Document [original]

Dynamics of single clusters in intense

light pulses studied with ion spectroscopy

and light scattering

vorgelegt von

Diplom-Physikerin

Leonie Fl¨uckiger

geb. in Bad Soden am Taunus

von der Fakult¨at II – Mathematik und Naturwissenschaften

der Technischen Universit¨at Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

– Dr. rer. nat. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Mario D¨ahne

Gutachter: Prof. Dr. Thomas M¨oller

Gutachter: PD. Dr. Tim Laarmann

Tag der wissenschaftlichen Aussprache: 16. Juli 2015

Berlin 2015

to my friends and family

iii

Abstract

The advent of x-ray free-electron lasers (FELs) has added a new twist to the field of

interaction between ultrafast laser pulses and nanoscale matter. The vision to image non-

crystalline targets in flight with atomic resolution in space and time is now within reach.

This thesis explores the laser induced dynamics of clusters with extreme ultraviolet (XUV)

radiation from the FLASH FEL in Hamburg as well as with infrared (IR) laser pulses from a

Ti:Sapphire system. An infrared laser focusing unit and a motorized in-vacuum incoupling

system were designed for the experiments in this thesis. IR and XUV pulses were guided

into the interaction region where they intersect the cluster beam. Large single xenon

clusters were produced in supersonic expansion under extreme conditions reaching a size

range between 10 and 1000 nanometer in radius. A method of coincident single-shot single-

particle imaging and ion spectroscopy was applied, which allows circumventing constrains

of signal averaging due to cluster size distributions and FEL power density profiles. A set

of filtering and sorting algorithms was developed to handle the large amount of collected

data demanded by this method.

The laser-induced cluster evolution is highly dependent on quasi-free electron density and

temperature. Nanoplasma dynamics were investigated dependent on cluster size and ma-

terial composition as well as laser intensity and wavelength to gain insight into their corre-

lation with experimental parameters. Astonishingly similar ion time-of-flight spectra were

found for very different conditions, i.e. metal and rare-gas clusters as well as IR and XUV

radiation. This reveals that very large clusters have universal dynamics in common: only

the outermost atomic layers explode and strong recombination takes place in the inner

core.

For time resolved investigation, a two color pump-probe technique was employed. The

XUV irradiated cluster expanded to a density where the Mie resonance condition was

matched and probed by the IR pulse. The average charge state created in clusters of

well-defined size did not change with FEL intensity. Furthermore, the average charge state

before recombination is derived from analytical calculations using the nanoplasma model.

In a reversed pump-probe scheme the IR-induced expansion was imaged. A plasma-driven

surface melting could be traced in a decreasing scattering signal at large angle. The

verification with basic 2D fast Fourier transforms revealed that the central part of the

cluster stays intact on a picosecond timescale. A slow evolution of the cluster is also

witnessed from ion signal with high kinetic energies, even a nanosecond after IR irradiation.

A novel type of scattering patterns - speckles - traces a slowly expanding neutral core,

driven by the hot electron gas in the nanoplasma. From the average speckle size the

average cluster radius at the time of detection can be gained. A modulation of the speckle

intensity envelope results from a density fluctuation inside the disintegrating cluster. The

key features of the measured speckle pattern could be reproduced in scattering simulations

using a numerical scalar approach.

Kurzfassung

Die Wechselwirkung von ultrakurzen Laserpulsen mit Nanoteilchen wird gegenw¨artig in-

tensiv untersucht. Freie-Elektronen-Laser (FEL) im R¨ontgenbereich erlauben seit kurzem

v¨ollig neuartige Untersuchungen. Durch ihre extrem intensiven Pulse wird es m¨oglich

werden nicht-kristalline Partikel mit r¨aumlich und zeitlich atomarer Aufl¨osung abzubilden.

Im Rahmen dieser Dissertation wurden Cluster mit extrem-ultravioletter (XUV) Strahlung

des FLASH-FEL in Hamburg abgebildet, sowie laserinduzierte Prozesse in der Probe mit

infraroten (IR) Pulsen untersucht. F¨ur die Experimente wurden ein Fokussier- und ein

motorisiertes, vakuumtaugliches Einkoppelsystem entworfen und aufgebaut. In der Wech-

selwirkungszone wurden IR und XUV Pulse mit dem Clusterstrahl ¨uberlappt. Die Xenon-

cluster wurden in ¨

Uberschallexpansion hergestellt und erreichten Gr¨oßen von 105−1010

Atomen. Die Methode der Einzelclusterstreuung wurde mit Ionenspektroskopie kom-

biniert, wodurch eine Mittlung der Messsignale ¨uber die Clustergr¨oßenverteilung und das

Leistungsdichen-Profils des Lasers umgangen werden konnte. Um die enormen Daten-

menge, welche mit dieser Methode einhergeht, zu handhaben, wurden eine Reihe von Filter-

und Sortieralgorithmen entwickeln. Im Einzelnen wurden folgende Ergebnisse erzielt:

Die laserinduzierte Entwicklung des Clusters ist stark abh¨angig von der Dichte und Tem-

peratur der quasi-freien Elektronen im Nanoplasma. Die Nanoplasmadynamiken wurden

in Abh¨angigkeit von der Clustergr¨oße und der Laserintensit¨at, sowie des Clustermaterials

und der Laserwellenl¨ange untersucht. Die detektierten Ionenspektren weisen erstaunliche

Ahnlichkeit auf, was darauf hinweist, dass sich f¨ur sehr große Cluster die Dynamiken uni-

versal verhalten. Nur die ¨außersten Atomlagen explodieren vom Cluster ab, w¨ahrend im

inneren Teil Elektronen und Ionen rekombinieren.

F¨ur eine zeitaufgel¨osten Untersuchung wurde die Zweifarben Pump-Probe Technik angewen-

det. Der XUV bestrahlte Cluster wurde zu einer Dichte expandiert, bei der die Mie Reso-

nanz auftritt, welche von dem IR Puls abgefragt wurde. In einer Clustergr¨oßen-abh¨angigen

Untersuchung konnte der mittlere Ladungszustand vor der Rekombination bestimmt wer-

den.

Durch Umkehr der Pump-Probe Reihenfolge war es m¨oglich die unterschiedliche Zerfallssta-

dien der IR induzierten Clusterexpansion mittels koh¨arenter R¨ontgenbeugung abzubilden.

Aus einem Abnehmen der Streusignalintensit¨at bei hohen Winkeln konnte ein Abschmelzen

der Cluster-Oberfl¨ache gefolgert werden. Das konnte mittels einfacher, schneller 2D Fouri-

ertransformationen best¨atigt werden, welche gleichzeitig zeigen, dass der zentrale Teil des

Clusters auf einer Pikosekunden-Zeitskala intakt bleibt. Diese langsame Entwicklung des

Clusterkerns wurde durch Ionensignal mit hohen kinetischen Energien best¨atigt - selbst

eine Nanosekunde nach Initialisierung der Expansion. Speckle-Muster in den Streubildern

zeigen den langsam expandierenden neutralen Zentralpart, der in erster Linie durch einen

Anstieg der Temperatur und nur zum geringen Teil durch Coulombkr¨afte auseinander

driftet. Aus der mittleren Speckle-Gr¨oße l¨asst sich der mittlere Radius des Clusters zur Zeit

seiner Abbildung bestimmen. Eine Modulation der Einh¨ullenden der Speckle-Intensit¨at re-

sultiert aus Dichte-Fluktuationen innerhalb des zerfallenden Clusters. Durch numerische

Streusimulationen konnten die Hauptcharakteristika des gemessenen Speckle-Bildes repro-

duziert werden.

Contents

1 Introduction 1

2 Theoretical concepts and previous experiments 5

2.1 Generation of large clusters in supersonic expansions . . . . . . . . . . . . . 5

2.1.1 Free jet flow and cluster growth . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Cluster size estimation by semi-empirical scaling laws . . . . . . . . 8

2.1.3 Temporal profile of a pulsed cluster jet . . . . . . . . . . . . . . . . . 10

2.2 Basic concepts and previous results for light scattering on clusters . . . . . 12

2.2.1 Fundamentals of light propagation . . . . . . . . . . . . . . . . . . . 12

2.2.2 Diffraction and scattering from spherical objects . . . . . . . . . . . 17

2.2.3 XUV scattering experiments on large clusters . . . . . . . . . . . . . 21

2.3 Cluster dynamics induced by highly intense laser pulses . . . . . . . . . . . 23

2.3.1 Initial ionization mechanisms and cluster charging . . . . . . . . . . 25

2.3.2 Nanoplasma dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3.3 Energy redistribution and disintegration of excited clusters . . . . . 32

3 Experimental Setup 41

3.1 Generation of XUV and IR pulses . . . . . . . . . . . . . . . . . . . . . . . 42

3.1.1 XUV pulse generation at the free-electron laser facility FLASH . . . 42

3.1.2 IR pulse generation at FLASH . . . . . . . . . . . . . . . . . . . . . 45

3.1.3 Spatial and temporal overlap in pump-probe setup . . . . . . . . . . 47

3.2 Experimental chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.1 Vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2.2 Cluster source for large xenon cluster generation . . . . . . . . . . . 51

3.2.3 Coincident photon and ion detection . . . . . . . . . . . . . . . . . . 53

vii

viii Contents

4 Results: Cluster evolution in intense XUV and IR pulses 59

4.1 Data processing and filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.1.1 Filtering by CCD image . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.1.2 Filtering by ion time-of-flight spectrum . . . . . . . . . . . . . . . . 65

4.2 Universal dynamics in large cluster nanoplasmas . . . . . . . . . . . . . . . 66

4.2.1 Ionization and ionic motion in XUV irradiated xenon clusters . . . . 66

4.2.2 Relationship between material characteristics and ionization dynam-

ics, studied in a comparison of xenon, silver and argon clusters . . . 70

4.2.3 Multistep vs field ionization: XUV and IR irradiated clusters . . . . 73

4.3 Probing the Mie plasmon resonance . . . . . . . . . . . . . . . . . . . . . . 76

4.3.1 Driving collective electron motion in xenon clusters . . . . . . . . . . 77

4.3.2 Relationship between exposed power density and resonance condition 81

4.3.3 Cluster size dependent resonance development . . . . . . . . . . . . 83

4.4 Imaging IR induced explosion . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.4.1 Imaging cluster surface ablation . . . . . . . . . . . . . . . . . . . . 88

4.4.2 Ionization of clusters under surface ablation . . . . . . . . . . . . . . 93

4.4.3 Expansion of a neutral cluster core on the nanosecond timescale . . 96

5 Summary and outlook 109

Appendices 113

A Small angle scattering code 115

List of Figures 119

List of Tables 121

Bibliography 122

Acknowledgements 136

Chapter 1

Introduction

The human eye can perceive movies with mircosecond resolution. However, a laser-

irradiated molecule takes only femtoseconds to disintegrate into single atoms. In order

to make this dissociation process visible to the human eye, many single images taken with

femtosecond exposure time and repetition rate need to be played back in a time-laps movie.

The realization of such a molecular movie has been far from reach for a long time. Only

in this century, with the invention of ultrafast, highly brilliant x-ray free-electron lasers

(FELs), imaging of nanoworld objects became feasible approaching atomic resolution in

space and time [1,2]. First proof-of-principle experiments on solid targets were performed

at the FLASH facility in Hamburg [3,4]. Soon, they were followed by many others (e.g.

[5,6]) and the field of femtosecond coherent diffraction imaging and holography evolved.

While high-resolution imaging of fixed solid-state targets was previously possible at syn-

chrotron sources by averaging scattering patterns over a long time range, the imaging

of single, free, unsupported, and thus naturally-grown and non-reproducible samples is

a ground-breaking novelty [7]. From the diffraction patterns it became possible to map

the shape and geometry of nanoparticles [8,9,10,11,12]. Also, fingerprints of ultrafast

electronic excitation during femtosecond exposure could be read from the scattered light

[10].

However, one single image still does not make a movie. A sequence of independent single-

shot still pictures is needed to resolve atomic motion. In a pioneering x-ray pump /

x-ray probe experiment, the fastest movie in the world was recorded by superimposing

two subsequent x-ray holograms from the same sample on one detector [13]. These were

later disentangled in post processing and resolved the sample at consecutive times. The

experimental setup and reconstructed images are presented in figure 1.1 a. A different

approach has to be used to circumvent the complicated process of disentanglement and

to gain an extended time-series of more than two ’photographs’. In an optical pump /

x-ray probe setup, the initiated evolution of separate identical copies of the sample could

be captured in individual pictures at different delay times [14], as presented in figure 1.1 b.

With this dynamic imaging method, ultrafast transient states in small particles can be

directly recorded. They can contribute to a detailed understanding of molecular motion

and chemical reactions.

Imaging nanoobjects by femtosecond x-ray scattering can thus not only reveal the geom-

etry and shape of the sample, but also give access to the light-induced dynamics on the

2 Chapter 1. Introduction

Reconstruction

Autocorrelator

FEL pulse

Sample

Split FEL pulse

CCD-detector

t = t0+50 fs

t = t0

(iii) Sample

(ii) FEL beam

(i) Pump laser

(iv) Mirror

(vi) Transmitted

beam

(v) CCD camera

-5 ps 10 ps

20 ps 140 ps

a) b)

Figure 1.1: Experimental design and scientific results of two pioneering dynamic imaging experi-

ments on solid targets. a) In x-ray pump / x-ray probe setup (blue and red pulse) two holograms

from the same target are overlapped on one detector and disentangles in post-analysis. From [13].

b) In optical pump / x-ray probe setup (green and violet beam) a series of scattering patterns is

recorded from different targets with the same shape at varying delay times. From [14].

timescale of atomic motion. However, dynamic imaging experiments become increasingly

complicated on unsupported particles. Therefore, this thesis contributes to this field by

investigating electronic excitation and ionic motion of free nanosamples and developing the

experimental techniques required. As object of investigation clusters were chosen. Clus-

ters are well established as nano-labs for laser interaction with finite targets. Due to their

simple electronic and geometric structure, they are intriguing research objects for both

theorists and experimentalists. Intra- and interatomic processes can be identified and con-

tributions from surface and bulk atoms disentangled by tuning the cluster size from several

tens to millions of atom. Time-resolved laser-cluster interaction is studied in this thesis

by investigating the interplay of single large xenon, argon and silver clusters with ultrafast

infrared (IR) and extreme ultraviolet (XUV) pulses. Ultrafast electron excitation, plasma

formation and recombination processes are addressed with elastic light scattering and ion

spectroscopy. To investigate atomic movement on a picosecond timescale, a pump probe

scheme is applied.

The text is organized as follows. The second chapter gives a quick introduction into the

basics of cluster generation, light scattering on nanoobjects, and dynamics arising from

cluster-light interaction. In chapter 3the experimental setup is described, focusing on

the laser pump-probe setup, the cluster source, and the ion and scattering detectors. The

major part of this thesis is dedicated to the data analysis and results, presented in chapter 4.

Ion spectra and diffraction patterns are examined for insight into nanoplasma dynamics.

Theoretical calculations and simulations strengthen the physical interpretations gained

from the analysis. A short summary and outlook on possible future experiments is subject

to chapter 5.

4 Chapter 1. Introduction

Chapter 2

Theoretical concepts and previous

experiments

A comprehensive introduction of the theoretical background of laser-cluster interaction

and an overview of state-of-the-art experiments will be given, to provide a framework for

the investigations of this thesis. First, the mechanism to produce rare-gas clusters in a

supersonic expansion, semi-empirical scaling laws, and the time characteristics of a pulsed

cluster jet are described in chapter 2.1. The key to understanding the functions and char-

acteristics of particles often lies in their structure which can be resolved by imaging with

x-ray scattering. The scattering processes fundamental for coherent diffraction imaging are

addressed in chapter 2.2. Imaging samples by means of x-ray scattering always induces ion-

ization and plasma formation. The nanoplasma evolution and expansion dynamics are the

main topics investigated in this work. Initial ionization and subsequent dynamic processes

occurring within the cluster are subject to chapter 2.3.

2.1 Generation of large clusters in supersonic expansions

Clusters, i.e. aggregates consisting of a finite number of atoms, are well established in

contemporary studies of laser-matter interaction. They bridge the regime between single

atoms and extended solids, since they show solid-like behavior while atomic effects are still

relevant. They allow to research physical and chemical properties as a function of size

and with varying surface to bulk ratio by tuning their size from a few to several millions

of atoms. Rare-gas clusters are often favored in experiments due to their uncomplicated

generation in supersonic nozzle expansion.

Section 2.1.1 focuses on cluster growth processes. The dependence of the cluster size on

experimental parameters and corresponding prediction of cluster size via scaling laws is

subject to section 2.1.2. Since the clusters investigated in this thesis were produced in a

pulsed source, the temporal evolution of a cluster beam in a pulsed expansion is addressed

in 2.1.3.

6 Chapter 2. Theoretical concepts and previous experiments

2.1.1 Free jet flow and cluster growth

Rare-gas clusters are produced in a supersonic expansion of atomic gas into vacuum. Since

rare-gas clusters have small binding energies Ebind in the order of only several meV, low

temperatures T0are needed (kBT0<Ebind) to produce stable clusters. From a reservoir

with low T0and with high background pressure p0, the gas expands through a nozzle with

diameter dinto a vacuum reservoir with significantly lower pressure. In the high pressure

reservoir the thermal atom motion is randomly directed and atom velocities are Boltzman

distributed. The mean free path for an ideal gas is given by

λ=kBT0

√2·p0·σ(2.1)

with Boltzmann constant kBand collision cross-section σ. The atomic beam becomes

aligned along the expansion direction by the adiabatic expansion of the gas through a

narrow orifice. If the mean free path is smaller than the nozzle diameter d, the beam into

vacuum is supersonic (λ<d)1, which means that the mean velocity vis higher than the

speed of sound c. The random thermal energy is transformed into directed kinetic energy.

Faster atoms transfer parts of their energy to slower atoms via collisions. The resulting

relative velocities of the atoms are small, which is equivalent to a strong adiabatic cooling

of the beam. In the cold atomic beam, the atoms aggregate and clusters will form [15].

The ratio of stream velocity vto local speed of sound cis also referred to as the Mach

number M=v/c. In the area behind the nozzle the Mach number is larger than one

(M>1), e.g. the expansion velocity is faster than the speed of sound. This area is called

the ’zone of silence’, as indicated in figure 2.1. Outside this zone, shock waves are formed

which reflect the expansion. They are thin non-isentropic regions of large gradients of

velocity, pressure, temperature, and density. To the sides of the supersonic beam they

are referred to as barrel shock. Downstream, the so-called Mach disk delimits the zone of

silence of the gas jet. Its distance from the nozzle exit is given by [16]

dM=2

3rp0

pback ·d. (2.2)

It marks the transition from supersonic flow (M>1) back to subsonic flow (M<1) and

destroys the generated clusters. A differential pumping stage can be used in order to lower

the background pressure and therefore shift the Mach disk further away from the cluster

source. Conical skimmers with sharp and narrow edges are often used to guide the cluster

beam from one pressure stage to the next. The position of the skimmer has to be chosen

carefully. On the one hand, the skimmer needs to be close enough to the nozzle, to be

located within the zone of silence [17]. On the other hand, the skimmer transmission

increases with distance as the mean free path decreases. Therefore, the skimmer needs to

be far enough away from the nozzle, so that λ > dSkimmer.

In microscopic description, the cluster growth process in the supersonic gas jet starts with

three-body collisions. Two atoms are sticking together and the third one takes the binding

energy away:

A + A + A = A2+ A∗.(2.3)

1For λ > d the beam is effusive.

2.1. Generation of large clusters in supersonic expansions 7

M = 1

p0, T0

M≪1

M≫1M < 1

M > 1

Jet boundary

Compression waves

Zone of silence Flow

Mach disk

shock

Barrel shock

Expansion fan

Figure 2.1: Scheme of the supersonic expansion of a free jet, adapted from [16]. Randomly

directed atoms are forced through a nozzle behind which the beam gets directed, relative velocities

are low, and clusters can form. Shockwaves and the Mach disk form a boundary to the vacuum

background. Within the ’zone of silence’ clusters can travel without getting destroyed.

The newly formed dimer is further used as nucleation seed growing by subsequent monomer

addition. The inner energy of the cluster increases with every monomer attached and atoms

evaporate off the cluster to reach thermal equilibrium. The number of atoms in the beam

decreases with ongoing cluster growth, which leads to a lower probability for monomer

addition. Instead, further down the beam, the growth process is taken over by cluster-

cluster coagulation.

The size of the clusters produced is determined by the number of collisions. More specifi-

cally, the growth process dependent on the probability of the collisions and on the duration

of the timespan at which collisions occur. Those are dependent on three parameters: the

backing pressure p0, the gas temperature T0and the shape of the nozzle. Higher backing

pressure leads to a higher number of collisions in the beam and therefore to more and larger

clusters. A higher temperature leads to a higher beam velocity which results in a lower

collision frequency and therefore leads to smaller clusters [18]. The shape of the nozzle

used for the supersonic expansion is important. Small nozzle orifices lead to a divergent

beam with low collision rates. Less divergent beams have higher directed densities which

favors the nucleation process, so that larger nozzle diameters result in larger cluster sizes.

Throughout the years several nozzle geometries were proposed and examined for efficient

cluster generation. Sonic, laval, conical, and trumpet shaped nozzles were used most com-

monly (see e.g. [19,20]). The geometry determines the flow field gradients. If it is chosen

such that the gas flow is constricted in transversal direction, the local pressure is higher

and the probability of collision increases [19]. Also the on-axis beam flux is higher [20],

which is especially important for experiments using a skimmer.

Due to the statistical formation process, the final size of the clusters exhibits a broad

distribution. The shape of the size distribution shows an exponential decay at small average

sizes where the production process is dominated by monomer addition. For large average

sizes resulting from the coagulation of larger clusters, the size distribution further evolves

to a log-normal shape. It follows the formulation [21]

f(n) = 1

√2πσN e−(lnN−µ)2

2σ2(2.4)

where σis the logarithm of the geometric standard deviation and µis the logarithm of the

geometric mean.

8 Chapter 2. Theoretical concepts and previous experiments

2.1.2 Cluster size estimation by semi-empirical scaling laws

The size of the produced clusters is determined by the applied gas stagnation pressure p0,

the gas temperature T0, and the geometry of the nozzle. These parameters together define

the condition for the gas flow and therefore the condition for atom condensation [22]. Semi-

empirical scaling laws were established in order to predict the mean generated cluster size

hNiin dependence on these parameters. The first scaling laws were developed by Hagena

for mono-atomic rare-gas clusters [22] and were later transformed for metals [23]. It was

shown that these simple laws can also be applied to hydrogen-bonded molecular systems

if the correct values of the degrees of freedom fwere used2.

A dimensionless scaling parameter Γ was introduced to correlate different initial expansion

conditions, which result in the same cluster size for the same gas [24]. The scaling parameter

combines the applied gas stagnation pressure p0, the gas temperature T0, and the nozzle

diameter d:

Γ = p0·T(q/4−3/2)

0·dq.(2.5)

The variable qwas determined in various experiments and changes for different materials.

For monoatomic gases it holds q= 0.85 [24].

Developing the correlation further, in order to be able to compare cluster sizes from par-

ticles of different gases, a reduced scaling parameter Γ∗was defined. It includes the char-

acteristic variables rch =3

pm/ρ and Tch = ∆h0

0/kB, where mis the atomic mass, ρis the

density of the solid, and ∆h0

0is the enthalpy of sublimation at 0 K:

Γ∗= Γ ·r(q−3)

ch ·T(q/4−3/2)

ch .(2.6)

The parameter Γ∗is a measure of the degree of condensation in the beam. Therefore,

cluster beams produced from different materials under different conditions but with the

same Γ∗should have the same mean cluster size hNi. In simplified form it can be rewritten

as [25,26]

Γ∗=Kch ·p0·dq

T(5/2−q/4)

(2.7)

with p0in mbar, deq in µm, and T0in K. The factor Kch is called specific gas constant and

combines all material specific values:

Kch =100 ·(10−6)q

kB·r(q−3)

ch ·T(q/4−3/2)

.(2.8)

The Kch values for rare gases are listed in table 2.1. The increase of the specific gas

constant from helium to xenon implies a higher clustering probability.

Table 2.1: Calculated specific gas constants Kch for the rare gases helium, neon, argon, krypton

and xenon, from [25]. A high clustering probability is mirrored by a high Kch value.

He Ne Ar Kr Xe

Kch 3.85 185 1646 2980 5554

2For monoatomic gases f= 3 and for diatomic gases f= 5.

2.1. Generation of large clusters in supersonic expansions 9

The orifice diameter dneeds to be replaced with the so-called equivalent nozzle diameter

deq in equation 2.7, to account for different nozzle geometries. The half opening angle αof

the cone is taken into account for conical nozzles. The equivalent nozzle diameter is then

given by

deq =G·d

tan α.(2.9)

The factor Gis dependent on the type of gas. For monoatomic gases f G= 0.736 [22]. For

arbitrary gases it can be calculated by [21]

G= 0.5(f+ 1)−(f+1)/4Af/2(2.10)

with fthe degrees of freedom for the gas and the constant A= 3.22 [27]. In the experiments

performed throughout this thesis a conical nozzle with d= 200 µm and α= 4◦was used,

corresponding to an equivalent nozzle diameter of deq = 2105 µm.

The mean number of atoms per cluster hNiis deduced from the reduced scaling parameter

Γ∗by [23]

hNi=C·Γ∗

1000B

.(2.11)

The values for the parameters Cand Bchange for different size regimes (see table 2.2).

Throughout this thesis only large clusters are addressed3which fall in the regime 104<Γ∗

<106.

In the basic assumption that large rare-gas clusters exhibit spherical shape, the mean

radius hRiof the produced clusters can be gained from the mean number of atoms hNiin

the cluster by

hRi=3mahNi

4πρ 1/3

(2.12)

with atomic mass maand solid density ρ. The expression reduces to hRi=3

phNi·0.24 nm

for xenon clusters with ρ= 3.781 ·103kg/m3and ma= 131.293 ·1.660 ·10−27 kg. Figure

2.2 shows the average cluster radii for xenon clusters in dependence on stagnation pressure

and gas temperature, produced with the nozzle applied in the experiment. The vapor

pressure curve is indicated by a white dotted line. Clusters produced from experimental

conditions above the curve are expanded from the liquid phase. If too low temperatures

are applied and the stagnation pressure exceeds the vapor pressure, the gas freezes in the

nozzle and cluster production is disturbed [25]. While the generation of small rare-gas

clusters is mostly uncomplicated, the production of large clusters in a size range of several

ten to hundred nanometer in radius is more challenging. The high stagnation pressure

Table 2.2: Values for the parameters Cand Bin equation 2.11. In different sizes range Buck and

Krohne (small) [26], Hagena (medium) [23], and Dorchies (large) [28] found the listed values.

350 <Γ∗<1800 1800 <Γ∗<104104<Γ∗<106

C3.84 33 100

B1.64 2.35 1.8

3p0= 9.8 bar, T0= 180 K, deq = 2105 µm, Γ∗= 2.472 ·105.

10 Chapter 2. Theoretical concepts and previous experiments

Temperature [K]

Pressure [bar]

100 300200 250150

Cluster

Radius

[nm]

100

Figure 2.2: Average cluster radius in dependence on gas temperature and backing pressure for a

nozzle with equivalent diameter of deq = 2105 µm and xenon gas, as calculated from equation 2.11.

With backing pressure the average size increases, while it decreases with higher temperature. The

experimental condition for the experiments described in this thesis is indicated by a star.

needed to produce large clusters leads to poor vacuum. In order to keep the background

pressure low, strong vacuum pumps are needed and cluster generation is often performed

in a pulsed jet instead of a continuous jet.

2.1.3 Temporal profile of a pulsed cluster jet

In a pulsed cluster jet, the concentration of the beam changes in time and space. Good

knowledge of the temporal profile of the cluster jet is necessary to predict the generated

cluster size. Up to date, two major studies investigated the temporal profile of pulsed jet

[29,30] and will be introduced in the following.

In the first study [29], the cluster flow of ensembles of xenon clusters in a pulsed expansion

were investigated with the Raleigh scattering method for three different source geometries.

One configuration had no reservoir between valve and nozzle and the other two had a small

(15 mm3) and a large (38 mm3) reservoir respectively. As presented in figure 2.3 a, the time

resolved spectra from xenon clusters show one plateau for the source without reservoir and

two peaks for the geometries with reservoir. The second peak presumably results from

larger clusters forming late in the pulsed beam. Apparently large clusters mainly grow

if a preroom is present. It was interpreted by the authors that the gas remaining in the

preroom after valve closing can serve as condensation nuclei upon a second reopening of

the valve.

In the second study [30], a similar temporal behavior was found but a different explanation

for the underlying physical processes was used. In an experimental setup similar to the one

presented in this thesis in chapter 3, single large xenon clusters were investigated with x-

ray scattering method allowing to precisely determine the radius of every detected cluster.

The size of the preroom in the source was kept constant but the expansion conditions

were varied from large clusters (case A), over medium sized clusters (case B), to atomic

2.1. Generation of large clusters in supersonic expansions 11

no preroom small preroom large preroom

Figure 2.3: a) Temporal jet profile for ensembles of xenon clusters produced in sources with

different preroom (reservoir between valve and nozzle) sizes. From [29]. The Rayleigh scattering

signal gives information about the size and amount of xenon clusters in the beam. Two plateaux

are visible in the graph taken with a large and small preroom respectively, while the spectrum taken

with a source without preroom shows only one plateau. b) Temporal jet profile for single xenon

clusters. From [30]. The second plateau in the atomic case hints towards a valve rebounce. The

large cluster size at the end of each plateau in case A and B respectively, indicate that the cluster

size is independent of the rebounce but results from the closing of the valve.

beams. The temporal profiles presented in figure 2.3 b show a broad plateau followed by

a pronounced peak for all three cases. The second peak in the atomic case identifies that

the valve opened twice due to a rebounce, since here the second peak cannot result from

large clusters late in the beam.

In case A, two additional small peaks are present following the plateau and the major peak.

The scattering experiment on single clusters makes it possible to determine the cluster size

directly. It shows that in these small peaks only large clusters are present, e.g. that they

appear late in the beam before the closing of the valve. A pressure shock wave arising from

the valve closing might shift the initial expansion conditions towards much more extreme

values, leading to larger clusters. Condensation in the preroom seems to be rather unlikely,

as the gas temperature in front of the nozzle throat is still high. Hence, the large clusters

detected at late times in the temporal profile can also appear if the valve does not exhibit

a rebounce.

12 Chapter 2. Theoretical concepts and previous experiments

2.2 Basic concepts and previous results for light scattering

on clusters

For the investigations in this thesis, clusters of different size and shape were illuminated by

highly intense laser pulses. For a profound understanding of the underlying processes, this

chapter gives an introduction to light propagation in matter. In section 2.2.1, the funda-

mentals of absorption and refraction are discussed. This approach is complimented by the

microscopic treatment of light scattering. The basic concepts of elastic light scattering are

for simplicity firstly described by scattering on free electrons and electrons bound to atoms.

The formalism is later extended to multi-atomic particles. Afterwards, coherent diffrac-

tion on finite targets is introduced, distinguishing between optically thick and optically

thin objects. The second part (chapter 2.2.2), concentrates on diffraction and scattering

from spherical particles. Starting with Fraunhofer diffraction from a single aperture, the

system is subsequently extended to arbitrary two-dimensional shapes. Then, Mie theory for

three-dimensional spheres is highlighted shortly, including properties of matter. Finally, in

section 2.2.3, several previous experiments using light scattering on clusters are reviewed.

They have made use of this method in order to study the geometry and light-induced

dynamics of clusters.

2.2.1 Fundamentals of light propagation

This section gives a short introduction into the fundamentals of light propagation. For

a more detailed description the reader is referred to the literature [31,32,33]. Light

propagation is described by the Maxwell’s equations which are expressed in differential

form as [34]

∇·D=ρ

∇·B= 0

∇×E=−∂B

∂t (2.13)

∇×H=J+∂D

∂t

where Dis the electric displacement, Bis the magnetic induction, Eis the electric field

vector, and His the magnetic field vector. ρand Jare the free charge density per unit

volume and free current density per unit area respectively. Monochromatic solutions to

the Maxwell equations are plane harmonic waves. The electric field amplitude of a linearly

polarized, electromagnetic plane wave is expressed as [33]

E(r, t) = E0ei(kr−ωt)(2.14)

where rindicates the position, ωthe light frequency, and tthe time. The wave vector

kis related to the wavelength λby |k|= 2π/λ. The amplitude of the wave oscillates

sinusoidally and the phase of the wave φ=kr −ωt indicates the instantaneous state of

this oscillation at point r.

In free space in the absence of any charges, e.g. in vacuum, the Maxwell equations can be

rearranged to derive the homogeneous wave-equation for the electromagnetic field in scalar

2.2. Basic concepts and previous results for light scattering on clusters 13

form [35]

∇2E−ε0µ0

∂2E

∂t2= 0.(2.15)

The permittivity of free space ε0and the magnetic permeable µ0can be expressed in terms

of the phase velocity for propagation in vacuum, e.g. the speed of light, as c= 1/√µ0ε0.

Wave propagation in medium - index of refraction

If a wave is propagating through a medium instead of vacuum, the materials’ refractive

index nhas to be taken into account4. In this case, the phase velocity is vp=c/n, or in

terms of the wave frequency vp=ω/k, which leads to the dispersion relation k=ωn/c.

The complex refractive index describes refraction and absorption of a material and is often

written as [33]

n= (1 −δ) + iβ. (2.16)

The real part accounts for the change in phase velocity of the propagating wave compared

to that in vacuum and the imaginary part accounts for the attenuation of the wave propa-

gating through medium. Based on the electric field amplitude of an electromagnetic wave

in vacuum (2.14), the plane wave solution for the Maxwell equations in dielectric isotropic

medium holds

E(r, t) = E0ei(kr−ωt)ei(1−δ)kr−βkr .(2.17)

This solution consists of a superposition of two plane waves, one in vacuum and one in the

medium of the refractive index n.

In a medium, due to absorption the wave amplitude decreases exponentially with increas-

ing distance in the direction of propagation. The decay of intensity is described by the

Lambert-Beer law as I=I0·e−µd with I0the incident beam intensity, µthe linear absorp-

tion coefficient, and dthe thickness of the material. The imaginary part of the refractive

index is related to the linear absorption coefficient via µ= 2kβ = 4πβ/λ. The intensity

decreases by a factor of eover a distance [33]

labs =1

µ=λ

4πβ (2.18)

also denoted as penetration depth into a thick material.

The refractive index of a medium is dependent on the light frequency. Close to atomic

resonance frequencies the imaginary part βis larger, which implies that the attenuation is

stronger there, due to an increased absorption probability. For optical light, nis typically

larger than 1, while in the extreme ultraviolet regime it is usually close to but slightly

smaller than 1. On the microscopic level, a photon absorbed by an atom transfers its

energy to an electron, which in turn is transferred into an excited bound state or a free

state above the ionization potential. If the photon is not absorbed it is either transmitted

or scattered. Therefore, even though they are different processes, absorption and scattering

are not independent and the factors δand βare related5.

4Note that in vacuum n= 1.

5The real and imaginary part of the refractive index delta and beta are connected by the Kramers-

Kronig-relations (see for example [35]), relating the processes of absorption and scattering.

14 Chapter 2. Theoretical concepts and previous experiments

If a free propagating wave impacts on an interface to a medium, the wave is scattered at

many scatterers within the material. The superposition of all scattered waves gives the

reflected wave. It is moving with phase velocity vptowards one direction, given by the

Snells law: cos α=ncos α0, where αand α0are the incident and the refracted angle [33].

In all other directions the scattered amplitudes result to zero. Hence, the real part of

the refractive index relates the angles of incidence and refraction when the plane wave is

refracted at the interface between free space and medium.

A scattered wave exhibits a relative phase shift respective to the incoming wave given by

[32]

∆φ=2πδ

λ∆r. (2.19)

If (1 −δ)>1, the incoming and outgoing waves are in phase. If the the real part of the

refractive index is smaller than unity, both waves are not in phase and the phase velocity

inside the medium is larger than the speed of light6. This leads to the phenomenon of total

internal reflection. In a scattering experiment, however, the phase cannot be detected,

since only the scattered intensity is recorded, which is the modulus squared of the electric

field amplitude

I=|E(r, t)|2.(2.20)

Elastic wave scattering

In this section the scattering probability of free electrons will be acquired. In a classical

approach an impacting electromagnetic wave forces a free electron to oscillate. The

electronic charge accelerates in the external field and its oscillating motion can be described

by the Lorentz force −eE. An electric dipole is produced. Upon its vibration the electron

acts as a source and radiates a scattered wave. The electron acceleration is derived by

Newtion’s equation of motion mea(r, t) = −eE(r, t), where meis the electron mass. With

this and Maxwell’s equations (2.14), the radiated field is deduced to [35]

E(r, t) = −e2

4π0mec2

rE0sin θei(kr−ωt)(2.21)

with scattering angle θand the classical electron radius re=e2

4π0mec2.

For linearly polarized light, the intensity distribution of the scattered wave from the dipole

induced by the oscillating electron dipole is depicted in figure 2.4. It is doughnut-shaped

with a central hole in direction of the oscillation. A measure to characterize the strength

of the scattered field is the total scattering cross-section σ. It is defined by the ratio of the

average total power radiated by an oscillating electron ¯

Pto the average incident power ¯

σ=¯

|¯

S|.(2.22)

For a single free electron it holds σ=8

3πr2

e, which is also denoted as Thomson cross-section.

The amplitude of the light scattered by a single atom can be given in fractions of the

scattering amplitude of a single free electron. The ratio of scattering amplitude of an atom

6The group velocity however is still smaller than c.

2.2. Basic concepts and previous results for light scattering on clusters 15

asin2Θ

(a) (b)

Figure 2.4: Donought-shaped intensity distribution of the radiation from a dipole which is induced

by an electron oscillating in an electric field. From [32]. The central hole lies in direction of the

oscillation a.

to the scattering amplitude of a free electron is given by the complex atomic scattering

factor f(q, ω). It is dependent on the light frequency and the scattering vector q=kout−kin

with |q|= 2|k|sin(θ/2) = 4π/λ ·sin(θ/2). In spherical coordinates the scattering vector is

composed of [36]

qx=q·cos(θ/2) cos(ϕ),

qy=q·cos(θ/2) sin(ϕ),(2.23)

qz=−q·sin(θ/2) (π≥θ≥0; 2π > ϕ ≥0)

The atomic scattering factor accounts for the fact that the electrons in the atom are bound

and have different contributions to the scattering signal. It introduces binding forces and

damping and is composed of a real and an imaginary part f(q) = f0(ω)−f00(ω), where

f0(ω) accounts for the binding of electrons to the atom and f00(ω) for the absorption of

photons. The field radiated from an atom is given by [33]

E(r, t) = −re

rf(q, ω)E0sin θei(kr−ωt).(2.24)

Hence the total scattering cross-section for an atom is σ=8

3πr2

e|f(ω)|[33].

One topic of this thesis is the light interaction with clusters, composed of many atoms.

In principle, in a system with several atoms, the wave scattered from one atom can be

scattered by a second atom and so on. However, if this multiple scattering is neglected,

the scattering amplitude from an object consisting of Natoms is simply calculated as the

summation of the scalar electric fields from an arrangement of Npoint scatterers [36]:

A(q, ω) =

j=1

ξj(q, ω)e−i(qrj−ωt)(2.25)

where rjis the central position of the jth atom, and ξj(q, ω) is the specific scattering

efficiency for each scattering atom. It contains the atom specific form factor fj(q, ω), the

distance between particle and detector L, and the differential Thomson cross-section dσ

dΩof

a free electron: ξj(q, ω)2=|fj(q, ω)|2(1

L2)dσ

dΩ[36]. The scattered wave is a superposition

of dipole radiations, building a spherical wave front.

Real and imaginary part of the atomic form factor fcan be expressed in terms of the

real and imaginary part of the refractive index n, to connect microscopic and macroscopic

16 Chapter 2. Theoretical concepts and previous experiments

description [33]

f0(ω) = 2π

nareλ2δ , f00(ω) = 2π

nareλ2β. (2.26)

Here nais the particle density and rethe electron radius.

Diffraction in the far-field

If the wavelength of the light is larger than the irradiated object, the outgoing wave is

best described by scattering, as it is the case of atoms in extreme ultraviolet (XUV) light

or clusters in infrared (IR) light. For clusters in XUV light, the obstacle is larger than

the wavelength. Here the outgoing wave is best described by diffraction. For objects

with complicated geometry exact solutions of Maxwell equations are mostly not available,

therefore approximations need to be used. The detector distance Lis much larger than

πR2/λ for all experiments performed in this work, which means that the experiments are in

the far-field limit [32]. In this Fraunhofer regime the scattered waves can be approximated

as scalar functions, which behave asymptotically like plane waves.

In the small-angle scattering limit |q|<< k, the relation of complementarity holds, which

is also known as Babinet’s principle. It states that diffraction from an obstacle can be

treated as diffraction from an equally shaped aperture in an infinitely extended screen.

Additionally, the far-field scattering pattern, which holds the geometry information of the

scatterer, can be described by the 2D Fourier transform of the object’s electron density

projected onto a plane perpendicular to the incoming wave propagation direction [33]

I=E(r, t)2=

eikr

rZρ(r)eiqr d3r

.(2.27)

This becomes evident in the definition of the atomic form factor as the integral over the

electron density of the atom ρ(r), which gives the probability that an electron is positioned

at a certain position rof the atom [33]

f(q) = ZAtom

ρ(r)eiqr d3r.(2.28)

Comparing equations 2.27 and 2.28 clearly shows that the atomic scattering factor is simply

the Fourier-transform of the atomic electron density. Therefore a simple and effective

method to estimate the two-dimensional outline of a particle shape from its small-

angle far-field scattering pattern is to compare the Fourier transform of estimated particle

shapes with measured scattering distributions as done in several experiments (c.f. [11] and

chapter 4.3.1).

Only for small scattering angles, e.g. where the projection vector npis approximately

parallel to kin , the assumption is valid that just a single projection plane is recorded in

the scattering pattern. If a large angle range is detected, several projection planes under

various angles are contained in the diffraction patterns, as schematically depicted in figure

2.5 b. If also large angles are detected in a 2D scattering pattern, the three-dimensional

shape of a particle is encoded. The 2D information can be extended to a 3D object by

accounting for the object depth with a multislice method [12].

2.2. Basic concepts and previous results for light scattering on clusters 17

npnp

kout

kin kin

a) b)

Projection plane Projection plane

Figure 2.5: Schematics of small and wide angle scattering. From [12]. a) In small-angle scattering

geometry the spatial information in beam propagation direction is not resolved, because the scat-

tering vector qand the projection plane are oriented perpendicular to the beam. The projection

vector npis approximately parallel to kin . b) In wide-angle scattering geometry 3D information is

contained in the pattern because the projection plane is rotated considerably.

To simulate a wide-angle scattering pattern, the 3D object is subdivided into a stack of

2D binary arrays with their normal vectors nporiented parallel to the direction of wave

propagation, which contain the particle electron density ρ(x, y, z=j) at the respective slice

of number j. The phase φof each object slice, accounting for the speed and direction of

light propagation, is given by [12]:

φj(x, y) = (pk2−(x2+y2)−k)·j(2.29)

where kis the wave vector. Subsequently, the Fourier transform is performed independently

for each array. Finally all Fourier transforms are phase corrected and summed up to one

final pattern [12]

F=|F(ρ(x, y, z=j))|+ei(φj+φslice).(2.30)

In contrast to small-angle scattering patterns, the wide-angle images are often not point-

symmetric. This is owed to the fact that the Fourier transform of a symmetric function

is always real, while the Fourier transform of an asymmetric function is imaginary [33].

In the diffraction patterns itself this behavior is manifested in a transition from broken

point-symmetry to point-symmetry from large to small angles [12] (see also figure 2.8).

2.2.2 Diffraction and scattering from spherical objects

Rare-gas clusters grown by monomer-addition and by coagulation7are often round in shape

(cf. section 2.1). For the simple case of spherical objects one can state precise calculations

which will be highlighted in the following.

As stated earlier, due to Babinet’s principle, the far-field diffraction pattern from a circular

disk is equal to the one from a circular aperture. The latter is the well known Airy

pattern. The intensity distribution in the far-field of an aperture with radius Ris given by

[33]

I=I0·

2J1(kR sin θ)

kR sin θ

(2.31)

7if the cluster is still warm enough and not frozen in an intermediate state.

18 Chapter 2. Theoretical concepts and previous experiments

Figure 2.6: Binary array with one circular object. The corresponding ring-shaped diffraction

pattern is called Airy pattern. The diffraction pattern from two point objects exhibits fringes.

Two circular objects lead to a diffraction pattern with an Airy pattern amplitude which is in itself

modulated by a set of interference fringes.

where J1is a first order Bessel function. The position of the first minimum θmin is found

at k·R·sin(θmin)=3.83. With this relationship the radius of a spherical cluster Rcan

in simple approximation be deduced from the angle of the first minimum in the recorded

scattering pattern as [32]

R= 0.61 ·λ

sin(θmin).(2.32)

In this formula the material dependent absorption or phase shift are not accounted for, even

though they have an additional influence on the position of the minimum. Nevertheless,

for the scope of this thesis equation 2.32 is of sufficient accuracy and has therefore been

used in the analysis in section 4.1.1 to determine the radius of the clusters to study the

size dependence of light-cluster interactions.

As introduced in section 2.1.1, clusters not only grow by monomer addition but from a cer-

tain size onwards also by coagulation. Thereby they sometimes freeze and build dumbbell-

shaped twin clusters, triple clusters, and so on, up to hailstone-shaped nano-particles. The

projection of these objects can be described by multiple circular apertures arranged on

a flat screen. A set of apertures cm, which all have the same radius and are not in contact

with each other, build an overall aperture function ρ(x, y) = Pmcm(x, y). The diffracted

amplitude from this system is given by the Fourier transform of the aperture function [37]

F(kx, ky) = F(ρ(x, y)) = Z Z ρ(x, y)ei(kxx+kyy)dxdy (2.33)

The diffraction amplitude from the individual opening, defined as C0(kx, ky) = F(c0(x, y)),

is the above introduced Airy pattern. With the addition theorem of the Fourier transforms

the diffraction amplitude from all aperture openings becomes F(kx, ky) = PCm(kx, ky).

Taking the shifting theorem Cm(kx, ky) = C0(kx, ky)ei(kxxm+kyym)into account, the overall

2.2. Basic concepts and previous results for light scattering on clusters 19

diffracted amplitude can be expressed as [37]

F(kx, ky) = C0(kx, ky)

m=1

ei(kxxm+kyym)

→ F(ρ(x, y)) = F(c0(x, y))

m=1

ei(kxxm+kyym)(2.34)

This equation expresses that the total scattering pattern comprises of the Airy pattern

amplitude which is in itself modulated by a set of interference fringes, as visible from

figure 2.6. The appearance of the fringes is determined by the arrangement of the single

aperture positions. The pattern becomes increasingly complicated with increasing aperture

number.

Mie theory

The elastic scattering from a three-dimensional sphere has been described by Gustav

Mie in the context of his research on small gold colloids [38]. Based on the Maxwell

equations (see set of equations 2.14), the Mie theory describes exactly the interaction

between a plane electromagnetic wave and a homogeneous, dielectric, spherical particle,

independent of distance of detection, and detected angle range. The scattered wave depends

on the ratio of particle radius to light wavelength and the refractive index of the particle. It

becomes possible to determine the radius and the refractive index of the particle by fitting

radial profiles of experimentally recorded scattering patterns with Mie calculations. The

entire derivation of the solution is complicated and described in detail in several books

[39,40,41]. Here, only a short introduction and illustration of the main principles are

given.

In vector form the fields inside and outside the object are described as superposition of

partial waves. All partial waves have to be solutions of the wave equation which directly

follow from the Maxwell equations. As boundary condition the energy at the surface needs

to be conserved. The scattering field Esin matrix form as a function of the incoming field

Eiis written as [39]

Eks

E⊥s=eik(r−z)

ikrS2S3

S4S1 Eki

E⊥i(2.35)

with angular scattering functions S1, S2, S3, and S4and wave vector k. For fully polarized

light S3=S4= 0. The remaining scattering functions are infinite series. For computations,

a cutoff at a certain degree m8yields good approximations [39]:

S1=X

2m+ 1

m(m+ 1)(amπm+bmτm), S2=X

2m+ 1

m(m+ 1)(amτm+bmπm) (2.36)

where amand bmare scattering coefficients and πmand τmare angular functions of the

respective degree.

8To avoid confusion, it is necessary to note that in the book of Bohren and Huffman [39] the refractive

index is denoted mand the degree of the series is denoted n, while in this thesis they are named the other

way around. This denotation was chosen because in most literature like e.g. [32,33]nis used for the

refractive index.

20 Chapter 2. Theoretical concepts and previous experiments

10-5

10-4

10-3

10-2

10-1

100

101

102

403020100

Re = 1 - 0.02

Re = 1 - 0.01

Re = 1 - 0.001

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

403020100

ß = 0.1

ß = 0.01

ß = 0.005

scattering angle [degree]

scattering intensity [arb. u.] scattering intensity [arb. u.]

a) b)

Figure 2.7: a) First five angular functions parallel and perpendicular to the propagation direction

of the incoming beam. From [39]. With higher orders the lobes shift towards forward direction. b)

Mie profiles of a 50 nm radius sphere exposed to 13.5 nm light. Their dependence on the real and

imaginary part of the refractive index are depicted. With increasing real part 1 −δ(phase shift)

the minima shift towards higher scattering angles (from red to blue). With increasing imaginary

part β(absorption) the minima get shallower (from red to blue).

The scattering coefficients depend on spherical Bessel functions J, H and its derivatives

J0, H0and are calculated by [39]

am=nJm(nx)J0

m(x)−Jm(x)J0

m(nx)

nJm(nx)H0

m(x)−Hm(x)J0

m(nx), bm=Jm(nx)J0

m(x)−nJm(x)J0

m(nx)

Jm(nx)H0

m(x)−nHm(x)J0

m(nx).

The angular functions πmand τmare defined as [39]

πm=Pm

sin θ, τm=dPm

dθ (2.37)

with Pthe Legendre polynomial. The first five modes are plotted in figure 2.7 a.

The number of degrees calculated before truncation is dependent on the particle size in

respect to the wavelength of the incoming light. With increasing order, the maximum

scattered light shifts forward and the scattering lobes become finer. With increasing sphere

size higher orders become increasingly important. For spheres with larger radius the first

minimum shifts towards smaller angles, as already evident from the Airy pattern equation

2.32. In the scope of this thesis, Mie theory is used to determine the average radius

of a cluster if the first minimum is not detected and therefore the Airy equation is not

applicable.

2.2. Basic concepts and previous results for light scattering on clusters 21

The index of refraction influences the depth of the fringe minima, as depicted in figure

2.7 b. For spheres with a diameter of 100 nm irradiated with 13.5 nm wavelength light the

following effect becomes visible for the diffraction pattern in forward direction: With in-

creasing real part - e.g. phase shift - the minimum shifts towards higher scattering angles,

while with increasing imaginary part - e.g. absorption - the minimum gets shallower. Mie

theory includes sharp boundary conditions, since the refractive index for the object’s mate-

rial is taken to be constant and changes abruptly at the surface layer between vacuum and

obstacle. It is a static theory which neglects dynamic effects like e.g. light-induced changes

in the electronic structure or the density of the sphere. Therefore, even though Mie theory

gives exact solutions for an ideal, homogeneous and spherical particle, the values gained

from Mie fits for the refractive index can only serve as an estimate.

2.2.3 XUV scattering experiments on large clusters

Several single-shot single-cluster experiments have been performed at free-electron lasers

up to date [42,10,11,30,12,43,44]. Their main goal was to investigate

•the cluster morphology, which gives indication about the cluster growth process,

•light induced ultrafast electron dynamics, imprinted in the scattering pattern by

modifying the optical constants, and

•light induced cluster ionization and fragmentation dynamics.

XUV scattering experiments on xenon clusters of about 50 nm in radius produced in a

supersonic expansion from the gas phase have identified two coexisting pattern geometries:

concentric ring patterns and fringe patterns with underlying substructures [11]. Scattering

simulations, using the Fourier transform of particle 2D projections, identified that these

images result from spherical particles and more complex shaped obstacles like dumbell-

shaped twin clusters. Figure 2.8 a shows outlines of twin clusters in various degrees of

coalescence and the resulting scattering pattern simulations, matching experimental results.

In a second experiment, even triple clusters and more complicated hailstone-like particles

were found for larger clusters up to a micron radius [30]. From these final cluster shapes,

new aspects of the cluster growth process became comprehensible. While small clusters

arrange in monomer-addition, larger clusters grow in coagulation and, depending on their

temperature, can freeze out in intermediate states, resulting in complex geometries.

In more advanced scattering simulations based on scalar theory and using the Born ap-

proximation, even three-dimensional particle information was extracted from the recorded

images of multiple clusters in the interaction region [11]. Not only the particles’ size but

also their relative position, orientation, and distance within the focal volume was evaluated.

The structure of free silver clusters produced in a magnetron sputtering source was cap-

tured in another XUV scattering experiment [12]. The highly symmetric patterns, as

reprinted in figure 2.8 b, point towards particle shapes of regular polyhedra. Broken point-

symmetry in some of the wide-angle scattering patterns reveals that 3D information is

encoded (see section 2.2.1). With multi-slice Fourier-transform simulations the orienta-

tion towards the beam axis and the full 3D shape of the individual particles was assigned.

22 Chapter 2. Theoretical concepts and previous experiments

Figure 2.8: a) Measured scattering patterns from xenon twin clusters of different geometries. From

[11]. Scattering simulations by FFTs of 2D masks illustrate the various degrees of coalescence. b)

Measured wide-angle scattering patterns from free silver clusters. From [12]. Some patterns ex-

hibit broken point-symmetry which indicated that three dimensional information about the cluster

structure is contained. The particles architecture and orientation in space was determined with

multi-slice Fourier transform simulations.

Theoretically predicted energetically preferred equilibrium shapes - like truncated octa-

hedra - were identified as well as morphologies already known from deposition studies -

like decahedra. Apart from these shapes, around hundred nanometer sized silver clusters

with icosahedral and flat hexagonal (truncated twinned tetrahedra) shape were identified.

Hence, XUV scattering is currently the only method to reveal, that silver clusters with

metastable geometry exist in way larger sizes than previously expected.

The modulation in the profile along the azimuth over a fixed polar angle, contains infor-

mation about the particle symmetry. Information about light-induced cluster dynamics

are encoded in the intensity profile along one polar axis. This fact was used in a scattering

experiment on single xenon clusters, to investigate the ultrafast (10 fs) sample response

dependent on the laser power density [10]. It was found that for low laser focal flux, the

envelope of the intensity profile followed a (qR)−4dependence, known as Porods law in

small-angle x-ray scattering (see figure 2.9 a). With rising power densities the envelope

increasingly deviated from this law, which was explained by an increase in the imaginary

part of the refractive index. This showed directly, that the impact of the laser beam can

change the electronic configuration within the cluster and therefore the ultrafast ionization

processes in the particle.

2.3. Cluster dynamics induced by highly intense laser pulses 23

Intensity [arb. units]

3 4 5 6 7 8 9

2 3 4 5

R = 120 nm

P = 5*10

W/cm

R = 117 nm

P = 2*10

W/cm

R = 155 nm

P = 4*10

W/cm

Porod's law

m=-4

Mie fit for high qR

Mie fit for low qR

Detector

saturation

a) b)

scattered intensity [arb.u.]

scattering angle [°]

Figure 2.9: a) Scattering profiles from clusters irradiated with different power densities reveal

information about the particles refractive index. From [10]. b) An overmodulation in scattering

profile difference spectra points towards an internal refractive core-shell system within the cluster.

From [45].

Within 10 fs, the atomic form factors change with increasing degree of ionization, evident

from a deformation of the scattering amplitude envelope [10]. Using longer XUV pulses of

100 fs, a supermodulation of the fringe pattern appears. It gives evidence of a refractive

core-shell system in the cluster. This is probably caused by sharp resonances of xenon

ions at 91 eV photon energy, which lead to the formation of a core and a shell region

with different refractive indices inside the cluster [45]. Difference spectra of radial profiles

from clusters irradiated with increasingly bright light pulses are shown in figure 2.9 b. The

supermodulation minimum shifts to larger angles with laser flux which indicates that a

possible shell-region becomes increasingly thicker.

On an even longer time scale of several picoseconds, the scattering pattern vanishes com-

pletely as demonstrated in a recent IR-pump / x-ray-probe experiment [46,43] (see also

section 4.3.1). It was shown that with increasing pulse delay time the scattering signal

decreases gradually from high to low scattering angles. This signature is attributed to a

softening of the single particle surface, due to the explosion of highly charged ions gradually

evolving from the cluster surface towards the cluster center.

2.3 Cluster dynamics induced by highly intense laser pulses

Since the advent of highly intense optical lasers in the sixties, many experimental and the-

oretical studies were performed in order to gain a profound understanding of laser-matter

interaction. Already introduced in sections 2.1 and 2.2, clusters can serve as convenient

24 Chapter 2. Theoretical concepts and previous experiments

Figure 2.10: Exempli-

fication of the three-

phase model for a cluster

in XUV light, adapted

from [52,45]: (I) Initial

ionization of a neutral

cluster in the rising edge

of a laser pulse. Onset

of nanoplasma forma-

tion. (II) Laser-electron

and electron-electron in-

teractions in the cluster

nanoplasma during the

laser pulse. (III) Energy

redistribution and relax-

ation after the pulse is

gone. Lowering of clus-

ter density by disinte-

gration.

Cluster ionization,

charge up

Electrons are trapped,

nanoplasma

Disintegration,

relaxation, recombination

(II) During

the pulse

(III) After

the pulse

(I) Beginning

of the pulse

nano-labs. In the optical regime ensembles of small clusters are well studied. Compre-

hensive reviews for the optical regime can be found in literature [47,48,49,50]. With

free-electron lasers emerging at the beginning of this century, coherent light pushing into

the sub-nanometer regime in ultrashort pulses became available. The new possibilities

sparked many studies on clusters in x-ray light. Work on light-cluster interaction in the

XUV domain has been recently reviewed [51,52].

These studies show that the interaction response of matter and light strongly depends on

several properties. The cluster component determines ionization potentials, resonant

transitions, as well as binding energies and different fragmentation dynamics are found for

homo- or heteronuclear samples [53,54,55,56]. With increasing cluster size bulk effects

start to dominate surface effects. Several factors are of importance for the laser beam:

the photon energy especially determines the mechanism of initial ionization, while the

intensity of the field accounts for the amount of deposited energy in the system. The

pulse length affects ionization and resonances and a spatial and temporal chirp may

influences ion energies [57]. This chapter intends to give an introduction on the manifold

dynamics taking place with emphasis on the interaction of rare-gas (especially xenon)

clusters with highly intense (1012 - 1015 W/cm2) XUV and IR pulses in the 100 fs duration

range.

For a comprehensive illustration of the complex processes occurring in laser-cluster interac-

tion it is useful to follow a three-phase model as often applied in literature [58,59,49,50].

The interaction is partitioned in three steps independent of the exact experimental param-

eters. These are schematically depicted in figure 2.10 on the example of irradiation with

XUV light. The outline of this chapter follows those phases:

(I) In the rising edge of the laser pulse, individual atoms are initially ionized and the

cluster charges up, developing a deep Coulomb potential (see 2.3.1).

(II) During the pulse, electrons get trapped in the cluster potential. Further energy

2.3. Cluster dynamics induced by highly intense laser pulses 25

transfer from laser to cluster as well as energy transfer within the cluster takes place.

The different mechanisms are introduced in 2.3.2.

(III) After the energy absorption from the laser field ends, energy is still redistributed

within the cluster. The particle expands and finally disintegrates, as will be discussed

in section 2.3.3.

2.3.1 Initial ionization mechanisms and cluster charging

Upon irradiation of a neutral cluster with the rising slope of a laser pulse, the light couples

to the compound atoms mostly as if they were isolated. This is especially the case for rare-

gas clusters, where electrons are strongly localized, and also in the case of core electrons

in metal clusters [49]. Instantaneously photon energy is absorbed and atoms get initially

ionized. Several excitation mechanisms - either directly via single photon absorption or

in non-linear processes - are possible dependent on the impacting laser power density and

photon energy. The electronic configuration of the atoms plays an important role in the

case of resonant excitation transitions. In this first phase the cluster environment is of

minor importance, hence for simplicity several mechanisms are introduced on the example

of atoms, following the reviews in [60,61,62,50]. Finally in the context of the cluster

environment a nanoplasma is build up, which is described in the last part of this section.

Initial ionization of single atoms

Single-photon ionization takes place if the photon energy ~ωexceeds the ionization

threshold Eip so that electrons are directly emitted into the continuum, as illustrated

in figure 2.11 a. This is for example the case for rare-gas atoms in extreme ultraviolet

(XUV) and x-ray light. In metal and water clusters, however, lower photon energies as

in the vacuum ultraviolet (VUV) regime are sufficient. Light sources with high photon

energies in the order of several tens of eV to one keV ionize mainly the inner electronic

shells. They are subsequently filled by Auger decays leading to multiply charged ions upon

absorption of a single photon (multiple single-photon ionization). During the pulse the

instantaneously refilled inner shells can be ionized many times. Multi-photon ionization

can take place via virtual states for energies smaller than the ionization potential (~ω <

Eip), promoting a bound electron over the vacuum level (see figure 2.11 b). This mechanism

proceeds over many laser cycles of the rapidly oscillating field.

At high laser intensities and low laser frequencies the strong laser field leads to a deforma-

tion of the potential combined from ionic and laser field. If the bending is strong enough

and the laser frequency sufficiently slow, an electron can escape the potential by tunnel-

ing through the barrier leading to tunneling ionization (see figure 2.11 c). The weakest

bound electrons exhibit the highest ionization probability. For even stronger fields the

potential bending is so strong that the barrier is suppressed below the bound state. No

tunneling is needed and above threshold ionization takes place (fig. 2.11 d).

The interaction of atomic electrons with electromagnetic radiation can be split in two

domains: the photon dominated regime where the field can be treated quantum me-

chanically as an ensemble of photons and the field driven regime where as many photons

26 Chapter 2. Theoretical concepts and previous experiments

hω <Eip

γ < 1

hω <Eip

hω >Eip

γ > 1 I>

Eip

16Z2

hω <Eip

γ < 1

hω <Eip

hω >Eip

γ > 1

a) b) c) d)

Figure 2.11: Schemes of photon dominated (a + b) and field driven (c + d) atomic ionization in a

laser field. From [63]. a) If the photon energy ~ωexceeds the ionization potential Eip single photon

or multiple single photon ionization occurs. b) Multi-photon ionization takes place if ~ω < Eip. c)

Tunnel ionization can occur if the laser field bends the atomic potential strongly. d) If the barrier

is suppressed below the bound state above-threshold ionization takes place.

participate that light is treated as classical field. Which regime is the prevailing depends

on the laser field strength and wavelength as indicated in figure 2.12. Here also the lasing

regimes reached by optical and free-electron lasers are indicated.

Both regimes can be quantitatively separated by the dimensionless Keldysh parameter

γ=ω/ωt[65]. It is introduced as the ratio of laser frequency ωto tunneling rate ωt. The

latter is given by [65]

ωt=eE0

p2meEip

,(2.38)

where eis the elementary charge, E0is the laser field strength, methe electron mass,

and Eip the ionization potential. If the tunneling rate exceeds the laser frequency (γ≤

1) the electron may leave the Coulomb potential by tunneling through the barrier and

therefore the interaction is in the optical field ionization regime. For γ1, in the so-

called perturbative regime occurring at high photon energies and low intensities, bound

electrons get excited by single or multi-photon absorption.

It is also useful to express the Keldysh parameter by the ponderomotive potential, which is

the cycle-averaged kinetic energy of a freely oscillating electron driven in an external laser

Figure 2.12: Photon energy over power density, illustrating the photon and field dominated

regimes with indicated regions reached by optical and free-electron lasers. From [64].

2.3. Cluster dynamics induced by highly intense laser pulses 27

Figure 2.13: Excitation steps and ionization channels in xenon atoms irradiated by 93 eV photons.

From [66].

field [60]

Upond =e2E2

4meω2=e2I

20cmeω2(2.39)

with I=c0E2

0/2 being the power density of the laser, 0the vacuum permittivity and cthe

speed of light. Several values of the ponderomotive potential are indicated in dependence

of photon energy and power density in figure 2.12. The transition between both regimes

approximately occurs where 2 ·Upond =Eip, as seen from the Keldysh parameter when

expressed as [60]

γ=ω

ωt

=sEip

2·Upond

.(2.40)

In the experiments performed for this thesis, ultrashort XUV pulses with 13.6 nm wave-

length (= 91 eV photon energy) are used. They exhibit a maximum power density of about

4.1·1014 W/cm2in the focal volume. With an ionization potential of Eip = 12.13 eV for

xenon atoms [67], a Keldysh parameter of 29 can be calculated using equation 2.40. There-

fore, the xenon-XUV interaction in this experiment is in the photon dominated regime.

In this regime the electronic structure of the target material significantly influences the

absorption efficiency. Depending on the electronic energy levels resonant excitations can

occur. For the applied photon energy of 91 eV the so-called giant resonance appears in

atomic xenon [66,68]. The ground state configuration of xenon is: Xe = [Kr] 4d10 5s2

5p6. Around 100 eV resonant 4d-f transitions with proceeding Auger decays lead to an

enhanced ionization with cross-sections from 23 Mbarn for neutral xenon up to 1000 Mbarn

for Xe6+ [69,70]. While for the first few charge states atoms are multiply and singly ionized

with only one photon, two photons are needed for ionization from Xe7+ onwards and three

from Xe10+ onwards by stepwise absorption of single photons, as schematically depicted in

figure 2.13.

Additionally, IR pulses with 800 nm wavelength are used in the experiments for this thesis.

With a power density of 1.1·1014 W/cm2, the IR-xenon interaction is in the field-driven

regime, as can be estimated from a Keldysh parameter of 0.9. Earlier experiments on

28 Chapter 2. Theoretical concepts and previous experiments

Figure 2.14: Concept of inner and outer ionization of excited electrons in the deepened cluster

potential. From [50]. If an electron is released from an ion but does not overcome the ionization

potential, it is quasi-free and called inner ionized. An electron leaving the cluster compound into

the continuum is called outer ionized.

atomic gas with these parameters yielded charge states up to Xe3+ in 200 fs pulses [71],

while in a later one Xe1+ was the highest charge state observed with pulses of 20 fs [72]. This

comparison reflects the non-negligible influence of the laser pulse duration and resulting

intensity and photon flux in the field driven regime.

Nanoplasma formation in clusters

The cluster environment is negligible for the initial ionization of a neutral cluster since the

atoms act as they are independent. However the cluster compound plays an increasingly

important role in the advancing processes. The liberation of each electron from the cluster

- either direct or via tunneling as in single atoms - leads to a deepening of the cluster

Coulomb potential. The individual potentials merge and atoms start ‘feeling’ each other as

depicted in figure 2.14. Electrons released from an ion which do not have sufficient kinetic

energy to overcome the potential are trapped. The efficient trapping of photoelectrons

often starts a few fs after irradiation and therefore already in the leading edge of the pulse

[50]. They trapped are referred to as inner ionized [58] or quasi-free. Together with

the ion background the cloud of quasi-free electrons forms a nanoplasma [47]. A dense

charged electron-ion system is created.

When ionized to that point, noble gas clusters become metallic since these electrons are

not bound to an ionic core but delocalized across the whole cluster. While for rare-gas

clusters a nanoplasma has to be created by inner ionization upon light irradiation, quasi-

free electrons are inherent to the system in metal clusters already in the ground state.

Quasi-free electrons in a cluster can absorb further energy during the light pulse. If they

absorb enough energy to overcome the potential, they subsequently get emitted and are

then denoted outer ionized [58]. With every expelled electron the potential barrier to

overcome gets higher and the energy span between inner and outer ionization grows. As

depicted in figure 2.10, the first phase is completed with the initial charging of the cluster.

In the next phase other processes dominate these initial processes, which are subject to

the next section.

2.3. Cluster dynamics induced by highly intense laser pulses 29

2.3.2 Nanoplasma dynamics

Clusters are able to absorb energy from laser pulses more efficiently than atomic gas. This

effect was found in several laser-cluster experiments investigating the emission of x-rays

[73], highly energetic ions [74], neutrons from fusion [75], and highly energetic electrons

[76]. The enhanced energy absorption in clusters compared to pure atomic gas results from

processes mainly occurring in the second phase, indicated in figure 2.10. Here, the laser

pulse interacts with an already charged cluster, where often a dense nanoplasma is present.

Like initial ionization procedures, nanoplasma dynamics can also be dependent on laser

wavelength and strength as well as on cluster size. Bound and quasi-free electrons in a

nanoplasma can absorb and exchange energy and get inner- and outer-ionized by several

different effects [48,77,50]. As in the atomic case, some plasma dynamics can be differ-

entiated in effects mostly driven by the laser field and in single-photon and multi-photon

effects. Additionally, also regime independent effects are possible, which are mainly deter-

mined by the intensity of the space charge and the amount and energy of the quasi-free

electrons. In most laser-cluster interaction scenarios many of these processes interact and

are highly linked to each other. Several reviews and books give a good introduction into

the complex mechanisms in the IR [47,49,62,61] and in the XUV regime [50,51,78]. It

has to be stressed, that many concepts in literature are valid for cluster sizes smaller than

the wavelength. This is neither the case for several 10 nm radius clusters in XUV light nor

for µm sized clusters in IR light, as both studied in this thesis. Still most models and ideas

are applicable to the experimental data in good approximation.

Plasma coupling regimes

In plasmas, electrons coherently driven by the external laser field give rise to collective

processes. But due to collisions of these electrons the collective motion can be destroyed

and random thermal motion takes the lead [77]. Which of these processes is dominant

during laser-cluster interaction, strongly depends on the temperature and density of the

plasma and can be deduced from the Debye number

ND=4π

3neλ3

D(2.41)

where neis the electron number density and λDthe Debye length [79]. The latter deter-

mines the length over which charge fluctuations are screened by the electron plasma. It is

defined as

λD=r0kBTe

nee2(2.42)

with kBthe Boltzman constant and Tethe electron temperature [79]. The number ND

gives the amount of electrons which contribute to the local screening. In a warm, dense,

strongly coupled plasma, where ND.1, the electron-ion interaction strength is large

and many collisions take place. For ND1, corresponding to hot temperature and low

density, the plasma is weakly coupled and collective motions are preserved.

A plasma can be characterized in two regimes, according to its particle density with respect

to the incoupling laser wavelength. The plasma frequency at which electron waves oscillate

30 Chapter 2. Theoretical concepts and previous experiments

Electric Field

Electrictron Cloud

Cluster

e-e-

Figure 2.15: Cluster driven by an electric field in resonance with the eigenfrequency of the electron

cloud motion. From [81]. In this state the nanoplasma receives a strong thermal excitation, which

leads to a maximized energy absorption from the laser.

in a plasma is given by [61]

ωp=snee2

0me

.(2.43)

If the laser frequency exceeds the plasma frequency (ω≥ωp), the plasma is underdense.

For xenon with a particle density neof 1.7 ·1028 m−3and therefore a plasma frequency of

7.4 ·1015 Hz, this is the case in 13.5 nm light (XUV) with ω= 2.2 ·1016 Hz. The plasma is

overdense for 800 nm radiation (IR) corresponding to ω= 3.7 ·1014 Hz, where ω≤ωp. If

the plasma is weakly coupled, e.g. exhibits hot temperature and low density, the laser and

plasma frequencies can be matched which results in an enhancement of collective electron

motion.

Collective processes

The Mie resonance plays a major role in the ionization of overdense nanoplasmas (ω≤

ωp) [49]. The natural collective oscillation frequency of an electron cloud is given in equation

2.43. Additionally, the quasi-free electrons are driven by the laser electric field, as depicted

in figure 2.15. With a light-induced expansion of the cluster (as subject to section 2.3.3),

the particle density drops and ωpis lowered. Eventually the eigenfrequency of the electron

motion matches the laser frequency [50]:

ωMie =ωp

√3=rρee

30me

(2.44)

with ρethe quasi-free electron density. Here the energy absorption from the laser is max-

imized due to the strong thermal excitation of the nanoplasma. This resonant collective

electron excitation was first experimentally demonstrated for small rare-gas cluster in IR

light [80]. Since this effect only applies for overdense plasmas it is photon energy dependent

and does not occur in clusters excited with XUV light. Apart from a strong wavelength

dependence, the effect of the Mie resonance is also highly influenced by cluster size.

In the approximation of the cluster as a uniform density sphere and an ionic motion with

2.3. Cluster dynamics induced by highly intense laser pulses 31

constant velocity, this resonance is reached after a resonance time [80]

τres =R

vn0

3ncrit 1/3−1.(2.45)

Here Ris the initial radius, vthe expansion velocity, n0the initial density, and ncrit the

critical density. For metal clusters and small rare-gas clusters this resonance can be probed

with a sufficiently long single laser in the range of femtosecond to nanaosecond duration.

But for larger rare-gas clusters in fs-pulses, a dual-pulse pump-probe scheme is required

to match the timescale of cluster expansion. During the expansion, the cluster density

has radial dependence. Hence, the critical density reaches different parts of the cluster

at different times. For large clusters the simple model was extended. It shows that the

resonance is moving inwards from surface to the cluster center with time [82].

Collisional processes

Other energy-exchanging processes are electron-ion and electron-electron collisions.

Fast quasi-free electrons transfer their kinetic energy to bound electrons and either pro-

mote them to an excited state by inelastic scattering or ionize them by electron-impact

ionization [49,50]. The corresponding cross-sections can be calculated from the empirical

Lotz formula [83]. Due to scattering of hot electrons on other quasi-free electrons, a local

quasi-equilibrium distribution establishes. This is the major mechanism leading to elec-

tronic thermalization and giving rise to an Maxwellian electron temperature distribution.

The importance of collision processes rises with cluster size, as in larger clusters bulk pro-

cesses become more prominent [84]. Collisions between ions can usually be neglected due

to the slow ionic motion, which usually exceeds the timescale of a femtosecond-laser pulse.

Collisions of laser-driven electrons with plasma ions - referred to as inverse brems-

strahlung heating (IBS) - is a highly photon energy dependent process. Inner ionized

electrons gain momentum in the laser field and transpose it to thermal energy by scatter-

ing on bound electrons. As a result the plasma gets heated. The averaged energy gain

with time interval dE/dt scales with λ8/3[85]. Therefore, it is most significant in the IR

regime but also has relevance in the VUV range. A IBS contribution was calculated for a

wavelength of up to 62 nm [86]. However, this value could not be validated in experiments

[87]. For XUV fields the oscillations are too fast for electrons to gain sufficient velocity

and IBS is negligible.

Cluster size effects

As the last paragraph already indicated, many nanoplasma dynamic effects change in

significance with cluster size and too simple models loose their accuracy. While for small

clusters the charges can be treated as homogeneously distributed, this does not hold for

larger clusters. Here, electron screening gains importance with increasing size. Trapped

electrons migrate to an energetically favorable state in the cluster center where the cluster

potential is deepest. The charge of the atomic ions is highest at the cluster boundary and

declines towards the middle. The electron cloud screens the ionic background and for a

32 Chapter 2. Theoretical concepts and previous experiments

temperature Tclose to zero a fully net-neutral core is established up to a radius of

Rel =R·Qel

Qion 1/3

(2.46)

with Qel and Qion the overall charge of the electrons and ions respectively [51]. This non-

equilibrium plasma is maintained during the entire laser-matter interaction period. The

time to reach a balanced state by electron-electron collisions is in the order of picoseconds

and therefore exceeds the pulse length for femtosecond lasers [62].

Experimentally this non-homogeneous charge distribution was revealed in ion spectra of

Ar-Xe core-shell clusters [56]. Xenon atoms building the cluster core were surrounded by

an argon shell. While argon charges 4+ and higher were detected, highly charged xenon

ions were virtually absent. This behavior was described by thermalization of the quasi-free

electrons and a subsequent recombination of the plasma core (see also 2.2.3).

Explicit treatment of the electromagnetic wave propagation is negligible for small clusters

and microscopic processes, such as collisions and plasma microfields, are of major impor-

tance. The electrostatic approximation breaks down for larger cluster sizes in the range

of the wavelength. Here the so-called propagation regime is entered [79] where clusters

opacity plays an increasingly important role and the plasma penetration depth δphas to

be taken into account. For an overdense plasma with frequency ωpit is given by [32]

δp=c

ωp

.(2.47)

Throughout this thesis clusters composed of xenon, argon, and silver atoms are investi-

gated. The corresponding penetration depth into the clusters with solid density is about

40 nm for xenon, 25 nm for argon, and 7 nm for silver particles.

2.3.3 Energy redistribution and disintegration of excited clusters

In the final stage of the three-phase-model (fig. 2.10), the light pulse goes to zero and

no more energy absorption takes place. The energy inside the highly excited cluster is

redistributed by charge transfer. Radiative and non-radiative relaxation and recombination

events take place and fluctuations in charge states even out. Due to repulsive forces and

hydrodynamic pressure the sample disintegrates on a timescale of picoseconds [43] and

beyond [88]. The expansion of the ionic background results in adiabatic cooling of the

electron cloud. Eventually the cluster fragments and reaches a final state, which can be

measured in electron and ion spectra. Due to the dynamics in the previous stages, cluster

ions exhibit higher kinetic energies than ions from atomic gas.

Cluster disintegration

Ionic motion might start already during laser-cluster interaction. After the laser pulse has

gone and energy deposition into the cluster has stopped, the cluster disintegrates. Initial

cluster ionization and subsequent energy transfer in the cluster (e.g. the charge of the

cluster), the number of trapped electrons, and their temperature determine the expansion

dynamics. There are two limiting cases: (i) explosion due to repulsive Coulomb forces

2.3. Cluster dynamics induced by highly intense laser pulses 33

Hydrodynamic expansionCoulomb explosion

neutral

charged

positively charged

sphere

thin bipolar

sheath

Figure 2.16: Schematic depiction of the cluster state determining the rivaling expansion mecha-

nisms, adapted from [89]. (i) A net-positively charged cluster results in Coulomb explosion. (ii) A

net-neutral cluster with a thin ambiploar shell leads to hydrodynamic expansion.

between ions and (ii) expansion by hydrodynamic pressure of the hot electron gas in a

plasma. A sketch of the charge distribution in the cluster before disintegration in both

regimes is presented in figure 4.27 a and b respectively. Intermediate regimes can occur in

non-homogeneously charged clusters.

If the net charge of the cluster is positive due to previous outer ionization of electrons,

unneutralized ions repel each other and are driving the cluster apart in a Coulomb ex-

plosion. Hence, the intensity of the laser field needs to be high enough to strip at least

one electron from an atom before ionic motion sets in [61]. The timescale on which the

cluster expands depends on the average charge state q. In a homogeneous expansion the

sample doubles its radius during the time [50]

tCoul = 2.3·p2π0mir3

e·q=rmi

niq2e2(2.48)

with midenoting the ion mass, rsthe Wigner-Seitz radius, and nithe atom density. For

xenon with rs= 0.24 nm the time holds tCoul = 190 fs/q. The ions fly apart very quickly in

the electric field of their own space charge, holding high kinetic energies. Coulomb explosion

mostly occurs for smaller clusters [49], while for larger clusters a different mechanism is

dominant.

In a cluster where most electrons are inner ionized and a dense nanoplasma is formed,

the cluster can be highly charged but still being almost net-neutral due to the screening

of quasi-free electrons in the sample. The cluster is driven apart by the thermal energy

of the activated, hot electrons instead of repulsive inter-particle Coulomb forces. If the

electron cloud is treated as an ideal gas with temperature Teand electron density ne, its

hydrodynamic pressure of phydr =nekBTe[47] is forcing the nanoplasma to drive apart

in a hydrodynamic expansion. In this regime, the time a spherical cluster with initial

cluster radius Rneeds to double in size is given by [48]

thydr =R·rmi

qkBTe

.(2.49)

The timescale is slower than in a Coulomb explosion and therefore the released charge ions

hold lower kinetic energies.

The experimental determination in which of both regimes the cluster is fragmenting is

not trivial. In early experiments on ensembles of clusters, it was proposed to identify the

dominating regime by the dependence of the kinetic energy on ion charge [90,91]. It was

claimed that while in the Coulomb case the final kinetic energy scales quadratically with

34 Chapter 2. Theoretical concepts and previous experiments

the charge state (Ekin(q)∼q2), it scales linearly for the quasi-neutral case (Ekin(q)∼q).

Experiments on water clusters however indicate that this method is often ambiguous [55].

A theoretical study showed, that this behavior is only valid for the average charge state [92],

e.g. for Coulomb explosion hEkin(q)i ∼ hq2iand for hydrodynamic expansion hEkin(q)i ∼

hqi. This was validated in an experiment on single clusters for the hydrodynamic case [44].

A different theoretical study suggested that ion energy spectra are not well suitable for

the identification of the expansion mechanism [52]. This study also gives a more reliable

measure for the regime in which the excited cluster disintegrates: the so-called frustration

parameter [52]

α=ntot

nout

.(2.50)

It is defined as the ratio of all (inner and outer) ionized electrons ntot to outer ionized

electrons nout. In [52] the ionization is calculated in the photon-dominated regime with

ntot =IτσN/(~ω), where Iis the laser power density, τthe laser pulse length, σthe

atomic cross-section for the dominant ionization channel, and Nthe number of atoms in

the cluster. The number of outer ionized electrons is calculated by [52]

nout =4π0

e2R·(~ω−Eip).(2.51)

For α≤1 the cluster is strongly charged and Coulomb explosion takes place, while for α

1 the majority of electrons is trapped and the major expansion mechanism is hydrodynamic

expansion.

In many cases the expansion is a combination of both limiting mechanisms. As soon as there

is a plasma the cluster will always expand in a hydrodynamic expansion due to screening

by quasi-free electrons. But the shell will explode in a Coulomb explosion since the outer

ions remain unscreened after electron migration towards the cluster center [93,94]. In a

laser wavelength dependent theoretical study on small argon clusters it was shown that

there is a smooth transition from a more hydrodynamic to a predominantly Coulombic

regime with increasing photon energy [52].

Recombination and relaxation processes

After the laser pulse is gone, the inner-ionized electrons relax either in three-body [95] or

in many-body recombination [96]. An electron is captured by an ion in the vicinity of a

second or more electrons respectively. The number of recombinations NRis dependent on

the ion density Ni, on the electron density Ne, and on the electron Temperature Te. For

Ni=Ne=N0, the number of recombinations evolving with time tcan be expressed as

[97]

NR(t) = N0· 1−1

p1 + t/τr!.(2.52)

The recombination time is defined as τr= 1/(2αrN2

0) with the electron temperature de-

pendent factor αr= 8.75 ·10−27T−4.5

ecm6s−1. Recombination is most effective when the

nanoplasma is dense and cold.

The evolution of electron relocalization with cluster expansion is subject of a theoretical

study [98]. Small (N= 923) xenon clusters in ultrafast (30 fs), XUV (92 eV) pump-probe

2.3. Cluster dynamics induced by highly intense laser pulses 35

pulses were investigated with molecular dynamic (MD) simulations. It was found that

three-body recombinations mainly take place in the early stage of cluster expansion, and

are suppressed for long delays. The pump pulse generates a warm and dense nanoplasma

which cools down during cluster expansion, as depicted in figure 2.17. These results prove

evidence for the findings in an experimental study [99]. The number of recombination

processes is also highly dependent on the location within the cluster nanoplasma. Shell-

dependent recombination probabilities were found which are most efficient in the cluster

center.

Fluorescence spectroscopy is a versa-

Temperature k T [eV]

102 3 4 5 6 7 8 9 10 11

10-4

10-3

10-2

10-1

2000 fs

1000 fs

3000 fs

t = 3000 fs

t = 1000 fs

t = 100 fs

N =1

Density [10 m ]

30 -3

1/fs

1/ps

1/ns

Quantum

Strongly coupled Weakly coupled

TBR

100 fs

500 fs

Figure 2.17: Evolution of nanoplasma density and

temperature in a pump-probe setting calculated with

MD simulations. From [98].

tile tool to resolve charge states be-

fore recombination, which are hidden

in ion spectra. Ion spectra from clus-

ters consisting of a xenon core and an

argon shell illuminated by an XUV

pulse revealed a highly charged outer

layer but only little charged ions from

the recombined core [56]. Correspond-

ing fluorescence spectra resolved mul-

tiply charged xenon ions from the in-

ner cluster part, revealing that these

were initially as highly activated as

shell atoms [100]. This experiment

proofed that the charge states gener-

ated during the laser-cluster interac-

tion might significantly differ from the

final charge state distribution, due to

strong recombination.

However, recombination processes can also be efficiently suppressed, for example during

ionization heating. This was demonstrated with 800 eV photons by using a new experimen-

tal approach [101]. Ion spectra and scattering patterns were recorded simultaneously from

one single cluster in the interaction region. With this method, signal averaging over the

cluster size distribution due to statistical cluster growth process and the focal intensity pro-

file was ruled out. The striking observation in this paper is that exclusively highly charged

atomic ions were detected from high laser intensities of about 1016 W/cm2onwards. The

absence of low charge states is attributed to inefficient electron-ion recombination in a

initially hot nanoplasma. Since this effect occurs only for the highest intensities it could

not be resolved for experiments on ensembles of clusters. There, most particles are hit in

the focal wings with low intensities.

Large clusters in IR and XUV light

Up to date, many experiments and theoretical studies were performed for small rare-gas

and metal clusters in laser light, consisting of up to a few 10000 atoms. Those experiments

helped to develop a fundamental understanding of the underlying dynamics. Less experi-

mental and theoretical data is available for larger clusters from 105atoms onwards, since in

this size range sample generation becomes increasingly challenging and calculations com-

36 Chapter 2. Theoretical concepts and previous experiments

Figure 2.18: Microscopic

particle-in-cell simulation

for a 30 nm radius xenon

cluster irradiated with an

800 nm laser pulse. From

[102]. Shown are the calcu-

lated spatial distributions

of total (a), tunnel (b) and

impact ionization (c) rates,

as well as mean charge

states (d), electric field in-

tensity (e) and fast elec-

trons (f) at the point of res-

onance condition. Laser-

induced plasma waves are

responsible for the inhomo-

geneous distributions.

putationally costly. Nevertheless, also in this domain some experiments were performed,

which could shed light on several aspects of laser-cluster interaction. This section tries to

give a short introduction to the current understanding of phenomena occurring in large

clusters from 105atoms onwards and to point out the topics which are still under discus-

sion. The focus is on the interaction of large xenon and argon clusters with IR and XUV

light.

Dynamics of large clusters at 800 nm: The photon energies in the infrared regime

(1.55 eV at 800 nm wavelength) are for most rare-gases too low for laser-cluster interaction

to be in the photon-dominated regime. Clusters are initially ionized by tunnel or above-

threshold ionization in sufficiently intense laser fields (see section 2.3.1). Subsequently inner

ionization occurs ‘from top to bottom’, i.e. from outer to inner atomic levels. The plasma

dynamics are dominated by the oscillating external laser field which drives the quasi-free

electrons back and forth over a long range within the sample. Electrons are repeatedly

forced to recollide with ions leading to inverse bremsstrahlung heating. Initially the plasma

frequency is much higher than the laser frequency. Upon cluster expansion the plasma

density drops and eventually Mie resonance is reached. This results in an enhanced energy

absorption and increased ionization. For large clusters, the critical density is expected to

be reached after picoseconds. Therefore, a dual-pulse experiment is needed to probe the

resonance condition with femtosecond-laser pulses. Eventually the cluster fragments due

to ionic motion. Large clusters usually disintegrate in a Coulomb explosion of the outer

shell and a hydrodynamic expansion of the inner part, due to electron migration towards

the center where a screened core is built.

From energy spectra the electron temperature can be deduced, like in an experiment per-

formed on ensembles of Xe150000 clusters irradiated with 5 ·1015 W/cm2intensity Ti:Sa

pulses [55]. A temperature of 600 eV was fitted to the electron kinetic energy distribution.

An enhancement of electron emission in the Mie resonance with shift to higher kinetic en-

ergies, and therefore more efficient heating, was observed. The emission spectra show high

angular dependence due to asymmetric barrier lowering parallel to the laser polarization.

A computational study with a microscopic particle-in-cell code (MicPIC) investigated the

2.3. Cluster dynamics induced by highly intense laser pulses 37

resonant Mie plasmon excitation of a R = 30 nm preionized xenon cluster in 800 nm light

with moderate laser intensities of <1014 W/cm2[102]. It was revealed that during the

probe pulse attosecond plasma-waves are generated by hot electrons. Those waves recollide

with the cluster surface and subsequently migrate to the cluster center where they collide

with each other. Non-homogeneous electric field fluctuations arise, which exceed the driving

laser intensity by more than 2 orders of magnitude (see figure 2.18). This results in an

enhanced impact ionization creating charge states up to Xe10+.

A one-color dual-pulse experiment with intensities of 5 ·1015 W/cm2on large argon clusters

(up to R= 5 nm) investigated the disintegration after irradiation [103]. In ion kinetic

energy spectra after single-pulse excitation a cluster size dependency was revealed in an

increase of the maximum energy proportional to the 1.6 power of the cluster source backing

pressure. This leads the authors to the conclusion that the cluster explodes in a Coulomb

explosion, because the kinetic energy of nanoplasma-expelled ions should be independent

of the cluster size.

The anisotropy in ion emission was calculated for a R = 17.5 nm argon clusters with PIC

code [104]. It shows that anisotropy is less important for large clusters because electron

collisions become more relevant. They also investigate resonant heating. The resonance

appears when the period of an energetic electron in the confining electrostatic potential

matches the laser frequency. The electron oscillation period, however, depends on the laser

intensity. Therefore, a threshold intensity in the order of 1015 W/cm2has to be reached

for this resonance. This is not the case in the experiments performed for this thesis and

can therefore be ruled out.

Dynamics of large clusters at 13.5 nm: Cluster dynamics in short-wavelength pulses

differ fundamentally compared to the optical regime. The laser field is oscillation fast

compared to the tunneling time of an electron. Tunnel and above-threshold ionization are

negligible in the XUV regime. Also IBS heating is ineffective in the XUV regime due to

a low ponderomotive potential. Additionally, the plasma is underdense from the begin-

ning such that resonant collective heating cannot occur. Unlike in IR pulses, cluster ion

charges do not exceed atomic ion charges. Instead, the sample is initially ionized in di-

rect single-photon absorption. Subsequent Auger cascades fill the inner-shell vacancies and

further electrons are ejected. The nanoplasma is heated via ionization heating [105,52].

Higher charge states are generated by electron-collision ionization or multi-photon absorp-

tion. At 90 eV collisional cross-sections for 5s and 5p states are higher (500 Mbarn) than

photoionization cross-sections (20 Mbarn) [106]. An experiment on small xenon clusters

revealed that the electron energy distribution shows two major peaks: one from directly

photoionized electrons and one from plasma electrons with a temperature of about Te=

20 eV [42].

The first experiment on single, giant (R = 30 - 600 nm) xenon clusters in single-shot mode

at 13.6 nm light revealed new insights into energy redistribution processes and cluster

explosion [45]. The data is depicted in figure 2.19. The newly developed method of photon

imaging coincident with ion time-of-flight spectroscopy allowed to sort single cluster data

for their size (deducted from the spacing of the rings in scattering patterns, see fig. 2.19 a)

and subsequently to arrange ion spectra according to exposed power density (fig. 2.19 b).

The central kinetic ion energy, extracted from the time-of-flight spectra, scales linearly

38 Chapter 2. Theoretical concepts and previous experiments

time of flight [µs]

ion yield [arb.u.]

Figure 2.19: Data taken in single-cluster single-shot experiments on giant xenon clusters with

13.6 nm pulses. From [45]. (a) Scattering patterns of clusters with different radii encoded. (b) Ion

spectra sorted for size and exposed power density. With increasing intensity higher charge states

rise and shift towards shorter flight times. (c) Corresponding kinetic energies deduced from the

flight times plotted over charge state reveal a linear dependency and an increase in energy with

cluster size.

with charge state (fig. 2.19 c). For all four size ranges an increase in power density from

approximately 3 ·1012 to 5 ·1014 W/cm2results in an increase in charge states by a factor

of 3 to 4. With increasing cluster radius (by factor 3.3 from 80 to 600 nm) the ion kinetic

energy per charge state grows only by a factor of 1.7. Apparently the laser focal power

density has more impact on the laser-induced cluster dynamics than the particle size.

Charge state resolved kinetic energy distributions reveal a narrow energy distribution and

missing low kinetic energies [44] (not shown in fig.2.19). This behavior was interpreted

as indicator for strong recombination in agreement with theoretical MD calculations on

small argon clusters [52]. From a calculated frustration parameter of 6 ·105deep in the

nanoplasma regime and narrow ion kinetic energy distributions for all charge states, the

2.3. Cluster dynamics induced by highly intense laser pulses 39

conclusion was drawn that for large clusters a thin outer shell comes off in hydrodynamic

expansion and the nanoplasma core recombines to full neutrality.

Short summary at present understanding

In laser-cluster interaction, the influence of many parameters (sample matter, and size; laser

intensity, pulse length, and photon energy) on complex processes in the cluster make it

hard to foresee the outcome of an experiment. General trends are a smooth transition from

mainly hydrodynamic to Coulomb expansion with increasing laser wavelength and intensity

as well as with decreasing cluster size. However, the assignment of process dominance from

experimental data proves to be nontrivial. Ruling out cluster size distribution and focus

averaging gives better access to underlying dynamics such as recombination frustration

and enables a charge state resolved analysis of ion kinetic energies.

Up to date not all processes during and after cluster irradiation are completely understood.

The key questions are:

•How and how fast does ultrafast ionization proceed and is a plasma built-up upon

irradiation?

•How fast is the energy redistributed inside? What is the role of collision and recom-

bination processes?

•How and on which timescale does the fragmentation of an irradiated particle pro-

ceed? What is the role of screening and recombination in the context of cluster

disintegration?

This thesis tries to contribute to answering these questions by investigating large, single

xenon, argon, and silver clusters in ultrafast, highly brilliant IR and XUV pulses.

40 Chapter 2. Theoretical concepts and previous experiments

Chapter 3

Experimental Setup

This thesis provides new insights into the dynamics of very large, individual xenon clusters

induced by ultrashort, highly intense light pulses. This chapter gives an overview of the

components used in the experiment and collection of raw data. The experiments were

performed in August 2011 at the Free-electron Laser in Hamburg (FLASH) at DESY in

Germany. FLASH provides ultrabright laser pulses of very short wavelength.

A schematic drawing of the setup is presented in figure 3.1. Femtosecond pulses of infrared

(IR) and extreme ultraviolet (XUV) light were coupled into the experimental chamber and

guided into the interaction region by a set of stray light apertures. Here, the pulses were in-

tercepted with single clusters, produced in supersonic expansion. Upon irradiation clusters

Figure 3.1: Scheme of the experimental setup. From left to right: XUV and IR beams from

the FLASH facility are colinearly coupled into the vacuum chamber. Straylight apertures guide

the beams into the interaction region. Here, they are intercepted with single large clusters. The

resulting ionized fragments are recorded with a time-of-flight spectrometer. Diffraction patterns

are captured by a scattering detector.

42 Chapter 3. Experimental Setup

are turned into a nanoplasma. The morphology and transient electronic states are captured

by XUV scattering. Fragments of the exploding clusters are recorded simultaneously with

an ion time-of-flight (TOF) spectrometer.

In a pump-probe setup, XUV and IR pulses initiate and probe the dynamics, expansion,

and disintegration of the xenon clusters. A detailed overview of the free-electron and

optical laser properties and the layout is given in section 3.1. The vacuum system, cluster

source, and detector systems are described in detail in section 3.2.

3.1 Generation of XUV and IR pulses

Research in the field of laser-matter interaction drastically increased with the emerging

of lasers, providing mono-energetic radiation with high coherence. Over the last decades

table-top lasers developed to become shorter in pulse length (down to attoseconds) al-

lowing to study processes with atomic resolution in time. Table-top Higher Harmonic

generation sources even reach the x-ray regime necessary to investigate matter with almost

atomic spacial resolution [107]. However, their peak brilliance is not sufficient for many

experiments involving imaging of individual nanoparticles. Accelerator-based synchrotron

sources deliver highly brilliant x-ray beams, but cannot compete with lasers when it comes

to pulse length. Free-electron lasers (FELs) opened up new possibilities by combining all

three characteristics, pushing into the x-ray regime with ultrashort pulses and additionally

providing high intensities [7].

In the experiments performed for this thesis, XUV laser pulses from the FEL where com-

bined with IR pulses from a table-top laser system in a pump-probe setup. A quick intro-

duction to the generation process of FEL pulses is given in section 3.1.1. The IR laser was

provided at FLASH and the system is described in section 3.1.2. For two color pump-probe

experiments, a good temporal and spacial overlap is critical. The setting and determina-

tion of the spacial and temporal overlap of the two individual pulses are explained in more

detail in section 3.1.3.

3.1.1 XUV pulse generation at the free-electron laser facility FLASH

For portraying individual non-crystalline nanoparticles by diffraction imaging, several re-

quirements need to be fulfilled by the illuminating light source [35]. A high photon flux is

crucial to gain a good signal-to-noise ratio from scattered photons. The light needs to be

monochromatic with a wavelength smaller than the particle, being in the XUV to x-ray

regime for nanometer sized targets. The length of the light pulse must be shorter than

the timescale of atomic vibrations and rotations in molecules and other targets which is in

the range of 10−12 s [108]. Sufficient coherence is important since interference of diffracted

waves is required. Presently, all of the above requirements combined are only fulfilled by

a short-wavelength FEL pulse.

FELs are fourth generation accelerator-based light sources using the principle of syn-

chrotron radiation generation by sending a beam of relativistic electrons through a mag-

netic structure referred to as Doppler frequency up-shifting of emitted radiation. Up to

date there are four FELs in user operation worldwide lasing in the XUV up to x-ray regime:

3.1. Generation of XUV and IR pulses 43

Figure 3.2: Schematic drawing of the current FLASH I and planned FLASH II setup, depicting the

constituent components required to generate a FEL beam [109]. See text for detailed description.

FLASH [110,111,112] where the experiments for this thesis took place, the Linac Coherent

Light Source (LCLS) in the US [113], the SPring-8 Angstrom Compact free-electron laser

(SACLA) in Japan [114], and the free-electron laser for multidisciplinary investigations

(FERMI) in Italy [115]. Development and planing are ongoing for further x-ray FEL facili-

ties like the European x-ray free electron laser (XFEL) [116], the SwissFEL [117], the PAL

XFEL in Korea [118], and for extensions of FLASH and LCLS. Detailed descriptions and

derivation of the theory behind FELs are found in literature (e.g. [119,120,121,122,123])

and a good illustration of the machine operation mode and setup at DESY is given in [124].

A short introduction into the principle of FEL radiation generation will be given here on

the basis of the FLASH layout depicted in figure 3.2.

The main components of a FEL are an electron injector, a particle accelerator, and a mag-

netic undulator as seen from left to right in figure 3.2. Free electrons are produced with

10 Hz repetition rate in a Radio-Frequency (RF) gun by illuminating photocathodes with

short ultraviolet (Nd:YLF) laser pulses. The photoemitted electrons are rapidly accelerated

to relativistic energies by radio-frequency fields. This cancels the repelling electric forces

between the equal charges by the attractive magnetic forces between the parallel currents.

The electron beam is further accelerated close to speed of light in superconducting linear

accelerators. The electrons are driven in klystrons by electromagnetic alternating fields of

more than 15 MV/m. Between the accelerating structures bunch compressors are shorten-

ing the electron pulses in length by two orders of magnitude. Here, the leading electrons

of the bunches gain less energy than the trailing ones. Forced through a magnetic chicane

the tail electrons travel a shorter distance and hence catch up.

The actual lasing process takes place in six undulator modules of 4.5 m each (sketched

in alternating green and red in fig. 3.2). Forced by a long arrangement of dipole magnet

pairs with alternating polarity, the electrons follow a wavelike orbit and emit photons

with each turn. The wavelength of the emitted light is dependent on the spacing of the

magnets (undulator period λU), the magnetic field B, and the energy of the electrons.

Continuous tuning of photon energy is realized at FLASH by adjusting the electron beam

energy. Electron beam and radiation co-propagate along the undulator interacting with

each other. The electron beam is bundled along its direction of propagation when the

undulator period λUis chosen such that the radiation field propagates (or slips) through

the electron pulse at one fundamental wavelength per undulator period, as sketched in

figure 3.3. The electrons are now emitting photons coherently [120]. At FLASH the

44 Chapter 3. Experimental Setup

Incoherent emission:

electrons randomly phased

Coherent emission:

electrons bunched at

radiation wavelength

Figure 3.3: Schema of FEL radiation emission from relativistic electrons and microbunching by

velocity slipping in an undulator [123]. a) When the electrons enter the undulator their phases

are randomly distributed and radiation is emitted incoherently. While passing the undulator the

electrons start bundling by velocity slipping and eventually start to radiate cohernently, if the

electrons are bunched at the radiation wavelength.

beam is spatially fully coherent across the entire focus diameter [125]. The temporal

coherence length holds a few femtoseconds [126]. The intensity of the emitted light scales

quadratically with the undulator period I≈N2. The radiation power grows exponentially

until saturation sets in.

FLASH is a so-called SASE laser, which stands for self amplified spontaneous emission.

Here, the lasing starts from shot noise and hence the spontaneous undulator radiation is

amplified at the beginning of the undulator. Due to the statistical process the photon

energy fluctuates. A different approach is to stimulate the lasing process with a monochro-

matic x-ray beam. The lasing process is then seeded. Due to the controlled FEL radiation

generation the pulses have well-defined profiles and bandwidths, leading to higher bril-

liance. Additionally, there is no temporal jitter with respect to the seeding laser. A seeded

FEL in operation is the FERMI FEL in Trieste [115].

At FLASH the electron beam is deflected behind the undulators by a magnet and dumped.

Downbeam the light axis follows a photon diagnostics section (indicated by a green box in

fig. 3.2), where each shot is characterized in non-invasive measurements. The fluctuations

in wavelength - due to the statistical SASE process - are recorded with a variable line

spacing grating spectrometer (VLS). Four gas monitor detectors (GMD) determine the

position and the intensity of each pulse. Two filter wheels for attenuation of the beam are

installed. Additionally, a gas attenuator can provide continuously variable intensities.

The beam is delivered to the user’s experimental endstations through a photon beam trans-

port system with gracing incidence carbon and nickel mirrors operating under high vacuum

conditions to prevent light absorption in air. At beamline 3, where the measurements were

3.1. Generation of XUV and IR pulses 45

Table 3.1: FLASH is a user facility since 2005 and has been upgraded several times. Listed are

the state-of-the-art radiation parameters in 2014 [127] and values of the 2011 experiment.

Parameter Current 2011

Wavelength 4.2 - 45 nm 13.6 nm

Average Single Pulse Energy 10 - 500 µJ 140 µJ

Pulse Duration (FWHM) <50 - 200 fs 100 fs

Photons per Pulse 1011 - 1013 1013

Spectral Width (FWHM) 0.7 - 2 % 1 %

Peak Power (from av.) 1 - 3 GW -

Average Power (example for 5000 pulses/s) up to 600 mW -

performed, tight focusing is established with ellipsoidal mirrors of 2 m focal length, result-

ing in a focus of r= 10 µm in radius [111]. For XUV pulses centered around λ= 13.6 nm

wavelength (corresponding to 91 eV) with t= 100 fs pulse length and E= 140 µJ pulse

energy, this leads to a power density Iin the focus of

I=E

2πr2t= 4.1·1014W/cm2.(3.1)

3.1.2 IR pulse generation at FLASH

The FLASH facility provides amplified Titanium:Sapphire (Ti:Sa) pulses which are tem-

porally synchronized with the FEL pulses for the performance of two color pump-probe

experiments. A detailed overview of the optical femtosecond laser system is given in [128].

The major components used for the experiments in this thesis are shortly introduced here.

A schematic drawing of the setup in the laser hutch is presented in figure 3.4.

The infrared laser pulses with a central wavelength of λ= 800 nm and bandwidth of 50 nm

are generated by a Ti:Sa ultrashort pulse oscillator (Kapteyn & Murnane Laboratories,

Model MTS). To perform well defined pump-probe experiments the oscillator is synchro-

nized to the FEL master clock with a jitter of under 70 fs root mean square (rms). The

oscillator seeds two amplifiers: a burst-mode optical parametric amplifier (indicated in

yellow in fig. 3.4) and a single-pulse chirped-pulse amplifier system (indicated in red in fig.

3.4). In the experiments performed for this thesis only the latter was used. It consists of

a regenerative and a 2-pass amplifier (Coherent, Hidra-25). The maximum output power

is 20 mJ at 50 fs pulse duration. For safe beam transportation the pulse is stretched and

later shortened with a compressor, leading to a pulse duration of 80 fs for the experiment

[129].

With temporal instabilities from the amplifier, the beam transport line, and the FEL

pulse jitter the overall temporal fluctuation between FEL and Ti:Sa adds to a total of

250 fs rms [130,131]. It is constantly monitored by a streak camera (Hamamatsu, C5680)

which records the arrival time of the optical laser pulse and the synchrotron radiation

pulse, radiated when the electrons are bent to get dumped. The relative jitter between

both pulses is saved in the data acquisition (DAQ) system. This enables to trace random

fluctuations and drifts in timing difference on-line and in post-analysis. The temporal

separation between FEL and IR pulses can be altered with a computer controlled delay

46 Chapter 3. Experimental Setup

Figure 3.4: Layout of the optical laser system at FLASH [128]. For the experiments in this thesis

only the single pulse amplifier was used.

state within a 3 ns range in steps of 10 fs. The position of the stage is linked to the bunch-

ID and also saved in the DAQ system. The optical pulses, delivered via a beamline system

to the experimental endstations, exhibit a beam diameter of 16 mm FWHM.

To couple the beam into the vacuum chamber and to focus it onto the interaction region

is in the responsibility of the users. Therefore, an optical setup was designed and imple-

mented on a breadboard positioned between vacuum chamber and beamline. The beam

was transported to the height of the optical setup with a periscope. For maximum trans-

mission, 2 inch diameter mirrors (Newport) were used. The IR beam entered the vacuum

system through a CF60 window flange. To achieve good spatial and temporal overlap in

pump-probe configuration (see next section) and due to the detector setup (see chapter

3.2.3), the incoupling geometry of the IR was collinear with the XUV beam. The Ti:Sa

pulses were reflected into the interaction region via a mirror in the FEL beam path, which

had a centered hole of 2 mm diameter to allow the FEL beam to pass. The mirror was

placed in a CF60 cube in the vacuum system and fixed on motorized in-vacuum stages for

full movement in all directions (three linear states with 8 mm hub (Mechonics) and two

angular stages (Newport) for pitch and tilt motion).

The focal length was chosen such that the power density in the interaction region was

maximum. Therefore, three aspects had to be taken into account:

•the focal length had to be short in order to get a tight focus,

•the divergence had to be small for the beam to fit through the detector hole, and

•the beam diameter had to be large on the hole of the incoupling mirror to keep the

power loss low.

3.1. Generation of XUV and IR pulses 47

Table 3.2: IR radiation parameters of the optical laser system in the laser hutch [128] and at the

experimental endstation in 2011.

General Parameters Value In Experiment Value

Central Wavelength 800 nm Focal length 750 mm

Max Pulse Energy 20 mJ Pulse energy in focus 0.8 mJ

Min Pulse Duration <50 fs Pulse Length 80 fs

Beam Diameter (FWHM) 16 mm focal diameter 90 µm

Repetition Rate 10 Hz Focal power density 1.1·1014 W/cm2

Energy Stability 3 % rms

To fulfill all three aspects, a clano-convex lens (Thorlabs, N-BK7) with focal length of

750 mm was chosen, resulting in a spot size of 5.5 mm diameter on the holey mirror, of

90 µm in the focal region, and of 1.4 mm at the detector hole. For focal spot positioning

along the beam axis, the lens was mounted on a linear stage (Thorlabs, 2 inch travel)

which was placed outside the vacuum due to the long focal length. In front of the vacuum

chamber the IR beam had a power of 1.4 mJ, which was reduced at the holey mirror by

40 %. The power behind the interaction region was measured to hold E= 0.8 mJ, resulting

in a focal power density of I= 1.1·1014 W/cm2with central wavelength λ= 800 nm, pulse

length τ= 80 fs, and estimated focal spot size d= 90 µm (see equation 3.1).

3.1.3 Spatial and temporal overlap in pump-probe setup

The pump-probe scheme is one of the most promising concepts to examine dynamic pro-

cesses on a picosecond time scale. While the pump pulse initiates the reaction of the

sample, the probe pulse observes the induced changes. In order to ensure that both pulses

hit the target, a reliable spacial overlap between IR and XUV pulse is required. In the

interaction region, the IR beam with focal spot size of 90 µm was overlayed onto the 20 µm

FEL beam with the help of a yttrium-aluminium-garnet (YAG) screen and a microscope.

The screen was moved into the interaction region with an UHV manipulator. While the

FEL focal position was fixed, the Ti:Sa focus was moved with two mirrors located on the

breadboard outside the vacuum. The beam profiles were imaged with a resolution of 7 µm

by a CCD camera (Basler) combined with a zoom-objective (Edmund, VZM 450i). This

setup succeeded in establishing a spacial overlap with a precision of about 10 µm in x- and

y-direction and about 300 µm in z-direction [132].

After setting the spacial overlap, the temporal overlap between IR and FEL pulses was

established in three steps. First, it was roughly set with a resolution of 100 ps by irradiating

a coaxial cable placed in both focal volumes. Upon impact the photons induced a current

in the inner conductor, which is sensitive to a broad photon energy range and exhibits a

fast rise time of 100 ps. The pulses induced by both laser beams are monitored with a fast

oscilloscope (LeCroy) and brought to overlap by movement of the IR delay stage in the

laser hutch.

In a second step, the temporal overlap was established more precisely with a resolution

of 1 ps, using molecular nitrogen (N2) as demonstrated in [133]. Via a metering valve the

vacuum chamber was flooded with gaseous nitrogen up to a pressure of p= 4·10−7mbar. By

48 Chapter 3. Experimental Setup

ion yield [arb.u.]

time of flight [µs]

1.85 1.87 1.89 1.91

0.65

0.70

0.60

0.55

N+

N2+

2δt≈

≈

+2.5 ps

-2.5 ps

δt

-0.5 0 0.5 1

N ion yield

-8

-6

-4

-2

temporal delay t [ps]

XUV/IR

IR/XUV

Figure 3.5: Temporal overlap determination with precision of one picosecond, adapted from [132]

and [133]. a) If the gaseous nitrogen is hit by an XUV beam it gets ionized and a high N2+

2signal

can be detected in ion TOF spectra (red curve). If a strong IR beam follows the XUV beam,

the XUV generated N2+

2dissociates into N+leading to a decrease in N2+

2signal (green curve). b)

Tracking the N2+

2ion yield over pump-probe separation time δt shows the isochronous arrival of

both laser pulses, where the Gaussian error function fit (blue line) decreases to half of the maximum

N2+

2signal.

pumping the gas with the XUV beam the molecular nitrogen was turned into molecular

nitrogen dications (N2+

2) due to core-level ionization and subsequent Auger relaxation.

As depicted in figure 3.5 a (red curve), a high N2+

2signal was detected in the ion TOF

spectrometer. When probing the XUV-ionized nitrogen molecule with the IR pulse, it

dissociates due to the intense optical field. As a result, the N2+

2signal decreases (see green

curve in fig. 3.5 a). To establish the temporal overlap, the IR delay stage was scanned.

The central N2+

2peak intensity was plotted over delay time and fit with a Gaussian error

function. The delay stage was positioned where the fit function decreased to the half

maximum (see blue curve in fig. 3.5 b).

Once the temporal overlap was established on a picosecond timescale, it was possible to

employ a third method as described in [134]. Here, the short-lived transient ion signal of

Xe3+ is indicating the isochronous arrival of both pulses with a resolution of 400 fs. Via the

cluster source gaseous xenon was leaked into the chamber. Around 90 eV photon energy,

xenon exhibits the 4d - f giant resonance [66] introduced in section 2.3.1. Irradiation with

one single XUV photon leads to double or triple charged xenon, due to 4d shell ionization

and subsequent Auger decay leaving two or three electron vacancies in the outer 5p shell,

respectively. The Xe2+ and Xe3+ ion TOF signals therefore scale linearly with the FEL

intensity1. Long-lived intermediate states just below the Xe3+ threshold can be pumped

by the IR pulse leading to a temporary increase in Xe3+ ion yield as evident from figure

3.6 a. The green curve shows a spectrum where the xenon gas is pumped with an IR and

probed with an XUV beam. When reversing the pump-probe scheme (blue curve), an

increase in Xe3+ ion yield exhibits the excitation of XUV generated Xe2+ states to Xe3+

states. In 500 TOF spectra taken at each delay time, the Xe3+ yield was integrated and

normalized to the Xe2+ yield. Plotted over pulse separation time δt the half maximum of

the Gaussian error function fit revealed the isochronous arrival time of both pulses with a

1In the production of higher charge states nonlinear processes like multiple-photon absorption are

involved.

3.2. Experimental chamber 49

3.2 3.4 3.6 3.8 4.0 4.2

time of flight [µs]

ion yield [arb.u.]

3+ Xe

t = +2.2 ps

t = - 2.1 ps

-4 -2 0 2 4 6

0.6

0.8

0.2

0.4

0.0

normalized Xe intensity

temporal delay t [ps]

Figure 3.6: Fine temporal overlap between IR and XUV pulse established with xenon gas, adapted

from [132]. a) Ion TOF spectra from xenon gas. Green curve: xenon is first exposed to IR and

after to XUV beam. Xe2+ and Xe3+ ion yield scale linearly with FEL intensity. Blue curve: if

the IR beam follows the XUV beam, XUV-excited intermediate states are pumped by the IR pulse

leading to an increase in Xe3+ ion yield. b) Isochronous pulse arrival time is extracted from the half

maximum of the Gaussian error function fit to the normalized Xe3+ ion yield plotted over pulse

separation time δt.

resolution of 400 ps (fig. 3.6 b). Once both laser pulses are well synchronized in time and

space, a good overlap with the cluster beam needs to be established as described in the

next section.

3.2 Experimental chamber

The experiments were performed in an ultrahigh-vacuum (UHV) chamber. Here, the clus-

ter beam was produced and laser-cluster interaction was detected. The requirements re-

garding the vacuum system are high, since cluster generation involves heavy gas loads and

residual detection requires good signal-to-noise ratio, e.g. high vacuum. To match all needs

the UHV chamber is separated into four parts, as described in detail in section 3.2.1.

The clusters were produced in a pulsed supersonic expansion (see 2.1). Large cluster sizes

in the range of several ten to hundred nanometer could be obtained by cooling the source

and applying high gas backing pressure. A key feature of this experiment is the ability

to study individual clusters to rule out the blurring of signals due to measurements on an

ensemble of clusters. Therefore, the jet was heavily skimmed such that only one single

cluster was detected in the interaction region at a time. The cluster source used for the

presented experiments is introduced in chapter 3.2.2.

A combined approach to simultaneously detect elastically scattered photons and frag-

mented cluster ions was applied to investigate light-matter interaction on different timescales.

It is introduced in 3.2.3. The positively charged ions were collected with an ion time-of-

flight spectrometer. A scattering detector recorded diffraction patterns and fluorescence

photons of the disintegrating clusters shot by shot. The detected data was stored together

in one file with an identifier from the FEL light pulse.

50 Chapter 3. Experimental Setup

Figure 3.7: Schematic diagram of the vacuum apparatus, adapted from [132]. I) The pressure

stage served as differential pumping stage between main chamber and beamline. II) In the main

chamber the interaction region and the detectors were located. Here, the background pressure

needed to be low in order to ensure a good signal-to-noise ratio in the measurements. III) In the

expansion chamber the clusters were generated by supersonic expansion of high pressure gas into

vacuum. Since the gas load under these conditions was heavy good vacuum pumps were needed. IV)

The extension chamber separated main and expansion chamber and served as differential pumping

stage. The gas throughput was kept low by two conic skimmers with small orifices of 0.5 and 1 mm

diameter.

3.2.1 Vacuum system

Clusters were produced under heavy gas load in the same chamber where experiments

under high vacuum conditions were performed. In order to keep undesirable background

signal in the measurements low, a smart vacuum system was needed. Hence, the chamber

was divided into four differentially pumped sections, as sketched in figure 3.7. A pressure

stage (I) was located between beamline and main chamber (II) where the laser beams were

intersected with the cluster beam and the scattering patterns and ion mass spectra were

detected. The clusters were formed in the expansion chamber (III) which was separated

from the main chamber by a set of small skimmers and a differentially pumped extension

chamber (IV). The whole vacuum setup was pumped by a set of turbo-molecular pumps

(TMP) and prevacuum pumps and constantly monitored with several pressure gauges

(Pfeiffer, Full range gauges and Pirani gauges connected to a Maxi Gauge controlling

unit). A safety system ensured controlled venting of the entire vacuum chamber, either

manually, or automatically if an error occurred at any of the vacuum pumps.

The pressure stage (fig. 3.7 I) served as incoupling stage for the IR laser, as already in-

troduced in section 3.1.3. Additionally, it ensured that the vacuum in the experimental

3.2. Experimental chamber 51

chamber was always better than in the beamline. This prevented residual carbon hydrates

from migrating into the beamline where they could coat the mirrors. Both vacuum sys-

tems were separated by a pressured valve which automatically closed if the pressure in the

pressure stage rose above the pressure in the beamline. Therefore, the valve was coupled

to the signal of the pressure gauge in the pressure stage and could only be opened if the

pressure was below pI= 10−6mbar. A TMP (Pfeiffer) was installed to achieve this pres-

sure, reaching down to pI= 10−8mbar. The TMP was coupled to a scroll pump (Franklin

Electric) providing a prevacuum of p= 10−2mbar.

In the main chamber (fig. 3.7 II) the jet of free clusters was channeled into the pulse trains

of the XUV and IR laser. The detection of scattered photons and fragmented ions as

residuals from the interaction demanded for low background pressure to ensure a good

signal-to-noise ratio in the measurements. With a large TMP (Pfeiffer, TMU1000PC)

background pressures of pII = 10−9mbar and pII = 10−6mbar were reached, without and

with cluster source switched on respectively. The prevacuum system was coupled with the

pressure stage. Gaseous residuals in the vacuum were analyzed with a quadrupole mass

spectrometer (MKS, e-Vision 2) which was also used for the alignment of the cluster source,

as described in section 3.2.2.

The clusters were generated in the expansion chamber (fig. 3.7 III) in supersonic expansion

with 5 Hz and backing pressure of 9.8 bar (see next section for setup of the cluster source).

Despite the heavy gas load, a background pressure of pIII = 10−4mbar was reached due to

two TMPs (Leybold, volume flow rate of 345 l/s) coupled to a strong prevacuum system.

This prevacuum system consisted of a roots (Oerlicon Leybold Vacuum, WSU251) and a

scroll (Edwards, XDS35i) pump, reaching a pressure of p= 10−3mbar without gas load

[132]. The same system was used for two TMPs, which were pumping the extension

chamber (fig. 3.7 IV) down to a pressure of pIV = 10−5mbar. The extension chamber was

located between expansion and main chamber. All three chambers were only connected

via two conical skimmers with orifice diameters of 0.5 and 1.0 mm respectively. These were

not only used to keep the gas throughput low, but also to extract only the central part of

the cluster beam, where the largest particles are present.

3.2.2 Cluster source for large xenon cluster generation

Large xenon clusters were generated in a cryogenic, pulsed cluster source, using the princi-

ple of supersonic expansion as introduced in the theoretical section 2.1. The main compo-

nents of the source were a nitrogen cooled cryostat, a solenoid driven pulsed valve, and a

conical nozzle. The commercial cryostat (CryoVac) was mounted on a flange with several

feedtroughs for liquid cooling material, temperature sensors, heat and valve control, and

gas inlet. The xenon gas was sent through a steel tube and cooled in a spiral around the

cryostat. From there, it was sent through the valve which was housed by a gold shield

where a temperature sensor and heat capacitors were located. The nozzle was directly

attached to the valve with an indium gasket to minimize leakage while optimizing heat

transport. To prevent clogging of the nozzle orifice, a sintered filter (Swagelock, 15 µm

pore size) was installed in front of the gas inlet.

To enable imaging of the clusters by XUV scattering, the samples had to be larger than

25 nm in radius, corresponding to about 110000 atoms in a spherical xenon cluster (see

52 Chapter 3. Experimental Setup

Buffer Spring

Main Spring

Teflon coated

Armature

Viton

Gasket

Body

Indium

Gasket

Nozzle

Holder

Conical

Nozzle

Coil Assembly

Tube Fitting

Gas Inlet

Valve Electronics

Poppet

Figure 3.8: Schematic depiction of the cut through the solenoid pulsed valve and the conic nozzle,

adapted from [135,136]. The atomic gas enters the valve from the left and exits it on the right when

the poppet in the armature is pulled back due to a magnetic filed induced in the coil assembly. The

gas expands in a supersonic expansion through the conic nozzle and thereby clusters are formed.

equation 2.12). To generate such large particles the xenon gas was cooled to T= 180 K.

A conic throat nozzle with an orifice diameter of 200 µm and a half cone angle of 4◦was

chosen for a relatively low but well directed gas flow. With a backing pressure of 9.8 bar the

resulting average number of atoms per cluster should have been hNi= 210000 according

to empirical scaling laws [28] (see also equation 2.11). Since the producible cluster size is

limited by the background pressure and pumping speed a pulsed valve was used to keep

the gas load low. Pulsed operation has considerable advantages towards continuous jet

flow:

•the stagnation pressure can be increased

•pumping requirements are reduced

•cleaner spectra with increased signal-to-noise ration can be detected and

•characterization of the velocity distributions in the jet is facilitated.

A schematic sketch of the solenoid valve (Parker General Valve Corporation, series 99) is

presented in figure 3.8. The valve is sealed by a vespel poppet pushed into the valve orifice

by the main spring. The poppet is located at the tip of a teflon coated, magnetic armature

which is pulled back by the induced magnetic field of a coil assembly when current is

applied. As long as the current is kept and the poppet is held back, the gas can flow freely

through the valve. Upon switching the current off, the poppet is pushed back into the

orifice by the main spring and the gas flow is stopped. The valve is controlled by a pulse

driver (Parker, IOTA ONE) which initiates valve opening with a -28 V opening pulse and

keeps it open with 250 mV holding voltage. An opening time of 5 ms was chosen for the

experiments. A minimum opening time of 1 ms is needed for the generation of clusters as

reported for similar experiments [137]. When the valve is closed between two pulses, the

dead reservoir between valve and nozzle is exhausted by pumping through the nozzle.

The repetition rate of the valve was set to 5 Hz which was half the frequency of the laser

pulses. For temporal synchronization of cluster beam and laser pulses the valve driver was

3.2. Experimental chamber 53

triggered with a TTL input from the FEL. The timing was controlled with a digital delay

generator (Stanford Research Systems), which received the timing pulse from the DESY

master clock and produced a preset beam duration after the desired delay. The XUV pulse

arrived 24 ms after the master signal in the interaction region [138]. In order to record

the temporal profile of the jet pulse, the delay was scanned between 0 and 14 ms after the

light entered the interaction region. The temporal profiles for the atomic beam and the

cluster beam are presented in figure 2.3 b. Atomic background spectra for reference and

optimization procedures were taken in the rising edge at 0.5 ms delay.

In order to establish single-cluster mode, the cluster jet had to be skimmed down in front

of the interaction region. The jet issuing from the cluster source was heavily skimmed

by a set of two conical skimmers downstream of the nozzle with 1 mm and 0.5 mm orifice

radius respectively. The shape of the skimmers is essential and follows the rules for skim-

mer design [17], which are introduced in section 2.1. The main part of the incoming gas

remained in the expansion chamber and only the central beam part containing the largest

clusters was guided into the interaction region. Precise adjustment of the cluster beam

axis was necessary to establish a clear path through both skimmers and spacial overlap

between cluster and laser beams. Therefore, the cluster source was mounted onto a me-

chanically translatable XYZ-manipulator and adjusted to a high dimer-to-monomer signal

ratio in a quadrupole mass spectrometer (QMS) downstream of the skimmers (see [45,132]

for detailed description of the alignment procedure). The dimer signal indicates whether

clustering is effective.

The narrow beam in the main chamber could additionally be cut with a skimmer slit which

is continuously variable in size. By varying the width of the skimmer slit, the number of

clusters in the focal volume was controlled. The slit consisted of two razor blades mounted

onto a piezo-driven shutter system (Piezosysteme Jena). The shutter closed upon applying

voltages up to 150 V. The resulting width varied between 0 and 1.5 mm. Reference values

between 0 and 10 V are monitored and converted into slit opening dslit by the following

calibration relation

dslit =a−b·U+c·U2(3.2)

with a= 1500 µm, b= 227.2 µm/V, and c= 7.3 µm/V2[132]. For single cluster experi-

ments, the skimmer voltage was adjusted to a read-out value of U= 8 V, corresponding to

a slit width of dslit = 150 µm.

3.2.3 Coincident photon and ion detection

Once the cluster source and the laser beams were set correctly and all beams intersected

in the interaction region, the residuals from the light-matter interaction were detected. A

combined approach was used to investigate different time scales: during the interaction

on a femtosecond timescale and after the pulse on a nanosecond timescale. With a scat-

tering detector elastically scattered photons were collected, which contain traces of the

change of the optical constants and therefore transient electronic configuration during the

pulse. Complementary data was recorded with an ion time-of-flight spectrometer. After

cluster explosion fragments were detected when ultrafast processes like electron collisions

and recombination were already finished. For easy data post-processing, both datasets

were stored coincidentally in one file [139], together with other information like e.g. laser

parameters.

54 Chapter 3. Experimental Setup

MCP

TOF

CCD camera

Mirror

XUV

Phosphor

screen

Window

flange

Cluster

beam

+2000V

Gating

switch

-1660V

-1260V

Scattering pattern

Figure 3.9: Scheme of the scattering detector setup, adapted from [132]. The elastically scattered

and fluorescing photons hit the front of the MCP where they induce electron avalanches. The

amplifies signal is converted into visible light by the phosphor screen. The out-of-vacuum CCD

camera records an image of the back of the phosphor screen through the window via the mirror

under 45 degrees. The camera trigger is synchronized to the FEL pulse. The TOF electrodes cast

a shadow on the detector limiting the detected diffraction pattern in vertical direction.

Scattering detector

The scattering patterns were captured by a 2D area detector (Photonis), used in several

previous experiments [42,10,30]. It is a robust and affordable solution which fulfills

the requirements of spacial resolution, dynamic range, x-ray sensitivity, and fast read-

out time. X-ray sensitive in-vacuum charge-coupled device (CCD) cameras are either

extremely expensive [140] or have insufficient resolution or readout rate. The here applied

detector uses an optical CCD-camera after conversion of the diffracted XUV light into

visible light and redirection of the image out of the vacuum chamber. The detector assembly

is composed of four major parts, as depicted in figure 3.9: (i) a multi-channel plate (MCP)

stack which transfers the XUV photon signal into electronic signal, (ii) a phosphor screen

which converts the electronic signal into visible green light, (iii) a mirror which reflects

the diffraction pattern out of the vacuum chamber, and (iv) a triggered out-of-vacuum

CCD camera to ultimately record the pattern. The first three detector components have a

central hole to pass the direct laser beam through and protect the components from beam

damage.

The large-area MCP stack consists of two MCPs twisted by 180 degrees to each other.

Both have a sensitive area of 75 mm diameter and channels with 25 µm under 8 degrees

to the surface. Due to this set-up, the detector has reduced detection probability at one

spot of under 8 degrees scattering angle (see scattering pattern in figure 3.9). A voltage of

3.2. Experimental chamber 55

-1660 V was applied to the MCP front, facing the interaction region, in order to accelerate

the electrons to the second MCP which was grounded on the back. Electrons produced

in the interaction region were repelled by the negative charge. To prevent the MCP from

detecting attracted ions, the voltage supply was gated by a fast high-voltage switch (Behlke)

from -1660 V to -1260 V after photon impact.

With +2000 V applied to the phosphor screen close behind the MCP stack the electrons

were accelerated towards the screen. Here the electronic signal was converted into green

light with a wavelength around 550 nm. The screen consisted of a fiberoptical plate coated

with P20-type phosphor. A mirror angled at 45 degrees reflected the diffraction image out

of the vacuum chamber through a CF60 flange window. The images were detected shot-to-

shot by an out-of-vacuum CCD camera (Basler, 1392 x 1040 pixel with 69 µm pixel size),

triggered synchronously with the arrival of the FEL pulses. An IR filter was installed at

the outcoupling window to protect the camera from direct IR light reflected in the mirror.

Great care needed to be taken to minimize stray light, originating from optical components

in the beampath. One circular aperture was positioned in the FEL path upstream from the

IR incoupling mirror. Additionally, a light baffle system for the IR path was constructed.

It consists of three circular apertures of 2.0, 1.5, and 1.1 mm diameter placed at 90, 70,

and 50 mm upstream from the interaction region respectively. Between the apertures the

beams were covered by black tubes to prevent IR reflexes from the vacuum chamber walls.

With the scattering detector mounted at a distance of 61.6 mm from the interaction region,

scattering angles from 4 degrees to a maximum angle of 31 degrees were covered. The

corresponding maximal momentum transfer is q= 4π/λ ·sin(θ/2) = 0.25 nm−1(with

λ= 13.5 nm), limiting the detection resolution to 2π/q = 25 nm. In vertical direction,

the maximum detected angle is limited to 11◦due to a shadow originating from the TOF-

spectrometer electrodes (see fig. 3.9).

Ion time-of-flight spectrometer

The ion mass spectra in this thesis were detected with an ion time-of-flight (TOF) spec-

trometer. The atomic and cluster ions created in the interaction region upon laser impact

were accelerated and guided towards a detector using electric fields. A schematic depiction

of the spectrometer principle is presented in figure 3.10 a. A difference in potential between

two electrode plates, located around the ion starting point, generates a field that pushes

the ions towards the time resolved detector. Between acceleration region (with length s)

and detector lies the drift region (with length d) where the ions fly in a field-free environ-

ment. TOF spectrometers are based on the principle that the acceleration of a particle in

a homogeneous electrical field depends on its mass-to-charge ratio (m/q) [141]. When the

mass mis known the charge qof the ion and their initial kinetic energy is determined by

the flight time tTOF elapsing between creation and detection. The flight time is given by

tTOF =rm

qr2·s·s1

+rd·s1

2·U1·s(3.3)

where U1is the repeller voltage.

The ion TOF spectrometer applied in this thesis is equipped with a bipolar detector and

introduced in detail elsewhere [93]. In principle it can detect both, ions and electrons,

56 Chapter 3. Experimental Setup

repeller

plate

extractor

plate

drift tube

MCP front

MCP back

scintillator

photomultiplier

grounded

+1000 V

+400 V

-2600 V

-1600 V

-600 V

TOF signal

mesh

aperture

d = 150 mm s=12mm

U = 0

Detector

Figure 3.10: a) Scheme of the TOF-spectrometer principle with measures of the used spectrom-

eter, adapted from [139]. Ions are accelerated upwards in the electric field around the interaction

region. They fly field-free in the drift region until they get post-accelerated toward the detector

behind the mesh. b) Depiction of the TOF design with voltages applied in the experiment, adapted

from [132].

depending on how voltages are applied. It consists of a repeller plate for acceleration of

particles and an extractor-plate. The extractor plate has a limiting aperture of 3.5 mm

diameter, so that only ions originating from the interaction region are collected and the

residual gas spectrum is cut out. Behind the repeller plate is a grounded drift tube made

out of µ-metal2. It is covered with a mesh in order to keep the inner tube field-free, and

a detector. The measures of the spectrometer are indicated in figure 3.10 a. Behind the

drift tube is a commercial detector (Burle Industires). It is composed of a MCP for signal

amplification, a scintillator crystal which converts the electronic signal into photons, and

a photomultiplier which enhances and reconverts the optical into electronic signal. The

voltages3applied during the experiment are indicated in figure 3.10 b.

The spectrometer is non-Wiley-McLaren [142] and can therefore also resolve initial ion ki-

netic energies. Ions with higher momenta are faster and recorded earlier in the flight-time

spectrum. For the conversion of flight time into kinetic energy the exact spectrometer

geometry needs to be taken into account. Xenon cluster flight-time spectra for the spec-

trometer design were modeled with SIMION in [45]. The resulting simulated conversion

function is linear

Eini = 1.8·10−8·t−2−444 ·q(3.4)

with tthe flight time and qthe charge. As plotted for the first five xenon cluster ion charge

states in figure 3.11 a, the kinetic energy is reciprocal to the squared flight time.

2µ-metal is a nickel copper alloy which effectively shields magnetic fields.

3With different voltages applied also electrons can be detected with this system.

3.2. Experimental chamber 57

a) b)

Figure 3.11: a) Time-to-energy conversion curves for the first five charge states and b) transmis-

sion function for the first eight charge states of xenon clusters simulated with SIMION [45].

When analyzing the TOF spectra for signal intensities, the spectrometer transmission has

to be taken into account. The transmission is dependent on the emission angle, charge

state, and momentum of the ions. The simulated transmission functions of the TOF

spectrometer for the first eight charge states are plotted in figure 3.11 b [45]. For ions

with low kinetic energies the detection probability is higher than for high kinetic energy

ions. The latter are thus underrepresented in the TOF spectra. Additionally higher charge

states are transmitted better, since their trajectories are stronger influenced by the electric

field. A prominent feature in the transmission function spectra are sharp peaks at high

kinetic energies. They result from an artifact owed to the detector geometry. In the TOF

spectra back-peaks are present, originating from ions which are initially ejected away from

the detector but later pushed towards it by the electric field of the repeller electrode. A

small aperture in the repeller plate distorts the field and leads to a lens effect, efficiently

focusing high energy ions onto the detector. Therefore, their transmission is high and

strong contributions from back-peaks can be found in TOF spectra of strongly excited

clusters.

58 Chapter 3. Experimental Setup

Chapter 4

Results: Cluster evolution in

intense XUV and IR pulses

The power of the approach of measuring matter-light interaction of single, free clusters

lies in the access to phenomena which are hidden when averaging over an ensemble of

clusters [42,10]. Together with the combined approach of elastic-light-scattering detection

and coincident ion spectroscopy, complementary aspects and different time scales of laser-

cluster interaction are accessed in unprecedented detail [101,44]. Precise morphological

characterization of non-periodic, nanoscale particles and analytical examination of the

individual degree of laser impact become possible with this method [11,12]. The great

wealth of recorded information holds the potential for extensive examinations. However, it

also demands for the design of new data-processing tools and filtering routines [143]. Their

development and implementation are subject to the first part of this chapter (section 4.1).

Cluster disintegration as a consequence of laser impact is the main topic of this thesis.

Single-pulse measurements with changing parameters are studied in detail in section 4.2 to

disentangle the particular influence of different materials and laser characteristics on the

particle evolution. Distinctions and analogies in cluster disintegration for varying particle

sizes and chemical components, as well as for tuned laser intensities and wavelengths reveal

interesting correlations in nanoplasma dynamics on the femto- up to picosecond timescale.

To trace the cluster ion motion, the experiment has been pushed further to an extended

timescale of up to nanoseconds by applying a pump-probe scheme (fig. 3.1). Single large

xenon clusters have been exposed to intense, extreme ultraviolet pulses to initiate an ex-

pansion process, which is topic of chapter 4.3. The simultaneous imaging of the clusters

upon pump-pulse impact allowed for good characterization of the initial particle condi-

tion. The subsequent gradual dilution of the sample was tracked with an infrared pulse by

probing the time of collective quasi-free electron motion driven by the laser field.

Finally, the disintegrating cluster was directly imaged in a reversed pump-probe setup.

A strong IR pulse triggered nanoplasma formation and evolution. It was followed by a

delayed XUV pulse, which recorded structural changes at consecutive points in time. The

emerging ’movie’ presents a variety of insights into different expansion states. Simulations

based on scalar theory of light scattering manifest the survival of large clusters on long

timescales (section 4.4).

60 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

4.1 Filtering and processing single-shot single-particle data

Single-shot single-particle measurements open up a wide range of new possibilities to pre-

cisely explore laser-induced nanoplasma dynamics on well-characterized systems. Up to

date most experimental studies of cluster-light interaction are performed on ensembles of

clusters (cf. [47,59,144]) - while almost all theoretical investigations deal with calculations

for single clusters (cf. [48,49,50]). This discrepancy often complicates a simple compar-

ison between measured and simulated data [145]. On the one hand, data from a cluster

ensemble exhibits spreading due to a size distribution resulting from the statistical growth

process of clusters (see section2.1). On the other hand, the Gaussian distribution of laser

intensity in the focal area adds further averaging of measured signals. This is caused by

the fact that clusters are hit in different places within the focus and therefore experience

different power densities.

Both resolution-lowering distributions are circumvent with the imaging of single particles

by XUV photon scattering, in contrast to experiments on cluster ensembles. Every in-

dividual shot is stored together with its FEL-allocated bunch-ID, giving the opportunity

to combine each hit with its corresponding pulse characteristics data in post analysis, as

introduced in section 3.2.3. The amount of photons scattered at one particle increases

with the amount of impinging photons. It therefore gives information about the imposed

laser power density (see 4.1.1). Additionally, the size of each individual target is precisely

recorded in its diffraction pattern. As consequence, size distribution averaging can be ruled

out which opens the possibility to study radius-dependent effects in great detail. Pioneer-

ing experiments on individual xenon clusters displayed a vast amount of target sizes and

shapes [146,11]. A different experiment was able to reveal the change of optical constants

dependent on laser intensity completely independent of size effects [10] and just recently

shock waves were observed in nanoplasmas [147]. These publications impressively prove the

necessity of single-particle detection to gain access to information concealed in ensemble

measurements.

A tremendous gain in information lies in the combined approach of collecting scattering

patterns and ion time-of-flight (TOF) spectra from the same sole sample. While nano-

plasma processes occurring on a femtosecond timescale are imprinted in CCD images, ion

spectra contain information about expansion mechanisms taking place picoseconds after

illumination (discussed in 4.1.2). Unexpected details about cluster fragmentation and elec-

tron recombination were revealed in the first experiment using this composite practice

[101]. This method allows to uncover previously hidden processes, but also demands for

the collection of a large amount of data to reach significant statistics with meaningful asser-

tion. Novel filtering and analyzing procedures for efficient, automated, and unsupervised

sorting are inevitable to process these huge amounts of data [143].

All measurements investigated in the scope of this thesis were taken at two different beam-

times at the free-electron laser FLASH in Hamburg. The first took place in 2011 and the

second a year later in 2012. All together over two Terabyte of data containing about a mil-

lion single shots were recorded to fulfill the needs of good statistics. In the first beamtime,

large xenon clusters were investigated with 13.6 nm wavelength FEL pulses and 800 nm

wavelength Ti:Sa pulses - either separate or consecutive in pump-probe configuration. In

one 16 h shift a total of 180 runs containing almost 100000 shots were recorded. By mea-

suring all data in one single shift it was ensured that all xenon clusters were produced

4.1. Data processing and filters 61

under very similar conditions and that laser specifications stayed relatively constant over

the whole experimental period. In the following year, only XUV pulses were used. This

time, additionally to xenon clusters, also silver and argon clusters were inspected. Due

to remodeling of the vacuum chamber by installing different cluster sources, the data was

collected over several days. With over 100000 shots recorded for each cluster component

meaningful statistics were gained to ensure a significant characterization of the studied

processes. During the course of this thesis, I wrote a whole set of filtering routines in

MATLAB [148] for handling of this massive amount of data. The three main filters are

sorting for

•cluster size, determined by fringe spacing from the scattering patterns,

•intensity of the CCD image, and

•high kinetic energies in ion TOF spectra.

The filters will be presented in the subsequent two sections.

4.1.1 Filtering by CCD image

Imaging in single-cluster mode was reached by cutting the cluster beam such that the

majority of shots in which clusters are hit by a laser pulse comprises only one single

cluster. A piezo-driven slit (see section 3.2.2) was set to the position where the minority

of the produced clusters gets through to achieve this condition. In this configuration, the

target beam was diluted so strongly that a vast amount of shots actually contained no

cluster but only atomic residual gas in the interaction region. Images resulting from pure

atomic signal in the focus had to be sorted out for analysis of laser-cluster interaction.

Four exemplary raw CCD images are shown in figure 4.1: the first two images, a and b,

show photons fluorescing and scattered from xenon and residual gas, hit by either an XUV

or by an IR pulse respectively. The hole which protects the detector from the direct laser

beam is visible in the center of the subfigures. In the first image (a), the high circular signal

around the hole arises from XUV photons secondarily scattered at the focusing mirror in

the beamline. In the second image (b), only little stray-light signal is seen to the left

side of the hole since the IR laser is focused by a lens (see section 3.2). Only IR light

falling directly through the hole of the detector can be detected since the detector MCP is

insensitive to the IR wavelength. The diffuse signal on the lower left side originates from

a reflection at the outcoupling window. The second set of images (c and d) depicts single

clusters hit by either an FEL or a Ti:Sa pulse respectively. Here, the shade from the TOF-

spectrometer electrodes falling on the round scattering detector becomes clearly visible.

The pattern from the XUV irradiated cluster (c) exhibits characteristic diffraction rings

due to strong forward scattering. In the last image (d), heterogeneous scattering signal

from the long-wavelength infrared in combination with fluorescence is visible. Under an

angle of 8 degrees the detector sensitivity is lowered due to the detector configuration as

introduced in section 3.2.3. All images exhibit a few dead camera pixels which do not

affect the analysis and are therefore ignored. Above the detector hole a stripe with low

detection signal is visible. It is attributed to a local degradation effect. It results from

ionized background gas in the chamber which is repelled from the lower TOF spectrometer

electrode (compare section 3.2.3).

62 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

XUV scattering

Atomic signal

Cluster signal

a) b)

c) d)

NIR fluorescence

Figure 4.1: CCD camera images showing scattered and fluorescing photons from xenon gas as well

as residual gas irradiated by a) an XUV pulse with maximum power density of 4 ·1014 W/cm2and

b) an IR pulse with with maximum power density of 1 ·1014 W/cm2. c) Scattering pattern from a

single xenon cluster hit by the XUV beam with minor fluorescence contribution. d) Fluorescence

from a xenon cluster irradiated the IR beam. Note that the MCP of the detector is insensitive to

elastic scattering in the IR wavelength regime. The red box indicates the region used to identify

the average scattering and fluorescence intensity.

The sum of pixel intensities over a suitable area of the detector (as indicated by a red box

in figure 4.1 d) was calculated for every shot in order to sort out ’atomic pictures’. Images

with intensity values falling under a certain threshold were rejected for further analysis. All

remaining images were cut to the scattering region to save memory and speed up filtering

algorithms.

After assuring that only patterns from clusters were left, a different type of image was

sorted out: patterns which result from more than one cluster in the interaction region.

The are often referred to as ’newton rings’ [11]. Here, three-dimensional information is

encoded in the 2D images (introduced in section 2.2.3). These types of images constitute a

whole interesting field of its own. Since they are not subject to this thesis they were sorted

out and neglected in the analysis.

Determination of cluster size from radial profiles

For spherical clusters the radius of the object is encoded in ring patterns of XUV photons

scattered, like the size of an aperture is contained in its airy disk [31]. For this thesis an

algorithm was developed for automatized extraction of the sample radius from each image

and is described in the following. The intensity value at each pixel is divided by a factor

of cos3(θ) to account for the flat detector [10,149]. First, the radial profile was generated

by averaging intensity values over scattering angle θ. The evaluated area was restricted to

a sector of the image to avoid including detector artifacts. In figure 4.2 four characteristic

scattering patterns and corresponding azimuthally integrated profiles are presented. In a

4.1. Data processing and filters 63

Scattering angle [deg]

Cluster radius [nm]

Count

100

30252015105

100

R = 100 nm

R = 60 nm

R = 30 nm

R = 500 nm

Scattering intensity [arb.u.]

a) b)

c) 600

500

400

300

200

100

2 3 4 5 6 7 8 9

100

2 3 4 5 6 7 8

maximum

at 34 nm

up to 700 nm

Figure 4.2: a) 3D plots of XUV scattering patterns from spherical xenon clusters with different

sizes and b) their corresponding radial profiles plotted over scattering angle θ. The respective

cluster size is determined from the angle of the first minimum for small clusters and from fringe

spacing for large clusters. c) The histogram of cluster radii reveals a log-normal distribution with

maximum at 34 nm radius and several very large clusters up to 700 nm radius.

second step, local minima and maxima of the profile were identified and their separation

was determined. If the first minimum was detected the radius was simply estimated by

the relation [31]

R=1.22 ·λ

2·θmin

(4.1)

with θmin the angle of the first minimum. A different approach was applied if the imaged

target was so large that the first minimum is overlaid by stray light or disappears in the

detector hole. Profiles were generated in Mie simulations for several radii ranging from 100

up to 700 nm. Subsequently, measured data was assigned to the simulated profiles by the

distance of profile minima. For cluster sizes above 700 nm radius, the interference fringes

were too fine to get resolved due to the detector spacial resolution. In line with recent

findings [44], smaller particles are round in shape reflected by circular scattering patterns

(fig. 4.2 a bottom). Particles of larger sizes exhibit a rough surface, since they freeze out in

64 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

100

30252015105

detector intensity [arb. u.]

scattering angle [deg]

a) b) c)

Figure 4.3: a) Illustration of a Gaussian focal density distribution with FWHM of 20 µm. Clusters

in the size range of several ten to hundred nanometer can be exposed to varying positions within the

focal volume. b) Scattering patterns of equally sized clusters exhibit various amounts of scattered

photons. c) Radial profiles of both patterns set in direct comparison reveal a difference in intensity

of scattered photons by a factor of 1.5.

non-spherical shapes during their growth by coagulation (fig. 4.2 a, see also section 2.2.3).

For xenon clusters measured in the 2011 experiment, the radii of all single clusters were de-

termined from XUV only and XUV/IR pump-probe data. They are depicted as histogram

in figure 4.2 c. A log-normal distribution with maximum of 34 nm radius was fitted. This

result corresponds well with pertinent scaling laws [28]. Xenon clusters of 34 nm radius

consist of N≈2.6·106atoms while the scaling law predicts hNi= 2.0·106for the expansion

conditions applied in the experiment (p= 9.8 bar, T= 180 K, deq = 2105 µm). Extraordi-

narily large sizes with radii of several hundreds of nm originate from valve closing in pulsed

cluster generation as stated in 2.1.3 [44]. Due to the missing detector resolution the size

of clusters larger than 700 nm cannot be resolved and are indicated in the histogram (fig.

4.2 c) as 700 nm radius clusters.

As a matter of course this procedure only works for patterns recorded from particles ir-

radiated with a short-wavelength pulse. For IR data the radius cannot be extracted due

to missing minima in forward scattering direction. All experiments were performed in one

long experimental run with stable cluster source conditions, switching back and forth be-

tween laser settings to ensure that the cluster size distribution is alike for data taken with

IR pulses only or in IR/XUV pump-probe configuration.

Experienced power density dependent scattering intensity

The clusters range in a size scale of several tens to hundreds of nanometers. In comparison,

the focus spot of the FEL beam was about 20 µm FWHM [111]. Hence, each cluster

experiences a different power density dependent on its position within the laser focus (see

figure 4.3 a).

The exposed power density a cluster experiences was 4.1 ·1014 W/cm2in the focal maximum

of the FEL pulse. It drops to zero outside the wings. The main quantity of the clusters

are hit in the sides [97]. Exemplary two CCD images with equal ring spacing from clusters

of same radius are presented in figure 4.3 b. The slopes of both patterns are set in direct

comparison in figure 4.3 c. They reveal a disparity in signal intensity by a factor of 1.5. The

4.1. Data processing and filters 65

difference in brightness is a direct indication for the discrepancy in scattered photons due

to the different extend of irradiation. A direct determination of absolute power densities

from an averaged detector intensity is not possible since clusters of different size scatter

with varying strength. Additionally, the electronic configuration within the cluster changes

with FEL impact, which results in a change in the scattering-profile slope [10]. The overall

amount of scattered photons increases with higher exposure power density value. Therefore,

the method of filtering for sample radius and subsequently for detector intensity has proven

to be a versatile tool to investigate cluster-size and power-density dependent nanoplasma

dynamics [101,45].

This method is not applicable for images recorded from particles irradiated with 800 nm

light only. The CCD images exhibit homogeneously distributed fluorescence instead of ring

patterns (see figure 4.1 d). Still the screen intensity gives a hint about the rage of the size

of exposed cluster and impacted laser intensity. An earlier experiment with photonenergy-

sensitive pnCCD detectors revealed that with raising power density of an infrared laser, the

fluorescence yield increases due to higher ionization and subsequent radiative decay [46].

Furthermore, larger clusters scatter more intensely. Therefore, the assumption is justified

that the brightest CCD images result from very large clusters hit in the focal center.

4.1.2 Filtering by ion time-of-flight spectrum

Ion TOF spectra from atomic gas and from

150

100

6420

150

100

150

100

Time of flight [µs]

Ion yield [arb.u]

H+

light

peak

H+9+

Figure 4.4: Single-shot ion time-of-flight spec-

tra of (a) xenon atoms and (b+c) single xenon

clusters exposed to a 91 eV FEL pulse. Spectra

differ significantly. By filtering on characteristic

features (Ekin 0, areas marked in red) atomic

and cluster data can be reliably separated.

clusters differ significantly. In figure 4.4

three exemplary ion spectra of xenon ir-

radiated by XUV pulses only are shown.

Single-shot atomic data is plotted in figure

4.4 a. It exhibits pronounced peaks which

are even isotope resolved. Singly ionized

xenon is almost not detected due to Auger

processes and missing recombination as al-

ready discussed in section 2.2.1. Charge

states up to Xe9+ are detected for a focal

power density of 4.1 ·1014 W/cm2. Cluster

spectra are presented in figure 4.4 b and c.

The peaks are broadened towards shorter

flight times from accelerated cluster ions

which override the residual gas peaks. The

assignment of single charge states becomes

difficult because the peaks merge into each

other. For a cluster hit in the focal wing

Xe1+ is the most pronounced peak (fig.

4.4 b), while for a strongly exposed cluster

the distribution is shifted to higher charge

states (fig. 4.4 c). Sorting according to ion

yield at flight times where no atomic sig-

nal is detected (indicated by the light red

areas in fig. 4.4) is a very reliable filter to

distinguish cluster data from atomic data.

66 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

In addition to ions, scattered light under 90 degrees was collected by the MCP of the TOF

spectrometer causing a light peak in the spectrum. Compared to the ions arriving at the

detector on a nano- to microsecond timescale, the light is detected almost instantaneously.

It was therefore used for calibration of the spectra to zero flight time. Further, the light

peak yield can be utilized to measure how well the cluster was hit in the focal area of

the laser pulse. Graph 4.4 b from a cluster exposed to the focal wing does not show a

light peak. However, a light peak is present in the spectrum of a cluster encountering the

focal center (4.4 c). While the scattering detector detects light from a broad region in the

experimental chamber, the TOF spectrometer only collects photons originating from the

interaction region, due to a small aperture in the drift tube. Since it is a time-resolved

signal the light peak also shows a fluorescence tail, especially in pump-probe data taken

at late delay times (cf. chapter 4.4). This helps to distinguish scattering and fluorescence

signal, which is not possible with the scattering detector.

4.2 Universal dynamics in large cluster nanoplasmas

The previous chapter explains how single-shot single-particle data was prepared and sorted

for further analysis. Based on that, this chapter focuses on the complicated dynamics of

clusters induced by irradiation with an ultrafast and highly brilliant laser pulse. With the

method of single-cluster imaging with coincident ion spectroscopy, it became possible for

the first time to disentangle the contributions from various experimental parameters to

laser-cluster interaction with unprecedented detail. In this chapter, several comparative

analyses focus on the expansion mechanism of single, large clusters. First, insights into

the affect of cluster size and laser intensity are given by the analysis of a single-shot

experiment on extremely large xenon clusters excited by 13.6 nm light discussed in section

4.2.1. Subsequently, in section 4.2.2 the material response is compared for xenon, argon,

and silver clusters of similar diameter under similar laser conditions by investigating their

ion kinetic energies. In a third study, the influence of the laser photon energy is examined

in detail in section 4.2.3, by means of ion spectroscopy on xenon clusters in single XUV

and single IR pulses respectively.

4.2.1 Ionization and ionic motion in XUV irradiated xenon clusters

The affect of laser intensity and cluster size on the laser-matter interaction is in principle

identified from theoretical models [49,50] as introduced in chapter 2.3. With increasing

cluster size and laser intensity hydrodynamic expansion becomes more probable, while

with smaller cluster size and laser intensity the clusters are more likely to disintegrate in

Coulomb explosion [52]. Which of the two is the prevailing expansion mechanism can be

estimated by the frustration parameter α(see equation 2.50). It is given by the ratio of

photoactivated ntot to photoionized nout electrons [52]. In the case of xenon clusters in

XUV light, where the photon energy exceeds the ionization threshold, cluster atoms are

photoionized and field driven effects are either not present or negligible.

In this section, large xenon clusters exposed to 91 eV laser pulses will be analyzed in

size and focal intensity resolved manner. As introduced in section 4.1, examined cluster

sizes are ranging between 25 and 1000 nm and the peak FEL pulse power density holds

4.2. Universal dynamics in large cluster nanoplasmas 67

4.1 ·1014 W/cm2. Upon XUV photon impact the amount of outer-ionized electrons before

frustration nout is calculated with equation 2.51 in the photon dominated regime. The

maximal kinetic energy is hereby not defined by the difference between photon energy and

ionization potential (~ω−Eip), but by the Auger electrons with ≈32 eV [42,52]. Therefore,

we get

nout(photon) = 32 ·4π0

e2·R= 22.22 ·R[nm] (4.2)

For the entire cluster-size range, nout varies between ≈550 and ≈22200 electrons. Note that

secondary processes like ionization heating, electron thermalization, and electron-impact

ionization are neglected in this calculation. The total amount of outer ionized electrons

most probably exceeds the values calculated here.

The amount of overall (outer- and inner-) ionized electrons ntot can be determined by ab-

sorption cross-sections with equation 2.51 introduced in chapter 2.3.3. However, in 13.6 nm

wavelength light very large clusters are optically thick and the laser cannot penetrate the

entire particle. The absorption length of xenon is labs =λ/(4πβ) = 24 nm (see equation

2.18) with β= 0.0445. Therefore, a simple calculation via atomic absorption cross-section

might give misleading results. Instead, ntot can be simply approximated by geometric

cross-sections. It is estimated that every atom is charged twofold by photoionization with

succeeding Auger excitation, as long as the number of photons impacting on the laser is

larger than the number of atoms in the cluster [66]. This is the case for a laser pulse

with focal power density of 4.1 ·1014 W/cm2where the number of photons is estimated as

nPhoton = 1.7·1010 [45]. The number of atoms in a xenon cluster of solid state density is

calculated by

N=4πρR3

3ma

= 72.67 ·(R[nm])3(4.3)

with ρ= 3.781 ·103kg/m3and ma= 131.293 ·1.660 ·10−27 kg for xenon clusters (compare

equation 2.12). This results in N= 1 ·106and N= 7 ·1010 for clusters with 25 and

1000 nm radius respectively. Only a very small fraction of all excited electrons leaves the

cluster. The frustration parameter is calculated as

α=ntot

nout

=2N

nout

.(4.4)

For the experimentally detected cluster-size range the frustration parameter results between

α≈2000 and α≈3·106. It is deep in the nanoplasma regime (α >100) and therefore

the expansion is expected to be far in the hydrodynamic limit for all data analyzed in this

section.

While the nanoplasma model was established for clusters exposed to infrared laser light, it

also holds for clusters in the XUV regime. This was demonstrated in earlier experiments

[93,150] and theoretical calculations [52]. The majority of activated electrons resides quasi-

free in the cluster compound as the approximation above shows. These charges redistribute

to lower the total energy stored in the clusters [56,151]. The electrons move towards the

center of the sample where they screen the positive cluster charges while at the surface the

ions stay partially unscreened. Thus a net-neutral core with a highly charged surface is

built.

The dense, cold nanoplasma in the net-neutral core allows for recombination via many-

body collisions. At the same time hydrodynamic expansion takes place upon the pressure

68 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

of the energetic quasi-free electrons. The cluster expansion starts at the outer surface and

proceeds layer-wise towards the cluster center [52]. While an ion at the cluster surface is

strongly accelerated during dissociation, an ion at the center is screened by the surrounding

electrons and hardly obtains kinetic energy. Therefore, the kinetic energy distribution,

detected e.g. in ion TOF spectra, mirrors the spacial distribution of the ion within the

cluster [151]. Recombination processes are manifested in TOF spectra by a missing of low

kinetic energy contributions in higher charge states, as well as by a strong contribution of

lower charge states. While these features predicted by theory are washed out in ion spectra

detected on ensembles of clusters, they are evident from single-cluster ion spectra as will

be demonstrated in the following section.

Expansion signatures in size and intensity characterized single-cluster ion spec-

tra

Here, an extended analysis of scattering patterns and ion TOF spectra from very large,

single xenon clusters in highly intense, ultrashort (100 fs) XUV pulses with 91 eV photon

energy is presented. A similar study was performed and analyzed in previous work [45].

It gives a good description on how to analyze single-shot coincident measurements. The

results of this study are the fundamentals for further investigation in this thesis and its

understanding is a prerequisite for the following sections. Data analysis methods developed

in [45] were applied to the data set collected for this thesis and are presented in the

following.

After determining the cluster-size distribution (see section 4.1.1), single clusters in a size

range between 100 nm and 1 µm radius were picked for further investigation. They were

grouped in three categories with radii of (200 ±100) nm, (500 ±200) nm, and larger than

700 nm. Three representative scattering patterns revealing the size of the investigated clus-

ters are presented in figure 4.5 a. Within the three groups all shots were sorted according

to the intensity of the recorded scattering pattern. It gives an indication of the sample

position within the Gaussian focal distribution of the laser pulse and therefore the exposure

power density (see section 4.1.1). Ion spectra were sorted accordingly and several selected

single-cluster ion spectra are shown in figure 4.5 b.

Several features in the sorted single-cluster ion TOF spectra illustrate power density and

cluster size dependent effects in nanoplasma dynamics. Within one cluster-size range a

redistribution from lower to higher charge states takes place with rising exposure power

density (fig. 4.5 b). The ion charge-state peaks shift towards shorter flight time and be-

come narrower for similar laser intensity but increasing target radius. This indicates that

the kinetic energy of the ions rises and develops towards an increasingly mono-energetic

distribution. The kinetic energy is a fingerprint of the ion position within the cluster [151].

Therefore, a narrow flight time distribution for one charge state is a strong indication that

these ions originate from a rather narrow cluster shell. Peak truncations at short flight

times - thus lower kinetic energies - point towards recombination processes taking place in

the dense cluster nanoplasma [52].

However, charge-state abundance and kinetic energy are not directly resolved in TOF

spectra. Accounting for spectrometer transmission and conversion to energy scale are

necessary to directly extract kinetic-energy distributions from the recorded TOF spectra.

4.2. Universal dynamics in large cluster nanoplasmas 69

R = 200 nm R = 500 nm R > 700 nm

time of flight [s]

Ion yield [arb.u.]

5+4+

3+ 2+ 1+

Figure 4.5: a) Single-cluster scattering patterns of single xenon clusters with about 200 nm and

500 nm radius, extracted from the fringe spacing in the pattern. in the last image the fringes are

too fine to be resolved due to the detector resolution. This indicates that the cluster is larger than

700 nm in radius. b) Ion time-of-flight spectra sorted first on cluster size and within one range to

assigned laser power density. The peak power density in the beam is 4.1·1014 W/cm2. While higher

charge-state yields rise dramatically with intensity the influence of the change in size is relatively

small.

A full characterization of the spectrometer used for this thesis is given in literature [152,

45]. In principle, every single ion spectrum needs to be simulated for a full charge-state

resolved kinetic-energy distribution. This procedure is extremely time consuming while the

information gain is relatively small. Instead, only the central kinetic energy in dependence

on the charge state is investigated here. The central kinetic energy is extracted from every

TOF spectrum depicted in figure 4.5 by polygon fits and subsequent adjustment to the

transmission function of the spectrometer as described in [45]. Plotted over charge state

in figure 4.6, a linear dependence is prominent for all shots.

Up to date there is an ongoing debate how the correlation of kinetic energy and ion charge

can contribute to distinguish between both limiting expansion scenarios: Coulomb explo-

sion and hydrodynamic expansion. It is often claimed that the mean kinetic energy hEi

scales linear with the ion charge in the case of hydrodynamic expansion, but quadratic for

Coulomb explosion:

hEHydroi ∝ q , hECouli ∝ q2.(4.5)

Several experiments on ensembles of clusters used this dependency to explain their explo-

sion mechanics [90,91,55,93]. However, from Monte Carlo classical particle-dynamics

simulations of a cluster undergoing Coulomb explosion, a quadratic dependence was only

70 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

charge state

central kinetic energy [eV]

R = 200 nm R = 500 nm R > 700 nm

4000

3000

2000

1000

543210 543210 543210

Figure 4.6: Central kinetic energies over charge state extracted from the TOF spectra presented

in figure 4.5. The color coding is maintained. With increasing exposed power density the central

kinetic energies are increasing and higher charge states appear. A linear dependence is found for

all spectra indicated by straight lines.

found for low charge states, while for higher charge states it was linear [92]. There, the

quadratic behavior was attributed to an artifact from the laser focal averaging. More re-

cent simulations using molecular dynamics calculations investigate single clusters [52]. The

authors suggest that ion spectra from clusters undergoing Coulomb explosion and hydro-

dynamic expansion do not significantly distinguish if recombination processes are taken

into account. However, the ion spectra contain only charge states up to 4+ and authors

do not comment on the linear/quadratic behavior discussion.

With the single-cluster ion spectra presented in this chapter it becomes possible to at-

tribute a linear correlation of mean kinetic energy and ion charge (fig. 4.6) to cluster in

hydrodynamic expansion (estimated with equation 4.4) without influence of laser power

density and cluster size averaging. Since the experiments performed here on very large

clusters in the XUV regime reside deep in the nanoplasma regime, no comment can be

given on the behavior for clusters undergoing Coulomb explosion. Therefore, single-cluster

imaging experiments in coincidence with ion spectroscopy has to be performed on smaller

clusters with higher photon energy, like it is available at the hard x-ray FELs, e.g. the

LCLS or SACLA.

4.2.2 Relationship between material characteristics and ionization dy-

namics, studied in a comparison of xenon, silver and argon clusters

The electron temperature and density inside an XUV laser excited cluster is strongly

influenced by the particle material. The excess energy, e.g. the remaining kinetic energy

of a photoelectron after ionization, varies for different chemical components due to the

respective electronic configuration. An attempt is made to understand the role of the

electronic configuration for large clusters in XUV light. Therefore, the well studied ion

spectra of individual xenon clusters are compared with TOF spectra from other materials,

taken under the same free-electron-laser conditions (wavelength: 13.6 nm, photon intensity:

150 µJ, focal spot size: 20 µm and pulse length: 100 fs).

4.2. Universal dynamics in large cluster nanoplasmas 71

43210

time of flight [µs]

ion yield [arb.u.]

R = 65 nm R = 90 nm R = 120 nm

1+ 1+ 1+

3+ 2+ 2+

4+ 4+

5+ 5+

Figure 4.7: Ion time-of-flight spectra of silver clusters, sorted by particle radius (independent

of the exact cluster shape) into groups of (65 ±12.5), (90 ±15), and (120 ±15) nm. Within one

size range spectra are arranged for exposed power density with a maximum of 4.1·1014 W/cm2.

Characteristic features are prominent, like an increase of high charge-state yield with laser focal

power (bottom to top) and a narrowing of charge-state flight-time distributions with cluster size

(left to right).

Xenon is a special case for 91 eV photon energy because of its 4dgiant resonance resulting in

high photoionization cross-sections (see chapter 2.3.1). The initial ionization proceeds from

inside out, starting in the 4d-shell followed by the 4s, 5s, and 5pshell [66]. Argon is chosen

for comparison since it is also a rare-gas and clusters are grown under similar conditions. It

is likewise Van-der-Waals bound, but has a different electronic configuration and therefore

no resonant energy absorption at 91 eV photon energy. The electron excess energy in argon

(E∗= 22 eV) is higher than in xenon (E∗= 20 eV) [42]. This leads to a higher electron

temperature and lower quasi-free electron density within the cluster. Contrary to xenon,

argon is ionized outside in. Another juxtaposition is made with silver because it has metal

bonding and already delocalized electrons in the ground state. In comparison with xenon

it has similar energy levels, leading to similar electron temperatures. Ionization proceeds

likewise from inside out. Xenon, argon, and silver clusters are expected to have a different

response to the light pulses because of different photoionization cross-sections and atomic

electron levels.

In a collaboration with the group of Prof. Meiwes-Broer from the University of Rostock first

scattering [12] and ion spectroscopy experiments were performed on large silver clusters

at FLASH. Due to a different cluster generation mechanism [153], the silver particles are

smaller than the xenon clusters and statistics are low for largest clusters. Like with xenon in

the previous section, silver shots are sorted according to sample radius and within one size

bucket sorted on intensity as presented in figure 4.7. Spectra are shown for radii ranging

between 65 and 120 nm and exposure power densities up to 4.1·1014 W/cm2. Comparison

72 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

76543210

Argon

Silver

Xenon

time of flight [µs]

ion yield [arb.u.]

a) b)

Figure 4.8: (a) Scattering patterns from single argon (R = 160 nm), silver (R = 120 nm) and

xenon (R = 280 nm) clusters exposed to a 100 fs XUV pulse. (b) Corresponding single-cluster ion

time-of-flight spectra. Despite different flight times due to particle mass, all three spectra exhibit

similar features. Charge states up to 5+ are detected and peak widths for higher charge states are

rather narrow.

of the spectra in figure 4.5 and 4.7 reveals that ion spectra are different for xenon and

silver particles, but the overall size and intensity dependence is similar. With increasing

cluster radius charge state peaks get narrower and more pronounced and higher charge-

state yields increase. Within one size range, the charge-state distribution shifts towards

higher values with increasing exposure power density. The fact that these characteristics

are equal for xenon and silver targets points towards very similar ionization processes

taking place independent of the bond type, the target geometry, and exact ground state

electron configuration.

Another juxtaposition is made with argon clusters. For argon, size and intensity resolved

analysis is disregarded for redundancy reasons. Rather a single ion TOF spectrum is set in

direct comparison with a single spectrum from a xenon and a silver cluster. As presented

in figure 4.8 all three images show comparable cluster radius and exposure power density.

Flight times are slower for heavier particles, and therefore the time axis differs for varying

materials, but the main features in the spectra are quite similar. All three particles are up

to fivefold ionized and, apart from the first charge state, flight-time distributions of single

charge-state peaks are rather narrow.

Since ion spectra mirror the final state after cluster fragmentation, no information about

initial cluster charging can be directly extracted from the spectra. However, the cluster

expansion dynamics and the resulting ion kinetic energies are determined by energetics of

the nanoplasma, which itself results from the initial cluster charging process. Photoion-

ization energies are different for xenon, silver, and argon (see table 4.1) and therewith

the following absorption cross-sections and Auger-decay rates. While xenon atoms exhibit

the 4dgiant resonance around 91 eV, resulting in high absorption cross-section (23 Mbarn),

photoionization processes in silver and argon are without any resonances. Their absorption

cross-sections at 91 eV photon energy are correspondingly small as can be seen from the

comparison in table 4.1.

4.2. Universal dynamics in large cluster nanoplasmas 73

Table 4.1: First three ionization energies (IPin eV) [32] and absorption cross-sections at 91 eV

(σin Mbarn) for xenon, silver, and argon atoms respectively [154]. Clusters sizes extracted from

figure 4.8 a respectively and corresponding total atom numbers N. Calculation of the amount of

outer photoionized electrons nout upon 91 eV pulse impact and the corresponding ratio from total

atom number to outer photoionized electrons.

Eip [eV] E1+

ip E2+

ip σ[Mb] R[nm] N nout N/nout

Xenon 12.1 21.0 31.1 23 280 1.6·1095200 3.1 ·105

Silver 6.5 20.8 35.5 2.03 120 4.2·109800 5.2 ·106

Argon 15.76 27.63 40.74 1.2 160 7.7·1082300 3.3 ·105

Despite varying initial ionization, for all materials only a small number of electrons nout gets

outer ionized before photoionization frustration sets in as calculated from equation 2.51.

The calculated numbers for clusters of the sizes presented in figure 4.8 are listed in table

4.1. Due to the very large cluster sizes initial ionization only contributes marginally to the

overall ionization and nanoplasma effects take the lead. Ionization heating and electron

impact ionization become dominant [105]. In a comparative paper where ionization of

silver and argon is calculated [84], electron impact ionization effects play a major role.

With increasing cluster size, the mean ionic charge number increases. Hence, for larger

clusters the impact ionization is more efficient during the cluster expansion compared to

smaller clusters. The ionization processeses in the nanoplasma have to have the same

impact as final spectra (fig. 4.8 b) show a high resemblance. Many nanoplasma processes

are independent of target material: electrons migrate to the cluster center, while an outer

shell comes off since it remains unscreened. The narrow distribution of the charge states

again hints on the explosion of a thin shell in hydrodynamic expansion. It seems that

with increasing cluster size, the amount of trapped electrons plays a major role. Plasma

dynamics become so dominant that the cluster dynamics become universal independent of

the particle material. This behavior is known from large clusters exposed to laser pulses

in the infrared regime [53]. Large xenon clusters in IR light will be the subject of the next

section.

4.2.3 Multistep vs field ionization: XUV and IR irradiated clusters

Above, expansion dynamics were examined in dependence on laser focal power density, clus-

ter size, and cluster component. In this section, cluster expansion is addressed regarding

illumination with a laser pulse of different photon energy. Therefore, ion spectra from large

xenon clusters exposed to near-infrared laser pulses (λ= 800 nm, I= 1.1·1014 W/cm2,

τ= 80 fs, see also section 3.2.2) are analyzed and set in comparison to the previously

analyzed spectra from clusters excited by extreme-ultraviolet laser pulses (λ= 13.6 nm,

I= 4.1·1014 W/cm2,τ= 100 fs). In both cases cluster charging proceeds through different

ionization processes. In contrast to 91 eV XUV photons, direct single-photon ionization of

xenon atoms is not possible for IR photons of 1.55 eV photon energy. At least eight pho-

tons are necessary for multi-step ionization of a single neutral xenon atom. In the infrared

regime, field driven effects like tunnel ionization are dominant.

To investigate the influence of initial ionization regime on cluster expansion, ion TOF

spectra of clusters in XUV pulses are now compared with spectra from clusters in IR

74 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

pulses. As stated earlier, in contrast to data recorded upon XUV illumination, size and

intensity resolved sorting is not possible for images and ion spectra upon IR excitation due

to missing interference fringes in scattering patterns (compare figure 4.1 d). Nevertheless,

the cluster size distribution should be equal to the one determined with XUV scattering

- with radii between 25 and 1000 nm and maximum distribution at 34 nm radius - since

xenon clusters are produced under the same expansion conditions (see figure 4.2 c for cluster

size distribution upon XUV irradiation). The intensity of the scattering images only gives

limited information. Images with moderate intensity might result from a large cluster hit

in the focal wing as well as from a small cluster exposed to the focal center. Therefore,

the most reliable filter is sorting for highest detector intensity which results from largest

clusters located in the focal center.

To map the higher value ends of size and

0.2

0.0

76543210 76543210

0.2

0.0

0.2

0.0

0.2

0.0

0.2

0.0

time of ﬂight [µs]

ion yield [arb.u.]

Figure 4.9: Averaged ion time-of-flight spectra

from single xenon clusters, irradiated either with

IR light (red graphs) or XUV light (blue graphs).

Average of (a) 1 to 10, (b) 11 to 25, (c) 26 to 55,

(d) 51 to 100, and (e) 101 to 200 brightest respec-

tively. Cluster sizes can only be determined from

corresponding single scattering patterns upon XUV

radiation, but not upon IR irradiation.

intensity distribution, the brightest 200

shots out of a total of 5000 shots are sub-

divided in five groups. Ion spectra coin-

cidentally recorded with the 10 brightest

scattering images are averaged for XUV

and IR exposure respectively and plotted

in figure 4.9 a. TOF spectra for decreas-

ingly bright pictures are averaged and pre-

sented in graphs 4.9 b-e. With increas-

ing photon detector intensity, the charge

distributions shift towards smaller flight

times in IR and XUV spectra. This in-

dicates an increasing energy absorption

independent of laser wavelength.

Apart from this common effect, signifi-

cant deviations between main features in

graphs from XUV and IR excitation are

prominent. Detected charge states are

higher for XUV exposure. This is most

likely a result from different initial cluster

charging mechanisms, namely photoion-

ization for 91 eV and tunnel ionization for

1.55 eV photon energy, as well as from dif-

ferent laser power densities (IXUV = 4.1·

1014 W/cm2and IIR = 1.1·1014 W/cm2).

For IR spectra the Xe1+ peak is the most

prominent. It exhibits higher kinetic en-

ergies than for the XUV spectra. For

xenon clusters in XUV light ionization

starts from inner shells proceeding to the valence levels via single photon absorption.

The opposite holds for the infrared case, with ionization from the outer to inner levels.

Therefore, lower charge states are produced first and higher charge states are generated by

subsequent heating and particle collisions.

4.2. Universal dynamics in large cluster nanoplasmas 75

Figure 4.10: Blue graphs: Single-cluster ion time-of-flight spectra from xenon clusters irradiated

with XUV pulses with peak power density of IXUV = 5 ·1014 W/cm2, sorted for cluster size and

exposed power density, as already presented in figure 4.5. Red graphs: Matching ion spectra from

clusters exposed to IR pulses with peak power density of IIR = 1 ·1014 W/cm2. Note that the size

for the clusters in IR light is unknown.

Although sorting for cluster size and laser power density is not possible for single-cluster

IR spectra, their investigation can uncover characteristics hidden in averaged spectra.

Comparison with single-shot XUV spectra exhibits an unexpected similarity for several

shots. Blue graphs in figure 4.10 present the size and intensity sorted single-cluster ion

spectra from xenon clusters under XUV radiation already plotted in figure 4.5. With the

help of a filter that compares all recorded spectra and subsequently sorts for similarity,

spectra from IR excited clusters are plotted on top of the most similar spectra from XUV

irradiated particles1. In direct comparison single spectra from clusters irradiated by XUV

or IR pulses reveal astonishing resemblance. Even though the initial excitation mechanisms

of the two pulses with different photon energies differ drastically, the overall deposited

energy seems to be the same resulting in similar cluster expansion. Due to the alike

appearance of the ion distributions, the linear increase in central ion kinetic energy over

charge state is equal. This indicates that large xenon clusters in strong IR pulses likewise

undergo hydrodynamic expansion of outer shell layers as predicted from earlier calculations.

The mechanism of initial ionization seems to be secondary, as long as a certain amount of

quasi-free electrons is trapped inside the cluster and the major part of the cluster is turned

into a nanoplasma. This is most likely the case for large clusters. Therefore, from a certain

particle radius on the expansion dynamics might be dominated by the large cluster size

instead of the laser photon energy. Independent of the regime of initial cluster charging,

the outer particle shell blisters off in hydrodynamic expansion and a recombined center

1Note that for highest intensities no matching shots are found, which is due to the lower power density

of the IR laser.

76 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

core remains. The detected ion distribution results in the same charge states with the

same kinetic energy distribution.

To conclude, similar expansion dynamics were found for large xenon, argon, and silver

clusters after the interaction with a strong XUV pulse. This suggests that the exact

electronic configuration of the cluster seems to play a minor role for the particle evolution

after nanoplasma formation. Similar dynamics were also found when large xenon clusters

were irradiated with strong IR pulses. Independent of the initial ionization regime (photon

dominated in XUV light and field driven in IR light), the dynamics seem to be mainly

determined by the large cluster size and similar exposed power density (IXUV = 4.1·

1014 W/cm2and IIR = 1.1·1014 W/cm2). Therefore, it is not a single cluster or laser

parameter that gives information about the final explosion process, but the ratio of outer

to inner ionized electrons. Hence, light-matter interaction under strongly different initial

situations can lead to astonishingly similar final results.

While recorded ion TOF spectra can give insight about the final state of the cluster after

fragmentation, the plasma evolution in intermediate states stays unidentified. The cluster

density is scanned in a dual-pulse experiment to trace the plasma disintegration step-by-

step, which is subject to the next section.

4.3 Probing collective electron oscillations in pre-expanded

clusters

Clusters are systems which exceed atoms and solids in efficient energy absorption from laser

radiation [47]. This effect is further drastically increased in resonance condition. Here, the

electron cloud inside a cluster is collectively oscillating driven by an external laser field as

demonstrated in several experiments on rare-gas and metal clusters [80,155,156]. This

so-called Mie resonance, introduced in chapter 2.2.2, is met when the frequency of the

collective electron oscillation ωPis close to the laser frequency ωL[38]. The resonance Mie

plasmon frequency is then given by ωMie =ωp/√3≈ωL/√3. Solid density xenon clusters

in IR fields are overcritical. This means that the density dependent plasmon oscillations are

faster than those of the driving laser field. Matching condition between laser and plasmon

frequency is reached by reducing the particle density due to the laser-induced expansion of

the cluster. For very large clusters, the evolution time until resonance condition with an

infrared pulse is met often exceeds the ultrashort pulse length. In this case the powerful

concept of the pump-probe technique can be applied to push the experiment to longer

timescales.

Since the Mie resonance occurs for a certain cluster density, the delay time ∆tat which

it occurs gives information about the expansion speed of the disintegrating cluster. This

fact is used here to further investigate the expansion behavior of large xenon clusters af-

ter XUV excitation. In dual-pulse configuration an FEL pulse (13.6 nm b= 91 eV, 100 fs,

4.1·1014 W/cm2) formed a nanoplasma, induced plasmons, and triggered the free target ex-

pansion. With a temporally delayed Ti:Sa pulse (800 nm b= 1.55 eV, 80 fs, 1.1·1014 W/cm2)

the Mie resonance condition was probed. The particle’s characteristic expansion time

∆tchar required for frequency matching is radius dependent as introduced in chapter 2.2.2.

The delay between the pulses was scanned in a wide range from 1 ps up to 1500 ps to

4.3. Probing the Mie plasmon resonance 77

account for the large cluster size distribution with radii from 25 nm to 1 µm. The initial

state of the single object was imaged by choosing XUV photons for the leading pulse. This

enables extraction of cluster size and exposed focal flux information from the scattering

patterns. This method opens the possibility to study the Mie plasmon resonance under

well characterized sample conditions, utterly impossible in earlier studies on ensembles of

clusters.

In this chapter, the resonance behavior is examined by means of highest charge-state yields

from single-shot single-cluster ion TOF spectra, which were recorded simultaneously with

scattering patterns. First, ion spectra from size-selected clusters are investigated as a

function of laser pulse delay, revealing a pronounced characteristic pulse separation time

for enhanced target ionization (section 4.3.1). Subsequently, the resonance behavior is

revisited for several intensities of laser focal power and discussed in the context of charge-

dependent cluster expansion (section 4.3.2). To conclude, in section 4.3.3, the influence of

the cluster radius on field-driven collective electron motion is investigated and compared

with hydrodynamic expansion theory. All results in this chapter were gathered together

with Mario Sauppe within the scope of his master thesis [132].

4.3.1 Driving collective electron motion in xenon clusters

As described in detail in chapter 3.2, free-electron laser pulses delivered by the FLASH

facility hold a peak power density of IXUV = 4.1·1014 W/cm2, pulse length of τXUV = 100 fs,

and a wavelength of λXUV = 13.6 nm. The thereto synchronized Ti:Sapphire laser pulses

hold IIR = 1.1·1014 W/cm2,τIR = 80 fs, and λIR = 800 nm. In this dual-pulse configuration

several fluctuations influenced the outcome of the detected single shots. Apart from cluster

sizes and exposed focal intensity varying from shot to shot, the laser beams exhibited spatial

and temporal jitter with each other. While the temporal jitter in the order of 250 fs [130]

is negligible in the time range examined, the spatial jitter has a larger impact. The 20 µm

and 90 µm focus of XUV and IR vibrated against each other, such that for some shots the

beams did not overlap completely. Therefore, a small amount of data was detected resulting

from clusters hit only by one single laser pulse - either FEL or Ti:Sa respectively. This fact

demands for accurate filtering routines. Scattering patterns from clusters only irradiated

by the IR pulse do not contain any fringe signal, but only homogeneously distributed

fluorescence. They are therefore easily recognizable as seen in figure 4.1 d. Scattering

patterns from exclusively XUV excited clusters do only contain fringe patterns but only

minor fluorescence and can be identified by the low signal at high scattering angles (see fig.

4.1 c). After precise sorting, data from single-pulse excited clusters was neglected which

decreases the overall statistics. For the further analysis only pump-probe data was taken

into account.

The previously introduced concept (see section 4.2.3) of basic filtering by investigating

best hits with highest detector intensity leads again to large clusters with highly excited

ions and large kinetic energies. This method is preferable for introducing approach since

differences in ion spectra are most prominent for large clusters as seen in chapter 4.2.1.

To make spectra comparable, highest excited clusters with 200 nm radius are chosen and

the resulting ionization of the cluster is evaluated as a function of the time separation

∆t between the pulses as depicted in figure 4.11. An increase of higher charge-state yield

(between 1 and 2 µs flight time) is visible with up to 12 ps delay. At the same time the lower

78 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

25x103

6543210

100

1000

Ion yield [arb.u.]

Temporal pulse separation [ps]

Time of flight [µs]

Figure 4.11: Single ion spectra of R = 200 nm clusters for different delays between leading XUV

and following IR pulse. Enhancement of high charge-state yield and kinetic energies with delay up

to 12 ps and subsequent decline hints on resonance feature. The same behavior is found for the

light peak measured at 0 µs flight time [132].

charge states gain in kinetic energy, indicated by the peak shift towards shorter flight times.

For longer delays, the ion distribution shifts back to lower charge states and the overall

signal decreases. The same rise-and-fall behavior is found for the light peak measured at

0µs flight time, consisting of scattered and fluorescence photons detected under 90 degrees.

Due to the statistical growth process leading to a log-normal cluster size distribution (see

fig. 4.2) statistics are very few for large clusters. No shots were found for R = 200 nm

at pulse separations of 20, 50, and 100 ps resulting in a big gap between the ion spectra

taken at 12 ps and 200 ps delay. Therefore, a qualitative analysis of the collective motion

of quasi-free electrons in clusters in this size range is not possible from this limited dataset.

Still the ion signals give strong evidence for resonant energy absorption in accordance with

theoretical predictions [157,158,159,49,50].

For better statistics, a size range around the most frequently detected radius of 34 nm

was chosen, from 27.5 to 40.5 nm, holding between 100 and 200 shots for each delay time.

Since the photon detector is not energy resolved, the signals resulting from XUV and IR

pulses respectively are hard to disentangle and sorting for exposed power density of both

pulses becomes extremely challenging. Sorting for detector intensity was renounced to

avoid misleading results by false assortment. All ion spectra measured for 34 nm xenon

clusters were averaged for each delay and plotted in figure 4.12 a. Every averaged spectrum

shows strong contribution from residual gas and uncondensed xenon atoms in the cluster

beam. They originate from single shots by clusters hit in the low-intensity focal wing.

Since those are the most frequently apparent their contribution is strongly prominent. In a

small region around short flight times between 1 and 2 ps cluster and atomic signal is well

separable. Averaged ion spectra at this high-charge-state region are set in comparison in

figure 4.12 b.

To extract pure cluster signal, each single-shot spectrum is integrated for flight times

where no background signal is detected as indicated by a red box in figure 4.12 b. In this

region, ions with higher charge states and kinetic energies than from pure xenon atoms

are measured. Subsequently, the single integrated values are averaged for each run. When

4.3. Probing the Mie plasmon resonance 79

time of flight [µs]

ion yield [arb.u.]

a) b)

8000

6000

4000

2000

6420

6,1 ps

3,8 ps

8,8 ps

3,7 ps

12,1 ps

21,6 ps

101,2 ps

1,9 ps

2,3 ps

51,5 ps

1,0 ps

time of flight [µs]

ion yield [arb.u.]

1000

800

600

400

200

2.01.81.61.41.2

Figure 4.12: a) Averaged ion spectra for xenon clusters of 34 ±6.5 nm radius taken with varying

pump-probe delays. Despite large atomic background signal an enhancement of high charge states

for certain delays is prominent. b) Zoom to the flight-time region where high charge states appear.

The maximum ion signal is obtained in spectra recorded at a temporal separation of ∆t= 8.8, 3.8,

and 6.1 ps. The red box indicates the integrated high-charge-state region.

plotted over delay (figure 4.13 a) it clearly shows that the enhanced ionization is a function

of temporal delay. The large error bars calculated by the standard deviation result from a

strong fluctuation of the high charge-state yield on a shot-to-shot basis. Highest ion signals

are detected at 6.1, 3.8, and 8.8 ps. This indicates that after these times the density of the

cluster has dropped sufficiently to reach coincidence between the frequency of collective

quasi-free electron motion in the cluster and the IR laser frequency. The delay time for

maximum resonance condition is determined by a log-normal fit [80]

I=I0+A·e−ln(∆t/∆tchar)

W2

(4.6)

with initial intensity I0, Amplitude Aand full width at half maximum W. A value of 6.3 ps

is found as indicated in figure 4.13 a.

The size of the expanded particle at point in time upon probing is disguised, even though

in the recorded scattering patterns the initial cluster radius is imprinted. For the resonance

condition, however, it can be calculated as demonstrated in the following. The so-called

Mie surface-plasmon corresponds to collective oscillations of the quasi-free electron cloud

against the ionic background. Its frequency is approximately given by [38,50]

ωMie =ωp

√3=re·ρion

30me

(4.7)

with the electron mass me, the vacuum permittivity 0, and the ion density ρion. A

nanoplasma is generated by the leading XUV pulse. It the quasi-free electrons oscillate

with the same frequency as the probing IR laser field (ωL= 3.7·1014 Hz), the energy

absorption is enhanced. This leads to the direct acceleration of electrons and strong thermal

excitation [160]. A critical ion density has to be reached to fulfill this resonance condition:

80 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

average charge state

critical expansion time [ps]

20151050

time delay [ps]

integrated ion yield [arb.u.]

400

300

200

100

6 8

2 4 6 8

100

b)a)

Figure 4.13: a) High charge-state yield of 34 ±6.5 nm radius clusters integrated over the flight

time range indicated by the red box in figure 4.12 b. Plotted over XUV/IR pulse separation time

∆tan increase in ion yield by one order of magnitude becomes prominent. Fitted with a log-

normal distribution the maximum appears at 6.3 ps. The maximum signal is accounted as evidence

of resonant collective electron excitation. b) Expansion time calculated with the uniform density

model over charge state. The initial radius is taken to be 34 nm and the electron temperature an

19.7 eV. The measured expansion time of 6.3 ps is indicated by a dotted red line.

ρion = 30meω2

L/e. The leading FEL pulse excites the cluster and initiates its expansion

by Coulomb and hydrodynamic forces. Accordingly the target density drops as a function

of time due to an increase in cluster volume

ρion(t) = Nhqie

V(t)(4.8)

with the number of atoms in the cluster N, the average charge state hqi, and the time

dependent cluster volume V(t). The latter is given by

V(t) = 4π/3·R(t)3.(4.9)

When combining equations 4.7,4.8, and 4.9, a critical radius is found where the resonance

condition is matched [50]

Rcrit =e2hqiNλ2

16π30mec21

3.(4.10)

For a cluster with R= 34 nm the number of atoms in the cluster is calculated to N= 2.9·106

from equation 2.12. To fully determine the critical radius the average charge state hqiin

the cluster is necessary.

Ion TOF spectra contain information about the final charge-state distribution of the dis-

integrated cluster. From the averaged ion spectrum measured at 6.1 ps time delay, which

is closest to the fitted maximum resonance time, the average charge state was extracted.

Furthermore, the flight-time was converted into mass-over-charge and the ion spectrum’s

center-of-gravity was determined to be m/q = 92.8 u. With a xenon mass of mXe = 131.3 u

4.3. Probing the Mie plasmon resonance 81

the average charge state can be derived as hqi= 1.4. Note that the transmission function of

the time-of-flight spectrometer for each charge state is not taken into account here, because

single charge states are hard to disentangle in the averaged spectrum (see fig. 4.12). Since

higher charges are better transmitted than lower ones, the value of m/q = 92.8 u might be

overestimated, e.g. the value of hqi= 1.4 is probably underestimated. Additionally, this

value has to be treated with care, because charge migration and recombination are taking

place before the final state is reached, which is recorded in the TOF spectra. A comparison

between ion and fluorescence spectra for similar xenon cluster and FEL properties demon-

strated that higher transient charge states are hidden in ion spectra [100]. Therefore, the

observed value of hqi= 1.4 can only hold as a lower limit for the average charge state

before expansion. An estimation of the average charge state before recombination can be

calculated from the charge state dependent expansion time.

As presented in section 4.2.3, the expansion for large xenon clusters irradiated by a

1014 W/cm2infrared pulse resides deep in the hydrodynamic regime. Therefore, the time

for a spherical cluster to expand to the critical radius can be calculated from the constant

plasma sound velocity v=phqikbTe/mito be [48,99]

texp = (Rexp −R)·rmi

hqikbTe

(4.11)

with electron temperature Te. In an experiment on an ensemble of N= 2000 atoms xenon

clusters in 90 eV FEL light with 5 ·1014 W/cm2power density, the electron temperature

was determined to be Te= 19.7 eV from electron TOF spectra [42]. With this temperature,

an initial radius of R= 34 nm, and by combining equation 4.11 with equation 4.10, the

critical expansion time was calculated for a range of average charge states and plotted in

figure 4.12 b.

As seen from figure 4.12 b, for low charge states the expansion time is slow and rises

drastically up to around hqi ≈ 4. From there it saturates and eventually decreases again

slowly towards high hqivalues. The maximum calculated value of 6.3 ps just matches the

measured peak expansion time of 6.3 ps (see fig. 4.12 a). The corresponding charge state of

hqi= 8.1 is much higher than the earlier deduced value of hqi= 1.4 predicted from the ion

TOF spectra. In comparison with the highest charge state detected of qmax>10 (see figure

4.13), it seems to be a possible value for the cluster before recombination and expansion.

However, it stays unclear which of the values is more realistic.

4.3.2 Relationship between exposed power density and resonance condi-

tion

In the previous section, laser-intensity effects were not directly addressed by averaging

single ion spectra of one cluster size but for all exposed power densities. The previous

calculations based on the hydrodynamic model suggest that the characteristic resonance

time is almost independent of the charge state from a certain threshold onwards (see graph

4.13 b). For sufficient photon fluxes it is therefore independent of the laser intensity of

the pre-expanding laser pulse. The model implies a homogeneous charge-state distribution

and does not take into account any radial dependencies. However, the quasi-free plasma

electrons migrate to the energetically preferred particle center and a shell-wise expansion

takes place as introduced in chapters 2.2.3 and 4.2.1. This effect becomes increasingly

82 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

important with large cluster sizes. Therefore, the validity of the calculation in figure 4.13 b

for the measured data needs to be revisited.

To examine the impact of the laser in-

time delay [ps]

high charge state yield [arb.u.]

600

500

400

300

200

100

6 8

2 4 6 8

100

high

medium

low

Figure 4.14: Integrated charge-state yields from

ion spectra of 34 ±6.5 nm radius clusters averaged

for three detector intensity regimes exhibit reso-

nance enhancement around the same laser pulse de-

lay time. Laser peak power densities are IXUV = 4.1·

1014 W/cm2and IIR = 1.1·1014 W/cm2. Adapted

from [132].

tensity on resonance condition, the size-

selected data from the previous section

was filtered further for detected photon

signal. Since the employed scattering

detector is not energy sensitive it is not

possible to distinguish between FEL and

Ti:Sa induced signal and hence to disen-

tangle XUV and IR exposed power den-

sities. Still the recorded frame intensity

makes a reasonable filter if the signal

is grouped in coarse enough fractions.

The data was arranged in three intensity

regimes with low (35 - 42 arb.u.), mod-

erate (42 - 49 arb.u.), and high (49 - 56

arb.u.) photon signal. As in the previ-

ous section, filtered ion spectra were in-

tegrated and averaged over high charge

states for each delay. The gleaned val-

ues are plotted in figure 4.14. It shows

that for all pulse separation times ∆t

the integrated high-charge-state yields

are largest for the data filtered for high-

est photon signal. This behavior is ex-

pected since a stronger scattering signal results from higher laser intensity. This leads to

stronger cluster excitation resulting in higher ionization (cf. section 4.2.1).

For all three intensity regimes a resonance enhancement in ion signal is observed around a

similar probe delay time. For a more precise analysis all data sets were fitted with a log-

normal distribution (equation 4.6). The resulting maximum values are 6.4 ps for high, 6.2 ps

for medium, and 6.4 ps for low excitation respectively. No clear dependence on the laser

intensity is found for the occurrence time of the Mie plasmon resonance. This observation

stands in good agreement with the previous calculation, predicting a similar characteristic

delay time for a wide range of average charge states, as soon as a certain threshold is

exceeded. Apparently, the approximations of the basic hydrodynamic expansion model of

a uniformly charged sphere are applicable in this case.

Non-homogeneous charge distributions in large clusters are reported to be reflected in

a broad temporal resonance distribution [49,50]. The uniformly-charged-sphere model

predicts the enhanced absorption to be completed after a femtosecond interval [47]. In

contrast, the resonance enhancement is calculated to be completed after several picoseconds

when a radial quasi-free electron distribution is included in calculations [82]. The charge

imbalance results in a non-uniform expansion of the cluster with faster outer side and slower

interior. Therefore, only those electrons in the layer where the density has sufficiently

dropped are collectively driven. This layer gradually moves from the outside to the cluster

center over a long time period. In the experiment performed on R= 34 nm xenon clusters

4.3. Probing the Mie plasmon resonance 83

2 3 4 5 6

100

35.25 nm 37.75 nm 40.25 nm

27.75 nm 30.25 nm 32.75 nm

delay time [ps]

high charge state yield [arb.u.]

critical expansiontime [ps]

cluster radius [nm]

40363228

Experiment

q = 8.1

q = 2.0

q = 1.4

Figure 4.15: a) Integrated ion yield over pump-probe separation time ∆tfrom averaged ion spectra

of different cluster sizes. Red curves are log-normal fits, revealing the relative peak delay times.

b) Peak resonance delay times (extracted from fits in (a)) over initial cluster radius. Calculated

expected characteristic resonance delay times for three different average charge states are indicated

by lines. Adapted from [132].

an enhanced resonance is detected between 4 and 9 ps with a fitted full width at half

maximum of W= 5 ps for all three intensity ranges (figure 4.14). In earlier experiment on

cluster ensembles [80], it was speculated that a broad resonance-time distribution might

result from a large cluster size distribution. By investigating single-cluster spectra of size-

selected particles, a size-average effect can be excluded here. Therefore, a broad resonance

time can be attributed to an shell-wise expansion as theoretically predicted [82].

4.3.3 Cluster size dependent resonance development

As evident from equation 4.10, larger clusters require more time to expand to frequency

matching condition. The data set from the previous section is split in six size regimes

from 27.75 up to 40.25 nm radius to study the radius-dependent resonance excitation time.

For better statistics and due to negligible influence it is refrained from intensity filtering.

For each temporal pulse separation and cluster-size range the single-shot high charge-

state yields are averaged and plotted in figure 4.15 a. Fitted log-normal distributions are

indicated as red lines. From bottom to top the delay times of maximum signal enhancement

shift towards higher values as expected for increasing particle size. While the size grows

by a factor of 1.45 the characteristic time develops with a factor of 1.8.

In figure 4.15 b, the experimental values are plotted together with model calculations for

different average charge states hqi. A value of hqi= 1.4, as extracted from averaged ion

spectra in section 4.3.1, underestimates the characteristic expansion time (blue line). The

calculated value of hqi= 8.1 (red line) delivers times exceeding those of the experiment.

The best compliance with the experiment is found for hqi= 2.0 (green line). With this

value the critical cluster radius Rcrit for all cluster sizes can be calculated assuming an

84 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

Table 4.2: Initial cluster radius R0deduced from fringe spacing in scattering patterns. Critical

expansion time texp extracted from figure 4.15 a. Critical cluster radius Rcrit calculated with

equation 4.10 and an average charge state hqi= 2.0. Resulting plasma velocity vexp, calculated

with v=phqikbTe/miand Te= 19.7 eV.

R0[nm] texp[ps] Rcrit [nm] vexp [m/s]

27.75 3.9 52.2 6300

30.25 5.1 56.8 5200

32.75 5.5 61.6 5200

35.25 5.9 66.3 5200

37.75 6.1 71.0 5400

40.25 7.0 75.6 5100

electron temperature of Te= 19.7 eV. Due to the knowledge of the initial radius before

excitation the expansion speed of the critical cluster layer up to resonance condition can be

calculated. The results are listed in table 4.2. For all initial sizes the speed was calculated

to be similar, fluctuating around 5500 m/s. In earlier drift measurements on xenon clusters

a velocity distribution with maxima at 3600 and 12000 m/s was detected [152]. This shows

that the here deduced results are realistic. This indicates that the fitted value of 2.0 is a

good estimate for the average charge state before recombination for clusters of R= 34 nm

in 80 fs IR pulses of 1014 W/cm2.

To conclude, the method of single-cluster imaging in coincidence with ion spectroscopy

allows to study the Mie plasmon resonance in unprecedented detail. By imaging the cluster

initial state with the pump pulse, the particles can be well characterized for size and

exposed focal flux. Independent of the latter, maximum ionization occurs 6.3 ps after XUV

excitation for particles with radius 34 ±6.5 nm. This indicates that the electron cloud is

driven resonantly by the strong IR laser field. The broad resonance time distribution of

5 ps is a signature of the layer-wise cluster expansion, e.g. the electron density dropping

to resonance condition shell-by-shell. In cluster radius-dependent observation larger initial

cluster sizes lead to longer expansion times until the critical radius is reached. From the

nanoplasma model an average charge state of hqi= 2.0 can be fitted to the data. Derived

from the thereby calculated critical radius the expansion speed of outer exploding shell is

determined.

What stays unrevealed is the destination of the cluster core after shell explosion. As

spectroscopy is blind to uncharged particles and therefore the recombined core, a different

approached is needed for its investigation. Since imaging provides access to neutral matter

the pump-probe setup is reversed in time. While the IR pulse initiates cluster expansion,

snapshots of the disintegrating sample are recorded with the succeeding XUV pulse for

several points in time. Combined they provide a movie of plasma evolution, subject to the

next chapter.

4.4 Imaging IR induced explosion

In the previous section the cluster expansion was initiated by an FEL-pump pulse and the

response was tracked with an IR-probe pulse. By examining of the characteristic time of

4.4. Imaging IR induced explosion 85

a) b)

Time-of-flight

spectrometer

Time-of-flight

spectrometer

XUV

pulse

Scattering

pattern

Fluore-

scence

Figure 4.16: Experimental scheme of the excitation mechanism. a) An IR-pump pulse excites a

single xenon cluster and induces a nanoplasma. The detected photon signal shows homogeneous

scattering and fluorescence. b) A variably delayed XUV pulse directly images the state of cluster-

electron distribution. By varying the arrival time of the pump pulse, the nanoplasma evolution is

mapped on an extended timescale up to nanoseconds. While ion spectroscopy is blind to neutral

cluster atoms, imaging gives access to investigate the recombined cluster core.

the ion-density dependent plasmon resonance the expansion speed was estimated. In this

chapter, the temporal pump-probe scheme of the two laser pulses is reversed. Thereby their

roles get interchanged: The IR pulse from the 800 nm Ti:Sa initiates cluster expansion and

cluster fragmentation is examined with the 13.6 nm XUV pulse from the FEL. Some aspects

of IR specific dynamics have been already discussed in detail in section 4.2.3. The electrons

in the cluster are field driven by the IR-pump pulse. Quasi-free electrons are produced by

inner field ionization processes, resulting in the build-up of a dense nanoplasma and a

disintegration of the particle’s outer ionic shell in a hydrodynamic expansion. At the

same time the inner core recombines and stays intact on a supra-femtosecond timescale.

The further development and the timescale of possible disintegration of the neutral core

is unknown. Therefore, the last key issue of this thesis is to investigate how the shell

disintegrates and what happens to the remaining core several pico- up to nanoseconds

after the excitation. While ion spectroscopy is blind to neutral cluster atoms, imaging

gives access to investigate the recombined cluster core. With the XUV as probe pulse

snapshots of the disintegrating sample are directly imaged for a detailed examination of

the nanoplasma evolution.

The pump-pulse delay with respect to the probe pulse was varied in 12 steps between 0.3 ps

and 1.5 nanoseconds to analyze the cluster expansion with good resolution on an extended

time range. 24000 scattering patterns and corresponding ion TOF spectra were recorded

from individual xenon clusters. Those were produced under the same expansion conditions

as stated in chapter 3.1, exhibiting a log-normal size distribution with the maximum at

34 nm radius and cluster radii up to 1 µm (see figure 4.2). In the previous section, the

initial cluster condition was mapped on the CCD image but no information about the final

state could be deduced from the scattering pattern. In this section, the setup is reversed as

schematically depicted in figure 4.16. No details can be directly extracted about the size

and shape of the cluster before excitation by the IR pulse. Only the state after expansion

is retained in the CCD images. With increasing delay time the disintegration of the cluster

86 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

1400 ps 1400 ps 1500 ps

500 ps

1000 ps

100 ps

100 ps 500 ps

20 ps

ii)

iii)

Figure 4.17: Three types of characteristic CCD images recorded from individual xenon clusters

excited by an IR pulse and subsequently probed by an XUV pulse. i) Ring structures hinting on

intact clusters. ii) Homogeneously distributed photon signal. iii) Speckle patterns. The respective

pulse separation time is denoted in each image. For a detailed description of the detector artifacts

visible in the scattering patterns see chapter 4.1.1 and figure 4.1.

should cause a dramatic change in scattering patterns due to IR induced electron-density

deformation and plasma-profile evolution.

Snapshots of manifold expansion states

A vast variety of images was recorded. Therefore, careful inspection and filtering of the

single-shot patterns had to be executed. A large amount of data exhibits shots where no

cluster is hit by any of either laser pulses, because of heavy cluster beam skimming. Other

data results from clusters hit exclusively by an FEL or an IR pulse respectively, due to

missing spacial overlap. These datasets were filtered and neglected for further pump-probe

investigations. Apart from those discarded shots three fundamentally different types of

scattering images were recognized on different timescales. A characteristic assortment of

the repertoire is depicted in figure 4.17. They are grouped in rows, depicting

(i) ring structures with additional fluorescence (fig. 4.17 i),

(ii) a rather homogeneously illuminated screen (fig. 4.17 ii), and

(iii) diffuse speckle patterns (fig. 4.17 iii).

These limiting cases mirror the different atom/ion-density distributions, present picosec-

onds after laser-cluster interaction. The discussion of the underlying physical principles,

leading to these patterns will be the topic of this chapter. It will lead to an overall picture

of the expansion dynamics taking place from a picosecond up to a nanosecond timescale.

The first characteristic type of scattering images appears over the entire time range from

0.3 ps up to 1500 ps delay time, though the vast majority is found at short delays. Due to

the visible fringe structure they have high resemblance with patterns from intact clusters

irradiated by an FEL pulse only. In addition they exhibit an enhanced background signal

reminding of CCD signal from exclusive Ti:Sa irradiate particles. As investigated in section

4.2.3, interaction of giant clusters with a moderate IR pulse results in skinning of a rather

4.4. Imaging IR induced explosion 87

NIR

100

3.5

200

500

1000

1500

XUV

Figure 4.18: Brightest CCD images of different runs. First row: clusters were exclusively hit

by an IR or XUV pulse respectively. Images below: clusters are imaged by the FEL pulse after

Ti:Sa excitation at different temporal delays, increasing from top to bottom and left to right as

indicated by the delay time in picoseconds. The gradual change in patterns mirrors the evolving

cluster disintegration. With increasing probe delay time the scattering fringe signal decreases and

fluorescence signal increases.

thin outer ionic shell and a remaining neutral nanoplasma which can efficiently recombine.

The visible ring structure in the scattering patterns indicates that the cluster core is still

to some extend intact, even picoseconds after the IR excitation. The timescale of the core

continuance will be analyzed in detail in section 4.4.1.

The rather constantly illuminated screen in the second type of images (fig. 4.17 b) resembles

data taken from clusters hit by an IR pulse only. For this reason they are hard to disentangle

from those and the corresponding ion spectra are necessary for reliable filtering. A loss of

information in the scattering pattern corresponds to a loss of order in the sample [161].

Hence, the absence of any fringes or speckles indicates an advanced destruction of the

particle. Also the intensity of the signal rises with pulse separation times, which will be

analyzed in more detail in section 4.4.2.

The third type of CCD images, as in the bottom row of figure 4.17, exhibits diffuse speckle

patterns not resembling any images detected from unmaimed rare-gas clusters. They strik-

ingly stick out from any patterns priorly presented and are very rare. They appear only

from a nanosecond delay onwards. Such speckle patterns are known from other fields, such

as particulate matter. They were detected from aggregates of spherical nanoparticles like

soot and aerosols [8,162] but never before from mono-atomic clusters. From an extended

analysis in section 4.4.3, they can be understood as images of the slowly expanding neutral

cluster core, which exhibits internal density fluctuations.

88 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

4.4.1 Imaging cluster surface ablation

Comparing the scattering patterns in figure 4.17, the question arises how the transition

between those extreme, limiting cases takes place. From the basic observation that with

delay time the amount of fringe patterns (as in fig. 4.17 i) decreases, while the quantity of

’homogeneously illuminated’ patterns (fig. 4.17 ii) increases, the conclusion can be drawn

that on a median timescale images of an intermediate state should be present. Indeed

patterns with vanishing fringe signal are existent, but accounting those to a corresponding

initial state and a matching final state is challenging, if not impossible.

Therefore, in figure 4.18 the most reliable

30252015105

scattering angle [degree]

scattering intensity [arb.u.]

XUV

NIR

1500

0.9

1000

500

200

100

8.7

5.7

3.8

2.2

Figure 4.19: a) Azimuthally averaged scattering

signal of the diffraction patterns shown in figure

4.18. For a juxtaposition the XUV only profile

is at the bottom (blue), while the IR only one is

at the top (red). Temporal delay increases from

bottom to top as indicated by numbers in picosec-

onds. The arrows are a guide to the eye to trace

the shift of envelope minimum towards smaller

angles for increasing delay.

assignment has been used to investigate on

which time scale large clusters get destruc-

ted by an IR laser as explained in the fol-

lowing. All CCD images recorded for one

delay time were filtered for the brightest

photon signal. The assumption thereby is

that largest clusters scatter most and clus-

ter most centrally placed in both beam foci

result in highest detector intensity. By this

method it is ensured that the biggest and

best hit clusters of each run are picked out.

For every delay time the scattering pattern

of those selected clusters are plotted in fig-

ure 4.18 in comparison with the most in-

tense shot for single pulse excitation (IR

and XUV only respectively). Pump-probe

patterns at shorter delay times up to 20 ps

show the familiar, fine fringe structures from

giant, hailstone-shaped xenon clusters. For

delay times up to 20 ps no major differences

to patterns from clusters in exclusive FEL

pulse imaging are observed, except from

the varying target geometries. From 50 ps

onwards the fringe pattern vanishes and a

drastic increase in background signal be-

comes prominent at larger scattering an-

gles. Whether this background arises from

fluorescence, inelastic, or incoherent scat-

tering cannot be determined since the de-

tector is not energy resolved. However, ion

time-of-flight spectra reveal an increase in

fluorescence signal with delay time, as will

be discussed later (see chapter 4.3.2 and figure 4.24). The drastic change in pattern appear-

ance between 20 and 50 ps is most probably arising from the deformation of the atom/ion-

density distribution which proceeds on a picosecond timescale.

More detail is revealed by the azimuthally integrated scattering profiles as presented in

figure 4.19 a. The fine fringes in the ring pattern are almost not resolved (compare with

4.4. Imaging IR induced explosion 89

figure 4.2) due to the very large cluster sizes and the detector geometry. However, the

profile envelope is clearly visible. For the FEL-only-shot this envelope appears to change its

slope around 20 degrees scattering angle. For the pump-probe hits this ’minimum’ evolves

towards smaller scattering angles with delay time, to around 7 degrees for the profile at

100 ps. On the same timescale the background signal at high scattering angles increases.

Its origin is discussed further below. From 200 ps delay onwards no more fringe signal is

detected. This leads to the conclusion that it has vanished to small angles below 4 degrees

which are not recorded with this setup2. From 500 ps onwards the profiles remarkably

resemble the ones recorded from clusters exposed to IR light only. However, the overall

detector intensity is higher for pump-probe data. This phenomenon will be elaborated and

interpreted in section 4.4.2.

Analysis of core melt-off by shell ablation

Previous single-shot XUV imaging experiments on xenon clusters demonstrated that ultra-

fast changes in electronic configuration - proceeding within femotseconds - are imprinted in

the scattering signal [10]. Within 10 fs, the atomic form factors can change with increasing

degree of ionization, evident from a deformation of the scattering amplitude envelope. Us-

ing 100 fs XUV pulses a supermodulation of the fringe pattern appears. This gives evidence

of a refractive core-shell system in the cluster. It is probably caused by sharp resonances of

xenon ions at 91 eV photon energy which lead to the formation of two regions with different

refractive indices inside the cluster [45]. Both publications ([10,45]) show that ultrafast

electronic changes affect the pattern intensity distribution. However, the fringe structure

itself, e.g. their spacing and radially integrated intensity distribution, is not drastically

altered. In contrast to those single-pulse experiments, the dual-pulse configuration used

in this work enters the timescales of atomic/ionic motion. Here, the changes in scattering

signal are more drastic. From the evolution of the scattering signal with varying temporal

pulse separation a precise conclusion about the evaluation of the nanoplasma profile can

be drawn. This was consistently demonstrated in an experimental [46] and a theoretical

study [163].

An IR-pump / x-ray-probe experiment on medium sized xenon clusters (20 nm in radius)

was performed recently at the hard x-ray free-electron laser LCLS. It was shown that higher

order scattering rings disappeared fast after a probe pulse delay time of only several hun-

dred femtoseconds [46]. The particles were pumped by a highly intense Ti:Sa pulse with

peak power density of 2 ·1015 W/cm2(almost 20 times more intense than in the present

experiment). The resulting high charge states exceeded Xe6+ by far. The fast stripping

of electrons from their parent ions resulted in a Coulomb explosion of the repulsive ionic

outer cluster layers and the cluster rapidly expanded. In small-angle Guinier-scattering

simulations on electron densities with Gaussian-like distribution - as reported for plasma

evolution in vacuum [164,165] - the vanishing of fringe signal at larger angles was repro-

duced. Moreover, the cluster size before illumination by the IR pulse was simulated. A

decrease of scattering signal at large angles by almost two orders of magnitude after 500 fs

was attributed to a core melt-down of 50 %. Additionally, it was revealed that the scat-

tering signal has completely blurred into background signal before complete destruction of

the cluster.

2Detector hole and stray light cover the region from 0◦to 4◦scattering angle.

90 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

a) b)

Figure 4.20: Adapted from [163]. a) MicPIC simulation for the electron and ion distribution of an

initially 25 nm radius hydrogen cluster at tree different time steps after excitation with an IR pump

pulse (λ= 800 nm, τ= 10 fs, I= 1015 W/cm2). b) Simulated corresponding scattering profiles

generated by an XUV probe pulse (λ= 10 nm, τ= 10 fs, I= 1016 W/cm2) at several delay times

after IR excitation. With increasing surface ablation higher order scattering maxima decrease in

intensity.

This signal drop in scattering intensity at large angles with cluster expansion was already

predicted by extensive theoretical calculations for hydrogen particles [163]. The evolution

of the radial ion and electron density several femtoseconds after excitation was computed

in MicPIC simulations on a hydrogen cluster excited by an IR pulse. Exemplary, results

for a 25 nm radius hydrogen cluster are shown in figure 4.20 a. First, an unscreened surface

layer bursts off the fully ionized particle in a Coulomb explosion. Eventually, the remaining

screened core - where ion and electron density coincide - undergoes hydrodynamic expan-

sion. At all time steps the simulated electron-density distribution was found to consist of

a uniform volumic mass core and an exponentially decaying shell. In total, it follows the

equation

ρ(r) = ρCore

[exp(r−rC

d·s) + 1]s(4.12)

with the density of the cluster core ρCore, the distance from the cluster center r, the radius

of the cluster core rC, the decay length of the melting surface d, and a sharpness factor s,

which ensures the correct transition between core and shell region [163].

In the same study, scattering patterns from an XUV pulse probing those density distri-

butions were calculated by the scattering fraction of the scattered electric field. They are

shown in figure 4.20 b where two major results are immediately visible. One the one hand,

the higher order maxima decrease in intensity with broadening of the surface layer and

smoothing of the edge between core and shell region. On the other hand, the minima shift

towards larger angles with delay time due to a reduction of the core radius. Due to this

behavior the amplitude envelope of the fringes gets steeper with surface ablation.

The results of this theoretical study were applied to the measured data presented in figures

4.4. Imaging IR induced explosion 91

1.0

0.5

0.0

12008004000

Scattering angle [deg] Scattering angle [deg]

Radius [nm]

Density [arb.u.]

Scattering intensity [arb.u.]

Core

994 nm

984 nm

940 nm

Surface

5 nm

20 nm

40 nm

0.1

100

30252015105

4x101

30252015105

500 ps

100 ps

50 ps

10 ps

XUV only

a) b)

Figure 4.21: a) Azimuthally integrated scattering patterns of clusters irradiated exclusively by

an FEL pulse or by an FEL pulse following a Ti:Sa pulse at different delay times respectively. Due

to the large particle size (>700 nm radius) the fringes are not resolved. The background signal

increases with delay and an intensity threshold is indicated by the black dotted line where fringe

signal is overlayed. The envelope of the scattering pattern gets steeper with temporal separation

between pump and probe pulse, as indicated by the red lines. Correspondingly crossing-points

of intensity threshold and envelope shift towards smaller angles with nanoplasma evolution. b)

Simulation of scattering patterns by 2D FFT of projected electron density arrays. Profile of an

intact cluster of R= 1000 nm radius with hard edge is depicted by the light gray pattern. Where

the blue envelope reaches an angle of 20 degrees an intensity threshold (black dotted line) is set.

Profiles with envelopes crossing this line are matched for angels of 11.5 and 7.5 degrees fitting the

measured data. Inset: Corresponding density profiles reveal the relatively small melted surface

compared with the remaining core.

4.18 and 4.19. The steepness of the scattering profile envelopes was analyzed to investigate

the change in electron-density distribution as function of expansion time. In figure 4.21 a

the profile for the XUV only excited cluster is set in direct comparison with clusters imaged

at 10, 50, 100, and 500 ps delay respectively. The two main tendencies observed are

•rising steepness of the intensity slope at low scattering angles with delay time and

•an arising of background signal at high scattering angles.

The second aspect is of minor interest for the understanding of the underlying physical

aspects of cluster expansion and will be discussed here only briefly. A minor background

arising from inelastic photon scattering is predicted by theoretical calculations [163], but

with orders of magnitude lower in intensity than the intensity of the elastically scattered

light3. A different publication reports on a previous dynamic pump-probe imaging ex-

periment, where a strong background signal with intensities in the order of the elastic

scattering intensities was also detected at high scattering angles and increasing with delay

time [161]. However, this experiment was not performed on isolated targets, but on several

3Note that contribution by fluorescence is neglected in this calculation.

92 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

extended membranes with the same pattern etched into them. The increase in background

signal with delay time was attributed to scattering from additional structure induced in

the membrane by the pump-pulse. Since this cannot be the case for finite targets, as in

the experimental data presented in figure 4.18 and 4.21 a, the background signal at high

angles is attributed to a composition of fluorescence and inelastic scattering. However, it is

not understood why it increases towards larger angles. Due to the high background signal,

the fringe envelopes are superimposed by the background signal from a certain intensity

threshold, indicated by the black dotted line in figure 4.21 a. Because the steepness of

the envelope rises with delay time, the scattering angle at which the envelope crosses this

threshold shifts towards smaller angles (indicated by the red dotted lines in fig. 4.21 a)

until it vanishes towards angles lower than those detected.

To further analyze the underlying plasma

Figure 4.22: Scattering profiles of patterns cal-

culated with Me’s theory from a spherical cluster

with 25 nm (red graph) and 250 nm (gray graph)

radius respectively from [163]. Despite the differ-

ent particle radius and resulting scattering fringe

spacing, the profile envelope is the same.

evolution, measured envelope changes have

been compared with theoretical simulations.

In scattering profiles from pristine spheri-

cal clusters the envelope steepness is inde-

pendent of the cluster size, evident from

Mie theory [38], as demonstrated in figure

4.22. This observation enables a qualita-

tive statement for the measured data with-

out prior knowledge of the initial cluster

radius before IR excitation and subsequent

cluster expansion. Several electron-density

distributions with increasing surface decay

length and correspondingly shrinking core

have been calculated to mimic the cluster

shapes at several time steps after IR irra-

diation. They are displayed in the inset of

figure 4.21 b. For their calculation the an-

alytic expression proposed by MicPIC the-

ory for nanoplasmas in hydrodynamic expansion [163] was employed (equation 4.12). In

the present experiment, however, the initial cluster size is unknown. The profiles presen-

ted in figure 4.21 a originate from the largest clusters produced, which exceed a radius

of 700 nm since the fringe spacing cannot be resolved (see section 4.1.1). Therefore, an

estimated initial radius of R= 1000 nm was used in all calculations in figure 4.21 b. Again,

note that the scattering envelope of a spherical particle is independent of the scatterer

size. Therefore, any arbitrary initial radius is applicable to study the amplitude envelope

changes.

In a simplified approach scattering profiles were simulated by 2D Fast-Fourier-transforms

(FFT) of the electron-density distribution projected onto the scattering plane. Scattering

fringes are plotted in gray in figure 4.21 b and envelopes are highlighted in color. The blue

density distribution in the inset of figure 4.21 b is calculated for a cluster with a surface

decay length of 5 nm and corresponding core of 994 nm. In order to make theory and

experiment comparable, an intensity threshold was set in figure 4.20 b where the higher

order maxima of the profile with blue envelope reach 20 degrees scattering angle. The

scattering angle at which envelope and threshold level cross is used as reference point to

find the matching density profiles. From density distributions with melting outer shells

4.4. Imaging IR induced explosion 93

(see inset in figure 4.21 b), profiles with envelopes crossing the background-threshold at

11.5 and 7.5 degrees were calculated, to simulate the data taken at 50 and 100 ps after IR

excitation respectively. The parameters for the density were chosen such that the overall

volume was kept constant. The resulting density distributions hold a cluster core of 984 and

940 nm with surface decay lengths of 20 and 40 nm respectively. With this basic simulation

the general trend of decrease in scattering yield at large angles with proceeding

cluster melting is well reproduced. It still is important to keep in mind that neither

initial cluster radius nor absolute values of slopes and threshold can be deduced from the

measured data in this experiment.

In conclusion, this simulation reveals that a cluster is not necessarily completely

destroyed when fringes are absent in measured scattering patterns. This ob-

servation agrees with the earlier presented result (section 4.2.3) that for large clusters in

infrared pulses only a thin cluster shell expands upon hydrodynamic pressure of the hot

electron cloud. The remaining core recombines to full neutrality after electrons migrate

to the energetically preferred cluster center. Information about the cluster evolution on

large timescales up to nanoseconds is probably prevented due to fringes hidden below 4

degrees, where scattering signal is missing due to the experimental setup. Even though

the decreasing core seems to be the major part remaining, its further fate is still unknown.

In corresponding ion TOF spectra the further existence of the cluster is witnessed on the

entire measured time scale up to 1.5 nanoseconds. TOF spectra are investigated in more

detail in the following section to get insight into the cluster dynamics on this extended

time scale.

4.4.2 Ionization of clusters under surface ablation

In this section, strongly (peak power densities of 1.1·1014 W/cm2) IR-excited clusters with

a substantial fraction of the core melted down are analyzed on an extended timescale up

to one and a half nanoseconds of pulse separation. Therefore, the data was filtered for

•shots where no diffraction rings are visible in the CCD images, but exclusively strong

fluorescence and diffuse scattering signal are detected (as in figure 4.17 ii). And for

•shots where high kinetic energies are detected in ion TOF spectra, as indicated by

red areas in figure 4.4.

From the analysis in the previous section it is concluded that the cluster surface is melted

to a degree where the resolvable fringe pattern falls into the detector center region at small

angles where residual stray light and the detector hole overlay the signal. Additionally,

these shots were filtered for corresponding TOF spectra which show clear evidence of cluster

signal, to ensure that data from pure atomic xenon was not taken into account.

Time evolution of detector intensity (scattered light and fluorescence)

For each remaining shot the averaged detector luminosity is plotted run-wise over temporal

pulse separation between IR-pump and XUV-probe pulse in figure 4.23 a. The overall

number of filtered images increases with delay time. A substantial quantity of hits exhibits

low and moderate intensity, mirroring the fact that the biggest amount of shots are recorded

94 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

delay time [ps]

detector intensity [arb.u.]

a) b)

100101102103

Figure 4.23: a) Integrated detector intensity for filtered shots in each run plotted over temporal

pulse separation between IR-pump and XUV-probe pulses. Averaged values for one run are indi-

cated by red stars. With increasing delay the high intensity shots gain in number and the maximum

single-shot detector intensity rises. b) Filtered CCD images with highest (top) and one of the lowest

(bottom) detector intensities respectively. The data was filtered on absence of scattering fringes

and high kinetic energy tails of charge states in TOF spectra. Inhomogeneities in the images arise

from residual scattering and detector artifacts as described in chapter 4.1.1 and figure 4.1.

from clusters hit in the focal wings and sides. The brightest images most probably result

from large clusters hit in both beams focal centers. The peak intensity as well as the

average luminosity increases with laser pulse delay time. Exemplary a high intensity and

a low intensity CCD image are depicted in figure 4.23 b.

Two effects can explain the change in detector intensity with delay time:

•scattering contribution and

•fluorescence contribution.

On the one hand, shortly after laser excitation most probably only small clusters are melted

to an extend where the scattering envelope has vanished towards small angles. Since the

initial size of the cluster is unknown in this experiment it is very likely that larger clusters

are filtered out by the special filter (no rings in scattering patterns, high kinetic energy

ions in TOF spectra) at small ∆tvalues because they are expected to need more time

for substantial surface ablation. Bigger clusters lead to higher detector intensities as they

scatter more strongly. However, as discussed in the previous section, with increasing delay

time shell ablation proceeds. This results in a decrease in scattering signal at high angles

and therefore to an overall decrease in detector signal.

On the other hand, in dense systems fluorescence is often suppressed due to quenching.

Excited states which are available for radiative decay become depopulated by electron

collisions. Upon particle expansion, these collisions become less probable and fluorescence

frustration is abolished, leading to higher photon signal. Additionally, in a dense system

photon reabsorption is frequent. Therefore, fluorescence is mostly collected from the cluster

outer layers. As introduced in section 2.3.3, a recent experiment on Ar-Xe core-shell

clusters revealed that fluorescence from the cluster core is emitted only from states with

short lifetime, while fluorescence from the shell is emitted from many states and therefore

4.4. Imaging IR induced explosion 95

has a stronger contribution to the overall detected photon signal [100]. Since the ablation

of the cluster evolves shell-wise on a long timescale, as analyzed in the previous section,

there is continuously a new outer cluster layer and the fluorescence is expected to gradually

increase until the process of shell ablation is completed.

Time evolution of ion TOF spectra (charge states and kinetic energies)

From the filtered scattering images where fringe signal is missing (cf. fig. 4.23 b and 4.17 ii)

only little information can be drawn. However, in the corresponding ion spectra salient

features mirror the nanoplasma evolution. The ion spectra averaged over every filtered

shot for every pump-probe separation time are plotted in figure 4.24 a. Zooming in at

zero flight time it shows that the light peak gains in height and width due to increased

fluorescence. This behavior is in agreement with the increasing luminosity of the scattering

screen described earlier. Looking at the entire TOF spectrum at short delay times (blue

spectra), the Xe1+ peak is most prominent with large contribution from high kinetic ions.

Towards later times it decreases and the distribution shifts towards higher charge states

(red spectra). At latest delays Xe7+ and higher are protruding. The charge-state increase

with ∆t becomes most prominent when plotting the spectra’s center-of-mass over delay

time, as presented in figure 4.24 b. In this depiction the TOF transmission functions for

each charge state are not taken into account due to the challenging assignment of charge

states for ion yields in averaged spectra (see section 3.2.3). Therefore, it is expected that

the average charge states in figure 4.24 b are slightly underestimated. However, the general

trend of increasing average charge state with delay time is contained.

The shift towards higher charge states is a strong indication for recombination suppres-

sion. This finding was recently simulated with molecular dynamics simulations for an

XUV/XUV pump-probe scheme on small xenon clusters [98]. Only in a dense, strongly

coupled nanoplasma three-body recombinations are effective. Here, the hot electrons can

release enough energy in collisions, so that recombination is possible. In a dilute plasma

however, collisions are less probable and electrons cannot cool down and have too high

energy to recombine. Therefore, in the late stages of cluster expansion the recombination

is not possible which results in overall higher charge states detected.

The second main characteristic feature in the averaged ion spectra is that with proceed-

ing delay time he overall spectrum resembles more and more an atomic one, irradiated

exclusively by an FEL pulse. For comparison a spectrum from pure xenon gas is plotted

at the top of figure 4.24 a. At large delay times, TOF peaks with high kinetic energies

reveal that cluster components are still present. This gives evidence that the evolution of

the excited nanoplasma lasts up to nanoseconds, even though not directly resolved in the

corresponding diffraction images (compare fig. 4.21).

With increasing delay time the signal becomes more ’atom-like’ because the cluster core be-

comes increasingly atom-like. While the cluster shell explodes off due to charge separation,

the recombined neutral cluster core exhibits no large kinetic energy when hit by the probe

pulse. An increasing ’atomization’ of the ion signal reveals an increasing ’atomization’ of

the cluster core. This means that the neutral core disintegrates after bonds are breaking

due to energy deposited in the cluster from the pump pulse.

The increase in light peak yield gives evidence that a transition from non-radiating recom-

96 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

876543210

0.3

0.9

2.2

3.8

5.7

8.7

100

200

500

1000

1500

atomic

0.200.100.00 2.22.01.81.61.41.2

100

1000

time of flight [µs] average charge state [e]

ion yield [arb.u.]

delay time [ps]

a) b)

Figure 4.24: a) Filtered and averaged ion TOF spectra, taken in IR/XUV pump-probe configura-

tion for varying delay times as indicated by numbers in picoseconds. The filter was set on absence

of fringes in CCD images and high kinetic energy contribution in corresponding TOF spectra.

Laser peak power densities were 1.1·1014 W/cm2and 4.1·1014 W/cm2for the IR and XUV pulses

respectively. For comparison an atomic spectrum from xenon gas irradiated with an XUV beam

only is included on top of the graph (black). b) Average charge state of each run, extracted from

the averaged TOF spectra’s center-of-mass. Note that the TOF transmission function is not taken

into account here, due to the challenging assignment of charge states for the ion yield in averaged

spectra.

bination and relaxation to radiative relaxation takes place. Strong shell ablation leading

to images of the second category (compare figure 4.17 ii) results from clusters well hit by

the pump IR pulse. A different picture arises for clusters less highly excited due to lower

exposed power densities, which are subject of the next section.

4.4.3 Expansion of a neutral cluster core on the nanosecond timescale

One nanosecond after excitation by the pumping infrared pulse some xenon clusters feature

a substantially new appearance. This is manifested in the third category of scattering

patterns recorded, as introduced in figure 4.17 iii. They exhibit an unordered speckle

structure - never before detected from spherical clusters. Some representative examples

with azimuthally averaged intensity profiles are presented in figure 4.25. The fact that they

appear earliest 500 ps after expansion initialization by the IR-pump pulse and the absence of

4.4. Imaging IR induced explosion 97

Scattering angle [degree]

Scattering detector intensity [arb.u.]

3x101

30252015105

Figure 4.25: Several characteristic patterns with unsystematic speckle distribution, recorded upon

XUV illumination 1.4 and 1.5 nanoseconds after IR excitation and their corresponding profiles of

azimuthally integrated scattering intensity. The profile slopes exhibit an overmodulation with

minima between 18 and 22 degrees scattering angle.

any ring structures indicates a different cluster evolution behavior than the above discussed

surface melt-down (section 4.4.1). The question arises how exactly a cluster disintegrates

after shell ablation and recombination of the cluster core to full neutrality.

The complexity of the speckle patterns prevents an exact retrieval of the disintegrating

cluster shape. Nevertheless, as this section will show, pattern frequency and intensity

envelope analysis allow to extract average parameters determining the particle appearance

encoded in the scattering patterns. Comparison with Mie theory indicates how to interpret

those speckle patterns. In ring-patterns from Mie calculations on spherical objects the

oscillation of the pattern yields information about the particle size [38]. Additionally, the

course of the amplitude is determined by the refractive index, which is directly coupled to

the material density. This chapter will show that the same correlation is valid for speckle

patterns. The shape and size of the speckles originate from the overall particle outline and

average diameter while the amplitude modulation is a direct consequence of fluctuations

in the particle density [166].

The arising of speckle appearance can be attributed to a ring break-up, originating from

a significant drop in particle density. Small-angle scattering simulations (SAXS) were

performed in three steps to visualize this behavior:

1. First, with the example of a linearly expanding dilute cluster with uniform density.

2. In a second step, this spherical cluster is subdivided in smaller units to account for

the density fluctuations in the evolving recombined plasma. The radius of the sub-

clusters in this model system exemplifies the size range of an internal cluster-density

modulation.

98 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

Step 1 Step 2 Step 3

DAtom

RClu DSub RSub RSub ﬂuctuating

Figure 4.26: Scheme of simulated model clusters. Step 1: Clusters are modeled with amorphously

distributed point scatterers of average distance dAtom within a sphere of radius RClu. Step 2: The

spherical cluster is subdivided in smaller sub-spheres with radius rSub and distance DSub. Step 3:

A size distribution is applied on the radii of the sub-clusters.

3. In a third step, a size distribution is applied to the sub-clusters to tune this approval

toward more realistic appearance.

A visualization of the model systems used in the three different steps is illustrated in figure

4.26. With the help of scattering simulations from these computed cluster geometries, it

will finally become possible to understand the underlying shape of the measured xenon

clusters.

Step 1: Small-angle x-ray scattering simulations from an expanding gas ball

Basic simulations with 2D-FFTs of projected sample outlines are a practical tool for fast

analysis of dense objects, where the distance between the single scatterers is smaller than

the impinging wavelength (as used for simulations in figure 4.21 b). Since the distance

between atoms is thereby not taken into account, more sophisticated modeling is needed

for dilute systems. An adequate method are small-angle scattering calculations from point-

scatterers with freely tunable separation. For the simulation a MATLAB code was written

based on the concept introduced in [36]. The formalism and code are described in detail in

appendix A. Point-scatterers representing xenon atoms were ordered on a three-dimensional

grid within a radius RClu (see fig. 4.26). The scatterer distance is denoted as dAtom. In order

to gain amorphous atom distribution the point-scatterer position was allowed to randomly

vary from its initial position on the grid by up to dAtom/2. The scattering signal was

calculated in scalar numerical approach [36]. The experimental values of XUV wavelength

λ= 13.6 nm, detector pixel size p= 0.069 mm, and distance between interaction region and

detector L= 61.64 mm, are used for all simulations. Therefore, simulated and measured

patterns are directly comparable. The angle resolution was set to 0.2 degrees in radial and

azimuthal direction respectively. All images were calculated up to 33 degrees scattering

angle.

A rigid sphere with equally expanding point-scatterers was implemented as model cluster.

While this model is a very basic approximation for the expansion of the neutral cluster

4.4. Imaging IR induced explosion 99

44.

20.

RClu = 100 nm RClu = 250 nm RClu = 1000 nm

dAtom = 5 nmdAtom = 12.5 nmdAtom = 50 nm

RClu = 100 nm RClu = 250 nm RClu = 1000 nm

dAtom = 5 nmdAtom = 12.5 nmdAtom = 50 nm

min

max

-20

-10

-30

angle [deg]

6.7

Figure 4.27: Simulation of light scattering on amorphously distributed scatterers. a) Cut through

atom distribution. Atomic distances dAtom are increasing from top to bottom and cluster radii RClu

from left to right. b) Corresponding calculated scattering patterns. For better visibility all images

are normalized to their maximum value. Therefore, absolute intensity values are not comparable.

With decreasing particle density (top to bottom) the ring-patterns vanish at high angles in favor

for speckles. Particle radius increase results in decrease of mean fringe spacing and speckle size

respectively.

100 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

core, it provides an intuitive understanding for the underlying mechanism. In a first step

the influence of cluster size and atomic distance on the diffraction image is investigated.

Figure 4.27 shows central cuts through modeled clusters (a) and their corresponding simu-

lated scattering patterns (b). From top to bottom dAtom is increased from 5 to 50 nm. For

dense particles (top row), coherent scattering gives pronounced interference ring patterns.

For larger atomic distances (center row), fringes break up at large angles and speckles

appear. Speckles arise from objects with amorphousness (for surfaces often denoted as

roughness) larger than the laser wavelength. Hence, the scattered exit waves do not inter-

fere constructively at the same scattering vector value q. In the bottom row of figure 4.27,

where dAtom is largest, the rings disappear almost completely towards low frequencies in

the pattern center and mainly ’homogeneous’ speckle patterns are visible. The angle where

the ring signal transforms into speckle signal is dependent on the average distance of all

point-scatterers to each other. This leads to the conclusion that the experimentally recor-

ded speckle images result from a cluster where the density has decreased sufficiently, such

that the laser wavelength becomes sensitive to the internal particle disorder and density

fluctuations.

The here presented simulations mirror the detector geometry used in the experimental setup

for this thesis. The maximum simulated scattering angle is 33 degrees. In the simulation

the average atomic distance has to increase from dAtom = 0.48 nm (Wigner-Seitz-radius of

solid xenon: rW= 0.24 nm) by one order of magnitude to dAtom = 5 nm for speckles to

become visible at maximum angles. For ring-structures to disappear completely up to 4

degrees - corresponding to the beamstop area in the detector - dAtom even has to rise to

50 nm (bottom row), e.g. by two orders of magnitude.

In figure 4.27 column-wise from left to right, the size of the particle is increased from a

radius of 100 to 1000 nm. While for dense targets the fringe spacing gets smaller (top

row), for dilute particles analogous the speckle structure becomes finer (bottom row). The

average size of the speckles is inversely proportional to the radius of the spherical cluster.

Laser speckle analysis is mainly common in rough surface examination [167]. Only in the

last years it gained in significance for imaging of finite target systems. From theoretical

calculations on a spherical object with rough surface [168] and independently on a two-

dimensional structure of spherical apertures [37] the relation between speckle and overall

cluster radius can be deduced to approximately

RClu ≈λL

πp

RSp

(4.13)

with the impinging wavelength λ, the distance between detector and interaction region L,

the detector pixel size p, and the mean speckle radius RSp.

For the determination of mean speckle size several approaches can be used, e.g. morpho-

logical analysis of binary images from pattern thresholding [169,37]. This procedure is

however not recommendable for patterns with an intensity modulation where lower in-

tensity speckles might be overlooked. One of the most frequently applied methods is to

extract the mean speckle size from the normalized autocovariance function4C(x, y) of the

scattering pattern intensity I(x, y) [170]

C(x, y) = hI(x, y)2i−hI(x, y)i2

P(hI(x, y)2i−hI(x, y)i2).(4.14)

4The normalized autocovariance function corresponds to the autocorrelation function.

4.4. Imaging IR induced explosion 101

Input radius [nm] Input radius [nm]

Speckle diameter [pixel]

Output radius [nm]

100

2 3 4 5 6 7 8 9

1000

2 3

FWHM

Squared

100

1000

100

2 3 4 5 6 7 8 9

1000

2 3

FWHM

Squared

a) b)

Figure 4.28: a) Full width at half maximum (FWHM, round symbols) and beam waist (1/e2,

squared symbol) of the mean speckle size, extracted from simulated scattering patterns plotted over

radius of model clusters. b) Corresponding calculated radii over radius of model clusters. The red

curve shows the dependence calculated with equation 4.13.

This technique was used here and cross-checked on simulated data. The sums of the

normalized autocovariances of all rows and columns in the pattern were fitted by a Gaussian

distribution. The full width at half maximum (FWHM) and the beam waist (1/e2) of

this Gaussian distribution were determined in pixels and converted to sphere radius with

equation 4.13. It is inevitable to cross-check the reliability of the applied method and

the utilized code. Therefore, the scattering patterns were calculated for several dilute gas

balls with varying cluster radius. Subsequently, the values of 2RSp were extracted from

the simulated data. In figure 4.28 mean speckle size and therefrom calculated radius are

plotted over the radius that was fed in the SAXS simulations. The red curve indicates

values calculated with equation 4.13. For small clusters of 100 nm radius, the extracted

size is slightly overestimated and the FWHM value fits better than the 1/e2value. For

larger clusters from 500 nm radius onwards, the size is underestimated and the beam waist

value gives a more correct result.

This method was also applied to the measured pattern presented in figure 4.29. Beamstop

and dead pixels were masked before calculation of the normalized autocovariance function.

A mean speckle size of 2RSp = 8.74 FWHM and RSp = 8.061/e2was extracted from

the pattern. Corresponding cluster radii of RClu = 884.8 nm and RClu = 960.2 nm are

calculated with equation 4.13, with λ= 13.6 nm, L= 61.64 mm, and p= 0.069 mm. A

simulated speckle pattern from a gas ball of this radius RClu = 950 nm is depicted in figure

4.29 as juxtaposition to the experimental data. The speckle sizes seem to match quite well.

Immediately apparent becomes the deviation of pattern intensity at high spatial frequencies

between measured and simulated images. The computed image exhibits a constant average

intensity distribution. In radial profiles of recorded images (see figure 4.25 b) the envelope

of the amplitude exhibits a modulation. The scattering intensity shows a decline up towards

around 20 degrees and stays relatively constant from this angle onwards. This behavior

demonstrates that the simple model of an equally expanding sphere shows some general

102 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

R=800

R=950

SimulationMeasurement

Figure 4.29: a) Diffraction pattern of a disintegrating xenon cluster imaged 1.4 ns after infrared-

laser excitation. b) SAXS simulations from a sphere of equally distributed amorphous point-

scatterers (as described in the text as Step 1) with dAtom = 50 nm and RClu chosen to be 950 nm.

The dark red circle indicates the area where the scattering signal is hidden due to stray light. The

mean speckle size matches well for calculated and recorded images. However, the relative intensity

distributions show clear deviations, e.g. the measured pattern exhibits an intensity modulation

which is absent in the simulation.

trend, but is insufficient to describe the entire cluster evolution witnessed in the experiment.

Step 2: SAXS simulations with density division in sub-clusters

The modulated diffraction-pattern envelope implies an underlying sub-structure in the

particle density distribution [166]. The above cluster model with on average equally spaced

point-scatterers was refined to get a handle on this density fluctuations. The sphere was

divided into several sub-clusters with internal amorphous atom distribution, as sketched in

figure 4.26 step 2. In a first loop the positions of the sub-clusters were arranged with spacing

DSub within a sphere of radius RClu. In a second loop the sub-spheres with radius rSub

and atomic distances dAtom were generated and arranged on the positions just calculated.

With the overall radius RClu and the atomic distance dAtom kept constant, the influence of

sub-cluster size rSub and spacing DSub on the scattering pattern is demonstrated in figure

4.30. Slices through the particle center are presented in (a) and corresponding calculated

scattering patterns in (b).

For all model systems in figure 4.30, the outer particle radius is kept constant at RClu =

250 nm5and the atomic distance within a sub-cluster is held at dAtom = 5 nm. From

top to bottom row the distance between debris centers DSub increases from 25 to 100 nm.

Analogous to a change in dAtom in figure 4.27, the overall particle internal disorder increases

together with the surface roughness. Hence, the scattering ring pattern at large scattering

angles vanishes in favor of speckles due to missing constructive interference at the same

propagation vector value. The average speckle size is not affected since it is only dependent

on the overall cluster radius RClu. The radius of the sub-clusters rsub raises column-wise

from 12.5 to 50 nm in figure 4.30. While in the left column of figure 4.30 b the simulated

images do not exhibit a clear envelope modulation, it becomes prominent in the second

column from a ring-shaped minimum at around 20 degrees. In the third column the first

minimum is shifted to smaller angles and higher order minima appear. The angle of the

first envelope minimum θmin is related to the size of the mean scatterer rSub by the Airy

pattern equation [32,33]:

rSub = 1.22 ·λ

2 sin(θmin).(4.15)

5For good visibility of the speckle size, a cluster radius of RClu = 250 nm was chosen for the simulations.

This is not to be confused with the measured size of RClu = 950 nm.

4.4. Imaging IR induced explosion 103

52.3

6.7

22.1

47.0

11.3

28*10³

233*10³

265*10³

2*10⁶17*10⁶

2*10⁶

rSub = 12.5 nm rSub = 25 nm rSub = 50 nm

DSub = 100 nm DSub = 25 nmDSub = 50 nmDSub = 100 nm DSub = 25 nmDSub = 50 nm

min

max

-20

-10

-30

angle [deg]

Figure 4.30: Simulation of scattering on spheres with amorphously distributed sub-spheres of

scatterers. a) Slices through the particle center. The radius of the sub-spheres rSub is increased from

left to right. The distance of the sub-spheres DSub in increased from top to bottom. Overall cluster

radius and atom spacing are kept constant (RClu = 250 nm and dAtom = 5 nm). b) Corresponding

scattering patterns. From top to bottom scattering rings in the pattern center break up in favor

for speckles. From left to right an overmodulation with decreasing fringe spacing appears. The

overmodulation’s first minimum θmin shifts to smaller angles with increasing sub-sphere radius.

104 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

With this relation the mean density fluctuation range can be deduced from measured

patterns. From a detected angle of about 20 degrees (see radial profiles in figure 4.25) a

value of rSub ≈25 nm is calculated with an XUV wavelength of 13.6 nm.

Following equations 4.13 and 4.15, simulations of a 950 nm radius sphere with 25 nm radius

sub-clusters should give a reasonable match with the measured pattern in figure 4.29. The

remaining unidentified parameters are the distances dAtom and DSub. The only information

known up to this point is that the distance between the sub-spheres DSub significantly

affects at which angle the ring pattern transforms into speckles. Since the transition is

not visible in the measured pattern, it is expected that it is located at angles lower than

4 degrees, which are covered with residual light. Therefore, only an upper limit for DSub

can be given.

To simulate cluster with certain den-

1011

1012

1013

1014

1015

302520151050

DSub: 100nm

dAtom: 5nm

DSub: 75nm

dAtom: 7.5nm

DSub: 50nm

dAtom: 10nm

DSub: 37.5nm

dAtom: 15nm

RClu: 950nm

rSub: 25nm

Scattering angle [deg]

Scattering intensity [arb.u.]

Figure 4.31: Scattering profiles from model clusters

with equal size (RClu = 950 nm) but of different density

distributions are presented, gradually varying from sys-

tems with few dense sub-spheres (red curve) to a cluster

with many dilute sub-spheres (violet curve). The amount

of atoms in the system stays constant at N= 1.9·106

atoms. Therefore, the density of the overall cluster does

not change. The radial profiles of the simulated scatter-

ing patterns demonstrate a stronger pronunciation of the

envelope modulation for stronger density fluctuations.

The length scale of the particle fluctuation is constant

for all envelopes (rSub = 25 nm).

sity, several combinations of dAtom

and DSub values are applicable. The

relative change in degree of density

modulation, e.g. the depth of the mod-

ulation minima, is influenced by the

ratio of the density of the sub-spheres

to the density of the entire cluster.

Several radial profiles of calculated

scattering patterns with differently

strong density modulation but con-

stant number of atoms N= 1.9·106

are depicted in figure 4.31. Note that

the length scale of the fluctuations

is kept constant by the sub-cluster

radius rSub = 25 nm (manifested in

the angle of the envelope minimum).

Also the speckle size stays equal due

to a constant cluster radius of RClu =

950 nm. With decreasing atomic dis-

tance and correlated increasing dis-

tance between the sub-clusters, the

envelope minimum becomes more pro-

nounced due to a stronger density

fluctuation. The observation that the

minimum in the recorded scattering

profile is rather weakly pronounced

(see figure 4.25 b) points towards a weakly developed density modulation.

4.4. Imaging IR induced explosion 105

Step 3: SAXS simulations with size distribution of the sub-clusters

A different effect which makes the min-

1011

1012

1013

1014

1015

302520151050

rSub: 25±20nm

rSub: 25±15nm

rSub: 25±10nm

rSub: 25±5nm

rSub: 25nm

RClu: 950nm

DSub: 50nm

dAtom: 10nm

Scattering angle [deg]

Scattering intensity [arb.u.]

Figure 4.32: Radial profiles of simulated scattering

patterns from model clusters with equal size (RClu =

950 nm) and equal internal density. Simulated scat-

tering profiles of model systems with a sub-cluster size

distribution. In step 3 of the simulation (details see

text) the radius of the sub-spheres rSub is allowed to

vary. While for small radius variations the minimum

of the envelope modulation in the scattering profile

is strong (violet curve), for a larger size distribution

the envelope minimum softens (red curve).

imum become less deep is a size distri-

bution of the sub-particles. The model

of a cluster divided into sub-spheres is

suitable to get an intuitive understand-

ing of the influence of density modu-

lations on diffraction patterns. How-

ever, it is certainly not appropriate to

model the exact cluster internal struc-

ture. The cluster model is once more re-

fined (see figure 4.26 step 3) by applying

a size distribution on the sub-clusters to

make the subject more realistic. Figure

4.32 presents several spectra from sim-

ulations with sub-particles fluctuating

around 25 nm radius. With increasing

size distribution the minimum in the

scattering envelope becomes less pro-

nounced (from blue to red curve). This

result points towards a wide variation

of density-modulation ranges inside the

measured particle. However, the mean

size range of the sub-clusters can be de-

termined from the amplitude envelope

outline of the recorded patterns, as ev-

ident from equation 4.15.

The complexity of speckle diffraction images makes their characterization a very challenging

task. Particle shape retrieval by direct comparison with theoretical calculations is often

intricate. The interplay of several length scales and distributions in real space and their

correlated effects on the pattern in Fourier space prevents exact determination of the

object’s architecture. Still the mean particle size and average density fluctuation

range are well extractable from speckle analysis.

Figure 4.33 presents the juxtaposition of a measured speckle pattern (in color see figure

4.25 b) with a simulated one. As introduced above, from the means speckle size an average

cluster radius of about 950 nm could be extracted from the measured pattern. The angle

of the first envelope minimum in the measured scattering pattern leads to an estimated

mean density fluctuation range of about 25 nm. To simulate the scattering pattern in figure

4.33 b a model cluster with the parameters RClu =950 nm, rSub =25 ±15 nm, DSub =50 nm,

and dAtom = 4 nm was generated and is depicted in figure 4.33 d. The model cluster con-

tains N= 3.2·107atoms. This corresponds to a cluster of R= 75.9 nm with solid-state

density. Speckle appearances and azimuthally integrated intensity profiles are rather well

matching. This simulation illustrates that despite the very approximative cluster model

the main sizes are well extractable from the speckle patterns.

106 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

Detector intensity [arb.u]

Scattering angle [degree]

RCluster = 950 nm rSub = 25 15nm

DSub= 50 nm dAtom= 4 nm

4x101

302520151050

1012

1013

Measurement

Simulation

a) measurement b) SAXS simulation

-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30

Scattering angle [degree] Scattering angle [degree]

c) d)

Figure 4.33: a) Typical speckle diffraction pattern recorded 1.4 ns after infrared laser impinge-

ment. See 4.25 b for color. b) Simulated pattern calculated in small angle x-ray scattering approach

from a d) modeled cluster with RClu =950 nm, rSub =25 ±15 nm, DSub =50 nm, and dAtom = 4 nm.

c) With this system SAXS simulations can well reproduce the measured speckle pattern in size and

slope.

Conclusion

The evolution of expanding single xenon clusters was imaged. Large individual clusters

were produced in supersonic expansion of 10 bar xenon at 180 K trough a conical nozzle,

resulting in a log-normal size distribution between 25 and 1000 nm radius with a maximum

at 34 nm radius. The particles were turned into a nanoplasma by a high power IR pulse

with peak intensities of 1.1·1014 W/cm2. The expansion was imaged with an ultrashort

FEL pulse of 4.1·1014 W/cm2. By snapshotting several points in time, ranging from

femtoseconds up to nanoseconds, two different expansion mechanisms were identified.

•Following strong particle excitation and nanoplasma formation, quasi-free electrons

migrate to the energetically preferred particle center. Efficient recombination leads to

a net-neutral core embedded in a highly charged shell. At the picosecond timescale

the xenon cluster gets skinned. Depending on the laser power density, a decrease

of scattering signal at high detection angles with increasing time delay mirrors the

accompanied softening of the cluster surface.

•The remaining net-neutral nanoplasma can efficiently recombine and stays in the in-

teraction region up to nanoseconds. In slow motion its density decreases and internal

density fluctuations build up. Diffraction images of speckle patterns are representa-

tive of this second stage of cluster expansion. Analysis of measured average speckle

size and pattern intensity envelope modulation reveal the mean cluster size and range

4.4. Imaging IR induced explosion 107

of internal density fluctuations at the time of detection. Simulations indicate that

after a nanosecond the neutral cluster core remains as expanded gas ball with mea-

surable internal density fluctuations.

These findings from dynamic diffraction imaging extend the picture of laser-matter inter-

action into the nanosecond time scale. Here structural principles are discovered, which are

up to date unexplored in homogeneous clusters.

108 Chapter 4. Results: Cluster evolution in intense XUV and IR pulses

Chapter 5

Summary and outlook

In this thesis, the ionization and expansion dynamics of large, single xenon clusters irradi-

ated with highly brilliant laser pulses was studied. The method of single-shot single-cluster

imaging in coincidence with ion time-of-flight (TOF) spectroscopy was applied. It enables

to characterize laser-particle interaction in unprecedented detail by eliminating the influ-

ence of the laser focal volume intensity and particle size distribution. Very large clusters

were produced in supersonic expansion of 180 K xenon gas with 9.8 bar backing pressure

trough a conic nozzle of 200 µm orifice and 4◦half opening angle. The resulting particle

radius was ranging between 25 and 1000 nm. The experiments were performed at the free-

electron laser in Hamburg (FLASH) at beamline 2. Ultrashort (100 fs) extreme ultraviolet

(XUV) pulses delivered were focused to a spot size of 20 µm. The maximum power density

in the focal volume reached about 4.1·1014 W/cm2. Additionally, an infrared (IR) laser

with wavelength of 800 nm and pulse length of 80 fs was used. With a focal spot size of

90 µm power densities around 1.1·1014 W/cm2were reached.

Three different excitation schemes were applied in order to examine different processes and

timescales of laser-cluster interaction:

1) Particles were irradiated by either a single IR or a single XUV pulse only.

2) The cluster disintegration was induced by an XUV pump pulse and probed with an

IR pulse in order to map the Mie resonance in the cluster nanoplasma.

3) Cluster fragmentation was initiated with an IR pulse and different disintegration

states were snapshotted with a delayed XUV pulse.

In the first part, the response of the cluster was investigated in dependence on the cluster

size and material, as well as the laser power density and wavelength. For clusters irradiated

with IR or XUV pulses only, almost identical TOF spectra with similar charge state yields

and kinetic energy distributions were found. Also xenon, argon, and silver clusters in

FEL pulses resulted in similar TOF spectra.This reveals that from a certain cluster size

on the cluster dynamics are universal, almost independent of laser wavelength and cluster

component. This behavior leads to the conclusion that initial ionization mechanisms play

a minor role and nanoplasma processes like e.g. electron collisions take the lead.

109

110 Chapter 5. Summary and outlook

In the second part, the timescale of the experiment was extended up to one and a half

nanoseconds with pump-probe technique. The XUV pulse induced cluster disintegration

and therefore a lowering of the overdense particle density. The temporal delay of the IR

pulse was scanned with respect to the FEL pulse arrival time in order to probe the Mie

resonance. A characteristic peak delay time of 6.3 ps was found for cluster sizes ranging

around 34 nm in radius. The large peak width and therefore plasmon lifetime of 5 ps is

an indication for a shell-wise density decrease. By mapping the focal volume it could be

shown that the characteristic delay time does not change significantly with XUV laser

power density. This behavior is in agreement with calculations using the nanoplasma

model. With the same model the average charge state hqiwas determined to hqi= 2.0,

fitted to radius dependent peak delay time measurements. The delay time increases from

3.9 ps to 7.0 ps for clusters of average 28 nm radius to 40 nm radius.

In the third part, the disintegration of large xenon clusters irradiated with intense IR pulses

was imaged by XUV scattering. Following strong particle excitation and nanoplasma for-

mation, quasi-free electrons migrate to the energetically preferred particle center. Efficient

recombination leads to a net-neutral core embedded in a highly charged shell. On the

picosecond time scale, a major part of the xenon cluster has been skinned by a rather

thin outer ionic shell in a fast expansion. This shell-ablation is mirrored in the recorded

diffraction patterns by a vanishing of fringe signal and decrease in scattering signal at high

scattering angles within tens of picoseconds. In basic simulations using 2D Fourier trans-

formations of particle outlines with softened surface these changes were identified as pro-

ceeding shell ablation, leaving a shrinking cluster core behind. The remaining net-neutral

nanoplasma can efficiently recombine and stays in the interaction region up to nanoseconds.

Its density decreases slowly and density fluctuations occur, leading to speckle patterns with

intensity modulations which appear from 500 ps on. Despite the high complexity of the

speckle patterns, it was shown that the overall particle size and internal density fluctua-

tion range can be derived by simple image analysis procedures. The findings from dynamic

diffraction imaging extend the picture of laser-matter interaction in to the nanosecond time

scale, where structural signatures were identified which were up to date not explored in

homogeneous clusters.

In the dynamic imaging experiments of this work, which used an IR pump pulse, the initial

cluster size and exposed focal flux are not well characterized since the initial image of the

particle is missing. An experimental improvement could be achieved by additional imaging

of the cluster at the time of pump-pulse arrival. Therefore, the IR pulse would have to

be substituted by an XUV pulse in order to record an initial scattering pattern which

facilitates a precise determination of the initial cluster state. The entire process of cluster

dynamics could be filmed by capturing the initial and various intermediate states of the

complete sample disintegration process. Up to date two major criteria limit this approach:

(1) To follow the entire sample disintegration both, XUV-pump and XUV-probe beams

need to be separated on an extended timescale up to nanoseconds. (2) Two separate

images need to be recorded which are only separated by picoseconds. In our group, we

have launched a project which addresses both limitations and will make ultrafast ‘movies’

of free nanoparticles feasible in future experiments.

XUV/XUV pump-probe experiments are currently possible at the FLASH facility with

the autocorrelator split-and-delay unit at beamline 2 [171]. Here, one beampath can be

temporally delayed from −3 ps up to +15 ps with respect to the other. The temporal

111

Figure 5.1: Schematic setup of the ‘X-ray movie camera’. From [172]. The FEL beam is split and

both beam paths are delayed with respect to each other. They are focused onto the particle from

opposite sites consecutive producing separate diffraction patterns on two opposing detectors.

delay range is limited due to setup which is based on grzing incidence reflection. To

push XUV/XUV experiments toward a longer timescale, a more compact split and delay

unit has been developed in our group and will be installed permanently into beamline 1

at FLASH until July 2015. The DESC (Delay Stage for CAMP) system is based on

multilayer mirrors. While multilayer mirrors only allow for a narrow wavelength range

to be reflected, they effectively shorten the beampaths due to normal incidence reflection

leading to a more compact geometry. With the DESC system XUV/XUV pump-probe

experiments in a range up to several 100 ps will be feasible.

The second limiting criteria for the recording of molecular movies up to date is the read-out

time of the scattering detector. In collinear pump-probe geometry both scattering patterns

consecutively fall on the same detector where they superimpose and are recorded as one

image. To circumvent this problem, in our group an ‘X-ray movie camera’ is envisioned

and will be commissioned at FLASH in October 2015. Here, in a pump-probe setup the

XUV beam is split and delayed and both pulses are focused onto the particle from opposite

sites, see figure 5.1. Two separate diffraction patterns are recorded consecutively from two

opposing detectors, similar as proposed in [173]. The overlay of both scattering patterns

is minimized due to the geometry under 180 degrees. The knowledge about initial cluster

size determined from the first image and at a later point in time from the second image

would enable to determine the exact cluster disintegration process. The here presented

setup will open the possibility to record a fast ‘movie’ from an unsupported nanoparticle

in free flight.

112 Chapter 5. Summary and outlook

Appendices

113

Appendix A

Small angle scattering code

All small angle scattering simulations in this thesis where performed in MATLAB with a

code adapted from [36]. To model a xenon cluster with amorphously distributed atoms the

following procedure was used: Point-scatterers were ordered at positions with coordinates

rx,ry, and rzon a three-dimensional grid with distance dAtom. Only the atoms within a

sphere of radius RClu were taken into account. To distribute the atoms amorphously they

were randomly displaced by a maximum of dAtom/2 in all three directions in space from

their initial position.

%% IA Generate model cluster as sphere of point-scatterers on a 3D grid

clear; clc;

RClu=35; % radius of the core

dAtom=7; % distance between atoms

atom=1;

box=2*RClu+1;

Cluster=zeros(box,4);

for x=(-RClu:dAtom:RClu)

for y=(-RClu:dAtom:RClu)

for z=(-RClu:dAtom:RClu)

rx=x; ry=y; rz=z;

R=sqrt(rx^2+ry^2+rz^2);

if R <= RClu

Cluster(atom,1)=rx+(0.5-rand(1)*dAtom);

Cluster(atom,2)=ry+(0.5-rand(1)*dAtom);

Cluster(atom,3)=rz+(0.5-rand(1)*dAtom);

atom=atom+1;

end

AtomInClu=atom-1;

ClusterIn=Cluster(1:AtomInClu,:);

scatter3(ClusterIn(:,1),ClusterIn(:,2),ClusterIn(:,3));

set(gca,’DataAspectRatio’,[1 1 1]);

115

116 Appendix A. Small angle scattering code

To model a xenon cluster with internal density fluctuations, the above model was refined

by subdividing the cluster into several sub-spheres. Therefore, first the positions of the

sub-spheres were ordered on a three-dimensional grid with distance DSub within the cluster

of radius RClu and the positions were randomly displaced by a maximum of DSub/2 in all

three directions in space from their initial position. Subsequently on these positions sub-

spheres with radius rSub are generated with point-scatterers of distance dAtom with random

displacement of maximal dAtom/2.

%% IB Generate sphere of point scatterers subdivided into sub-spheres

clear; clc;

RClu=35; rSub=8; % radius of entire cluster and of sub-sphere

dAtom=4; dSub=20; % distance between atoms and between sub-spheres

box=RClu*2+1; sub=1; Position=zeros(box,4);

for rx=(-RClu:dSub:RClu)

for ry=(-RClu:dSub:RClu)

for rz=(-RClu:dSub:RClu)

R=sqrt(rx^2+ry^2+rz^2);

if R <=RClu

Position(sub,1)=rx+((0.5-rand(1))*dSub);

Position(sub,2)=ry+((0.5-rand(1))*dSub);

Position(sub,3)=rz+((0.5-rand(1))*dSub);

sub=sub+1;

end

SubInCluster=sub-1; Pos=Position(1:SubInCluster,:); clear sub

AtomInClu=zeros(SubInCluster,1);

for sub=1:SubInCluster

atom=1; box=RClu*2+1; Cluster=zeros(box,4);

PosX=Pos(sub,1); PosY=Pos(sub,2); PosZ=Pos(sub,3);

for rx=(-rSub:dAtom:rSub)

for ry=(-rSub:dAtom:rSub)

for rz=(-rSub:dAtom:rSub)

R=sqrt(rx^2+ry^2+rz^2);

if R <= rSub

Cluster(atom,1)=rx+PosX+((0.5-rand(1))*dAtom);

Cluster(atom,2)=ry+PosY+((0.5-rand(1))*dAtom);

Cluster(atom,3)=rz+PosZ+((0.5-rand(1))*dAtom);

atom=atom+1;

end

AtomInClu(sub)=atom-1; ClusterSub=Cluster(1:AtomInClu(sub),:);

b=sum(AtomInClu); a=b-AtomInClu(sub)+1;

ClusterIn(a:b,:)=ClusterSub;

end

117

To simulate the scattering from the model cluster, the scattering from each point-scatterer

is calculated in azimuthal and radial direction, respectively, for a chosen angle range (Nθ,

Nϕ) with chosen accuracy (∆θ, ∆ϕ). The scattering vector value is wavelength and angle

dependent |q|= 4π/λ ·sin(θ/2) and is in spherical coordinates composed of

qx=q·cos(θ/2) cos(ϕ),

qy=q·cos(θ/2) sin(ϕ),(A.1)

qz=−q·sin(θ/2) (π≥θ≥0; 2π > ϕ ≥0)

The amplitude of the light scattered by a single point-scatterer is calculated in fractions

of the scattering amplitude of a single free electron. The ratio of scattering amplitude

of an atom to the scattering amplitude of a free electron is given by the complex atomic

scattering factor. It is f=−2.61 + i·32.92 for xenon at 91.5 eV photon energy [?].

The scattering amplitude from the entire model cluster consisting of Natoms is simply

calculated as the summation of the scalar electric fields from an arrangement of Npoint

scatterers:

Nθ,Nϕ

θ,ϕ

Aθ,ϕ =

Nθ,Nϕ

θ,ϕ

Nx,Ny,Nz

x,y,z=1

f·ei(Qxrx+Qyry+Qzrz)(A.2)

The intensity of the scattering signal is proportional to the squared modulus of the ampli-

tude:

I= 4π|A|2(A.3)

% % II Calculate scattering crossection of the model cluster

Lambda=13.5; % laser wavelength

FAtom=-2.61+1i*32.92; % atomic scattering factor

DThe=2.0; The1=0; The2=33.0; % theta increment and lower/upper bounds

DPhi=2.0; Phi1=0; Phi2=360.0; % phi increment and lower / upper bounds

NThe=round(1+(The2-The1)/DThe);

NPhi=round(1+(Phi2-Phi1)/DPhi);

PatternAngle=zeros(3,NThe,NPhi);

for i=1:NThe

for j=1:NPhi

TheSc=The1+(i-1)*DThe;

PhiSc0=Phi1+(j-1)*DPhi;

if PhiSc0<0, PhiSc=PhiSc0+360; end

if PhiSc0>=0, PhiSc=PhiSc0; end

kapa=(4*pi*sin(pi*TheSc/(180*2)))/Lambda;

Qx=kapa* cos((pi*TheSc)/(180*2))* cos((pi*PhiSc)/180);

Qy=kapa* cos((pi*TheSc)/(180*2))* sin((pi*PhiSc)/180);

Qz=-kapa*sin((pi*TheSc)/(180*2));

argu=ClusterIn(:,1).*Qx+ClusterIn(:,2)*Qy+ClusterIn(:,3)*Qz;

Amplitude=sum(FAtom.*exp(1i.*argu));

Intensity=(4*pi*abs(Amplitude))^2;

PatternAngle(1,i,j)=TheSc;

PatternAngle(2,i,j)=PhiSc;

PatternAngle(3,i,j)=Intensity;

end

118 Appendix A. Small angle scattering code

List of Figures

1.1 Pioneering dynamic imaging experiments . . . . . . . . . . . . . . . . . . . 2

2.1 Supersonic expansion of a free jet . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Cluster size dependence on gas temperature and gas backing pressure . . . 10

2.3 Temporal jet profile for single and ensembles of xenon clusters . . . . . . . . 11

2.4 Intensity distribution of the radiation from a dipole . . . . . . . . . . . . . . 15

2.5 Small-angle and wide-angle scattering geometry . . . . . . . . . . . . . . . . 17

2.6 Airy pattern and diffraction from multiple circular apertures . . . . . . . . 18

2.7 Mie Scattering: Angular functions and intensity profiles . . . . . . . . . . . 20

2.8 Cluster morphology determined from scattering patterns via 2D Fourier

transforms and MSFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.9 Scattering profiles in dependence on laser power density . . . . . . . . . . . 23

2.10 Three phase model of laser-cluster interaction . . . . . . . . . . . . . . . . . 24

2.11 Schemes of photon dominated and field driven atomic ionization in a laser

field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.12 Photon energy over power density, illustrating the photon and field domi-

nated regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.13 Excitation steps and ionization channels in xenon atoms . . . . . . . . . . . 27

2.14 Concept of inner and outer ionization . . . . . . . . . . . . . . . . . . . . . 28

2.15 Motion of the electron cloud in the laser electric field . . . . . . . . . . . . . 30

2.16 Schematic depiction of the cluster state determining the rivaling expansion

mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.17 Evolution of nanoplasma density and temperature in a pump-probe setting

calculated with MD simulations. From [98]. . . . . . . . . . . . . . . . . . . 35

2.18 Spatial distribution of ionization rates . . . . . . . . . . . . . . . . . . . . . 36

119

120 List of Figures

2.19 Single-shot single-cluster scattering pattern and ion spectra of giant xenon

clusters in 13.6 nm pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1 Scheme of the experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2 Schematic drawing of the FLASH setup . . . . . . . . . . . . . . . . . . . . 43

3.3 FEL radiation emission in an undulator . . . . . . . . . . . . . . . . . . . . 44

3.4 Optical laser layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.5 Temporal overlap determination with precision of one picosecond . . . . . . 48

3.6 Fine temporal overlap between IR and XUV pulse established with xenon gas 49

3.7 Schematic diagram of the vacuum apparatus . . . . . . . . . . . . . . . . . 50

3.8 Schematic depiction of the solenoid pulsed Parker valve . . . . . . . . . . . 52

3.9 Scheme of the scattering detector setup . . . . . . . . . . . . . . . . . . . . 54

3.10 Scheme of the TOF-spectrometer principle . . . . . . . . . . . . . . . . . . . 56

3.11 Time-to-energy conversion and transmission function of the time-of-flight

spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.1 CCD camera images showing scattered and fluorescing photons . . . . . . . 62

4.2 XUV scattering patterns and corresponding cluster sizes . . . . . . . . . . . 63

4.3 Scattering patterns from clusters hit in different positions within the focal

volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.4 Single-shot ion time-of-flight spectra of xenon . . . . . . . . . . . . . . . . . 65

4.5 Ion time-of-flight spectra from single xenon clusters sorted on cluster size

and focal power density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.6 Central kinetic energy over charge state . . . . . . . . . . . . . . . . . . . . 70

4.7 Ion time-of-flight spectra from single silver clusters sorted on cluster size

and focal power density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.8 Comparison of ion TOF spectra from single argon, silver, and xenon clusters 72

4.9 Compare averaged ion spectra of xenon cluster irrdiated by XUV and IR

light respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.10 Compare single ion spectra of xenon cluster irrdiated by XUV and IR light

respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.11 Single ion spectra of R = 200 nm clusters for different delays between leading

XUV and following IR pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

List of Figures 121

4.12 Averaged ion spectra for xenon clusters of 34 nm radius taken with varying

pump-probe delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.13 Integrated high charge-state yield over time delay and calculated cluster

expansion time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.14 Intensity dependent charge-state yield over delay time . . . . . . . . . . . . 82

4.15 Integrated ion yield over pump-probe separation time from averaged ion

spectra of different cluster sizes . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.16 Experimental scheme of the excitation mechanism . . . . . . . . . . . . . . 85

4.17 Three types of characteristic CCD images . . . . . . . . . . . . . . . . . . . 86

4.18 Brightest CCD images of different runs with varying delay time . . . . . . . 87

4.19 Scattering profile of the brightest images for each delay . . . . . . . . . . . 88

4.20 MicPIC IR pump - XUV probe simulation from [163]. . . . . . . . . . . . . 90

4.21 Measured and simulated scattering profiles of clusters with melting surface 91

4.22 Scattering profiles of patterns calculated with Me’s theory . . . . . . . . . . 92

4.23 Integrated detector luminosity for filtered shots . . . . . . . . . . . . . . . . 94

4.24 Averaged filtered ion TOF spectra over delay time . . . . . . . . . . . . . . 96

4.25 Characteristic patterns with unsystematic speckles . . . . . . . . . . . . . . 97

4.26 Scheme of simulated model clusters . . . . . . . . . . . . . . . . . . . . . . . 98

4.27 Simulation of light scattering on amorphously distributed scatterers . . . . 99

4.28 Determination of mean speckle size . . . . . . . . . . . . . . . . . . . . . . . 101

4.29 SAXS simulations reveal the expanding particle mean radius . . . . . . . . 102

4.30 Scattering simulations on spheres with sub-spheres of scatterers . . . . . . . 103

4.31 Radial profiles of simulated scattering patterns from model clusters of dif-

ferent density distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.32 Radial profiles of simulated scattering patterns from model clusters with

with a sub-cluster size distribution . . . . . . . . . . . . . . . . . . . . . . . 105

4.33 Measured speckle pattern and matching simulation . . . . . . . . . . . . . . 106

5.1 Schematic setup of the ‘X-ray movie camera’ . . . . . . . . . . . . . . . . . 111

List of Tables

2.1 Calculated specific gas constants Kch for the rare gases helium, neon, argon,

krypton and xenon, from [25]. A high clustering probability is mirrored by

a high Kch value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Values for the parameters Cand Bin equation 2.11. In different sizes range

Buck and Krohne (small) [26], Hagena (medium) [23], and Dorchies (large)

[28] found the listed values. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 FLASH is a user facility since 2005 and has been upgraded several times.

Listed are the state-of-the-art radiation parameters in 2014 [127] and values

of the 2011 experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 IR radiation parameters of the optical laser system in the laser hutch [128]

and at the experimental endstation in 2011. . . . . . . . . . . . . . . . . . . 47

4.1 First three ionization energies (IPin eV) [32] and absorption cross-sections

at 91 eV (σin Mbarn) for xenon, silver, and argon atoms respectively [154].

Clusters sizes extracted from figure 4.8 a respectively and corresponding to-

tal atom numbers N. Calculation of the amount of outer photoionized elec-

trons nout upon 91 eV pulse impact and the corresponding ratio from total

atom number to outer photoionized electrons. . . . . . . . . . . . . . . . . . 73

4.2 Initial cluster radius R0deduced from fringe spacing in scattering patterns.

Critical expansion time texp extracted from figure 4.15 a. Critical cluster

radius Rcrit calculated with equation 4.10 and an average charge state hqi=

2.0. Resulting plasma velocity vexp, calculated with v=phqikbTe/miand

Te= 19.7 eV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

122

Bibliography

[1] R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu. Potential for

biomolecular imaging with femtosecond X-ray pulses. Nature, 406:752–757, 2000.

[2] J. Schneider. FLASH - from accelerator test facility to the first single-pass soft x-ray

free-electron laser. Journal of Physics B: Atomic, Molecular and Optical Physics,

43:194001, 2010.

[3] S. Eisebitt, J. L¨uning, W.F. Schlotter, M. L¨orgen, O. Hellwig, W. Eberhardt, and

J. St¨ohr. Lensless imaging of magnetic nanostructures by X-ray. Nature, 432:885–888,

2004.

[4] H. N. Chapman, A. Barty, M. J. Bogan, S. Boutet, M. Frank, S. P. Hau-Riege,

S. Marchesini, B. W. Woods, S. Bajt, W. H. Benner, R. A. London, E. Plonjes,

M. Kuhlmann, R. Treusch, S. D¨usterer, T. Tschentscher, J. R. Schneider, E. Spiller,

Th. M¨oller, Ch. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der

Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. M. Seibert, F. R. N. C.

Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu. Femtosecond Diffractive

Imaging with a Soft-X-ray Free-Electron Laser. Nature Physics, 461:839–843, 2006.

[5] H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R.

Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, Ch. Jacobsen, and

D. Shapiro. High-resolution ab initio three-dimensional x-ray diffraction microscopy.

Journal of the Optical Society of America. A, Optics, image science, and vision,

23(5):1179–1200, 2006.

[6] S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N.

Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. Cui, M. R. Howells, D. A. Shapiro,

J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert. Massively

parallel X-ray holography. Nature Photonics, 2:560–563, 2008.

[7] M. J. Bogan, W. H. Benner, S. Boulet, U. Rohner, M. Frank, A. Barty, M. M. Seib-

ert, F. Maia, S. Marchesini, S. Bajt, B. Woods, V. Riot, S. P. Hau-Riege, M. Svenda,

E. Marklund, E. Spiller, J. Hajdu, and H. N. Chapman. Single particle X-ray diffrac-

tive imaging. Nano Letters, 8:310–316, 2008.

[8] M. J. Bogan, D. Starodub, C. Y. Hampton, and R. G. Sierra. Single-particle coherent

diffractive imaging with a soft x-ray free electron laser: towards soot aerosol mor-

phology. Journal of Physics B: Atomic, Molecular and Optical Physics, 43:194013,

2010.

123

124 Bibliography

[9] M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. J¨ons-

son, D. Odi´c, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty,

J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Mar-

tin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, J.-M. Claverie, C. Bostedt, J. D.

Bozek, S. Boutet, A. A. Miahnahri, M. Messerschmidt, J. Krzywinski, G. Williams,

K. O. Hodgson, M. J. Bogan, C. Y. Hampton, R. G. Sierra, D. Starodub, I. Anders-

son, S. Bajt, M. Barthelmess, J. C. H. Spence, P. Fromme, U. Weierstall, R. Kirian,

M. Hunter, R. B. Doak, S. Marchesini, S. P. Hau-Riege, M. Frank, R. L. Shoeman,

L. Lomb, S. W. Epp, R. Hartmann, D. Rolles, A. Rudenko, C. Schmidt, L. Fou-

car, N. Kimmel, P. Holl, B. Rudek, B. Erk, A. H¨omke, C. Reich, D. Pietschner,

G. Weidenspointner, L. Str¨uder, G. Hauser, H. Gorke, J. Ullrich, I. Schlichting,

S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K.-U. K¨uhnel, R. Andritschke,

C.-D. Schr¨oter, F. Krasniqi, M. Bott, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover,

H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, H. N. Chapman, and J. Ha-

jdu. Single mimivirus particles intercepted and imaged with an X-ray laser. Nature,

470:78–81, 2011.

[10] C. Bostedt, E. Eremina, D. Rupp, M. Adolph, H. Thomas, M. Hoener, A. R. B.

De Castro, J. Tiggesb¨aumker, K. H. Meiwes-Broer, T. Laarmann, H. Wabnitz,

E. Pl¨onjes, R. Treusch, J. R. Schneider, and T. M¨oller. Ultrafast x-ray scattering

of xenon nanoparticles: Imaging transient states of matter. Physical Review Letters,

108:093401, 2012.

[11] D. Rupp, M. Adolph, T. Gorkhover, S. Schorb, D. Wolter, R. Hartmann, N. Kimmel,

C. Reich, T. Feigl, A. R. B. De Castro, R. Treusch, L. Str¨uder, T. M¨oller, and

C. Bostedt. Identification of twinned gas phase clusters by single-shot scattering

with intense soft x-ray pulses. New Journal of Physics, 14:055016, 2012.

[12] I. Barke, H. Hartmann, D. Rupp, L. Fl¨uckiger, M. Sauppe, M. Adolph, S. Schorb,

C. Bostedt, R. Treusch, C. Peltz, S. Bartling, T. Fennel, K.-H. Meiwes-Broer, and

T. M¨oller. The 3D-architecture of individual free silver nanoparticles captured by

X-ray scattering. Nature Communications, 6(6187):1–8, 2015.

[13] C. M. G¨unther, B. Pfau, R. Mitzner, B. Siemer, S. Roling, H. Zacharias, O. Kutz,

I. Rudolph, D. Schondelmaier, R. Treusch, and S. Eisebitt. Sequential femtosecond

X-ray imaging. Nature Photonics, 5:99–102, 2011.

[14] A. Barty, S. Boutet, M. J. Bogan, S. Hau-Riege, S. Marchesini, K. Sokolowski-Tinten,

N. Stojanovic, R. Tobey, H. Ehrke, A. Cavalleri, S. D¨usterer, M. Frank, S. Bajt,

B. W. Woods, M. M. Seibert, J. Hajdu, R. Treusch, and H. N. Chapman. Ultrafast

single-shot diffraction imaging of nanoscale dynamics. Nature Photonics, 2:578–578,

2008.

[15] I. Yamada, J. Matsuo, N. Toyoda, and A. Kirkpatrick. Materials processing by gas

cluster ion beams. Materials Science and Engineering: R: Reports, 34(6):231–295,

2001.

[16] G. Scoles, D. Brassi, U. Buck, and D. Laine. Atomic and Molecular Beam Methods:

Volume 1. Oxford University Press, New York, 1988.

Bibliography 125

[17] H. C. W. Beijerinck, R. J. F. Van Gerwen, E. R. T. Kerstel, J. F. M. Martens,

E. J. W. Van Vliembergen, M. R. Th. Smits, and G. H. Kaashoek. Campargue-type

supersonic beam sources: Absolute intensities, skimmer transmission and scaling

laws for mono-atomic gases He, Ne and Ar. Chemical Physics, 96:153–173, 1985.

[18] O. F. Hagena. Cluster Formation in Expanding Supersonic Jets: Effect of Pressure,

Temperature, Nozzle Size, and Test Gas. The Journal of Chemical Physics, 56:1793,

1972.

[19] D. Pentlehner, R. Riechers, B. Dick, A. Slenczka, U. Even, N. Lavie, R. Brown, and

K. Luria. Rapidly pulsed helium droplet source. Review of Scientific Instruments,

80:1–9, 2009.

[20] U. Even. Pulsed Supersonic Beams from High Pressure Source: Simulation Results

and Experimental Measurements. Advances in Chemistry, 2014(636042):1–11, 2014.

[21] C. Bobbert, S. Sch¨utte, C. Steinbach, and U. Buck. Fragmentation and reliable size

distributions of large ammonia and water clusters. Physical Journal D, 192:183–192,

2002.

[22] O. F. Hagena. Nucleation and growth of clusters in expanding nozzle flows. Surface

Science, 106:101–116, 1981.

[23] O. F. Hagena. Cluster ion sources (invited). Review of Scientific Instruments,

63(1992):2374–2379, 1992.

[24] O. F. Hagena. Condensation in free jets: Comparison of rare gases and metals.

Zeitschrift f¨ur Physik D Atoms, Molecules and Clusters, 4:291–299, 1987.

[25] R. Karnbach, M. Joppien, J. Stapelfeldt, J. W¨ormer, and T. M¨oller. CLULU: An

experimental setup for luminescence measurements on van der Waals clusters with

synchrotron radiation. Review of Scientific Instruments, 64:2838–2849, 1993.

[26] U. Buck and R. Krohne. Cluster size determination from diffractive He atom scat-

tering. The Journal of Chemical Physics, 105:5408, 1996.

[27] E. L. Knuth. Dimer-formation rate coefficients from measurements of terminal

dimer concentrations in free-jet expansions. The Journal of Chemical Physics,

66(1977):3515–3525, 1977.

[28] F. Dorchies, F. Blasco, T. Caillaud, J. Stevefelt, C. Stenz, A. Boldarev, and

V. Gasilov. Spatial distribution of cluster size and density in supersonic jets as

targets for intense laser pulses. Physical Review A, 68:1–8, 2003.

[29] L. Shao-Hui, L. Bing-Chen, N. Guo-Quan, and X. Zhi-Zhan. Investigation of the

time characteristics of a pulsed flow of large rare gas clusters. Chinese Physics,

12:856–860, 2003.

[30] D. Rupp, M. Adolph, L. Fl¨uckiger, T. Gorkhover, J. P. M¨uller, M. M¨uller, M. Sauppe,

D. Wolter, S. Schorb, R. Treusch, C. Bostedt, and T. M¨oller. Generation and

structure of extremely large clusters in pulsed jets. Journal of Chemical Physics,

141:044306, 2014.

126 Bibliography

[31] M. Born and E. Wolf. Principles of optics electromagnetic theory of propagation

interference and diffraction of light. Pergamon Press, New York, 2nd edition, 1999.

[32] D. Attwood. Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Appli-

cations. Cambridge University Press, 2000.

[33] J. Als-Nielsen and D. McMorrow. Elements of Modern X-ray Physics. John Wiley

and Sons, New York, 2nd edition, 2011.

[34] J. D. Jackson. Classical Electrodynamics. John Wiley and Sons, New York, 3rd

edition, 1998.

[35] S. P. Hau-Riege. High-Intensity X-Rays - Interaction with Matter. Wiley-VCH Verlag

GmbH & Co. KGaA, Weinheim, Germany, 2011.

[36] A. R. B. De Castro, E. Eremina, C. Bostedt, M. Hoener, H. Thomas, and T. M¨oller.

Numerical simulation of small angle scattering (SAXS) for large atomic clusters.

Journal of Electron Spectroscopy and Related Phenomena, 166-167:21–27, 2008.

[37] Z. Ulanowski, E. Hirst, P. H. Kaye, and R. Greenaway. Retrieving the size of particles

with rough and complex surfaces from two-dimensional scattering patterns. Journal

of Quantitative Spectroscopy and Radiative Transfer, 113(18):2457–2464, 2012.

[38] G. Mie. Contributions to the optics of turbid media, particularly of colloidal metal

solutions. Annalen der Physik, 25(3):377–445, 1908.

[39] C. F. Bohren and D. R. Huffman. Absorption and scattering of light by small particles.

Number 6. Wiley Science Paperback Series, Chichester, UK, 1998.

[40] M. Quinten. Optical Properties of Nanoparticle Systems: Mie and beyond. Wiley-

VCH, 2011.

[41] U. Kreibig. Hundert Jahre Mie-Theorie. Optische Eigenschaften von Nanopartikeln.

Physik in unserer Zeit, 39(39):281–287, 2008.

[42] C. Bostedt, H. Thomas, M. Hoener, T. M¨oller, U. Saalmann, I. Georgescu, C. Gn-

odtke, and J. M. Rost. Fast electrons from multi-electron dynamics in xenon clusters

induced by inner-shell ionization. New Journal of Physics, 12, 2010.

[43] T. Gorkhover and et al. Femtosecond visualization of structural dynamics in single

nanoparticles. to be published, 2015.

[44] D. Rupp and et al. Explosion dynamics of single clusters resolved for particle size

and laser power density. to be published, 2015.

[45] D. Rupp. Ionization and plasma dynamics of single large xenon clusters in superin-

tense XUV pulses. PhD thesis, Technische Universit¨at Berlin, 2013.

[46] T. Gorkhover. Ultrafast light induced dynamics of Xe nanoparticles studied with a

combination of intense infrared and x-ray pulses. PhD thesis, Technische Universit¨at

Berlin, 2014.

[47] T. Ditmire, T. Donnelly, A. Rubenchik, R. Falcone, and M. Perry. Interaction of

intense laser pulses with atomic clusters. Physical Review A, 53(5):3379–3402, 1996.

Bibliography 127

[48] V.P. Krainov and M.B. Smirnov. Cluster beams in the super-intense femtosecond

laser pulse. Physics Reports, 370:237–331, 2002.

[49] U. Saalmann, C. Siedschlag, and J. M. Rost. Mechanisms of cluster ionization in

strong laser pulses. Journal of Physics B: Atomic, Molecular and Optical Physics,

39(4):39–77, 2006.

[50] T. Fennel, K.-H. Meiwes-Broer, J. Tiggesb¨aumker, P. G. Reinhard, P. M. Dinh, and

E. Suraud. Laser-driven nonlinear cluster dynamics. Reviews of Modern Physics,

82:1793–1842, 2010.

[51] U. Saalmann. Cluster nanoplasmas in strong FLASH pulses: formation, excita-

tion and relaxation. Journal of Physics B: Atomic, Molecular and Optical Physics,

43:194012, 2010.

[52] M. Arbeiter and T. Fennel. Rare-gas clusters in intense VUV, XUV and soft x-ray

pulses: Signatures of the transition from nanoplasma-driven cluster expansion to

Coulomb explosion in ion and electron spectra. New Journal of Physics, 13:053022,

2011.

[53] P. G. Reinhard and E. Suraud. Introduction to Cluster Dynamics. Wiley-VCH Verlag,

Weinheim, Germany, 2004.

[54] J. Posthumus. Molecules and Clusters in Intense Laser Fields. Cambridge University

Press, 2009.

[55] V. Kumarappan, M. Krishnamurthy, and D. Mathur. Explosions of water clusters in

intense laser fields. Physical Journal A, 67:063207, 2003.

[56] M. Hoener, C. Bostedt, H. Thomas, L. Landt, E. Eremina, H. Wabnitz, T. Laarmann,

R. Treusch, A. R. B. De Castro, and T. M¨oller. Charge recombination in soft x-ray

laser produced nanoplasmas. Journal of Physics B: Atomic, Molecular and Optical

Physics, 41:181001, 2008.

[57] Y. Fukuda, Y. Kishimoto, T. Masaki, and K. Yamakawa. Structure and dynamics

of cluster plasmas created by ultrashort intense laser fields. Physical Review A -

Atomic, Molecular, and Optical Physics, 73:031201, 2006.

[58] I. Last and J. Jortner. Quasiresonance ionization of large multicharged clusters in a

strong laser field. Physical Review A, 60(3):2215–2221, 1999.

[59] H. Wabnitz, L. Bittner, A. R. B. De Castro, R. D¨ohrmann, P. G¨urtler, T. Laarmann,

W. Laasch, J. Schulz, A. Swiderski, K. von Haeften, T. M¨oller, B. Faatz, A. Fateev,

J. Feldhaus, C. Gerth, U. Hahn, E. Saldin, E. Schneidmiller, K. Sytchev, K. Tiedtke,

R. Treusch, and M. Yurkov. Multiple ionization of atom clusters by intense soft

X-rays from a free-electron laser. Nature, 420:482–485, 2002.

[60] I. V. Hertel and C.-P. Schulz. Atome, Molek¨ule und optische Physik 1: Atomphysik

und Grundlagen der Spektroskopie. Springer, 2010.

[61] T. Ditmire. Strong Field Physics. In Handbook of Optics: Optical Properties of

Materials, Nonlinear Optics, Quantum Optics, chapter 21. McGraw-Hill, 2009.

128 Bibliography

[62] V. P. Krainov and B. M. Smirnov. Femtosecond excitation of cluster beams. Physics-

Uspekhi, 50:907–931, 2007.

[63] I. Georgescu. Rare-gas clusters in intense VUV laser fields. PhD thesis, Technische

Universit¨at Dresden, 2008.

[64] N. Bigaouette. Computational investigation of intense short-wavelength laser inter-

action with rare gas clusters. PhD thesis, University of Ottawa, 2014.

[65] L. Keldysh. Ionization in the field of a strong electromagnetic wave. Soviet Physics

Jetp, 20(5):1307, 1964.

[66] A. Sorokin, S. V. Bobashev, T. Feigl, K. Tiedtke, H. Wabnitz, and M. Richter.

Photoelectric effect at ultrahigh intensities. Physical Review Letters, 99:213002, 2007.

[67] A. Kramida, Y. Ralchenko, J. Reader, and NIST ASD Team. NIST Atomic Spectra

Database (version 5.1) [online], 2013.

[68] M. Richter, M. Y. Amusia, S. V. Bobashev, T. Feigl, P. N. Jurani´c, M. Martins, A. A.

Sorokin, and K. Tiedtke. Extreme ultraviolet laser excites atomic giant resonance.

Physical Review Letters, 102:163002, 2009.

[69] A. Aguilar, J. D. Gillaspy, G. F. Gribakin, R. A. Phaneuf, M. F. Gharaibeh, M. G.

Kozlov, J. D. Bozek, and A. L. D. Kilcoyne. Absolute photoionization cross sections

for Xe4+, Xe5+, and Xe6+ near 13.5 nm: Experiment and theory. Physical Review

A - Atomic, Molecular, and Optical Physics, 73(3):032717, 2006.

[70] J.-M. Bizau, J.-M. Esteva, D. Cubaynes, F. Wuilleumier, C. Blancard, A. La

Fontaine, C. Couillaud, J. Lachkar, R. Marmoret, C. R´emond, J. Bruneau, D. Hitz,

P. Ludwig, and M. Delaunay. Photoionization of Highly Charged Ions Using an ECR

Ion Source and Undulator Radiation. Physical Review Letters, 84(3):435–438, 2000.

[71] S. Larochelle, A. Talebpour, and S. L. Chin. Non-sequential multiple ionization of

rare gas atoms in a Ti:Sapphire laser field. Journal of Physics B: Atomic, Molecular

and Optical Physics, 31(6):1201–1214, 1999.

[72] K. Yamakawa, Y. Akahane, Y. Fukuda, M. Aoyama, N. Inoue, H. Ueda, and T. Ut-

sumi. Many-electron dynamics of a Xe atom in strong and superstrong laser fields.

Physical Review Letters, 92:123001, 2004.

[73] A. McPherson, A. B. Borisov, K. Boyer, and C. K. Rhodes. Competition between

multiphoton xenon cluster excitation and plasma wave Raman scattering at 248 nm.

Journal of Physics B: Atomic, Molecular and Optical Physics, 29(7):291–297, 1999.

[74] T. Ditmire, E. Springate, J. Tisch, Y. Shao, M. Mason, N. Hay, J. Marangos, and

M. Hutchinson. Explosion of atomic clusters heated by high-intensity femtosecond

laser pulses. Physical Review A, 57(1):369–382, 1998.

[75] T. Ditmire, J. Zweiback, V. P. Yanovsky, T. E. Cowan, and G. Hays. Nuclear fusion

from explosions of femtosecond laser-heated deuterium clusters. Nature, 398:489–492,

1999.

[76] E. Springate, S. Aseyev, S. Zamith, and M. Vrakking. Electron kinetic energy mea-

surements from laser irradiation of clusters. Physical Review A, 68(5):053201, 2003.

Bibliography 129

[77] L. Ramunno, C. Jungreuthmayer, and T. Brabec. Intense laser-cluster interaction in

the strong coupling regime. Laser Physics, 17(5):618–624, 2007.

[78] B. Ziaja, Z. Jurek, N. Medvedev, S.-K. Son, R. Thiele, and S. Toleikis. Photoelectron

spectroscopy method to reveal ionization potential lowering in nanoplasmas. Journal

of Physics B: Atomic, Molecular and Optical Physics, 46:164009, 2013.

[79] C. Varin, C. Peltz, T. Brabec, and T. Fennel. Light wave driven electron dynamics

in clusters. Annalen der Physik, 526(3):135–156, 2014.

[80] J. Zweiback, T. Ditmire, and M. Perry. Femtosecond time-resolved studies of the

dynamics of noble-gas cluster explosions. Physical Review A, 59(5):3166–3169, 1999.

[81] http://nanocomposix.eu/pages/plasmonics.

[82] H. M. Milchberg, S. J. McNaught, and E. Parra. Plasma hydrodynamics of the

intense laser-cluster interaction. Physical review E, Statistical, nonlinear, and soft

matter physics, 64:056402, 2001.

[83] W. Lotz. An empirical formula for the electron-impact ionization cross-section.

Zeitschrift f¨ur Physik, 206:205–211, 1967.

[84] P. Hilse, M. Moll, M. Schlanges, and T. Bornath. Laser-Cluster-Interaction in a

Nanoplasma-Model with Inclusion of Lowered Ionization Energies. Laser Physics,

19(3):428–436, 2008.

[85] V. P. Krainov. Inverse stimulated bremsstrahlung of slow electrons under

Coulomb scattering. Journal of Physics B: Atomic, Molecular and Optical Physics,

33(8):31585–1595, 2000.

[86] I. Georgescu, U. Saalmann, and J. M. Rost. Attosecond resolved charging of ions in

a rare-gas cluster. Physical Review Letters, 99:183002, 2007.

[87] C. Bostedt, H. Thomas, M. Hoener, E. Eremina, T. Fennel, K. H. Meiwes-Broer,

H. Wabnitz, M. Kuhlmann, E. Pl¨onjes, K. Tiedtke, R. Treusch, J. Feldhaus, a. R B De

Castro, and T. M¨oller. Multistep ionization of argon clusters in intense femtosecond

extreme ultraviolet pulses. Physical Review Letters, 100:133401, 2008.

[88] L. Fl¨uckiger, D. Rupp, M. Adolph, T. Gorkhover, M. Krikunova, M. M¨uller, T. Oelze,

Y. Ovcharenko, M. Sauppe, S. Schorb, C. Bostedt, S. D¨usterer, M. Harmand,

H. Redlin, R. Treusch, and T. M¨oller. Infrared laser-induced cluster evolution imaged

by x-ray scattering. in preparation, 2015.

[89] N. K. Kandadai. Interaction of Clusters with Ultra Short X-Ray Free Electron Laser

Pulses. PhD thesis, The University of Texas at Austin, 2012.

[90] M. Lezius, S. Dobosz, D. Normand, and M. Schmidt. Explosion Dynamics of Rare

Gas Clusters in Strong Laser Fields. Physical Review Letters, 80:261–264, 1998.

[91] M. Lebeault, J. Viallon, J. Chevaleyre, C. Ellert, D. Normand, M. Schmidt, O. Sub-

lemontier, C. Guet, and B. Huber. Resonant coupling of small size-controlled lead

clusters with an intense laser field. European Physical Journal D, 20:233–242, 2002.

130 Bibliography

[92] K. Ishikawa and T. Blenski. Explosion dynamics of rare-gas clusters in an intense

laser field. Physical Review A - Atomic, Molecular, and Optical Physics, 62:063201,

2000.

[93] H. Thomas, C. Bostedt, M. Hoener, E. Eremina, H. Wabnitz, T. Laarmann,

E. Pl¨onjes, R. Treusch, A. R. B. De Castro, and T. M¨oller. Shell explosion and core

expansion of xenon clusters irradiated with intense femtosecond soft x-ray pulses.

Journal of Physics B: Atomic, Molecular and Optical Physics, 42:134018, 2009.

[94] B. Ziaja, F. Wang, H. Wabnitz, E. Weckert, and T. M¨oller. Ionization and expan-

sion dynamics of atomic clusters irradiated with short intense VUV pulses. In AIP

Conference Proceedings, volume 1161, pages 105–112, 2009.

[95] T. Fennel, T. D¨oppner, J. Passig, Ch Schaal, J. Tiggesb¨aumker, and K. H. Meiwes-

Broer. Plasmon-enhanced electron acceleration in intense laser metal-cluster inter-

actions. Physical Review Letters, 98:143401, 2007.

[96] C. Jungreuthmayer, L. Ramunno, J. Zanghellini, and T. Brabec. Intense VUV laser

cluster interaction in the strong coupling regime. Journal of Physics B: Atomic,

Molecular and Optical Physics, 38:3029–3036, 2005.

[97] E. Ackad, N. Bigaouette, S. Mack, K. Popov, and L. Ramunno. Recombination

effects in soft-x-ray cluster interactions at the xenon giant resonance. New Journal

of Physics, 15:053047, 2013.

[98] M. Arbeiter, C. Peltz, and T. Fennel. Electron-relocalization dynamics in xenon

clusters in intense soft-x-ray fields. Physical Review A, 89:043428, 2014.

[99] M. Krikunova, M. Adolph, T. Gorkhover, D. Rupp, S. Schorb, C. Bostedt, S. Roling,

B. Siemer, R. Mitzner, H. Zacharias, and T. M¨oller. Ionization dynamics in expanding

clusters studied by XUV pumpprobe spectroscopy. Journal of Physics B: Atomic,

Molecular and Optical Physics, 45(10):105101, 2012.

[100] L. Schroedter, M. M¨uller, A. Kickermann, A. Przystawik, S. Toleikis, M. Adolph,

L. Fl¨uckiger, T. Gorkhover, L. N¨osel, M. Krikunova, T. Oelze, Y. Ovcharenko,

D. Rupp, M. Sauppe, D. Wolter, S. Schorb, C. Bostedt, T. M¨oller, and T. Laar-

mann. Hidden charge states in soft-x-ray laser-produced nanoplasmas revealed by

fluorescence spectroscopy. Physical Review Letters, 112:183401, 2014.

[101] T. Gorkhover, M. Adolph, D. Rupp, S. Schorb, S. W. Epp, B. Erk, L. Foucar, R. Hart-

mann, N. Kimmel, K. U. K¨uhnel, D. Rolles, B. Rudek, A. Rudenko, R. Andritschke,

A. Aquila, J. D. Bozek, N. Coppola, T. Erke, F. Filsinger, H. Gorke, H. Graafsma,

L. Gumprecht, G. Hauser, S. Herrmann, H. Hirsemann, A. H¨omke, P. Holl, C. Kaiser,

F. Krasniqi, J. H. Meyer, M. Matysek, M. Messerschmidt, D. Miessner, B. Nilsson,

D. Pietschner, G. Potdevin, C. Reich, G. Schaller, C. Schmidt, F. Schopper, C. D.

Schr¨oter, J. Schulz, H. Soltau, G. Weidenspointner, I. Schlichting, L. Str¨uder, J. Ull-

rich, T. M¨oller, and C. Bostedt. Nanoplasma dynamics of single large xenon clusters

irradiated with superintense X-ray pulses from the linac coherent light source free-

electron laser. Physical Review Letters, 108:245005, 2012.

[102] C. Varin, C. Peltz, T. Brabec, and T. Fennel. Attosecond plasma wave dynamics in

laser-driven cluster nanoplasmas. Physical Review Letters, 108:175007, 2012.

Bibliography 131

[103] S. Sakabe, K. Shirai, M. Hashida, S. Shimizu, and S. Masuno. Skinning of argon clus-

ters by Coulomb explosion induced with an intense femtosecond laser pulse. Physical

Review A - Atomic, Molecular, and Optical Physics, 74:043205, 2006.

[104] T. Taguchi, T. M. Antonsen, J. Palastro, H. Milchberg, and K. Mima. Particle in

cell analysis of a laser-cluster interaction including collision and ionization processes.

Optics express, 18(3):2389–2405, 2010.

[105] M. Arbeiter and T. Fennel. Ionization heating in rare-gas clusters under intense XUV

laser pulses. Physical Review A - Atomic, Molecular, and Optical Physics, 82:013201,

2010.

[106] M M¨uller, L Schroedter, T Oelze, A Przystawik, A Kickermann, M Adolph,

T Gorkhover, L Fl¨uckiger, M Krikunova, M Sauppe, Y Ovcharenko, S Schorb,

D Rupp, T Laarmann, and T M¨oller. Ionization dynamics of XUV excited clus-

ters: the role of inelastic electron collisions. submitted to Journal of Physics B:

Atomic, Molecular and Optical Physics, pages 1–14, 2015.

[107] R. L. Sandberg, A. Paul, D. A. Raymondson, S. H¨adrich, D. M. Gaudiosi, J. Holt-

snider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao,

Y. Liu, and F. Salmassi. Lensless diffractive imaging using tabletop coherent high-

harmonic soft-X-ray beams. Physical Review Letters, 99(9):098103, 2007.

[108] R. Moshammer, Th. Pfeifer, A. Rudenko, Y. H. Jiang, L. Foucar, M. Kurka, K. U.

K¨uhnel, C. D. Schr¨oter, J. Ullrich, O. Herrwerth, M. F. Kling, X.-J. Liu, K. Moto-

mura, H. Fukuzawa, A. Yamada, K. Ueda, K. L. Ishikawa, K. Nagaya, H. Iwayama,

A. Sugishima, Y. Mizoguchi, S. Yase, M. Yao, N. Saito, A. Belkacem, M. Naga-

sono, A. Higashiya, M. Yabashi, T. Ishikawa, H. Ohashi, H. Kimura, and T. Togashi.

Second-order autocorrelation of XUV FEL pulses via time resolved two-photon single

ionization of He. Optics Express, 19(22):21698, 2011.

[109] http://flash.desy.de/.

[110] W. Ackermann and et al. Operation of a free-electron laser from the extreme ultra-

violet to the water window. Nature Photonics, 1:336–342, 2007.

[111] K. Tiedtke, A. Azima, N. Von Bargen, L. Bittner, S. Bonfigt, S. D¨usterer,

B. Faatz, U. Fr¨uhling, M. Gensch, Ch Gerth, N. Guerassimova, U. Hahn, T. Hans,

M. Hesse, K. Honkavaar, U. Jastrow, P. Juranic, S. Kapitzki, B. Keitel, T. Kracht,

M. Kuhlmann, W. B. Li, M. Martins, T. N´u˜nez, E. Pl¨onjes, H. Redlin, E. L.

Saldin, E. a. Schneidmiller, J. R. Schneider, S. Schreiber, N. Stojanovic, F. Tavella,

S. Toleikis, R. Treusch, H. Weigelt, M. Wellh¨ofer, H. Wabnitz, M. V. Yurkov, and

J. Feldhaus. The soft x-ray free-electron laser FLASH at DESY: Beamlines, diagnos-

tics and end-stations. New Journal of Physics, 11:023029, 2009.

[112] R. Treusch and J. Feldhaus. FLASH: New opportunities for (time-resolved) coherent

imaging of nanostructures. New Journal of Physics, 12:035015, 2010.

[113] P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann,

P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher,

J. Frisch, S. Gilevich, J. Hastings, G. Hays, Ph. Hering, Z. Huang, R. Iverson,

132 Bibliography

H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Rat-

ner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch,

W. White, J. Wu, G. Yocky, and J. Galayda. First lasing and operation of an

˚angstrom-wavelength free-electron laser. Nature Photonics, 4(9):641–647, 2010.

[114] D. Pile. X-rays: First light from SACLA. Nature Photonics, 5(8):456–457, 2011.

[115] E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio,

and F. Parmigiani. The FERMI@Elettra free-electron-laser source for coherent x-ray

physics: Photon properties, beam transport system and applications. New Journal

of Physics, 12:075002, 2010.

[116] M. Altarelli. The European X-ray free-electron laser facility in Hamburg. In Nuclear

Instruments and Methods in Physics Research, Section B: Beam Interactions with

Materials and Atoms, volume 269, pages 2845–2849, 2011.

[117] B. D. Patterson, R. Abela, H. H. Braun, U. Flechsig, R. Ganter, Y. Kim, E. Kirk,

A. Oppelt, M. Pedrozzi, S. Reiche, L. Rivkin, T. Schmidt, B. Schmitt, V. N. Strocov,

S. Tsujino, and A. F. Wrulich. Coherent science at the SwissFEL x-ray laser. New

Journal of Physics, 12:035012, 2010.

[118] E. S. Kim and M. Yoon. Beam dynamics in a 10-GeV linear accelerator for the X-ray

free electron laser at PAL. IEEE Transactions on Nuclear Science, 56(6):3597–3606,

2009.

[119] C. Schm¨user, P. Dohlus, M. Rossbach, and J. Behrens. Free-Electron Lasers in the

Ultraviolet and X-Ray Regime. Springer, Berlin, Germany, 2nd edition.

[120] E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov. Coherence properties of the

radiation from X-ray free electron laser. Optics Communications, 281:1179–1188,

2008.

[121] J. Feldhaus, J. Arthur, and J. B. Hastings. X-ray free-electron lasers. Journal of

Physics B: Atomic, Molecular and Optical Physics, 38:799–819, 2005.

[122] Z. Huang and K. J. Kim. Review of x-ray free-electron laser theory. Physical Review

Special Topics - Accelerators and Beams, 10:034801, 2007.

[123] B. W. J. McNeil and N. R. Thompson. X-ray free-electron lasers. Nature Photonics,

4(12):814–821, 2010.

[124] Deutsches Elektronen-Synchrotron. FLASH - The Free-Electron Laser in Hamburg.

2007.

[125] I. A. Vartanyants, A. P. Mancuso, A. Singer, O. M. Yefanov, and J. Gulden. Coher-

ence measurements and coherent diffractive imaging at FLASH. Journal of Physics

B: Atomic, Molecular and Optical Physics, 43:194016, 2010.

[126] R. Mitzner, B. Siemer, M. Neeb, T. Noll, F. Siewert, S. Roling, M. Rutkowski,

A. A. Sorokin, M. Richter, P. Juranic, K. Tiedtke, J. Feldhaus, W. Eberhardt, and

H. Zacharias. Spatio-temporal coherence of free electron laser pulses in the soft x-ray

regime. Optics express, 16(24):19909–19919, 2008.

Bibliography 133

[127] http://flash.desy.de/.

[128] H. Redlin, A. Al-Shemmary, A. Azima, N. Stojanovic, F. Tavella, I. Will, and

S. Dsterer. The FLASH pumpprobe laser system: Setup, characterization and op-

tical beamlines. Nuclear Instruments and Methods in Physics Research, Section A:

Accelerators, Spectrometers, Detectors and Associated Equipment, 635:88–93, 2011.

[129] Private Communication with Stefan D¨usterer.

[130] P. Radcliffe, S. D¨usterer, A. Azima, H. Redlin, J. Feldhaus, J. Dardis, K. Ka-

vanagh, H. Luna, J. Pedregosa Gutierrez, P. Yeates, E. T. Kennedy, J. T. Costello,

A. Delserieys, C. L S Lewis, R. Ta¨ıeb, A. Maquet, D. Cubaynes, and M. Meyer.

Single-shot characterization of independent femtosecond extreme ultraviolet free elec-

tron and infrared laser pulses. Applied Physics Letters, 90:131108, 2007.

[131] A. Azima, S. D¨usterer, P. Radcliffe, H. Redlin, N. Stojanovic, W. Li, H. Schlarb,

J. Feldhaus, D. Cubaynes, M. Meyer, J. Dardis, P. Hayden, P. Hough, V. V. Richard-

son, E. T. Kennedy, and J. T. Costello. Time-resolved pump-probe experiments be-

yond the jitter limitations at FLASH. Applied Physics Letters, 94:2009–2011, 2009.

[132] Mario Sauppe. Untersuchung der Ionisationsdynamik von Xenonclustern mit

zeitaufgel¨oster Massenspektroskopie und mit Streumethoden. Master thesis, Tech-

nische Universit¨at Berlin, 2013.

[133] J. M. Glownia, J. Cryan, J. Andreasson, A. Belkacem, N. Berrah, C. I. Blaga, C. Bost-

edt, J. Bozek, L. F. DiMauro, L. Fang, J. Frisch, O. Gessner, M. G¨uhr, J. Hajdu,

M. P. Hertlein, M. Hoener, G. Huang, O. Kornilov, J. P. Marangos, A. M. March,

B. K. McFarland, H. Merdji, V. S. Petrovic, C. Raman, D. Ray, D. A. Reis, M. Trigo,

J. L. White, W. White, R. Wilcox, L. Young, R. N. Coffee, and P. H. Bucksbaum.

Time-resolved pump-probe experiments at the LCLS. Optics express, 18(17):17620–

17630, 2010.

[134] M. Krikunova, T. Maltezopoulos, A. Azima, M. Schlie, U. Fr¨uhling, H. Redlin,

R. Kalms, S. Cunovic, N. M. Kabachnik, M. Wieland, and M. Drescher. Time-

resolved ion spectrometry on xenon with the jitter-compensated soft x-ray pulses of

a free-electron laser. New Journal of Physics, 11:123019, 2009.

[135] J. Jha. A Study of Dynmics in Laser-cluster Interaction. PhD thesis, Tata Institute

of Fundamental Research, Mumbai, 2007.

[136] Parker General Valve Operation. Solenoid Pulsed Valve Manual.

[137] G. Chen, B. Kim, B. Ahn, and D. Kim. Pressure dependence of argon cluster size

for different nozzle geometries. Journal of Applied Physics, 106:053507, 2009.

[138] Private Communication with Sven Toleikis.

[139] M. Adolph. Cluster-light interaction and imaging of cluster growth processes. PhD

thesis, Technische Universit¨at Berlin, 2014.

[140] L. Str¨uder, S. Epp, D. Rolles, R. Hartmann, P. Holl, G. Lutz, H. Soltau, R. Eckart,

C. Reich, K. Heinzinger, C. Thamm, A. Rudenko, F. Krasniqi, K. U. K¨uhnel,

C. Bauer, C. D. Schr¨oter, R. Moshammer, S. Techert, D. Miessner, M. Porro,

134 Bibliography

O. H¨alker, N. Meidinger, N. Kimmel, R. Andritschke, F. Schopper, G. Weidenspoint-

ner, A. Ziegler, D. Pietschner, S. Herrmann, U. Pietsch, A. Walenta, W. Leitenberger,

C. Bostedt, T. M¨oller, D. Rupp, M. Adolph, H. Graafsma, H. Hirsemann, K. G¨artner,

R. Richter, L. Foucar, R. L. Shoeman, I. Schlichting, and J. Ullrich. Large-format,

high-speed, X-ray pnCCDs combined with electron and ion imaging spectrometers in

a multipurpose chamber for experiments at 4th generation light sources. Nuclear In-

struments and Methods in Physics Research, Section A: Accelerators, Spectrometers,

Detectors and Associated Equipment, 614(3):483–496, 2010.

[141] E. W. Schlag. Time-of-Flight Mass Spectrometry and its Applications. Elsevier

Science, 1st edition, 1994.

[142] W. C. Wiley and I. H. McLaren. Time-of-flight mass spectrometer with improved

resolution. Review of Scientific Instruments, 26(12):1150–1157, 1955.

[143] J. Andreasson, A. V. Martin, M. Liang, N. Timneanu, A. Aquila, F. Wang, B. Iwan,

M. Svenda, T. Ekeberg, M. Hantke, J. Bielecki, D. Rolles, A. Rudenko, L. Foucar,

R. Hartmann, B. Erk, B. Rudek, H. N. Chapman, J. Hajdu, and A. Barty. Automated

identification and classification of single particle serial femtosecond X-ray diffraction

data. Optics Express, 22(3):2497, 2014.

[144] S. Das, P. M. Badani, P. Sharma, and R. K. Vatsa. Size and wavelength dependent

photoionisation of xenon clusters. Chemical Physics Letters, 552:13–19, 2012.

[145] M. R. Islam, U. Saalmann, and J. M. Rost. Kinetic energy of ions after Coulomb

explosion of clusters induced by an intense laser pulse. Physical Review A - Atomic,

Molecular, and Optical Physics, 73:38–41, 2006.

[146] C. Bostedt, M. Adolph, E. Eremina, M. Hoener, D. Rupp, S. Schorb, H. Thomas,

A. R. B. De Castro, and T. M¨oller. Clusters in intense FLASH pulses: ultrafast

ionization dynamics and electron emission studied with spectroscopic and scattering

techniques. Journal of Physics B: Atomic, Molecular and Optical Physics, 43:194011,

2010.

[147] D. D. Hickstein, F. Dollar, J. A. Gaffney, M. E. Foord, G. M. Petrov, B. B. Palm,

K. E. Keister, J. L. Ellis, C. Ding, S. B. Libby, J. L. Jimenez, H. C. Kapteyn, M. M.

Murnane, and W. Xiong. Observation and control of shock waves in individual

nanoplasmas. Physical Review Letters, 112:115004, 2014.

[148] MATLAB, 2010.

[149] R. A. Kirian. Structure determination through correlated fluctuations in x-ray scat-

tering. Journal of Physics B: Atomic, Molecular and Optical Physics, 45:223001,

2012.

[150] K. Hoffmann, B. Murphy, B. Erk, A. Helal, N. Kandadai, J. Keto, and T. Ditmire.

High intensity femtosecond XUV pulse interactions with atomic clusters. High Energy

Density Physics, 6(2):185–189, 2010.

[151] H. Iwayama, A. Sugishima, K. Nagaya, M. Yao, H. Fukuzawa, K. Motomura, X.-J.

Liu, A. Yamada, C. Wang, K. Ueda, N. Saito, M. Nagasono, K. Tono, M. Yabashi,

Bibliography 135

T. Ishikawa, H. Ohashi, H. Kimura, and T. Togashi. Inhomogeneous charge redis-

tribution in Xe clusters exposed to an intense extreme ultraviolet free electron laser.

Journal of Physics B: Atomic, Molecular and Optical Physics, 43(16):161001, 2010.

[152] H. Thomas. Wechselwirkung von Edelgas-Clustern mit intensiven Pulsen weicher

R¨ontgenstrahlung vom Freie-Elektronen-Laser FLASH. PhD thesis, Technische Uni-

versit¨at Berlin, 2009.

[153] H. Hartmann, V. N. Popok, I. Barke, V. Von Oeynhausen, and K. H. Meiwes-Broer.

Design and capabilities of an experimental setup based on magnetron sputtering

for formation and deposition of size-selected metal clusters on ultra-clean surfaces.

Review of Scientific Instruments, 83:073304, 2012.

[154] http://ulisse.elettra.trieste.it/services/elements/WebElements.html.

[155] S. Zamith, T. Martchenko, Y. Ni, S. Aseyev, H. Muller, and M. Vrakking. Control

of the production of highly charged ions in femtosecond-laser cluster fragmentation.

Physical Review A, 70:011201, 2004.

[156] T. D¨oppner, T. Fennel, T. Diederich, J. Tiggesb¨aumker, and K.-H. Meiwes-Broer.

Controlling the coulomb explosion of silver clusters by femtosecond dual-pulse laser

excitation. Physical Review Letters, 94:013401, 2005.

[157] B. N. Breizman, A. V. Arefiev, and M. V. Fomytskyi. Nonlinear physics of laser-

irradiated microclusters. 12:056706, 2005.

[158] C. Siedschlag and J. M. Rost. Surface-plasma resonance in small rare-gas clusters by

mixing ir and vuv laser pulses. Physical Review A - Atomic, Molecular, and Optical

Physics, 71:031401, 2005.

[159] M. Kundu and D. Bauer. Optimizing the ionization and energy absorption of laser-

irradiated clusters. Physics of Plasmas, 15:033303, 2008.

[160] T. Fennel, L. Ramunno, and T. Brabec. Highly charged ions from laser-cluster

interactions: Local-field-enhanced impact ionization and frustrated electron-ion re-

combination. Physical Review Letters, 99:233401, 2007.

[161] A. Barty. Time-resolved imaging using x-ray free electron lasers. Journal of Physics

B: Atomic, Molecular and Optical Physics, 43:194014, 2010.

[162] N. D. Loh, C. Y. Hampton, A. V. Martin, D. Starodub, R. G. Sierra, A. Barty,

A. Aquila, J. Schulz, L. Lomb, J. Steinbrener, R. L. Shoeman, S. Kassemeyer,

C. Bostedt, J. Bozek, S. W. Epp, B. Erk, R. Hartmann, D. Rolles, A. Rudenko,

B. Rudek, L. Foucar, N. Kimmel, G. Weidenspointner, G. Hauser, P. Holl, E. Peder-

soli, M. Liang, M. S. Hunter, L. Gumprecht, N. Coppola, C. Wunderer, H. Graafsma,

F. R. N. C. Maia, T. Ekeberg, M. Hantke, H. Fleckenstein, H. Hirsemann, K. Nass,

T. A. White, H. J. Tobias, G. R. Farquar, W. H. Benner, S. P. Hau-Riege, C. Reich,

A. Hartmann, H. Soltau, S. Marchesini, S. Bajt, M. Barthelmess, P. Bucksbaum,

K. O. Hodgson, L. Str¨uder, J. Ullrich, M. Frank, I. Schlichting, H. N. Chapman,

and M. J. Bogan. Erratum: Fractal morphology, imaging and mass spectrometry of

single aerosol particles in flight. 489(7416):460–460, 2012.

136 Bibliography

[163] C. Peltz, C. Varin, T. Brabec, and T. Fennel. Time-Resolved X-Ray Imaging of

Anisotropic Nanoplasma Expansion. Physical Review Letters, 133401:133401, 2014.

[164] Y. V. Medvedev. Expansion of a finite plasma into a vacuum. Plasma Physics and

Controlled Fusion, 47(7):1031–1046, 2005.

[165] P. Mora. Collisionless expansion of a Gaussian plasma into a vacuum. Physics of

Plasmas, 12(May 2014):1–8, 2005.

[166] F. Van der Veen and F. Pfeiffer. Coherent x-ray scattering. Journal of Physics:

Condensed Matter, 16:5003–5030, 2004.

[167] J. W. Goodman. Speckle phenomena in optics: theory and applications. Roberts &

Company, 2007.

[168] G. Zhang, Z. Wu, and Y. Li. Speckle size of light scattered from 3D rough objects.

Optics Express, 20(4):4726, 2012.

[169] J. C. Auger, G. E. Fernandes, K. B. Aptowicz, Y. L. Pan, and R. K. Chang. Influence

of surface roughness on the elastic-light scattering patterns of micron-sized aerosol

particles. Applied Physics B: Lasers and Optics, 99:229–234, 2010.

[170] Y. Piederri`ere, J. Le Meur, J. Cariou, J. Abgrall, and M. Blouch. Particle aggregation

monitoring by speckle size measurement; application to blood platelets aggregation.

Optics express, 12(19):4596–4601, 2004.

[171] M. W¨ostmann, R. Mitzner, T. Noll, S. Roling, B. Siemer, F. Siewert, S. Eppen-

hoff, F. Wahlert, and H. Zacharias. The XUV split-and-delay unit at beamline

BL2 at FLASH. Journal of Physics B: Atomic, Molecular and Optical Physics,

46(16):164005, 2013.

[172] D. Rupp. X-ray movie of FEL-induced dynamics in individual nanoparticles. FLASH

Beamtime Proposal, 2014.

[173] K. E. Schmidt, J. C H Spence, U. Weierstall, R. Kirian, X. Wang, D. Starodub,

H. N. Chapman, M. R. Howells, and R. B. Doak. Tomographic femtosecond X-ray

diffractive imaging. Physical Review Letters, 101(11):1–4, 2008.

Acknowledgements

Diese Arbeit w¨are nicht ohne die Hilfe und den Beistand vieler lieber Menschen entstanden.

Daher m¨ochte ich mich bedanken bei:

Thomas M¨oller - f¨ur die M¨oglichkeit unter Dir als Doktorvater zu Promovieren. F¨ur den

großz¨ugigen Freiraum und die Unterst¨utzung meiner Ideen aber auch die konstruktive und

richtungsweisende Kritik. F¨ur das sympathische Team das Du um Dich gesammelt hast

und die angenehme Arbeitsatmosph¨are die Du verbreitest.

Tim Laarmann - f¨ur die Rolle des Zweitgutachters dieser Arbeit. F¨ur eine wunderbare

Fluoreszenzmesszeit und die tollen daraus resultierenden Paper.

Dani - f¨ur Deine unersch¨opfliche Energie und Deinen ¨uberbordenden Enthusiasmus. Du

hast es immer wieder geschafft mich auch in frustrierenden Situationen anzuspornen und

zu motivieren. Danke f¨ur all die n¨otigen Kopfw¨aschen mit viel Feingef¨uhl und die wun-

derbare, unbezahlbare Betreuung. Es hat jeder Zeit viel Spass gemacht mit und von Dir

zu lernen, Experimente durchzuf¨uhren, Auswertungsprogramme zu coden und zuk¨unftige

Forschungsvorhaben zu erspinnen. — Maria M. - f¨ur die herzliche Aufnahme und Einf¨uhrung

in die AG M¨oller. F¨ur etliche lustige Stunden bei Balzac, in der Denkzelle und auf Messzeit.

F¨ur Dein Interesse, Deinen Beistand und Deine liebensw¨urdige Menschlichkeit. F¨ur die

richtigen Fragen zur richtigen Zeit und Dein viel zu untersch¨atztes Fachwissen, dass Du

auf Knopfdruck mit mir geteilt hast und nat¨urlich f¨ur die zahlreichen Stunden die Du mit

der Korrektur dieser Arbeit verbracht hast.

Mario - f¨ur die gute Zusammenarbeit bei der Auswertung der XUV/IR Daten und die

zahllosen Abbildungen die du mir zur Verf¨ugung gestellt hast. Dein wunderbarer Humor

hat selbst nach endlosen Nachtschichten bei mir zu Lachkr¨ampfen gef¨uhrt. — Yevheniy

- for sharing the office with me throughout my entire thesis. I really appreciate the ple-

sant atmosphere and all the interesting discussions with you and the tons of chocolate

that helped me survive the final months of my thesis. — Robert - F¨ur jede Menge gute

Ideen zu allen m¨oglichen Komponenten wann immer ich an experimentellen Aufbauten

gebastelt habe und f¨ur all die Teile die ich mir jederzeit aus deinem Labor leihen durfte.

— Tais - f¨ur das L¨ochern mit Advocat‘s Devil Fragen, die einen selbst auf den fiesesten

Referee perfekt vorbereiten. — Alex - f¨ur das Testen und die richtigen Fragen zu meinem

Rekonstruktionsprogramm w¨ahrend Deiner Bachelorarbeit. — Marcus - f¨ur das geniale

Datenausleseprogramm FoxIT. — Andre - f¨ur die Herzlichkeit die Du in der Gruppe ver-

breitest.

dem Rest der (Ex-)AG-M¨oller f¨ur die tolle Zusammenarbeit: Andrea, Bruno, Christoph,

Dave, Jan, Lena, Maria K., Ramona, Schorbi, Tim, Tobi, Toli und Yussuf. — dem Team

der IOAP-Werkstatt - allen voran J¨orn und Fabian - f¨ur all die sch¨onen Teile die durch Euch

aus meinen Zeichnungen zur Wirklichkeit wurden. — dem FLASH-Team und allen Kollab-

orationspartnern f¨ur die gute und erfolgreiche Zusammenarbeit: Harald, Stefan, Marion,

Rolf, Sven, Holger, Lasse, Andreas K., Andreas P., Karl-Heiz Meiwes-Broer, Thomas Fen-

nel, Hannes, Ingo, Christian, Mathias

meiner Familie und meinen Freunden - Mama, Papa, Annette, Cori, Kathi, Marcel - die

mich durch alle H¨ohen und Tiefen begleiten und jederzeit f¨ur mich da sind. — Veri - for

proofreading in finest Oxford english — Jochen - f¨ur den endlosen mentalen R¨uckhalt und

den nie abreißenden Klapperdraht