New J. Phys. 18 (2016)043017 doi:10.1088/1367-2630/18/4/043017
PAPER
Time-resolved x-ray imaging of a laser-induced nanoplasma and its
neutral residuals
L Flückiger
1,2
, D Rupp
1
, M Adolph
1
, T Gorkhover
1,3
, M Krikunova
1
, M Müller
1
, T Oelze
1
, Y Ovcharenko
1,4
,
M Sauppe
1
, S Schorb
1,3
, C Bostedt
3,5
, S Düsterer
6
, M Harmand
6,7
, H Redlin
6
, R Treusch
6
and T Möller
1
1
Institut für Optik und Atomare Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
2
ARC Centre of Advanced Molecular Imaging, Department of Chemistry and Physics, La Trobe University, Melbourne, 3086, Australia
3
SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
4
European XFEL GmbH, Notkestraße 85, D-22607 Hamburg, Germany
5
Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA
6
Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, D-22607 Hamburg, Germany
7
Institute of Mineralogy, Materials Physics and Cosmochemistry, 4 Place Jussieu, F-75252 Paris, France
E-mail: l.fl[email protected]
Keywords: clusters, free-electron laser, pump–probe experiment, time-resolved imaging, nanoplasma
Supplementary material for this article is available online
Abstract
The evolution of individual, large gas-phase xenon clusters, turned into a nanoplasma by a high power
infrared laser pulse, is tracked from femtoseconds up to nanoseconds after laser excitation via
coherent diffractive imaging, using ultra-short soft x-ray free electron laser pulses. A decline of
scattering signal at high detection angles with increasing time delay indicates a softening of the cluster
surface. Here we demonstrate, for the first time a representative speckle pattern of a new stage of
cluster expansion for xenon clusters after a nanosecond irradiation. The analysis of the measured
average speckle size and the envelope of the intensity distribution reveals a mean cluster size and length
scale of internal density fluctuations. The measured diffraction patterns were reproduced by scattering
simulations which assumed that the cluster expands with pronounced internal density fluctuations
hundreds of picoseconds after excitation.
1. Introduction
Gas phase clusters are ideal systems to investigate the interaction between intensive light pulses and matter and
in particular to follow the underlying processes of the formation and control of highly excited plasma states
[1,2]. It is of fundamental interest tounderstand those many-particle dynamics [3–10]but it has also interesting
applications ranging from surgery [11]and controlled material processing [12]over strategies for supressing
radiation damage in single-shot diffractive x-ray imaging of biomolecules [13–15]to the generation of neutron
pulses by the ignition of nuclear fusion in deuterium clusters [16]. Hence for example in time-resolved
measurements and calculations on clusters in intense IR pulses the significance of collective heating processes
was found [17–19], which are the underlying principle for the highly efficient energy absorption of clusters in
this wavelength regime [20].
With the advent of short-wavelength FELs, a new regime of intense light–matter interaction opened up, with
novel opportunities for achieving high spatial and temporal resolution. The new imaging method of
femtosecond coherent diffraction imaging emerged [21,22]. For the first time it has become possible to image
isolated, non-crystalline, finite targets in flight [23–25], allowing to investigate nanoparticle geometries [26,27]
and in particular ultrafast structural changes with high spatial and temporal resolution [25,28]. Coherent
diffractive imaging on single clusters has opened new avenues, especially for intense laser matter studies, because
the elastic light scattering directly maps the electronic structure of the sample, i.e. the scattering response of the
transient electronic structure [25]and the evolving nanoplasma after pulsed laser excitation [29].
OPEN ACCESS
RECEIVED
29 November 2015
REVISED
7 March 2016
ACCEPTED FOR PUBLICATION
22 March 2016
PUBLISHED
13 April 2016
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© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
The light induced dynamics—depending on the intensity of the light pulse—proceeds on several time scales.
For strong pulses, immediately after photon absorption electrons are emitted and the particle gets ionized
[4,30]. Electron trapping by the deepening Coulomb potential [30], subsequent charge migration from the
cluster surface towards its center, and the beginning of recombination take place on a femtosecond time scale
[31–33]. Ion motion finally leads to sample disintegration. Its characteristics strongly depend on the power
density. This process is usually completed after several picoseconds in small clusters [33–35]. For large cluster
sizes the highly charged plasma evolves in shell ablation and subsequent cluster core recombination [36–39].
Theoretical work [40]and initial experiments [29,41]provide evidence that surface softening proceeds within
several hundred femtoseconds. The dynamics and the behavior of the remaining cold center part are however
unknown. Theory has severe problems to model the complex dynamics up to long timescales, since they are
challenging and extremely time consuming.
We performed single-shot single-cluster scattering experiments on individual large xenon clusters. By
removing the averaging over cluster size and laser intensity, via sorting the single-shot images in post-analysis,
the blurring of clear signatures is avoided [42–44]. In order to entirely follow the long-term expansion dynamics
of the cluster, imaging experiments were pushed up to the nanosecond time scale in a pump–probe setup. The
cluster expansion initiated by an ultrashort infrared (IR)pulse [45]was imaged with a soft x-ray FEL pulse from
the FLASH facility at DESY [46]. With this method we were able to directly image two fundamentally different
stages of cluster evolution.
•On a picosecond time scale, scattering patterns exhibit decreasing fringe signal at high scattering angles. This
indicates a softening of the cluster surface while the center part stays intact.
•After a nanosecond, speckle patterns reveal the survival of the cluster core. Image analysis points towards the
core remaining as diluting neutral particle with internal density modulation.
Diffraction patterns from these extreme evolution states give unprecedented access to an up-to-date unseen
phase of radiation-induced cluster dynamics.
2. Experiment
A schematic diagram of the experimental geometry is presented in figure 1. Extremely large individual xenon
clusters are produced in a pulsed supersonic expansion through a cooled conical nozzle (180 K, 200 μm
diameter, 4°half opening angle)with 10 bar backing pressure. Production of such large particles is
experimentally challenging and triggered the development of a new experimental approach for rare-gas cluster
generation [47]. The source setup and valve operation scheme are described previously [47]. For imaging in
Figure 1. Schematic diagram of the experimental geometry showing the collinearly incoupled laser beams intersecting the single-
cluster beam in the interaction region. An ion time-of-flight spectrometer records the ionized fragments. Scattered photons are
collected with a scattering detector comprising of a multi-channel plate (MCP)and a phosphor screen. The phosphor screenis imaged
with an out-of-vacuum CCD (not depicted here)via a mirror under 45°. Some artefact like dead pixels and decreased detection
efficiencies appear in the recorded images which are described in more detail in the supplementary material. Diffraction patterns of
individual xenon clusters imaged by soft x-rayscattering reveal the particle size and shape. With the applied source setupa wide size
range was produced with the majority of clusters holding a size of 35 nm radius (a)but ranging up to extreme sizes (b)–(d), some even
larger than 700 nm in radius (d).
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New J. Phys. 18 (2016)043017 L Flückiger et al
single-particle mode the cluster beam was heavily skimmed down until only one single particle was intercepted
with the light pulses in the interaction region [25,26,43].
The FLASH free-electron laser facility delivered soft x-ray pulses with 13.6 nm wavelength and about 100 fs
pulse length in single-bunch mode [46,48]. We used the focused branch of the FLASH beamline, BL2, where the
FEL power density reached peak intensities of up to 4×10
14
Wcm
−2
. Far-field scattering patterns were recorded
with the detector system described in [25]at a distance of 61.6 mm behind the interaction region, recording
scattering angles up to 32°. The central part up to 4°is not detected due to a central hole in the detector setup,
preventing beam damage. A gating scheme was applied to ensure that only photons were detected (see
supplementary material for details). To take the flatness of the detector into account, all images were intensity
corrected with a factor of
q
-
cos
3
()
[25]. From the single-pulse scattering patterns each cluster size was
individually determined by fringe spacing analysis [47]. The statistical nature of the growth process results in a
broad log-normal size distribution. Its maximum is identified at 35 nm radius. A representative pattern from a
cluster of this size is shown in figure 1(a). Most prominent but less abundant are patterns resulting from very
large clusters up to a micron in radius, shown in figures 1(b)–(d). Smaller particles are predominantly round in
shape reflected by circular scattering patterns. For largest particle sizes the fine interference fringes were not
resolvable with our detector setup. In line with recent findings [47]they exhibit a rough surface since they freeze
out in non-spherical shapes during their growth by coagulation.
Imaging of nanoplasma evolution was established with pump–probe technique. Synchronized to the FEL
pulses, 800 nm Ti:Sapphire pulses of 80 fs duration [45]were collinearly coupled into the vacuum chamber via a
holey mirror (see figure 1). The IR pulses were vertically polarized and their focal power density was determined
to be about 10
14
Wcm
−2
. The IR pump-pulse focal area with a FWHM of 90 μm was overlapped with the 20 μm
soft x-ray probe pulse using an in-vacuum microscope. Isochronous pulse arrival (‘time zero’)was established
with sub ps-resolution by tracing the ion yield of the transient Xe
3+
charge state [49]with an ion time-of-flight
spectrometer. The relative timing jitter between Ti:Sa and FEL pulse was about 0.4 ps, as measured with the
streak camera setup at FLASH [50]. In order to gain insight into manifold steps of the nanoplasma evolution
upon IR excitation, the pump pulse arrival time was scanned in a wide range from 0.5 ps up to 1.5 ns before
inception of the probe pulse, i.e. the instant of time when the particle was imaged.
The method of single-shot imaging requires a large amount of data to be collected in order to ensure
meaningful statistics. Despite opening new possibilities it also demands novel filtering routines [51]. From the
evolution-initiating IR pulse only a fluorescence is recorded and not a scattering pattern. Therefore, in the
pump–probe experiment the initial cluster size and exposed power density is not well defined. However, the
final state of the excited cluster, at probe time, is detected by the FEL pulse. A reliable filtering method was
needed to make patterns of different final states comparable, despite missing knowledge of the initial state. A
very basic but effective method was to filter scattering patterns with highest detector intensity. It was assumed
that these images resulted from the largest clusters, as they scatter significantly stronger than smaller ones.
Additionally we presume that the strong scattering intensity is an indication that the cluster was exposed to
maximal FEL power densities. There the higher number of impinging photons should result in a larger number
of scattered photons. Note that the current detector system used was not a single photon counter detector and
that the photon signal was converted to electronic and optical signal before data storage [25]. Therefore no
absolute values can be given for the detector intensity. Nevertheless, sorting of relative diffraction pattern
intensities makes a reliable filter as shown in earlier experiments [25].
3. Results
The analysis of laser induced nanoplasma evolution is divided in two phases to account for the different
expansion processes occurring during a nanosecond time interval. First the evolution of the outer cluster shell is
investigated (section 3.1)and subsequently the whereabouts of the center part are examined in detail
(section 3.2).
3.1. Surface ablation
In this section the gradual change in scattering patterns with cluster evolution on a picosecond time scale is
analyzed. Figure 2depicts snapshots of different individual xenon clusters recorded without pre-irradiation (a)
and at various delay times after sample excitation with the IR pump pulse (b)–(e). As mentioned above, the initial
cluster state upon IR laser excitation cannot be directly extracted from the recorded images. To eliminate the
influence of particle size and focal position, for each delay time, the scattering pattern with highest detector
intensity is chosen. It is assumed that these patterns result from the largest xenon clusters (700–1000 nm radius)
in the size distribution intercepted at the central FEL focus position. These large clusters grow by coagulation of
smaller particles and can freeze out in intermediate states resulting in mostly spherical particles with grainy
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New J. Phys. 18 (2016)043017 L Flückiger et al
substructure [47]. These hailstone-shaped particles lead to characteristic fringe patterns in the diffraction images
(figure 2(a)). At early delays (figure 2(b)) the fringe structure is visible over a wide angle range, showing that
conjecturably the grainy substructure on the particle surface is still intact after 10 ps. Immediately visible from
comparison of figures 2(b)–(e)is the loss of fine structure at higher scattering angles with proceeding delay.
From 50 ps onwards (figure 2(c)) it gradually blurs and vanishes starting from the outer detector region towards
the center. At the same time a background signal arises with stronger contribution at high angles.
For a qualitative analysis of the particle evolution in time, the recorded scattering patterns depicted in
figure 2are azimuthally integrated and their profiles are plotted in figure 3(a). The fine interference rings cannot
be resolved due to the detector resolution; therefore the size of the clusters cannot be extracted. However the
cluster evolution can be extracted from the changing of the intensity envelopes.
With increasing delay time a background signal arises, especially at high scattering angles. Its origin is
unknown but might result from fluorescence and inelastic scattering. In the literature an increase in background
signal at high scattering angles due to inelastic scattering was predicted by theoretical models [40]. A similar
appearance in photon intensity at large angles was reported in an earlier dynamic imaging experiment [52].
The key observation in the here presented patterns is that the envelope slopes of the scattering signal at small
angles get steeper with increased delay time, which we attribute to coherent diffraction signal from the evolving
cluster. This observation is also found in a recent experiment studying a different size regime of xenon clusters
[29]and is well explained by theoretical calculations on hydrogen clusters [40]. In both works the intensity
lowering of higher order fringe maxima in scattering patterns from a spherical cluster is attributed to surface
ablation.
We conducted comparative calculations following the theory in [40]to understand the correlation between
surface ablation and decrease of fringe intensity in much more detail. They show that only a few percent of the
cluster need to melt off to result in such a steepening of the radial profiles. To find a suitable choice for the
parameters in the calculation is not unambiguous since the initial radius of the cluster is unknown. The
following assumptions were made. To mimic the cluster shapes at several time steps after IR irradiation, various
electron density distributions with increasingly softened surface and corresponding shrinking full-density core
Figure 2. Scattering patterns from xenon clusters imaged with the soft x-ray pulse without pre-irradiation (a), and at several delay
times after the IR pulse excitation (b)–(e). Each pattern is the most intense out of all images recorded at the indicated delay time. This
selection is based on the assumption that sorting for intensity filters the largest and best hit particles and thus comparable initial
conditions. Exclusive probe pulse imaging (a)shows an intact particle with radius larger than 700 nm. In pump–probe configuration
(b)–(e)with increasing delay time the low frequency information is blurred revealing proceeding particle surface ablation. The bright
diffuse spot at around −20°on the left side of the scattering patterns is an artifact originating from reflections of the IR laser on the
out-of-vacuum CCD camera (see supplementary material for details).
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New J. Phys. 18 (2016)043017 L Flückiger et al
are calculated and displayed in the inset of figure 3(b). For the calculation of the electron density distribution an
analytic expression proposed by MicPIC theory for nanoplasmas in hydrodynamic expansion [40]was
employed:
⎡
⎣⎤
⎦
=
+
-
nr n
exp 1
,1
rr
ds
s
Core
Core
()
() ()
where n
Core
is the core density, r
Core
the core radius, dthe decay length of the melting surface, and san additional
sharpness factor. In a simplified approach scattering profiles were simulated by 2D fast Fourier transforms
(FFTs)of the electron density distribution projected onto the scattering plane and presented in figure
8
3(b).No
absolute photon intensities are measurable with this detector setup. Thus, to be able to compare theory and
experiment, scattering slopes are not directly compared, but a rather different approach is used: an intensity
threshold was set where the recorded scattering signal merges with background noise, as indicated by the black
dashed lines in figure 3(b). The scattering angle, at whichenvelope and threshold level cross (indicated by red
dashed lines in figure 3(b)), was used as reference point to find the matching density profiles. The slope of a
scattering envelope from a spherical object is independent on the particle size [53]. Therefore any arbitrary initial
radius is applicable to study the intensity envelope changes. As discussed above, the initial cluster size cannot be
extracted from the recorded images, but since profiles are filtered on brightest image presumably resulting from
largest clusters in the beam, an initial radius of 1000 nm was assumed.
Three electron density distributions with increasing surface ablation and, correspondingly, with the reduced
core-size were calculated (inset in figure 3(b)). Thereby the overall particle volume was kept constant, e.g. the
integral under the outline was always kept the same. With increasing surface melt-off and decreasing core the
scattering profiles become steeper. From the profile simulated for the scattering pattern recorded 100 ps after IR
excitation (orange profile), it becomes evident that only a minor part of the core needs to melt off before the
characteristic scattering fringes of large clusters are almost completely vanished. The absolute values in this
calculation are not viable but the simulation clearly show that in our setup the scattering patterns vanish much
faster than the clusters themselves.
Our findings confirm earlier studies performed with ion spectroscopy on large argon clusters in IR light [36].
It showed that for moderate IR intensities (10
14
Wcm
−2
)the cluster is skinned with the layer of certain thickness
depending on the laser power. A recent study on large xenon clusters in soft x-ray light indicates a similar
behavior [39]. A thin, highly charged cluster shell expands upon hydrodynamic pressure of the nanoplasma
electron cloud. The remaining core recombines to full neutrality [39]after electrons migrate to the energetically
preferred cluster center [13]. Here we show that these disintegration dynamics of such large xenon clusters can
Figure 3. (a)Azimuthally integrated scattering pattern profiles reveal an increase in envelope steepness with delay time. Additionally
the scattered background level increases with delay time especially at high angles. (b)Inset: several cluster electron density
distributions for particles with increasingly softened surface. Calculated increasing shell ablation results in decreasing core radius
since the overall particle volume is kept constant. (b)Full image: profiles of 2D FFTs from the projected densities show the correlation
between shell ablation and scattering signal decrease at high scattering angles. Scattering fringes are plotted in gray and envelopes are
highlighted in color. With evolving surface softening the scattering envelope increases in steepness.
8
In this approximation absorption effects are neglected.
5
New J. Phys. 18 (2016)043017 L Flückiger et al
be directly imaged. From the above simulation we can estimate that after 100 ps a substantial part of the cluster
core can still be intact, even though the coherent scattering signal has already vanished towards small scattering
angles and is overlaying with background signal, especially at high detection angles. The further fate of the
recombined inner part of the cluster [39]however, is fully unknown. The disintegration of the central part of the
cluster is subject of the next section.
3.2. Core disintegration
3.2.1. Measured speckle patterns
On a long timescale, from 500 ps on, a novel kind of pattern shows up as presented in figure 4(a). These speckle
patterns from fragmenting xenon clusters were to our knowledge never detected before from atomic clusters but
are mainly known from imaging of colloid systems [28,54,55]. All three patterns exhibit a characteristic speckle
distribution with distinct speckle size and intensity. As these images are low in overall scattering intensity
(compare with figure 2(e)), they probably result from small clusters. Note that the cluster size distribution is
broad with a maximum of 35 nm radius, as stated in the experimental section.
Figure 4(b)presents the azimuthally integrated intensities of the speckle patterns in figure 4(a). A change in
the slope of the intensity envelope is seen in the experimental scattering profiles around 20°.
A detailed analysis of the speckle pattern can provide information on the particle shape [56]and density [57].
In the case of dense spherical objects the analysis of the intensity profiles would give information of different
object properties. in full analogy, the ring spacing corresponds to the particle size, while the intensity envelope
depends on the materials refractive index, which is coupled to the electron density [53]. In a similar way, the
mean size of speckles is inversely proportional to the average radius of the overall object [56,58]and the slope of
a speckle distribution is correlated with the average characteristic length scale of the internal structure which
induces scattering [57].
Structural information from scattering patterns can in principle be gained by reconstruction with phase
retrieval methods [59]. However, for disintegrating targets this procedure is challenging, especially if important
information at small scattering angles is missing due to the hole in the scattering detector. Recent experiments
demonstrated that reconstruction gets extremely difficult with increasing loss of detailed structure in the sample
[52]. Instead of phase retrieval methods we therefore performed simulations which can provide new insight into
the main characteristic of the sample disintegration. We start with a systematically analysis to understand main
features of speckle patterns (section 3.2.2)and as a second step try to modulate measured scattering patterns in a
simplified model (section 3.2.3).
Figure 4. (a)Characteristic speckle patterns, recorded upon soft x-ray irradiation of single clusters 1.5 ns after IR laser excitation. (b)
Corresponding azimuthally integrated scattering intensities show a modulation in the amplitude envelope with change of slope at
around 20°scattering angle and lower.
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New J. Phys. 18 (2016)043017 L Flückiger et al
3.2.2. Method: small-angle x-ray scattering (SAXS)simulations
We systematically computed scattering patterns from model clusters with SAXS simulations in numerical scalar
approach [60].Inafirst step, scattering from a sphere with amorphously distributed point-scatterers has been
investigated. In a second step, the cluster has been further divided into sub-spheres to account for internal
density fluctuations. By tuning the parameters of the overall cluster size, atomic distance, sub-sphere size, and
their spacing, the response on the scattering pattern are systematically studied and presented in figures 5and 6.
Scattering from a ‘gas ball’, with in average equal atom spacing significantly smaller than the impinging laser
wavelength, results in ring patterns (figure 5(a)). The fringe spacing is inversely proportional to the overall
particle radius R
Cluster
, as evident from Fraunhofer diffraction. Please note that absolute scattering intensities
scale with the number of scatterers. For better visibility all simulated scattering patterns are normalized to their
respective maximum intensity and absolute values are not directly comparable. With increase in distance
between the point scatterers D
Atom
(from figures 5(a)to (b)) ring patterns break up and transform into speckles,
gradually evolving from large to small scattering angles. This is equivalent to the transition from a homogeneous
to an inhomogeneous sample, leading at the same time to an increase in surface roughness. Analogous to
interference rings from dense objects the speckle size decreases with growing sphere size (see figure 5(b)top to
bottom). The average particle radius can be determined from the mean speckle size by [56,58]
l
p
=RL
R2
Cluster
Speckle
·
·()
with λthe impinging wavelength, Lthe distance between detector and interaction region, and R
Speckle
the mean
speckle radius on the detector (the detector pixel size multiplied by half the number of pixel length an average
speckle occupies). Note that if the distance between the atoms becomes larger than the transversal coherence
length of the laser beam, speckles can not be resolved [61].
Fluctuations in the particle density have been implemented in the simulation by modeling spherical sub-
clusters of point-scatterers with radius R
Sub
and distance between their center points D
Sub
(figures 6(a)and (b)).
They lead to modulations in the diffraction amplitude envelope, as indicated by red dashed lines in figures 6(a)
and (b). From the Airy pattern formula [62]
l
q
=R1.22
2sin 3
Sub
min
·
·() ()
the average fluctuation range is inversely correlated to the angle of the first order minimum
q
min of the scattering
envelope modulation. As simulations emphasize, with increasing sub-cluster radius the modulation minimum
shifts towards smaller scattering angles (from figures 6(a)to (b)). Note that the speckle size is unaffected by the
density modulation (compare figures 5and 6).
Figure 5. Emergence of speckle patterns: central cuts through modeled cluster geometries of small (left half: R=100 nm)and large
(right half: R=250 nm)particles and corresponding SAXS simulations. For better visibility the pattern intensities are normalized to
their respective maximum value. Therefore absolute values for different simulations are not comparable in this depiction. (a)A dense
particle with smooth surface gives ring-patterns known from Mie theory. (b)For a dilute particle with rough surface the scattering
images contains speckles with constant intensity distribution.
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New J. Phys. 18 (2016)043017 L Flückiger et al
3.2.3. Cluster evolution determined from speckle analysis
The size of the cluster debris, at a nanosecond after IR irradiation, can be characterized with the measured
speckle patterns by the dependencies stated above. Exemplifying we discuss pattern II and IV in figure 4(a). The
mean speckle size can be deduced with several image analysis methods. Here we performed the normalized
autocovariance of the speckle pattern [63]. The width of its intensity profile at 1/e
2
of the maximum intensity
provides a reasonable measurement of the average width of a speckle [63]. In our experimental setup with
wavelength λ=13.6 nm and detector distance L=61.6 mm, the average speckle in pattern II covers in length
8.06 pixels of the detector, related to a mean speckle radius of R
Speckle
=0.28 mm due to a detector pixel size of
p=0.069 mm. This corresponds to a cluster radius of about 950 nm (see equation (2)). For pattern IV the mean
speckle radius is 0.33 mm (9.61 pixel)analogous to a mean cluster radius of about 800 nm. A change of slope in
the amplitude envelope is found at approximately 20°(see envelope II in figure 4(b)). This corresponds to about
25 nm range in density fluctuations, which is mimicked by sub-cluster radius in this simulation. For pattern IV it
is challenging to determine a minimum due to the low schattering signal. However, a simulation with
=
R
52 30
Sub ()
nm seems to fit best.
The overall particle density determined by the atomic and sub-cluster distance, cannot be directly extracted
from the measured pattern. This is because the important central part of the pattern up to 4°is missing, due to
the detector center hole and stray light out of the beamline, as introduced in the experimental section and
encircled by a red ring in figures 7(a)and (b). For small scattering vector values, e.g. towards the central part, the
particle looks dense. For larger angles the scattering signal is sensitive to the distance of the scatterers. Therefore
the scattering angle of the transition between ring pattern and speckle structure is correlated to the density of the
cluster (figure 5(a)). This enables us to give a lower limit of the particle density in the cluster. A model cluster
with a distance of 50 nm between sub-sphere centers and 4 nm distance between atoms within the sub-spheres
fits a transition from ring to speckle pattern below 4°angle. For pattern IV a model with
=
D
10 nm
Atom
and
=
D
104 nm
Sub has been used.
Figure 7(b)shows a suitable simulation with these values, of a R
Sphere
=950 nm cluster, divided in sub-
spheres of in average R
Sub
=25 nm. To make the model more realistic, we included a distribution of density
modulation length. Therefore, the sub-cluster size has been distributed between 10 and 40 nm radius
(figure 7(c)) which results in a less pronounced amplitude modulation (figure 7(d)). Azimuthally integrated
intensity profiles reveal that the slope can be reproduced properly (figure 7(d)). The method of SAXS
simulations on clusters with internal density fluctuations shows that even though the complexity of the speckle
patterns makes an exact particle characterization impossible, the characteristic length scales of the evolving
cluster can be extracted.
Figure 6. Emergence of intensity modulation: central cuts through modeled cluster geometries of small (left half: R=100 nm)and
large (right half: R=250 nm)particles and corresponding SAXS simulations. Pattern intensities are normed to their respective
maximum value. (a)Internal density modulations result in a modulation of the amplitude envelope visible as ring-shaped
superstructure at high angle, indicated by red dashed circles. (b)With increasing range of density modulation the envelope minima
shift to smaller angles. For the simulations inc and d the atomic distance iskept constant at 5 nm.
8
New J. Phys. 18 (2016)043017 L Flückiger et al
4. Conclusion
We explored cluster evolution by snapshotting time-slices of laser induced disintegration in pump–probe
configuration, pushing to extreme time regimes from several pico- up to 1.5 ns. After initiation of the expansion
with an intense IR laser pulse, xenon clusters in the size range of several ten to hundred nanometers in radius
were imaged with a soft-x-ray FEL pulse in single-shot single-particle mode. We identified two different kinds of
scattering patterns on different time scales: fringe patterns, where the scattering signal vanishes at high scattering
angles with increasing delay time within tens of picoseconds, as well as speckle patterns, which appear from 500
picoseconds onwards.
We attribute these two types of patterns to different stages of the expansion:
•Following strong particle excitation and subsequent electron trapping in the deepening Coulomb potential a
quasi-neutral nanoplasma is formed. Its surface ions undergo hydrodynamic expansion due to the pressure of
the plasma electrons [38]. The expansion evolves on a picosecond timescale layer-wise from the outside
towards the cluster center. This surface softening is mirrored by a decrease in scattering signal at high
scattering angles (see also [29,40]).
Figure 7. (a)Typical speckle diffraction pattern recorded 1.4 ns (II)and 0.5 ns (IV)after IR laser impingement. (b)Simulated pattern
calculated in scalar numerical small angle x-ray scattering approach from a =
R
950 nm
Cluster dilute gas ball with internal density
fluctuations on a size range of =
R
25 15
Sub (
)
nm and a cluster with =
R
800 nm
Cluster and =
R
52 30
Sub (
)
nm. (c)
Visualization of the model clusters used to calculate (b). Atomic distances are set to
=
D
4nm
Atom and sub-cluster distances to
=
D
50 nm
Sub , respectively =
D
10 nm
Atom and
=
D
104 nm
Sub
.(d)Radial profiles of measured and simulated data show the
elaborateness of input values. The intensity scale for measured and simulated data varies due to the ambiguous linearity of the
scattering detector.
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New J. Phys. 18 (2016)043017 L Flückiger et al
•Meanwhile the majority of excited electrons recombines and consequently the expansion driven by plasma
electrons finally stops. The remaining neutral cluster core stays in the interaction region up to nanoseconds.
Its density decreases slowly and density fluctuations occur, leading to speckle patterns with intensity
modulations.
We show that simple image analysis of the recorded speckle patterns has the potential to determine the
overall size and internal density fluctuation range of the examined object. Our findings from dynamic diffraction
imaging extend the picture of laser–matter interaction into the nanosecond time scale, where we identifed
structural signatures up to date not explored in homogeneous clusters.
Acknowledgments
The authors like to thank the DESY staff for their outstanding support during FLASH beamtime as well as
Thomas Fennel, Christian Peltz and Ivan Vartanyants for fruitful discussions. Financial support by the BMBF
grand 05K10KT2 is kindly acknowledged.
References
[1]Fennel T, Meiwes-Broer K H, Tiggesbäumker J, Reinhard P G, Dinh P M and Suraud E 2010 Rev. Mod. Phys. 82 1793–842
[2]Saalmann U, Siedschlag C and Rost J M 2006 J. Phys. B: At. Mol. Opt. Phys. 39 R39–77
[3]Snyder E, Buzza S and Castleman A 1996 Phys. Rev. Lett. 77 3347–50
[4]Wabnitz H et al 2002 Nature 420 482–5
[5]Laarmann T, de Castro A, Gürtler P, Laasch W, Schulz J,Wabnitz H and Möller T 2004 Phys. Rev. Lett. 92 143401
[6]Iwayama H et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 134019
[7]Varin C, Peltz C, Brabec T and Fennel T 2012 Phys. Rev. Lett. 108 175007
[8]Ziaja B, Chapman H N, Fäustlin R, Hau-Riege S, Jurek Z, Martin A V, Toleikis S, Wang F, Weckert E and Santra R 2012 New J. Phys. 14
115015
[9]Schütte B, Arbeiter M, Fennel T, Vrakking M J J and Rouzée A 2014 Phys. Rev. Lett. 112 073003
[10]Müller M et al 2015 J. Phys. B: At. Mol. Opt. Phys. 48 174002
[11]König K, Riemann I, Fischer P and Halbhuber K J 1999 Cell. Mol. Biol. 45 195–201
[12]Englert L, Wollenhaupt M, Haag L, Sarpe-Tudoran C, Rethfeld B and Baumert T 2008 Appl. Phys. A92 749–53
[13]Hoener M, Bostedt C, Thomas H, Landt L, Eremina E, Wabnitz H, Laarmann T, Treusch R, Castro A R B D and Möller T 2008 J. Phys.
B: At. Mol. Opt. Phys. 41 181001
[14]Iwan B et al 2012 Phys. Rev. A86 033201
[15]Schorb S et al 2012 Phys. Rev. Lett. 108 233401
[16]Ditmire T, Zweiback J, Yanovsky V P, Cowan T E and Hays G 1999 Nature 398 489–92
[17]Köller L, Schumacher M, Köhn J, Teuber S, Tiggesbäumker J and Meiwes-Broer K H 1999 Phys. Rev. Lett. 82 3783–6
[18]Zweiback J, Ditmire T and Perry M 1999 Phys. Rev. A59 3166–9
[19]Saalmann U and Rost J M 2003 Phys. Rev. Lett. 91 223401
[20]Ditmire T, Donnelly T, Rubenchik A, Falcone R and Perry M 1996 Phys. Rev. A53 3379–402
[21]Chapman H N et al 2006 Nat. Phys. 2839–43
[22]Neutze R, Wouts R, van der Spoel D, Weckert E and Hajdu J 2000 Nature 406 752–7
[23]Bogan M J et al 2008 Nano Lett. 8310–6
[24]Bostedt C, Adolph M, Eremina E, Hoener M, Rupp D, Schorb S, Thomas H, de Castro a R B and Möller T 2010 J. Phys. B: At. Mol. Opt.
Phys. 43 194011
[25]Bostedt C et al 2012 Phys. Rev. Lett. 108 093401
[26]Rupp D et al 2012 New J. Phys. 14 055016
[27]Barke I et al 2015 Nat. Commun. 66187
[28]Bogan M J et al 2010 Aerosol Sci. Technol. 44 i–vi
[29]Gorkhover T et al 2016 Nat. Photon. 10 93–7
[30]Bostedt C et al 2008 Phys. Rev. Lett. 100 133401
[31]Bostedt C, Thomas H, Hoener M, Möller T, Saalmann U, Georgescu I, Gnodtke C and Rost J M 2010 New J. Phys. 12 083004
[32]Saalmann U 2010 J. Phys. B: At. Mol. Opt. Phys. 43 194012
[33]Krikunova M et al 2012 J. Phys. B: At. Mol. Opt. Phys. 45 105101
[34]Krainov V and Smirnov M 2002 Phys. Rep. 370 237–331
[35]Arbeiter M, Peltz C and Fennel T 2014 Phys. Rev. A89 043428
[36]Sakabe S, Shirai K, Hashida M, Shimizu S and Masuno S 2006 Phys. Rev. A74 043205
[37]Thomas H, Bostedt C, Hoener M, Eremina E, Wabnitz H, Laarmann T, Plönjes E, Treusch R, De Castro A R B and Möller T 2009
J. Phys. B: At. Mol. Opt. Phys. 42 134018
[38]Arbeiter M and Fennel T 2011 New J. Phys. 13 053022
[39]Rupp D et al Phys. Rev. Lett. submitted
[40]Peltz C, Varin C, Brabec T and Fennel T 2014 Phys. Rev. Lett. 113 133401
[41]Hau-Riege S P et al 2010 Phys. Rev. Lett. 104 064801
[42]Islam M, Saalmann U and Rost J 2006 Phys. Rev. A73 041201 (R)
[43]Gorkhover T et al 2012 Phys. Rev. Lett. 108 245005
[44]Hickstein D D et al 2014 Phys. Rev. Lett. 112 115004
[45]Redlin H, Al-Shemmary A, Azima A, Stojanovic N, Tavella F, Will I and Düsterer S 2011 Nucl. Instrum. Methods Phys. Res. A635
S88–93
10
New J. Phys. 18 (2016)043017 L Flückiger et al
[46]Tiedtke K et al 2009 New J. Phys. 11 023029
[47]Rupp D et al 2014 J. Chem. Phys. 141 044306
[48]Ackermann W et al 2007 Nat. Photon. 1336–42
[49]Krikunova M et al 2009 New J. Phys. 11 123019
[50]Radcliffe P, Düsterer S, Azima A, Li W, Plonjes E, Redlin H, Feldhaus J, Nicolosi P, Poletto L and Dardis J 2007 Nucl. Instrum. Methods
Phys. Res. A583 516–25
[51]Andreasson J et al 2014 Opt. Express 22 2497–510
[52]Barty A et al 2008 Nat. Photon. 2415–9
[53]Mie G 1908 Ann. Phys., Lpz. 330 377–445
[54]Loh N D et al 2012 Nature 486 513–7
[55]Pedersoli E et al 2013 J. Phys. B: At. Mol. Opt. Phys. 46 164033
[56]Zhang G, Wu Z and Li Y 2012 Opt. Express 20 4726–37
[57]Veen F V D and Pfeiffer F 2004 J. Phys.: Condens. Matter. 16 5003–30
[58]Ulanowski Z, Hirst E, Kaye P and Greenaway R 2012 J. Quant. Spectrosc. Radiat. Transfer 113 2457–64
[59]Marchesini S, Chapman H N, London R A and Szoke A 2003 Opt. Express 11 2344–53
[60]DeCastro A, Eremina E, Bostedt C, Hoener M, Thomas H and Möller T 2008 J. Electron Spectrosc. Relat. Phenom. 166–167 21–7
[61]Vartanyants I, Mancuso P, Singer A, Yefanov O M and Gulden J 2010 J. Phys. B: At. Mol. Opt. Phys. 43 194016
[62]Als-Nielsen J 2011 Elements of Modern X-ray Physics (New York: Wiley)
[63]Piederrière Y, Le M J, Cariou J, Abgrall J and Blouch M 2004 Opt. Express 12 4596–601
11
New J. Phys. 18 (2016)043017 L Flückiger et al
