Citation: Keil, D.; Scharring, S.; Klein,
E.; Lorbeer, R.-A.; Schumacher, D;
Seiz, F.; Sharma, K.K.; Zwilich, M.;
Schnörer, L.; Roth, M.; et al.
Modification of Space Debris
Trajectories Through Lasers:
Dependence of Thermal and Impulse
Coupling on Material and Surface
Properties. Aerospace 2023,10, 947.
https://doi.org/10.3390/
aerospace10110947
Academic Editor: Pierre Rochus
Received: 29 September 2023
Revised: 30 October 2023
Accepted: 30 October 2023
Published: 7 November 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
aerospace
Article
Modification of Space Debris Trajectories Through Lasers:
Dependence of Thermal and Impulse Coupling on Material
and Surface Properties
Denise Keil 1,* , Stefan Scharring 1, Erik Klein 1,2 , Raoul-Amadeus Lorbeer 1, Dennis Schumacher 3,
Frederic Seiz 1, Kush Kumar Sharma 1,4 , Michael Zwilich 1, Lukas Schnörer 1, Markus Roth 5,
Mohamed Khalil Ben-Larbi 2,† , Carsten Wiedemann 2, Wolfgang Riede 1and Thomas Dekorsy 1
1Institute of Technical Physics, German Aerospace Center (DLR), Pfaffenwaldring 38–40,
70569 Stuttgart, Germany; stefan.scharring@dlr.de (S.S.); erik.klein@dlr.de (E.K.);
raoul.lorbeer@dlr.de (R.-A.L.); kushkumar.sharma@community.isunet.edu (K.K.S.);
m.zwilich@uni-muenster.de (M.Z.); lukas.schnoerer@dlr.de (L.S.); wolfgang.riede@dlr.de (W.R.);
thomas.dekorsy@dlr.de (T.D.)
2Institute of Space Systems, Technische Universität Braunschweig, Hermann-Blenk-Str. 23,
[email protected] (C.W.)
3GSI Helmholtzzentrum für Schwerionenforschung GmbH, Plasmaphysik/PHELIX, Planckstraße 1,
4ISU International Space University, 1 Rue Jean-Dominique Cassini, 67400 Illkirch-Graffenstaden, France
5Institute for Nuclear Physics, Technical University of Darmstadt, Schlossgartenstraße 9,
*Correspondence: denise.keil@dlr.de
†Current address: Chair of Space Technology, Department of Aeronautics and Astronautics, Technische
Universität Berlin, Marchstraße 12–14, 10587 Berlin, Germany.
Abstract:
Environmental pollution exists not only within our atmosphere but also in space. Space
debris is a critical problem of modern and future space infrastructure. Congested orbits raise the
question of spacecraft disposal. Therefore, state-of-the-art satellites come with a deorbit system
in cases of low Earth orbit (LEO) and with thrusters for transferring into the graveyard orbit for
geostationary and geosynchronous orbits. No practical solution is available for debris objects that
stem from fragmentation events. The present study focuses on objects in LEO orbits with dimensions
in the dangerous class of 1 to 10 cm. Our assumed method for the change of trajectories of space debris
is laser ablation for collision avoidance or complete removal by ground-based laser systems. Thus,
we executed an experimental feasibility study with focus on thermal and impulse coupling between
laser and sample. Free-fall experiments with a 10 ns laser pulse at nominally 60 J and 1064 nm were
conducted with GSI Darmstadt’s nhelix laser on various sample materials with different surfaces.
Ablated mass, heating, and trajectory were recorded. Furthermore, we investigated the influence
of the sample surface roughness on the laser-object interaction. We measured impulse coupling
coefficients between 7 and 40
µ
Ns/J and thermal coupling coefficients between 2% and 12.5% both
depending on target fluence, surface roughness, and material. Ablated mass and changes in surface
roughness were considered via simulation to discriminate their relevance for a multiple shot concept.
Keywords:
space debris; debris-trajectory modification; collision avoidance; high-power laser
application; space sustainability
1. Introduction
In 1978, Donald J. Kessler predicted a condition where space will be so congested that
a cascade of collisions between the space objects might cause a pollution of the orbits and,
therefore, make it unusable for future space applications [
1
]. Nowadays, we are closer
to that point than ever. Some scientists found indications that the collapse has already
Aerospace 2023,10, 947. https://doi.org/10.3390/aerospace10110947 https://www.mdpi.com/journal/aerospace
Aerospace 2023,10, 947 2 of 25
begun [
2
], while others still believe little time is left until the Kessler Syndrome de facto
appears [
3
]. Both research opinions are alerting and require mankind to act and protect
space. Losing space as a resource would deeply affect our daily lives. As [
4
] illustrates,
the loss of GPS could lead to an economic breakdown, just to mention one effect. NASA
most recently published a study where the damage due to space debris is expressed as
monetary numbers, showing how expensive it will be to not act [
5
]. Adilov et al. names
monetary losses of about USD 86–103 million in 2020 due to satellite collisions with space
debris [6].
In another study, Liou [
7
] shows that on today’s measures, the current post-mission
disposal is not enough to stop the growth of the fragment population in orbit. Only active
debris removal can reduce the population of unwanted objects and cause a sustainable
space environment in the future.
This leads to the question of how to remove debris from space. For bigger objects,
like defunct satellites, rocket bodies, or other mission-related objects, the European Space
Agency (ESA) works on ClearSpace1, which is a chaser system that hunts down and
deorbits them [
8
]. For the very first removal demonstration, ClearSpace1 is meant to
deorbit a Vega launch adapter named VESPA. Recently, the ESA reported about a new
object in VESPA’s vicinity, which most likely is the result of a fragmentation event of VESPA.
This underlines the urgency of trajectory modification and removal of larger debris objects
as well as the great danger that potentially undetected small debris objects pose to other
orbital objects [
9
,
10
]. This smaller class of fragments, namely with a size of a few decimeters,
cannot be chased efficiently. For this purpose, laser-ablative debris removal is proposed,
which can be operated either space-based [
11
,
12
] or ground-based [
13
]. In the concept of
ground-based lasers, a high-power laser system is based in a ground station. This laser
system transmits laser pulses, typically in the nanosecond regime, towards the designated
object in orbit. Each pulse causes ablation at the object’s surface and, thus, momentum
perpendicular to the surface. The relevant trajectory modification results from a multi-shot
interaction. For the final deorbit of an object, several 100 to 1000 passes of the object are
required, depending of the laser settings (mainly repetition rate and applied fluence) and
the target dimensions [14].
The present study is part of our feasibility studies regarding ground-based, laser-based
methods for modification of space debris trajectories, with the option for complete removal
of objects. In previous publications, we performed various simulative and experimental
studies [
15
–
17
]. In particular, the influence of the sample geometry on impulse coupling
was investigated [
17
]. In this work, we investigate a variation in materials and surface
properties aiming for measuring impulse and thermal coupling by simultaneously applying
approximately 10 J/cm2within 10 ns on sample surfaces.
This document is structured as follows: we will present the experimental framework
in Section 2, followed by an introduction to the experimental methods in Section 3. Finite
element simulations for thermal and impulse coupling will be presented in Section 4.
The results are summarized in Section 5, which is followed by the discussion section,
Section 6. The paper will close with a conclusion in Section 7and an outlook in Section 8.
2. Experiment
The experiment was conducted to gain knowledge about thermal and impulse cou-
pling depending on material and sample surface condition. The following sections will
describe the laser facility and the experimental set-up, including the samples and irradia-
tion parameters.
2.1. nhelix Laser Facility
The applied laser is the nhelix (nanosecond high energy laser for heavy ion experi-
ments) laser of the GSI (Gesellschaft für Schwerionenforschung) in Darmstadt, Germany.
nhelix provides 60 J pulse energy at a wavelength of 1064 nm and a pulse duration of 10 ns.
Aerospace 2023,10, 947 3 of 25
For the conducted experiment, laser fluences above the ablation threshold are required,
which is material-dependent and, beyond that, affected by the surface roughness. Based on
simulations, we have determined that for this given wavelength and at a pulse duration
of 10 ns, a fluence of 10 J/cm
²
is sufficient for the ablation of metal surfaces. Moreover,
momentum coupling is expected to be rather effective in this fluence regime. These
constraints have been kept identical to the previous experiment [17].
Due to damage in the last amplifier stage, nhelix comes with variations in its output
energy. We set 60 J, which leads to the nominal fluence of 10 J/cm
²
with the given laser
diameter of 28 mm at the target point. Our study covers a bandwidth of fluences between
3 and 20 J/cm
²
. Aside from energy fluctuations, inhomogeneous energy distribution
amongst the spot diameter as well as the true target hit angle also have to be considered.
Details are discussed in Section 3.1.
2.2. Experimental Setup
For the experiment, we adopted the set-up from the previous experiment by Lor-
beer et al. [
17
], cf. Figure A1 in Appendix A.1. We employ a dropping arm set-up where the
arm is accelerated by a spring, cf. Figure 1a. The arm is initially actuated by a spring, while
the sample experiences acceleration due to gravity alone. The arm is intercepted by a spring
plate which avoids it to move back and interact with the falling sample. The sample itself
is placed on a chair-like sample holder, cf. Figure 1b. For thermal measurements, a thermal
sensor is affixed to the sample backside. Charging contacts for the sensor are installed on a
fixed rail. The arm is held into position by an electromagnet, which is switched off when
the trigger sequence is started. The trigger signals for sample release, camera and laser,
as well as the oscilloscope are linked to a trigger box via BNC. This trigger box consists
of a micro-controller, type Arduino Leonardo. Timing nuances were adjusted manually
at the trigger box to achieve an optimum hit of the laser pulse at the target during its fall
through the beam propagation path. A mechanical button is installed to kick-start the
trigger sequence manually.
(a) (b)
Figure 1.
Experimental set-up, installed in the Z6 vacuum chamber at the GSI Darmstadt. (
a
) Set-up
displayed with expected sample trajectory. (
b
) Detailed image of the sample holder with sensor
charging and release mechanism.
With our choice of samples, we tried to cover a wide spectrum of debris materials.
We selected the materials listed in Table 1as they are expected to be highly abundant
throughout debris fragments in the size range of 1–10 cm [
18
]. We subsequently prepared
two sets of samples: one with a polished surface and another with a sandblasted surface.
All samples were prepared in a squared shape with an edge length of 2 cm and a thickness
of 0.8 mm.
Aerospace 2023,10, 947 4 of 25
Table 1. Predominant materials for small space debris >1 cm and their usage in space applications.
Material Space Application
Aluminum 6082 General structure material with multiple applications due to light
weight and good cost–benefit balance.
Copper Mainly electronic components
Stainless Steel AISI304 Rocket stages
Titanium 99% Structure elements like bolts and screws
2.3. Hemispherical Reflection of the Samples
To characterize the samples reflection behaviors, we carried out hemispherical re-
flection measurements applying an integrating sphere (Thorlabs 2P4, Thorlabs GmbH,
Bergkirchen, Germany), a laser light source at 1064 nm, and a photo diode (PD300IR, Ophir
Spiricon Europe GmbH, Darmstadt, Germany). The integrating sphere was installed so that
the samples are illuminated by the laser under an angle of incidence of 8
° ±
1
°
as proposed
by [
19
] in order to avoid a specular back-reflection leaving the sphere through the input
port, cf. Figure 2for details. Each measurement was individually calibrated by placing
the sample in an additional port and directly illuminating the closed integrating sphere.
With this procedure, we avoided distortion due to individual and imperfect reflection lobes
for real materials.
Figure 2. Integrating sphere set-up for hemispherical–directional reflectance measurements.
The third-Taylor method was applied for the measurements [
19
]. This method allows
for a direct comparison of the detected signals for reference
(Φtot
ref)
and sample
(Φtot
meas)
under consideration of the wall fraction
fw=Aw/A0
, where
Aw
is the wall area and
A0
the
whole surface of the sphere. For our specific case, the wall factor is 0.972. The reflectivity R
is given by
R=φtot
meas
fwφtot
ref
. (1)
3. Experimental Methods
3.1. Fluence Estimation
To accurately document the laser fluence per shot, a calorimeter probe directly con-
nected to an oscilloscope has been employed. The calorimeter is placed in the laser path
so that it is irradiated with approximately 1% of the laser power. Several calibration shots
on a second calorimeter probe at the sample position in the vacuum chamber were taken
Aerospace 2023,10, 947 5 of 25
to identify a factor to convert oscilloscope voltage data into energy emitted by the laser.
For detailed knowledge about the laser spot, we installed a second beamline, identical to
the one in the vacuum chamber. Approximately 1% of the laser light is transmitted through
the mirror, forwarding the other 99% of the laser beam towards the sample chamber. This
small fraction of the laser light is projected on a screen which is recorded by an Andor iXon
Ultra 897 camera, cf. Appendix A.2. The camera chip is protected by a neutral density filter
(ND 1.8). Via the distribution of the intensity per pixel, we can derive the laser profile per
shot. The integrated intensity over the area illuminated by the laser was also calibrated via
probe measurements, which provides an additional method to estimate the laser energy
per shot.
For fluence estimation per shot, we extracted the laser energy per pixel from the Andor
images, cf. Figure 3. In an ideal case, the laser would hit with a homogeneous profile
perpendicular to the sample surface and apply a vector of force in its center of gravity
(COG). Since reality is different, we extracted the relevant pixels contributing to the impulse.
For this, we converted the shadowgraph images (Figure 3b). into a mask and used a best-fit
function to match and apply it to the image array (Figure 3a). This provides us with the
relevant pixel area of the profile (Figure 3c). Thus, the sum of the energy per pixel area is
the true applied fluence Φtarget on the target surface, further referred to as target fluence.
(a) (b) (c)
Figure 3.
Relevant array extraction by applying the shadowgraph mask onto the laser profile.
(
a
) Image of the initial beam profile. (
b
) Shadowgraph image. (
c
) Masked beam profile only consider-
ing the pixels within the mask for fluence estimation.
3.2. Motion Tracking
For exact analysis of the sample trajectory before and after the laser shot, we installed
two high-speed cameras (M3 MotionScope and OS7, Integrated Design Tools Inc., Pasadena,
CA, USA) in a stereoscopic setup. These are triggered with the sample release, recording
the sample falling for a sequence of 0.5 s with a frame rate of 1000 fps on the M3 camera
and 2000 fps on the OS7 camera. Details are listed in Appendix A.3.
Camera calibration for triangulation, motion tracking, trajectory calculation, derivation
of COG, as well as linear and angular speed was performed via a self-made python tool.
To determine the imaging characteristics and relative positions in 3D space of the two high-
speed cameras, a calibration procedure adapted from Zhang was used [20,21]. To analyze
the movement of the falling sample, a semi-automatic motion tracking procedure was
applied. The sample corners were chosen as characteristic, well-observable object features.
Their locations were manually initialized as pixel coordinates in the first frame of each
high-speed camera footage. Then, the 2D-trajectories of the sample corners were obtained
by automated tracking of the initially chosen pixels in the subsequent frames based on
the optical flow method [
22
]. For each tracked object feature, the two 2D trajectories are
then combined via triangulation yielding its 3D trajectory [
21
,
23
]. The trajectories undergo
a correction where the y-axis of the trajectory is aligned with the direction of gravity.
The final trajectory data are then analyzed regarding translational velocity changes due to
the laser. For this, we used the first derivative of the displacement-time data of the COG
data points before and after laser interaction. For the y-component of the laser-induced
motion, gravitational acceleration
dvg=g·dt
is taken into account with g = 9.81 m/s
²
Aerospace 2023,10, 947 6 of 25
at sea level. For targets perpendicular to the beam,
dvy−dvg
would equal 0. The final
velocity increment results as follows:
dv =qdv2
x+dv2
z+ (dvy−dvg)2. (2)
3.3. Thermal Coupling
For measuring thermal coupling, we developed a thermal sensor, which is described in
detail in [
24
]. It is a lightweight micro-controller equipped with data storage, capacitors as
energy source, and four PT1000 elements that allow for wireless data collection. The sensor
is applied on the sample backside using thermal conductive tape. Only the PT1000 elements
are in contact with the material. The rest is in no thermal dependence. The sensor comes
with two contacts that allow for charging the sensor inside the vacuum chamber. When
the dropping arm is detached, the circuit is interrupted and the capacitors will start to
discharge. The sensor starts looping the measurements until the capacitors cannot provide
further energy. The data file is read out via a GUI and processed further.
3.4. Ablation Behavior
In order to determine the sample ablation behavior in dependence of material, laser
fluence, and surface properties, we weighed the samples before and after the experiment.
It is assumed that material losses due to hitting the chamber ground are neglectable for
the majority of cases. Thus, the measured difference equals the mass of ablated mate-
rial. Furthermore, we investigated the sample surface roughness, as we expect different
laser coupling in dependency of roughness due to a more diffusive reflection/absorption
behavior on rougher samples. Therefore, we created defined surfaces for each sample
material. Reference and ablated sample surfaces were investigated using a White Light
Interferometer (WLIM) Wyko NT9100 (Appendix A.5). The measured roughness R
a
at
3 positions of the sample surface were averaged.
4. Simulations
Laser ablation strongly depends on laser parameters and the irradiated material.
The main figures of interest here are the momentum coupling coefficient
cm
and the coeffi-
cient of residual heat ηres. Following [25], cmis given by
cm=M∆v
EL
=∆P
EL
, (3)
where
EL
denotes the laser pulse energy, and
∆P
,
∆v
are the change of momentum and
velocity, respectively, of the target with the mass Mafter ablation.
During the ablation process, laser pulse energy is converted not only into the heat and
kinetic energy of the ablation plume, but also a considerable amount of heat
∆Q
remains in
the target after ablation. For its consideration,
ηres
is defined as the coefficient of residual
heat given by
ηres =∆Q
EL
. (4)
Since the dependencies of
cm
and
ηres
from the incident laser fluence
Φ
are highly
non-linear, their prediction from simulations is of great interest for feasibility studies and
preliminary system design. In our case, we employ the simulation results for
cm
(
Φ
) and
ηres
(
Φ
) to compute theoretical values of velocity change
∆v
and temperature increment
∆T
for comparison with experimental data by employing the measured fluence distribution
Φ(x,y) on the target surface using
∆v=1
MZZ cm(Φ(x,y))Φ(x,y)dA (5)
Aerospace 2023,10, 947 7 of 25
and
∆T=1
McpZZ ηres(Φ(x,y))Φ(x,y)dA, (6)
where cpdenotes the specific heat of the target material.
From the combination of thermal and momentum coupling, the so-called thermo-
mechanical coupling coefficient ctm can be derived using [16]
ctm =cm
ηres , (7)
which gives the ratio of imparted momentum to the laser-induced heat that has to be
considered, in particular under highly repetitive laser irradiation where thermal limitations
of target integrity might be encountered.
4.1. Finite-Element Method (FEM) Simulation
As a starting point for our FEM simulations, implemented in COMSOL Multiphysics
®
6.1,
we have set up a one-dimensional model which consists of three domains, cf. Figure 4.
Figure 4.
Simulation domain for 1D FEM analysis of laser ablation. (
a
) Laser heating. (
b
) Laser
ablation. Note: graph is not to scale.
In our model, which is described in greater detail in [
26
], the incident laser pulse
irradiates the target at its surface where laser radiation is absorbed within a thin surface
layer (region II). Below this layer, the bulk material of the target (region I) is subsequently
heated. For laser fluences beyond the ablation threshold, the vaporized surface material
forms a plume (region III) propagating in the direction of the laser source. Laser light
absorption is computed within the surface layer (II) following the Lambert–Beer law
given by
∂zI=α·I, (8)
where the intensity
I0
of the incident laser light at the target surface is split into a fraction
Iabs = (
1
−R)·I0
, which is absorbed as described by Equation (5), as well as a fraction
of light reflected
Ire f l =R·I0
from the target surface. In these relations,
I
denotes the
(local) laser light intensity,
R
represents the target’s reflectivity, and
α
is the material’s
absorption coefficient. Once ablation of surface material is initiated, light absorption within
the ablation jet has to be considered as well; see below.
Optical properties of target and ablation jet depend significantly from the temperature
which is incorporated into our simulations based on the relations outlined in Appendix C.
Using Equation (3) as a source term, the heat transfer equation
ρcp∂tT−∂z(κ·∂zT) = ∂zI(9)
can be solved in domains I and II for the target temperature field
T(x
,
t)
. Note that the
material’s density
ρ
, its specific heat capacity
cp
, and its heat conductivity
κ
strongly
Aerospace 2023,10, 947 8 of 25
depend on the temperature. Moreover, the target’s reflectivity
R(T)
and its absorption
coefficient
α(T)
depend from the temperature as well, which gives a feedback from heat
transfer inside the material to the laser heating boundary condition in terms of a real
laser–matter interaction.
Thermophysical data as a function of the temperature has been taken from the COM-
SOL material database which comprises material data for heat conductivity from [
27
–
29
],
for heat capacity from [
30
–
33
], and for density from [
28
,
29
,
32
,
34
–
47
]. The temperature
dependency of the optical properties is calculated separately, cf. Appendix B. Numerical
solution of heat transfer takes into account for melting comprising the latent heat of fusion
as well as a smooth transition of the thermophysical and optical properties between the
two phases within a transition interval of
∆T=
200
K
around the melting temperature
Tm
to ensure numerical stability.
Ablation of surface material is computed following [
48
] using the Hertz–Knudsen
equation from which the surface recession rate vR(Ts) can be expressed as
vR(Ts) = ssti
ρrma
2πkBTs·ps(Ts), (10)
where
Ts
is the surface temperature,
ssti
is the sticking coefficient,
ma
the atomic mass,
kB
is Boltzmann’s constant, and
ps
is the saturation pressure at the surface given by the
Clausius–Clapeyron equation as
ps(Ts) = pbexpLb
kB1
Tb−1
T (11)
with the latent heat
Lb
of vaporization, the boiling temperature
Tb
, and the pressure
pb
for which
Tb
is given. From this, the process of material removal at the surface can be
quantified by the area density µaof ablated mass using ∂tµa=−vR·ρ.
Above the ablation surface, a thin film of saturated gas is immediately formed, the so-
called Knudsen layer [
49
]. Mathematically, this layer, which is not resolved spatially in
our simulations, is used to describe the discontinuity between target and ablation plume
as a region in which pressure, velocity, and temperature drastically change. According
to [
49
], at the interface between Knudsen layer and ablation jet we have a temperature
Tk=Ts/
1.49 where T
s
is the temperature at the target surface. Furthermore, the pressure
is given by
pK=
0.21
·ps
, where
ps
is the saturation pressure at the target surface and
is obtained for the particle escape velocity
vK=pγkBTK/ma
, where
γ
is the material’s
adiabatic index. These relations are used to characterize the inflow at the boundary of the
ablation jet which forms above the Knudsen layer. Furthermore, we employ that mass
conservation demands
−vR·ρ
ma
=vKρK
ma
=vKnK, (12)
where
ρK
and
nK
are the jet’s mass density and particle density at the end of the Knudsen
layer. The gas dynamics inside the jet can be described according to [
50
] by the Euler
equations of hydrodynamics with respect to continuity,
∂tn+∂z(nu) = 0, (13)
momentum balance,
∂t(ρu) + ∂z(ρu2+p) = 0, (14)
and energy balance
∂t(E+ρu2/2) + ∂z[u(E+ρu2+p)] = αp·I, (15)
Aerospace 2023,10, 947 9 of 25
where
n=n0+ni
is the particle number density of neutrals and ions, and u,
ρ
, and p are
the local particle velocity, density and pressure, respectively. E is the local internal energy
density given by
E=n3
2(1+ηi)kBT+ηiW1,0(16)
with the first ionization potential given by
W1,0
and
ηi
as the mean ionization fraction.
Moreover, the ideal gas rule is assumed valid here and reads as p= (1+ηi)·nkBT.
p= (1+ηi)·nkBT= (n0+2ne)kBT. (17)
The source term
αp·I
in the energy balance equation Equation (15) indicates laser
heating of the ablation plume. For laser light absorption in the plume, we restrain our
considerations to absorption by inverse Bremsstrahlung according to [
49
]. Finally, due to
the plasma absorption of the laser light in the ablation jet, the incident laser intensity at the
target surface is reduced, which is commonly referred to as plasma shielding.
4.2. FEM Configuration
For our simulations, we have employed the commercial FEM software COMSOL Mul-
tiphysics
®
, Version 6.1, together with the related Heat Transfer Module and the COMSOL
Material Library. The timespan of our simulation usually covered 100 ns, while in a few
cases as well as for fluences below the ablation threshold only the time interval of the
laser pulse was simulated. The simulations cover a laser fluence range over three orders
of magnitude from 0.1 J/cm
2
up to 100 J/cm
2
. For the temporal course of the laser pulse
intensity, we assume a Gaussian shape and start our simulations at the point in time where
the laser intensity negligibly low (between 30 ns and 34 ns before the pulse peak). We
use an initial timestep of 1 fs, which is dynamically enlarged up to max. 70 ps during
the ablation process and furthermore increased towards the end of the simulation. The
maximum element sizes for the target bulk have been chosen to amount to 1
µ
m with a
maximum element grow rate of 1.005. While heat transfer, cf. Equation (9), is computed
throughout the entire target with a thickness of 1 mm, laser absorption is only modeled
within a thin surface layer with a thickness of 5
×α−1
min
, which is between 135 nm (titanium)
and 230 nm (aluminum). Correspondingly, the spatial resolution of the mesh is far higher
in the absorption layer than in the bulk and amounts to between 0.31 nm and 0.46 nm.
Finally, the computation domain for the ablation plume extends 5 mm from the target
surface comprising 2000 mesh elements whose size increases linearly with the distance
from the surface.
4.3. Post-Processing and Validation
The figures of merit in laser-ablative thermo-mechanical coupling can then be obtained
in post-processing of the simulation results, where the momentum coupling coefficient
cm
is given by integration at the target/plume boundary as
cm=Rpadt
Φ, (18)
where
pa=−vR·ρ·vK+pK
denotes the pressure acting on the target surface generated
from the pressure
pk
in the Knudsen layer together with the recoil from the ablated particles
escaping with the jet velocity
vk
from the Knudsen layer. Furthermore, the coefficient of
residual heat ηres can be derived from
ηres =Eres(t1)−Eres(t0)
Φ, (19)
Aerospace 2023,10, 947 10 of 25
where the areal density of the residual heat
Eres
in the target can be derived from
the integration
Eres(t) = Zρ(x,t)H(x,t)dx (20)
with the specific enthalpy H.
While data on residual heat in laser ablation could not be retrieved for our laser
parameters, experimental data on momentum coupling in this parameter range have been
found in the literature, which serves for validation of our simulations. It can be seen from
the comparison in Figure 5that the results from our simulations are in general supported by
the experimental findings from the literature. While the results for titanium match quite well,
we observe, however, that
cm
is underestimated for iron at high fluences, for aluminum in
general, and in particular for copper, which might be attributed to the generalized assumptions
on plume pressure and temperature, cf. Equations
(A5)
and
(A6)
in Appendix B, which are
neither spatially nor temporally dissolved. Beyond that, deviations between simulation
and experimental results occur at the ablation threshold in particular for aluminum, copper,
and iron. While for the latter this deviation might stem from the thermo-physical behavior
of the irradiated steel being different from that of iron, the reason for the deviation with
aluminum and copper has not been clarified yet. Overall, however,
cm
data for aluminum
in this laser parameter region from different researchers exhibit a significant scatter among
each other.
Figure 5.
Comparison of experimental data on laser-ablative momentum coupling from the literature
with 1D-FEM simulation results at the same laser parameters. While pure metals serve as a reference
for Al [
51
] and Cu [
52
], results for alloys have been taken from [
53
] for comparison with Fe simulation
results (30CrMnSiA steel) and Ti (TC4 alloy), respectively. Whereas the numerical values of the
experimental data were provided alongside the paper in the case of [
51
], underlying numerical data
have been extracted from the graphs of [52,53] using WebPlotDigitizer 4.6 [54].
5. Results
In the following, we present our experimental and simulated results. Here, we firstly
separate the different observation channels for data analysis, namely the simulation and
measurement results of the velocity increment and the temperature increase as well as data
regarding surface ablation. Afterwards, we analyze the data as a whole set. All considered
laser shots are listed in Tables 2and 3. The list contains the four measurement parameters,
which are building the base of further discussion and of the coupling coefficient calculation.
Data not obtained are marked with “n.a.”. Fluences listed in brackets relate to shots where
no beam profile was available either due to poor signal in the Andor camera (shot 10 and 14)
or cases without shadowgraph available (shot 42). In case of poor signal, the oscilloscope
Aerospace 2023,10, 947 11 of 25
value was used for further processing. In case of unsuccessful shadowgraph, a comparable
shadowgraph of another shot was applied for the target fluence estimation.
Table 2.
Results for ablated mass
∆m
and respective roughness change
∆R
as well as for velocity and
temperature increments (
∆v
,
∆T
) for each polished sample at the given target fluence
Φtarget
. Note:
values marked with * are considered as outliers.
Shot-No. Material Φtarget ∆m∆Ra ∆v∆T∆Tcorr
[J/cm²] [µg] [nm] [m/s] [K] [K]
14
Aluminum
(11.73) 1290 218.71 0.267 0.55 0.58
36
Aluminum
5.22 160 163.86 0.613 n.a. n.a.
19 Copper 3.39 0 * 62.64 0.158 n.a. n.a.
23 Copper 6.32 21,070 * 53.36 0.126 0.80 0.84
39 Copper 10.48 20 83.94 0.141 n.a. n.a.
37 Steel 6.59 20 115.33 0.264 n.a. n.a.
42 Steel (8.84) 1920 125.97 0.333 0.84 0.88
18 Titanium 2.83 50 193.09 0.316 n.a. n.a.
21 Titanium 3.85 40 588.24 0.287 n.a. n.a.
38 Titanium 9.13 300 344.11 1.704 n.a. n.a.
43 Titanium 8.86 430 317.53 0.216 0.28 0.30
Table 3.
Results for ablated mass
∆m
and respective roughness change
∆R
as well as for velocity
and temperature increments (
∆v
,
∆T
) for each sandblasted sample at the given target fluence
Φtarget
.
Note: values marked with * are considered as outliers.
Shot-No. Material Φtarget ∆m∆Ra ∆v∆T∆Tcorr
[J/cm²] [µg] [nm] [m/s] [K] [K]
10
Aluminum
(10.72) 500 n.a. 0.788 n.a. n.a.
11
Aluminum
6.63 480 −620 1.044 0.20 0.21
44
Aluminum
12.412 790 −476.67 1.616 0.46 0.49
22 Copper 7.67 310 −65.33 0.619 n.a. n.a.
24 Copper 6.98 1090 −365.33 0.419 n.a. n.a.
45 Copper 4.17 850 −2 0.025 0.39 0.41
47 Copper 4.54 620 −32 0.095 0.85 0.89
30 Steel 2.33 360 +26.63 1.734 n.a. n.a.
31 Steel 9.89 480 +66.63 0.475 n.a. n.a.
46 Steel 8.41 30,330 * −46.7 0.199 0.44 0.46
25 Titanium 2.175 200 −159.97 0.047 n.a. n.a.
27 Titanium 2.023 540 −209.97 0.285 0.53 0.57
56 Titanium 7.205 870 −213.3 0.1637 0.52 0.55
5.1. Ablation Behavior
In order to evaluate the ablation behavior of the samples, we analyzed ablated masses
and the change in surface roughness between a surface before ablation and the sample.
The results are listed in Tables 2and 3. Samples which were exposed to similar fluences
range around similar mass losses and, thus, were well reproduced across the shots. We
find that the relation between ablated mass and fluence is not linear. This effect has been
described in the literature before [
49
]. Furthermore, we see that for polished samples,
discrepancies in ablated mass under similar conditions for copper and stainless steel
are immense.
These discrepancies are not reproduced in the roughness change, instead, changes in
surface roughness are rather low for both materials, while aluminum and titanium exhibit
relatively large changes. For roughness change, we find three cases. In case 1, the polished
samples became rougher, which is consistent throughout all polished samples. In the
second case, sandblasted surfaces become smoother. In case 3, sandblasted samples become
Aerospace 2023,10, 947 12 of 25
rougher. Case 3 only appears for stainless steel and within a narrow range of
±
100 nm; thus,
we consider these results as “no changes”. Regardless of the fluence, roughness changes
per material and sample above the ablation threshold are comparable.
Lastly, we investigated the hemispherical–directional reflectance as described in Section 2.3.
As a result, we found approximately a factor of 3 in reflectance between polished and
sandblasted surfaces for initial sample surfaces, referred to as reference samples, as listed
in Table 4. Comparing the sandblasted references and samples, the reflectances are almost
identical. In comparison, we found reduced reflectivity for polished samples between the
ablated sample surface and the reference. Here, we consider our sample materials fully
intransparent (transmission τ= 0) and, thus, the absorptivity A=1−R.
Table 4. Reflectances of the initial surfaces (reference) and the surfaces after ablation (sample).
Material Reference Reflectance Ablated Sample Reflectance
Polished Sandblasted Polished Sandblasted
Aluminum 0.85 0.37 0.79 0.33
Copper 0.94 0.41 0.84 0.46
Stainless Steel 0.63 0.2 0.62 0.22
Titanium 0.67 0.19 0.54 0.21
5.2. Laser-Induced Momentum and Heat
Thermal data were collected with the described sensor system (see Section 3.3). Mea-
surement data of all four PT1000 elements was averaged. To avoid external influences
due to surface contact of the sample with the vacuum chamber, we considered only the
first 350 ms, which is within the time frame of the samples’ free fall. Here, there are
100 ms before the laser interaction. To assure correct data in good approximation, we
recorded calibration curves for each sensor model in pre-experiments in our cleanroom
at DLR Stuttgart. For this, we applied the sensor together with the thermal tape on a
heated element in a vacuum chamber. The true temperature was logged by a calibrated
thermo-logger in close spatial proximity to the sensor also including the thermal tape. Not
all shots have been completed with the sensor applied. This is due to the fact that also
trajectories with pure targets, without the influence of the extra weight of the sensor were
demanded. Nevertheless, the sensor was designed to minimize weight while the relevant
components were placed to ensure a good overlap of the sample’s center of gravity with
the sensor’s one when the sensor is applied centric to the sample’s backface. More details
can be taken from [
24
]. Conclusively, one to three data points per material and surface are
provided, which still gives an indication of the thermal behavior. Furthermore, presumably
the laser-induced shock wave sometimes caused the sensor to detach from the sample’s
backside; thus, this data were not considered here. Discussion on mechanical shock is out
of scope for the present framework but will be considered in future work.
The measured residual heat
∆T
ranges between 0.2 K and 0.85 K, depending on
material, surface, and applied fluence, cf. Tables 2and 3. Thermal losses in the tape were
considered by calculating the heat
Q=cp·m·∆T
in sample and tape each, the corrected
value
∆Tcorr
is then used for further calculations. With these temperatures, an
ηres
between
2% and 12% have been calculated.
The velocity increment
∆v
is extracted from the high-speed video files by using the
motion tracking algorithm, cf. Section 3.2. The accuracy of the implemented motion
tracking algorithm was investigated by applying the second derivative on the fit function of
the gravity directed displacement vector. The chosen sequence is before the laser interaction
and ignores the first frames after release and the last ones before laser hit to ensure a stable
and continuous movement. The expected acceleration is a = g, which is gained to a good
approximation with an average acceleration of
a=
9.45
±
0.46 m/s
²
across all investigated
samples. A systematic error, explaining the offset of a to g = 9.81 m/s
²
, is expected due to
the short sequence under consideration. This leads to an average uncertainty of 5%, which
is expected for the measured velocities. Additionally, the triangulated tracks of the falling
Aerospace 2023,10, 947 13 of 25
sample are limited in their reproducibility due to the manual choice of the initial tracking
pixel and, in case of losing the tracked pixel, reselecting the very same pixel again. One
needs to note that due to overexposure from plasma, the tracked pixel always needs to be
re-initiated after ablation.
Equation (3) was used to calculate the momentum coupling coefficient. This coefficient
provides the information regarding how efficiently the laser energy is disposed into the
sample and converted to impulse. The sample mass
M
is measured with a precision scale
(cf. Appendix A.4) before and after the experiment. Laser energy E
L
is taken from the
measured spot profiles, described in Section 3.1. We used the calculated target energy and
fluence, respectively, for all further calculations. As the coupling coefficient scales linear
with the velocity increment, we also expect an error range of 5% for these results. Overall,
the calculated values for
cm
are between approximately 7 and 100
µ
Ns/J. Values higher
than 40 µNs/J for the given fluence range has been considered as outliers.
Fluence estimation of each shot shows a broad fluence range of 2 <
Φtarget
< 12.5 J/cm
2
,
which can be deduced to the imperfection of alignment during dropping and, therefore, not
exposing the sample surface completely and perpendicularly to the incoming laser beam.
Plotting
∆v
over
∆T
and comparing it with the respective calculated values shows
that the prediction of
∆v
is close to the measured values, cf. Figure 6. An underestimation
for all aluminum samples and sandblasted titanium samples as well as polished stainless
steel is found. Polished copper is well predicted. For the temperature increment, we found
higher discrepancies up to a factor of 3 to 5 between measurements and expected values
(cf. Equations (5) and (6) depending on most of the sample. A further error analysis is
performed in Section 6. Samples which provide two data points (Al, Cu, Ti; all sandblasted)
show consistency within each other.
Figure 6. Comparison of measured and calculated velocity and temperature increments.
5.3. Comparison with Simulations
The FEM simulation results for the laser parameters, mentioned in Section 2, are
depicted in Figure 7. The datafits of the simulation results have been computed using
the empirical fit functions from [
16
], cf. Appendix C, enabling us to derive the theoretical
values of imparted momentum and heat for the experimental targets, see below.
Aerospace 2023,10, 947 14 of 25
(a)
(b)
Figure 7.
FEM simulation results for (
a
) momentum coupling and (
b
) thermal coupling as a function
of incident fluence of a laser pulse with
τ
= 10 ns pulse duration at
λ
= 1064 nm wavelength. For data
fitting, empirical fit functions from [
16
] have been used. Simulation results for polished material are
denoted by full symbols, whereas the hollow symbols indicate results for computations where the
surface reflectivity was scaled according to the measurements; see text. Thermal and momentum
coupling derived from experimental results are depicted by full and hollow stars.
In the simulations, the initial reflectivity
Rsb
of the rough surfaces was assumed
to amount to
Rsb =RN
s
, where
Rs(T)
is reflectivity modeled for the solid phase, cf.
Appendix B. The exponent N has been derived from the experimental data shown in
Table 3, where similarly we assumed
Rsb =RN
pol
; hence, N virtually represents the average
number of reflections of a single ray on a rough surface.
Comparing the measured
cm
data with the simulations, one can see that simulation
and experiment are in good agreement, even though the experimental results underlie a
noticeable scatter. The aforementioned underestimation of
cm
(cf. Figure 5) is confirmed by
our measurements. While copper and stainless steel are mostly in good agreement, titanium
steel and aluminum are noticeably underestimated. The measured thermal coupling is in
general overestimated by the simulations for all samples.
5.4. Thermo-Mechanical Coupling Coefficient
The most interesting question of our research study was to identify how mechanical
coupling and thermo-coulpling are related. Therefore, we calculated
ctm
as described in
Aerospace 2023,10, 947 15 of 25
Equation (7). The results are displayed in Figure 8a. The calculated
ctm
for polished titanium
is in good approximation to the simulated values, while others are underestimated.
The simulation, cf. Figure 8b, firstly shows the obvious: the less energy is put into
heat, the more energy can be used to apply the desired velocity increment. This is valid
for all
ηres
> 0.1 for copper and titanium and
ηres
> 0.2 for aluminum and stainless steel.
Furthermore, it indicates that materials with higher heat capacity transform less energy
into momentum than samples with lower heat capacities. The measured data points are
too few to confirm this finding experimentally. However, considering the
ηres
being off by
a factor of 3 to 5 due to underestimation of the temperature increment, the measurement
points would align well. Here, too, aluminum and copper are predicted comparably well,
while stainless steel is underestimated and titanium overestimated.
(a)
(b)
Figure 8.
Comparison of (
a
) experimental thermo-mechanical coupling coefficients with simulated
data and (b) experimentally estimated and simulated coupling coefficients.
6. Discussion
Laser–matter-interaction experiments have been conducted at an experimental wave-
length of 1064 nm and an estimated fluence of 10 J/cm
²
. Pulse duration was set to 10 ns.
These settings were explicitly chosen since former studies indicate them as most reason-
able for a real-life scenario [
13
–
15
,
55
–
57
]. The existence of laser facilities like the National
Ignition Facility (NIF) [
58
] and the Laser Mégajoule (LMJ) [
59
] indicate that kJ-pulses at a
wavelength around 1
µ
m are technologically possible. These facilities operate on a nanosec-
Aerospace 2023,10, 947 16 of 25
ond base which gives a foundation for the assumption of a 10 ns pulse duration. Along
with this, fluences between 1 and 10 J/cm
²
are possible, which are in good agreement with
the required fluence for overcoming the ablation thresholds for metal materials [49].
During the laser–matter interaction, it was found that samples which have been ex-
posed to similar laser conditions show similar ablated masses and, thus, fulfil the expected
behavior. Surface roughness changes show a strong dependency on the initial state of
the sample surface and the sample material. This, we suspect, is due to the different
melting behavior of the materials. First of all, due to the inhomogeneous beam profile,
locally higher fluences can be expected, which would cause an imprint of the beam pro-
file’s “roughness” into a surface. This effect would be predominant on polished surfaces.
Secondly, a polishing effect on surfaces that have been sandblasted could be explained
by not melting the sample surfaces across a thickness higher than the roughness itself.
In other terms, only the roughness peaks are melting and thus flatten. Polishing effects are
most prominent for samples with a lower discrepancy between melting and boiling point,
e.g., for aluminum. For in-orbit applications, due to atmospheric aberrations, a “rough”
laser spot can be expected as well. Therefore, we expect target materials for laser-ablative
trajectory modification to alter their surface conditions towards higher roughness as well
while interacting with the laser source.
Integrating sphere measurements showed increasing absorbance of the laser energy
for increasing surface roughness. This can be explained by multiple reflections of the light
on microscopic scale. An increasing absorbance of the sample surfaces after the interaction
is observed for polished samples, except for stainless steel, while sandblasted samples
remain similar. Stainless steel’s behavior can be explained by the fact that it is the sample
which ablated the least material and conclusively is least responsive to laser momentum
transfer among the tested materials. Additionally, no measurable roughness changes were
found for it, which also indicates that its reflectivity and, thus, its absorbance, remain on
the same level.
Simulations regarding thermo-mechanical coupling have been conducted and com-
pared with experimental results. All in all, the experimental results for
∆v
and
cm
align well
with simulations. Experimental values for cmare scattering in good proximity around the
calculated curves. Offsets from the simulated data can be explained by inaccuracies from
the motion tracking due to noisy video files, losing and re-selecting the tracked pixel, and
tracking difficulties for tumbling objects, e.g., when the tracked point disappears for several
frames while the sample is flipping. The general underestimation of
∆v
is most likely
influenced by a systematic error that can be deduced from the slightly underestimated
values for gravitational acceleration. Furthermore, inaccuracies due to imperfect masking
of the spot profile could contribute here.
Temperature data
∆T
was overestimated by the simulation. To exclude artifacts due
to the sensor application by thermal tape, we computed the evolution of the temperature
distribution of target and tape using a simple one-dimensional FEM model. We found
equilibrium after approximately 100 ms, which is within the time frame of 250 ms after laser
hit and before the sample hits the chamber. The calculation shows that a small fraction of
the heat energy is stored inside the tape so that the temperature of the target itself (without
tape) is slightly underestimated by presumably less than 10%. The correction of the thermal
data approves this range. Effects of the bonding have been excluded, assuming perfect
bonding and no detachment during mechanical shock, which has been observed for some
measurements. Thus, only measurements that showed no detachment of the sensor in
the high-speed video files were considered. Nevertheless, reduced bonding, outside of
the detection of the camera, could lead to lower measured temperatures than the true
temperature. We observe higher discrepancies for sandblasted samples which could be
reasonable expecting higher mechanical shock due to better mechanical coupling.
Furthermore, the experimental result is strongly dependent on the angle under which
the target interacts with the laser. This situation is considered by extracting the target
fluence and assuming that the experimental data point under random laser–sample–
Aerospace 2023,10, 947 17 of 25
angle equals the data point of a simulated sample hit perpendicularly by a laser with
reduced fluence.
7. Conclusions
We conducted a laser–matter-interaction experiment at the site of GSI Darmstadt,
Germany, and compared the experimental data with results from FEM simulations. Metal
materials, namely aluminum, copper, titanium, and stainless steel, with two different,
defined surfaces were under investigation. We found higher thermal and mechanical
coupling of the laser for sandblasted surfaces, which, we conclude, is due to inter-surface
reflections in the microscopic pits of the surface. We found higher ablated masses for rough
surfaces, while the ablated mass depends on the material itself. The finding that the surface
roughness of polished samples increases significantly during the interaction suggests that
for a multi-shot interaction of the surface, the behavior would shift towards a rough surface
needs to be considered for ablative change of trajectory during multiple passes of a debris
particle. As the initial state of a material surface of a debris particle is unknown, the authors
recommend considering it as a rough surface for a conservative heating rates calculation
during trajectory modification. Furthermore, the experiments indicated higher applied
∆v
for rough surfaces. This would allow for a stronger trajectory modification of debris
particles with increasing surface roughness, either due to the laser–matter interaction itself
or interaction with its environment, but at the cost of a limited number of laser pulses per
pass due to the higher heating rates.
Thermo-mechanical coupling shows a material-dependent optimum value for an
ηres ≈
0.1 to 0.2 and a
cm
between 12
µ
Ns/J and 30
µ
Ns/J in simulations, considering the
experimental measurements being underestimated due to imperfect bonding of the thermal
sensor and its detachment due to mechanical shock. This led to an
ctm
ranging between
166 µNs/J and 5000 µNs/J.
We conclude that based on these findings, ground-based laser-ablative orbit mod-
ification appears to be feasible for metal debris fragments, especially since no sample
disintegrated for the tested fluences in our experiments. This, of course, should be verified
by further multi-shot experiments. Furthermore, we conclude a given relevance for object
identification for laser-ablative orbit modification.
8. Outlook
In this article, we only discussed single, plane, metal targets, while the analyses of
further samples from this experiment comprising composite materials, layered targets, and
plastics are in preparation to be published in the near future [60].
For future experiments, alternative ways of sample–sensor bonding would most likely
lead to more realistic measurements of
∆T
. Also, simulations of mechanical shock of a two
layer material could confirm the factor of delamination between sensor and sample.
To further validate the feasibility of laser-based trajectory modification, multi-material
and organic material simulations as well as mechanical shock simulations will be required
and, possibly, experimentally validated.
Author Contributions:
Conceptualization, D.K., S.S., R.-A.L., D.S. and M.R.; Data curation, D.K.,
E.K. and S.S.; Formal analysis, S.S. and E.K.; Funding acquisition, W.R. and T.D.; Investigation,
D.K., S.S., E.K. and D.S.; Methodology, D.K., S.S., E.K. (FEM simulation [
26
]), R.-A.L., D.S., F.S.
(thermal sensor [
24
]), K.K.S.(image processing [
23
]), M.Z. (image processing [
21
]) and L.S.; Project
administration and Resources, D.S., M.R., W.R. and T.D.; Software, S.S., E.K., F.S., K.K.S., M.Z. and
L.S.; Supervision, D.K., S.S., R.-A.L., M.R., M.K.B.-L., C.W., W.R. and T.D.; Validation, S.S., F.S.,
K.K.S., M.Z. and L.S.; Visualization, D.K., S.S., E.K., F.S., K.K.S., M.Z. and L.S.; Writing—original
draft, D.K. and S.S.; Writing—review & editing, D.K., S.S., E.K., R.-A.L., D.S., F.S., K.K.S., M.Z., L.S.,
M.R., M.K.B.-L., C.W., W.R. and T.D. All authors have read and agreed to the published version of
the manuscript.
Funding: This research was enabled by institutional funding.
Aerospace 2023,10, 947 18 of 25
Institutional Review Board Statement: Not applicable.
Data Availability Statement: Upon reasonable request.
Acknowledgments:
The authors gratefully want to thank Fabian Isensee and Ole Johannsen from
Helmholtz Imaging for assisting in optimization of the motion tracking algorithm. Further gratitude
goes to Anja Jenner for supporting our experiment preparation. We thank Martin Metternich and
Haress Nazary from GSI for supporting the experimental procedure. Also, we thank Samantha
Siegert for proofreading the manuscript.
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or
in the decision to publish the results.
Abbreviations
The following abbreviations are used in this manuscript:
MDPI Multidisciplinary Digital Publishing Institute
DLR German Aerospace Center
LEO Low Earth Orbit
GSI Gesellschaft für Schwerionenforschung
nhelix Nanosecond High Energy Laser for Heavy Ion Experiments
GPS Global Positioning System
NASA National Aviation and Space Agency
ESA European Space Agency
BNC Bayonet Neill Concelman, coaxial cable connector
ND Neutral Density
COG Center of Gravity
GUI Graphical User Interface
WLIM White Light Interferometer
FEM Finite-Element Method
Al Aluminum
Fe/Steel/AISI304 Iron/Stainless Steel
n.a. Not Available
EMCCD Electron Multiplying Charged-Coupled Device
ROI Region of Interest
pol Polished
sb Sandblasted
NIF National Ignition Facility
LMJ Laser Mégajoule
Appendix A. Equipment
Appendix A.1. Schematic Set-Up
The following schematic drawing, cf. Figure A1, shows the details of the experimental
set-up. It depicts where the elements of the set-up are positioned. One can see that the
dropping arm is mounted in the center of the vacuum chamber under an angle so that the
laser will not interact with the mechanical structure. This angle is compensated by the
rotation of the actual sample holder. The laser beam enters the chamber from above and
redirected towards the sample plane by a further mirror. A lens focuses the beam such
that the required laser diameter is provided in the sample plane. An identical light path is
installed outside the chamber for documenting the laser profile. The vacuum chamber is
illuminated by a light source from above as well. The high-speed cameras are positioned
as depicted.
Aerospace 2023,10, 947 19 of 25
Figure A1. Schematic of the experimental dropping arm set-up.
Appendix A.2. Andor iXon Ultra
The applied camera for documenting the laser profile is an Andor iXon Ultra 897
EMCCD camera. The integrated sensor is 512
×
512 pixels, which limits the resolution of
the laser spot increment that can be extracted. Each pixel has a size of 13 µm.
For calibration, the noise, consisting of sensor and environment prior to the experiment
is recorded, by taking a frame without releasing the laser. This is referred to as our
experimental background and is substracted from each data frame. To calibrate the true
distance in diameter on the dimensions of the chip, a scale paper with squares of 1 mm
size has been photographed. An algorithm then calculates the mm-to-pixel scale factor to
estimate the true dimensions of the laserspot.
Appendix A.3. High-Speed Cameras
For stereoscopic measurements of the sample trajectory, we used two high-speed
cameras (MotionScope M3 and OS7 IDT Vision). While the OS7 camera captured the
falling samples with a framerate of 2000 fps, the framerate of the M3 camera was limited to
1000 fps for the required region of interest (ROI). Both cameras had an illumination time
of 400
µ
s. The motion-tracking process was performed based on a framerate of 2000 fps,
and the pixel positions of each tracked object feature in the M3 frame were interpolated for
the instants between captured images. To assure parallel recording of both systems, both
cameras received the same trigger signal from the Arduino controller. Their temporal offset
was considered in the post-processing of the oscilloscope information, which recorded
the incoming trigger signal for each camera. The temporal offset between trigger instants
of both cameras was considerably low and evened out by interpolation. Both cameras
captured monochrome images, which came with the advantage of moderate requirements
to the lighting conditions.
Appendix A.4. Sartorius CPA225D
The applied analytical balance is a Sartorius CPA225D with a capacity of 40 g and a
readability of 10
µ
g with a reproducibility of +/
−
20
µ
g. For measuring the ablated mass,
Aerospace 2023,10, 947 20 of 25
the samples were weighted before and after experiment. For defining uncertainty, we
measured a “light sample” (polyimide foil), a “medium sample”, (PFTE) and a “heavy
sample” (titanium) frequently during the 3-week period of the experiment to validate the
stability of the data. All samples provided the same dimensions. Furthermore, we took a
series of 10 measurement to confirming data reproducibility, which led to the following
results, cf. Table A1.
Table A1. Balance accuracy.
Titanium PTFE Polyimide
Average mass [g] 1.447919 0.727215 0.029277
Stand. dev. [g] 5.4 ×10−61.2 ×10−56.4 ×10−6
Error [g] 1.7 ×10−63.8 ×10−62.0 ×10−6
Appendix A.5. White Light Interferometer (WLIM) Wyko NT9100
Our WLIM provided us with the possibility of a contactless measurement of the
sample surface roughness. The device allows for measurements between sub-nanometer
region up to the mm region. To achieve a good averaging across the surface, we applied
a low magnification of 2.5 and a sampling of 3.96
µ
m for rough samples and 971 nm for
polished samples. Data were taken at 3 points each.
Appendix B. Temperature Dependence of Simulation Parameters
Optical properties of target and ablation jet depend significantly on the temperature
which, in turn, has a strong impact on heat transfer during the laser pulse, thus constituting
the laser–matter interaction. These dependencies are incorporated in our simulations based
on the relations outlined in the following:
The reflectivity for perpendicular light incidence is calculated by
R= ((n−
1
)2+
k2)/((n+
1
)2+k2)
[
61
] and the absorption coefficient using
α=
4
πk/λ
, where
n∗=
n+ik =√ε∗
is the complex refractive index of the material. For the computation of the
temperature dependency of R and
α
in solid metals following [
62
],
n∗
has to be known for a
reference temperature
Tre f
. Then, R and
α
can be computed as a function of the temperature
T using
ne(T) = ρ(T)/ma·Nv
where n
e
is the electron density and N
v
denotes the number
of valence electrons per atom. From this, the plasma frequency
ωp
of the electron gas can
be derived by
ωp(T) = pe2(ne(T))/(mee0)
yielding the collision frequency
ωc
(T) in the
electron gas given by
ωc(T) = ωc(Tre f )T5RΘD/T
0z4
ez−1dz
T5
re f RΘD/Tre f
0z4
ez−1dz
, (A1)
where ΘDis the Debye temperature. Thus, the complex dielectric constant [49]
ε∗(T) = 1−ω2
p
ω2+ω2
c
+iω2
p·ωc
ω2+ω2
c·ω(A2)
can be computed where
ω= (
2
πc0)/λ
is the angular frequency of the laser light with the
wavelength
λ
and
c0
denotes the speed of light in vacuum. Eventually,
R(T)
and
α(T)
can
be obtained from ε∗(T)using the above-mentioned relations.
It should be noted, however, that this procedure demands proper initialization data
for
n∗(Tre f )
, otherwise backwards computation of
n∗
at the reference temperature T
re f
from Equations
(A1)
and
(A2)
yields inconsistency obtaining
˜
n∗
mod(Tre f ) = ˜
n∗[ε∗(Tre f )] 6=
n∗
exp(Tre f )
. Therefore, consistency with the model assumptions is achieved using
n∗
exp
and
˜
n∗
mod
as a starting point for an iteration to derive an adapted value of
n∗
mod(Tre f )
, which is
in line with the considerations given by Equations
(A1)
and
(A2)
. The resources employed
for the experimental data are [
63
] for Al, [
64
] for Cu, [
65
] for Fe, and [
66
] for Ti. For the
Aerospace 2023,10, 947 21 of 25
computation of R and
α
in the liquid phase, we follow Siegel’s approach [
67
], replacing
ΘD
in Equation (A1) with the Percus-Yevick temperature
ΘPY
. The temperature dependency of
ΘPY can then be computed using
ΘPY(T) = ΘPY(Tm)sT
Tm
3
sρ(T)
ρ(Tm)2
, (A3)
where the data for ΘPY(Tm)are taken from the tabulated values given in [67].
To compute the laser absorption inside the ablation jet, we determine the mean ioniza-
tion fraction
ηi
as a function of incident laser fluence
Φ
and pulse duration
τ
. Following [
25
],
we restrict our considerations on single-state ionization and solve the set of the general gas
equation, cf. Equation (17), together with the Saha equation:
ne=v
u
u
tn0·2u1
u02πmekBT
h23
2exp−W1,0
kBT(A4)
for the particle density
n0
of neutrals and
ne
of electrons, respectively, where
me
is the
electron mass in order to obtain
ηi=ne/(ni+n0) = ne/(ne+n0)
. In this computation,
the first ionization potential
W1,0
as well as the quantum mechanical weighting functions
u0
and
u1
are taken from [
68
]. As estimates for temperature T and pressure p in the plume
we employ Phipps’ approximations for the electron temperature, assuming local thermal
equilibrium (which is a rather rough, but nevertheless, bearing assumption), and the
ablation pressure given in [69] by
p=5.83A−1
8Ψ9
16 I3
4(λ√τ)−1
4, (A5)
and
T=2.98 ·104A1
8·(Z+1)−5
8Z3
4(Iλ√τ)−1
2(A6)
using
Ψ=A
2·3
pZ2(Z+1), (A7)
where
A
is the atomic mass number,
I=Φ/τ
denotes the laser pulse intensity assuming a
square laser pulse. Note that Equations
(A5)
–
(A7)
are not invariant as regards the employed
unit system but refer to me,kB, h, W1,0, p, I, and λgiven in cgs-units.
From these considerations,
ηi
(
Φ
) can be computed to eventually derive the absorption
coefficient αpdue to inverse Bremsstrahlung via [49]
αIB =C·λ3Z2nine
√T1−exp−¯hω
kBT, (A8)
where
C≈
1.37
·
10
−35
,
λ
is the laser wavelength (in microns),
ne
and
ni
are electron and
ion number density, respectively, and
Z=ne/ni
denotes the mean ionization state in the
plume. Note that
αIB
,
ne
, and
ni
are given in cgs-units in Equation (A8).
¯h=h/
2
π
is the
reduced Planck constant, while
ω= (
2
πc0)/λ
is the angular frequency of the laser light
where
c0
denotes the speed of light in vacuum. In sum, this allows us to compute the laser
light absorption inside the ablation jet for the specific laser irradiation parameters
λ
,
τ
,
and
Φ
as a function of particle density and temperature, which are variables solved for in
the FEM simulation.
Aerospace 2023,10, 947 22 of 25
Appendix C. Fit Functions
FEM simulation data on thermo-mechanical coupling have been fitted using the em-
pirical functions given in [
16
]. The respective fit parameters for momentum coupling with
cm(Φ)≈Φ−Φ0
∆Φ + (Φ−Φ0)·b·12.46 ·A7
16 ·√τ
λ·Φc
, (A9)
where
b
can be understood as the optimum magnitude of momentum,
∆Φ
is related to
the difference between the fluence for momentum coupling and the ablation threshold, c
indicates the impact of plasma shielding, and A is the atomic mass in amu. Fit results are
shown in Table A2. Note that
Φ
is given here in J/cm
2
, whereas SI units are used for all
other quantities. Moreover, Equation (A9) is valid for Φ⩾Φ0only.
Table A2.
Parameters from non-linear fits of Equation (A9) to the FEM simulation results shown
in Figure 7a for aluminum (Al), copper (Cu), iron (Fe), and titanium (Ti). Reflectivities obtained
from the method shown in Appendix Chave been employed for polished surfaces, denoted as “pol”,
whereas in the simulations for sandblasted surfaces, denoted as “sb”, we used the scaling method
described above.
Material Surface ∆Φ b c Φ0
[J/cm2][µNs/J] [-] [J/cm2]
Al pol 2.18 0.097 0.52 2.81
Al sb 4.33 0.093 0.65 1.54
Cu pol 1.88 0.105 0.39 7.68
Cu sb 4.45 0.104 0.59 2.89
Fe pol 2.17 0.110 0.44 1.99
Fe sb 2.24 0.108 0.47 1.49
Ti pol 5.27 0.321 0.36 1.47
Ti sb 4.57 0.320 0.35 1.34
For the coefficient of residual heat, we used
ηres(Φ)≈a0+a1Φ+a2Φ2
1+a3Φ+a4Φ2+a5Φ3(A10)
with arbitrary parameters
a(0−5)
which holds for
Φ⩾
0. The respective results are shown
in Table A3.
Table A3.
Parameter from non-linear fits of Equation (A10) to the FEM simulation results shown
in Figure 7b for aluminum (Al), copper (Cu), iron (Fe), and titanium (Ti). Reflectivities as obtained
from the method shown in Appendix C have been employed for polished surfaces, denoted as “pol”,
whereas in the simulations for sandblasted surfaces, denoted as “sb”, we used the scaling method
described above.
Material Surface a0a1a2a3a4a5
[-] [J−1cm2] [J−2cm4] [J−1cm2] [J−2cm4][J−3cm6]
Al pol 0.040 −0.045 0.015 −0.567 0.075 0.0061
Al sb 0.180 −0.037 0.054 −0.577 0.149 0.0291
Cu pol 0.024 −0.010 0.0013 −0.219 0.012 0.0003
Cu sb 0.257 0.049 0.0017 −0.130 0.039 0.0004
Fe pol 0.048 −0.074 0.067 −0.637 0.112 0.0344
Fe sb −0.049 2.417 1.364 6.140 −0.282 1.0584
Ti pol 0.036 0.161 0.102 −0.407 0.261 0.1224
Ti sb 0.402 −0.012 0.178 0.043 0.035 0.2141
Aerospace 2023,10, 947 23 of 25
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