Coulomb acceleration of protons with a free-electron laser · X-ray free electron lasers (XFELs)...
Transcript of Coulomb acceleration of protons with a free-electron laser · X-ray free electron lasers (XFELs)...
Coulomb acceleration of protons with a free-electron
laser
Prospects for nuclear fusion
Elsa Caroline Souto Gonçalves de Abreu
Dissertação para a obtenção do grau de mestre em
Engenharia Física Tecnológica
Júri
Presidente: Prof. João Seixas
Orientador: Profª. Marta Fajardo
Vogais: Prof. Luís O. Silva
Julho de 2007
2
Acknowledgements
A big thank you to Nicusor Timneanu, my (co)supervisor here in Uppsala, for all the
help and the discussions, and to Marta Fajardo, my supervisor in Lisbon, who first made me
think of coming to Uppsala, and who helped me to make it happen. Thank you Magnus
Bergh, for the big help with Cretin, and thank you Janos Hajdu for comments and motivation.
The experiments at FLASH would not have been possible without the help of our
collaborators: Ryszard Sobierajski, Thomas Möller and Matthias Höner, the LLNL/Uppsala
collaboration, Björgvin Hjörvarsson, and Libor Juha. Thank you all.
I would also like to acknowledge the European project TUIXS for financial support
during my stay in Uppsala.
And last but not least, thank you all of you who, inside or outside the lab, in Sweden
or in Portugal, helped me enduring the winter and enjoying the summer, during this year in
Uppsala.
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Index
Abstract 4 Resumo 5 Figures and tables 6 Abbreviations 8 1 Introduction 9 2 Theory 11
2.1 Fusion reactions 11 2.2 Ionization mechanisms 13 2.3 Simulation models 14
2.3.1 Molecular dynamics simulations 14 2.3.2 Non-LTE plasma simulations 15
3 Experiments: background information 17
3.1 XFEL: working principle 17 3.2 Experiments on solids 19 3.3 Experiments on gas clusters 22
4 Results and analysis, for solids 24
4.1 Experiments on solids 24 4.1.1 General analysis 25 4.1.2 Light ions energy analysis 28 4.2 Simulations 34 4.2.1 Interaction of the FEL pulse with solid samples 35 4.3 Preliminary results on gas clusters 42
5 Discussion 45 6 Conclusions and outlook 47 References 48 Appendix A 50 Appendix B 51
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Abstract
X-ray free electron lasers (XFELs) are a new kind of light source, capable of
producing super-brilliant, ultra-short X-ray pulses with more than 10 orders of magnitude
higher peak brilliance than pulses from synchrotron sources. This extremely high peak
brilliance allows us to deposit huge amounts of energies into the sample over a very short
time, and will revolutionize many areas of physics, chemistry and biology in applications like
the imaging of single biomolecules, or the creation of highly ionized dense states of matter.
Molecular dynamics simulations, performed in Uppsala in the context of imaging
biomolecules, have predicted the ejection of protons with unexpectedly high energies, of the
order needed for fusion reactions. These protons are expelled from a nanometer-sized
sample in a Coulomb explosion, caused by interaction with an XFEL beam. This motivated
experiments at the FLASH facility, in Hamburg to study the interaction of the XFEL beam with
both solid and clustered gas samples, and to look for signatures of highly energetic protons or
deuterons, produced during the Coulomb explosion of samples rich in hydrogen or deuterium.
The energies detected, in the solid case, were high enough to support the hypothesis of
fusion. These results were analyzed and compared to predictions from a plasma code.
Improvements are still needed, mainly in an experimental point of view, and some of
them are suggested here; however the way is opened for a very exciting new area of
research related to XFELs.
Key words: X-ray free electron laser (XFEL), fusion, Coulomb Explosion, TOF (time-of-flight),
plasma simulations, Molecular Dynamics
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Resumo
Os lasers de electrões livres emitindo nos raios-x (XFELs) são uma nova fonte
luminosa, capaz de produzir impulsos ultra-curtos e extremamente brilhantes, na gama dos
raios-x, com uma intensidade 10 ordens de grandeza superior à dos sincrotrões. Enormes
quantidades de energia são depositadas nas amostras num espaço de tempo muito curto, o
que constitui uma revolução em diversas áreas da física, química e biologia, nomeadamente
para a obtenção de imagens de biomoléculas ou para a criação de estados altamente
ionizados na matéria.
Em simulações de Dinâmica Molecular, realizadas em Uppsala, foram observados
protões altamente energéticos, com capacidade para participar em reacções de fusão. Os
protões provêm da explosão, por efeito do potencial repulsivo de Coulomb, de uma amostra
nanométrica atingida pelo feixe do XFEL. Os resultados das simulações levaram à realização
de experiências no FLASH, em Hamburgo, com o intuito de procurar assinaturas deixadas
por protões ou deuterões altamente energéticos, produzidos durante a explosão de amostras
– sólidos ou clusters de gases – ricas em hidrogénio e deutério. As energias detectadas no
caso dos sólidos são suficientes para justificar a hipótese de fusão. Estes resultados foram
analisados e comparados com simulações feitas usando um código de plasma.
São ainda necessários melhoramentos, nomeadamente do ponto de vista
experimental, e alguns serão sugeridos neste estudo. No entanto, a porta está aberta para
uma nova e fascinante área de investigação relacionada com os XFELs.
Palavras-chave: Laser de electrões livres nos raios-x (XFEL), fusão, explosão de Coulomb,
TOF (time-of-flight: tempo de voo), código de plasma, Dinâmica Molecular
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Figures and tables
Figures
Figure 1: MD simulation of radiation-induced Coulomb explosion of a small protein molecule
(lysozyme) 9
Figure 2: High-energy protons leaving the molecule very early during the explosion. 9
Figure 3: Simple schemes of the photoabsorption and Auger emission processes. 14
Figure 4: Detailed scheme of the FLASH line, where the XFEL beam is produced 17
Figure 5: Scheme of an undulator 18
Figure 6: Radiation from a non-relativistic and relativistic accelerated electron 18
Figure 7: Microbunching process 19
Figure 8: Picture of the sample holder, with the samples used in September 2006 20
Figure 9: Left: picture of the inside of the chamber, with the sample holder mounted, although
not in the final position. Right: scheme of the geometry of the interaction 20
Figure 10: Picture and scheme of the Warsaw TOF detector, used during the September
2006 experiments at FLASH 21
Figure 11: Setup of the March 2007 gas experiments at FLASH and scheme of the Berlin
TOF detector used 22
Figure 12: TOF spectra for NbH, NbDH and PMMA 24
Figure 13: First step in the determination of the present ion species 26
Figure 14: Nomarski differential interference contrast microscope (x100) pictures taken from
PMMA and NbDH samples 28
Figure 15: Top: Direct TOF output for a single FEL shot on an Nb sample. Bottom:
Corresponding energy distribution for H+ ions and a multiple Gaussian fit 29
Figure 16: Top: Direct TOF output for a single FEL shot on an NbD sample. Bottom:
Corresponding energy distribution of the H+, D
+, D2
+ and Nb
+ peaks from fitted Gaussians 30
Figure 17: Intensity dependence of the three hydrogen subpeaks, in Nb, based on three FEL
shots 31
Figure 18: a: Intensity dependence of the kinetic energy for the three kinds of H+ ions in NbH
(green) and Nb (red). b: Intensity dependence of the kinetic energy for the H+, D
+ and D2
+ ions
in NbDH. 32
Figure 19: Intensity dependence of the three peaks (from left to right: H, C and O) of the
PMMA, based on three FEL shots 34
Figure 20: Simulated beam intensity dependence for Nb, at 21nm, with and without taking the
continuum lowering effect into account 36
7
Figure 21: Top: simulated beam intensity dependence of the kinetic energy in PMMA. Bottom:
simulated dependence of the kinetic energy on the sample used, for fixed beam energy of
75!J. 37
Figure 22: Simulated ionization levels for Nb, at 21 nm, as calculated by Cretin, for a beam
energy of 20!J or 100!J 39
Figure 23: Dependence of the ion kinetic energy as a function of depth, for several beam
intensities, simulations performed on Nb. 39
Figure 24: Simulated electron temperature, average ionization and ion kinetic energy for Nb,
NbD, NbDH, NbH and PMMA, at 21nm, with a beam energy of 100!J. 40
Figure 25: Simulated absorption for Nb, NbD, NbDH, NbH and PMMA, at 21nm, with a beam
energy of 100 !J 41
Figure 26: Attenuation length for Nb and PMMA between 1 and 40 nm 42
Figure 27: Methane data for a backing pressure of 1.2 bar and 10 bar 43
Figure 28: Intensity depence of the H+ ions energy, for a backing pressure of 10 bar 44
Tables
Table 1: Cross section values for fusion reactions involving two hydrogen isotopes, at 10 keV
and 100 keV 12
Table 2: Ionization values for the ions relevant in the context of this experiment. 38
8
Abbreviations
XFEL X-ray Free Electron Laser
FLASH Freie Elektronen Laser in Hamburg
DESY Deutsches Elektronen Synchrotron
MD Molecular Dynamics
LTE Local Thermodynamic Equilibrium
SASE Self Amplified Spontaneous Emission
LINAC Linear Accelerator
PMMA Polymethyl Methacrylate
TOF Time Of Flight
GMD Gas Monitor Detector
FWHM Full Width at Half Maximum
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1 Introduction
X-ray free electron lasers (XFELs) can reach much higher beam intensities at much
shorter wavelengths than usual lasers, and allow huge amounts of energy to be deposited
into a sample during a few femtoseconds. FLASH (“Freie Elektronen Laser in Hamburg”),
located at DESY (“Deutsches Elektronen Synchrotron”), in Hamburg, is the only operational
FEL reaching into the soft x-ray regime [1]. Hard X-ray FELs (down to 1.0Å predicted) are
being built in Stanford, California (LCLS – Linac Coherent Light Source) [2], and in Hamburg,
Germany (European XFEL) [3], and should be ready for operation in 2009 and 2013,
respectively. A third XFEL is being constructed in Japan (SCSS – Spring-8 Compact SASE
Source), and has reached saturation at 40nm wavelength during initial operations [4].
X-ray frequencies induce different processes in materials than optical frequencies, in
a laser-matter interaction. Inner shell ionization processes, such as photoemission and Auger
electron emission or fluorescence, dominate over outer shell processes; on the other hand,
optical nonlinearities, such as multiphoton absorption and free carrier absorption (inverse
Bremsstrahlung) lose part of their relevance, at x-ray frequencies [5]. Processes like Coulomb
Explosion are thus altered, and must be studied in this new context.
Figure 1: MD simulation of radiation-induced Coulomb explosion of a small protein molecule (lysozyme). White balls: H, Gray: C, Blue: N, Red: O, Yellow: S. Integrated X-ray intensity: 3.10
12(12keV) photons/100 nm diameter spot. The picture shows the protein exposed to a 2 fs FWHM
X-ray pulse, and its disintegration followed in time. The atomic positions in the first structures are practically identical at this pulse length due to an inertial delay in the explosion. Hydrogen ions and
highly ionized sulphurs are the first to escape the immediate vicinity of the protein. The encircled stage is shown in detail in Figure 2.
Figure 2: High-energy protons leaving the molecule very early during the explosion (encircled
stage from Figure 1). The energy of the fast escaping protons strongly depends on their original chemical environment. In the case of lysozyme, two protons shoot out at very high energies already at the beginning of all simulations (they are outside the picture frame in Figure 1). These protons are attached to two specific sulphur atoms in the native protein, and leave in the same direction in a reproducible manner.
Molecular Dynamics simulation of Coulomb explosion of lysozyme. Two high energy protons from the vicinity of specific sulphurs leave the molecule very early. XFEL: 3x1012 (12 keV) ph/100 nm diameter
Molecular Dynamics simulation of Coulomb explosion of lysozyme. Two high energy protons from the vicinity of specific sulphurs leave the molecule very early. XFEL: 3x1012 (12 keV) ph/100 nm diameter
Molecular Dynamics simulation of Coulomb explosion of lysozyme. Two high energy protons from the vicinity of specific sulphurs leave the molecule very early. XFEL: 3x1012 (12 keV) ph/100 nm diameter
10
The use of XFELs has been proposed to achieve single-shot high-resolution images
of molecules [6], the final goal being to image macromolecules and living cells with atomic
resolution. Molecular dynamics (MD) simulations of the Coulomb explosion of a molecule [5,
7], presented in Figure 1, were made in the context of the imaging experiments. A sample is
hit by a 2 fs XFEL beam and loses its electrons. It then explodes, given the repulsive
Coulomb interaction between the remaining positive ions, but only after the end of the pulse,
i.e. an image taken during the illumination of the sample shows it unchanged. Figure 2
corresponds to the encircled stage in Figure 1, and shows the unexpected acceleration of
light ions, which follows the Coulomb explosion.
This observation set the possibility of accelerating protons or deuterons to KeV
energies, in a few femtoseconds, by means of the interaction of solid or clustered samples
with an XFEL beam. Deuterons accelerated to such energies are in good conditions to
undergo DD fusion reactions [5]. On a longer term, the aim will be to detect signatures of the
following reaction [8]:
D + D!3He + n , (1)
in the form of 2.45MeV neutrons and 0.82MeV alpha particles. The best candidates are
neutrons, neutral particles which can easily escape the interaction region, and which leave
with an energy characteristic of the reaction. Reaction (1) occurs along with a second one
D + D! T + p , (2)
with the same probability [8].
Intercluster fusion studies have been made, both theoretically [9] and experimentally
[9, 10] and so have intracluster fusion studies [11], on a theoretical level, based on the
interaction of ultra-intense optical/IR lasers with matter. However, in this case, the shift to x-
ray frequencies, keeping a high intensity and a pulse duration of a few femtoseconds, makes
the situation totally distinct, and opens the door to challenging new processes.
In the following sections, preliminary experiments are described, on the interaction of
an XFEL beam with solid samples and gas clusters. Very exciting results are presented and
analyzed, mainly in the case of the solids. Nevertheless, questions remain to be answered,
and improvements to be made, which are addressed later in this study.
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2 Theory
2.1 Fusion reactions
The aim of this study is to achieve fusion reactions, driven by the interaction between
an XFEL beam and a solid sample or a gas cluster. A brief summary of this kind of reactions
will therefore be given [8].
A nucleus of atomic number Z and mass number A has a mass whose value differs
from the sum of the masses of the protons and neutrons that constitute it by an amount
�
!m ,
given by:
�
!m = Zmp + (A " Z)mn "m , (3)
where
�
mp is the mass of the proton,
�
mn the mass of the neutron and
�
m the mass of the
nucleus.
�
!m is related to the nuclear binding energy B by
B = c2!m . (4)
The energy per nucleon,
�
B A , when plotted as a function of A, exhibits a maximum
for
�
A = 56. The existence of this maximum motivates fusion and fission reactions, since light
nuclei tend to fuse, and heavy nuclei to break, in order to reach a more stable configuration,
characterized by a higher value of
�
B A .
An important parameter in fusion reactions is the cross section
�
! , which has the
dimensions of an area, and measures the probability of occurrence of the reaction, per pair of
particles.
An average reactivity or reaction rate can be computed from the cross section
�
! and
the velocity
�
v of the incident nucleus (the target nuclei are assumed to be at rest), and is
given by:
!"v# = " (v) v f (v)dv0
$
% , (5)
where f is the velocity distribution of the incident particles.
Deuterium and tritium (two hydrogen isotopes) are generally used in fusion
experiments, instead of hydrogen, because of their higher cross-section at low temperatures.
Table 1 shows several cross section values for hydrogen isotopes fusion reactions, at
10KeV and 100KeV . Reaction b. is chosen for laboratory fusion experiments since its
cross section is higher than in reaction a., deuterium is easier to obtain than tritium, and both
products of the reaction are non-radioactive, and easy to detect (especially neutrons).
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Reaction !@10 keV
(barn)
!@100 keV
(barn)
�
!max
(barn)
�
!max
(KeV)
a.
�
p + p! D+ e+
+ "
�
3.6.10!26( )
�
4.4.10!25( )
b.
�
D+ D!3He + n
�
2.78.10!4
�
3.7.10!2
0.11 1750
c.
�
D+ D! T + p
�
2.81.10!4
�
3.3.10!2
0.096 1250
d.
�
D+ T!4He + n
�
2.72.10!2
�
3.43 5.0 64
e.
�
T + T!4He + 2n
�
7.90.10!4
�
3.4.10!2
0.16 1000
Table 1: Cross section values for fusion reactions involving two hydrogen isotopes, at 10 keV
and 100 keV. Also shown are the maximum value for the cross section, and the energy for which that
value is achieved. (Data from [8]) (
�
1barn =10!24cm
2)
Zweiback et al. [12] have derived the kinetic energy distribution from an exploding
cluster. Assuming that the cluster ionizes faster than it explodes, the potential energy of a
deuteron (charge e) on the surface of the cluster – which is the same as its kinetic energy
after the explosion – is given by Coulomb’s law:
E(r) =1
4!"0
eQcluster
r=
1
4!"0
1
re2 #q$n
4
3!r3 =
en#q$r2
3"0
,
i.e. Emax
=en!q"r
max
2
3#0
, (6)
where e is the elementary charge, Qcluster the charge of the cluster, n the particle density in
the cluster,
�
q the average charge of a particle,
�
rmax
the radius of the cluster, and
�
!0 is the
vacuum permittivity.
The aim is, therefore, to maximize n,
�
q and
�
rmax
. The use of an XFEL as a light
source (with short pulses) allows for a faster ionization of the sample, up to higher values,
which corresponds to an increase in
�
q , for given values of
�
rmax
and n; increasing
�
rmax
can
only be achieved by increasing the cluster size, while maintaining n, i.e. by optimizing the
parameters of cluster generation; the density n can be increased by compressing the clusters,
or by the use of solid samples. As described below, both approaches have been used, in the
experiments presented in this study, and will keep being used throughout the project. With
solid samples, high densities are attained much more easily than with gas clusters; on the
other hand, clusters are like “nano-labs” [13], which suffer very little from the influence of the
surroundings.
Ions located deeper inside the cluster will be characterized by a different potential
energy value, with a distribution such that
�
p(E)! E , for
�
E < Emax
, (7)
since p(r) = 4!r2n, r " r
max
13
This distribution can be shifted towards
�
Emax
if heteroclusters are used, since heavier
atoms will serve as a catapult for lighter ones, which will have their kinetic energy increased.
[14]
2.2 Ionization mechanisms
The goal of the current work is to study the energies of ions ejected from a sample,
after its ionization by an XFEL beam. Some ionization mechanisms must therefore be referred
to, from a general point of view, before the discussion itself.
One of the main ionization mechanisms consists of the photoelectric effect, depicted
in Figure 3. An incident photon removes a bound electron from an atom. This electron will
leave with a kinetic energy
�
Ek corresponding to the difference between the incident photon
energy
�
E! and the ionization energy of the bound level the electron came from
�
En:
Ek= E! " En
= h# " En
, (8)
where h is the Planck constant and
�
! the photon frequency.
In the case of hard X-rays, a hole is left in a low-laying orbital in the electronic
structure of the ionized atom, which is therefore in an excited state. Two ways are possible, to
go back to the ground state. On the one hand, a higher energy electron can fall to the lower
empty energy level by emitting a photon, whose energy corresponds to the difference
between the two electronic levels, in a process known as fluorescence. On the other hand,
the energy lost by the electron that fills the vacancy can be transmitted to another electron,
known as Auger electron (Figure 3), which in turn leaves the atom. It will have a kinetic
energy
�
Ek
A corresponding to the difference between the decaying electron initial energy level
�
En and the Auger electron initial energy level
�
En
A.
�
Ek
A= E
n! E
n
A. (9)
If the ionization process is fast, as happens when one has energetic photons and
high beam intensities, a plasma is formed in the interaction region, where the electrons have,
at first, a higher temperature than the ions, and a lower mass. They will thus fly out first, and
leave behind a highly positively charged material. The positive charges will then repel each
other and be accelerated, in a so-called Coulomb explosion. When heavier and more highly
charged ions are also present, this repulsion can act like a catapult for light ions, such as
hydrogen and deuterium,
14
Figure 3: Simple schemes of the photoabsorption (left) and Auger emission (right) processes.
During photoabsorption an incoming photon transfers its energy to a bound electron (from the inner
shell, in the case of hard x-rays), which leaves the atom. An electron coming from a higher orbital then
decays to fill the vacancy left by the photoelectron, and the gained energy can be used to remove an
electron – known as Auger electron – from an intermediate level (in the outer shell, in this case).
2.3 Simulation models
2.3.1 Molecular dynamics simulations
MD simulations have been performed, in an earlier stage, using the Gromacs code
[15].
Molecular dynamics aims at predicting macroscopic properties of systems, and follow
the kinetics of atomic and molecular processes, making use of realistic atomic models. More
generally, these simulations use as an initial input the potential of interaction, which depends
on atomic positions, and the positions r and velocities v of all atoms in the system. Different
forces are then computed: forces between non-bonded pairs (van der Waals and Coulomb
interactions), forces due to bonded interactions, and restraints (both for position and
distance). Finally, the atoms move according to Newton’s equations of motion, thus updating
the system configuration.
In spite of their accuracy in describing the “real” system, MD simulations generally do
not take into account complex processes such as collisional ionization, inverse
Bremsstrahlung, or continuum lowering, among others, which can be neglected in some
cases (for instance, inverse Bremsstrahlung at x-ray frequencies), but must be taken into
account for some energies and materials, when they are the more relevant.
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2.3.2 Non-LTE plasma simulations
Simulations were made using the code Cretin, developed at LLNL (Lawrence
Livermore National Laboratory), by Howard Scott [16]. Cretin is a radiation transfer plasma
code, which combines atomic kinetics and radiation transfer, and which can describe the
behavior of a non-LTE (non Local Thermodynamic Equilibrium) plasma. In each step it
updates the state of the system, based on initial input values of the density and temperature
of the plasma, and on the energy and intensity of the incident beam. The atomic populations
can be calculated either in a steady-state or a time-dependent mode.
Atomic kinetics is taken into account through a user-defined atomic model, and does
not include any radiation transfer or other non-local processes. A continuum-lowering model
is also available, which accounts for the effect of free electrons on the ionization potential of
the atom by shielding bound electronic levels, and therefore lowering the continuum level.
Radiation transfer is evaluated for continuum and line radiation, and couples back to atomic
kinetics. Spectral radiation is also calculated and allows the construction of detailed plasma
spectra. It is based on the plasma characteristics, but is not reused in the simulation.
This code can run in 0D to 3D. It includes a large number of switches and
parameters, which give it a wide versatility regarding the kind of processes to take into
account – such as continuum lowering, multiphoton ionization and time-dependence –, and
the specific values to assign to variables – such as the time step, the time between edits and
the minimum temperature – that are relevant for the description of the plasma or the
performance of the code.
Cretin can also be used as a postprocessor for a hydrodynamics code, using plasma
densities and temperatures as an input. One of its main applications lies in the study of ICF
(Inertial Confinement Fusion), where line emission from trace elements placed on the fusion
capsule is studied, in order to evaluate the extent of the hydrodynamics instabilities [17].
Cretin can also be used to study tokomak plasmas characteristics, in the context of MCF
(Magnetic Confinement Fusion), and to calculate the emission spectra of laser-produced
laboratory plasmas [17].
The code therefore corresponds to a static description, which does not include a
hydrodynamic expansion or a charge induced repulsion (leading to Coulomb explosion). In
our case, it was used to calculate the heating of the material – more specifically the electron
temperature – before the hydrodynamic motion occurs. During this time, the thermal energy of
the ions can be calculated from the electron-ion coupling coefficient. As opposed to what was
described in the examples above Cretin was thus used as a pre-processor rather than a post-
processor.
Combining these two approaches, or even trying to look at the problem through a
different perspective, with different simulation tools, can give a better insight of what is to be
expected from ongoing and future XFEL-based interaction experiments.
16
3 Experiments: background information
3.1 XFEL: working principle
Free electron lasers (XFEL) differ from usual lasers by the lasing principle they use.
Instead of relying on atomic or molecular bond states to produce coherent radiation they use
electrons, accelerated to relativistic speeds, which radiate when going through an undulator,
with carefully chosen characteristics.
FLASH is a high gain XFEL, based on the “Self Amplified Spontaneous (or
Stimulated) Emission” (SASE) principle. In this case the undulator is five to ten times longer
than in a synchrotron and the electron beam has a lower emittance (i.e. a better collimation);
a good amplification can thus be obtained after a single passage through the undulator. The
problem of having no reflective mirrors available for short wavelengths is then solved, these
mirrors being necessary for creating an optical cavity resonator, when outside the SASE
regime [18].
In detail, an electron beam (where the electrons are randomly distributed inside a
gaussian shape) is first created by a laser-driven RF (radiofrequency) gun, and is then
accelerated to relativistic speeds, in a superconducting LINAC (“Linear Accelerator”). There,
at specific energies, the electron bunches are longitudinally compressed by magnetic fields,
as shown in in Figure 4.
Figure 4: Detailed scheme of the FLASH line, where the XFEL beam is produced. The main
features are the electron bunch generator (RF gun), the linear accelerator, the long undulator magnet,
and the final bending magnet, which separates the emitted radiation from the electron beam. (Source:
DESY, Hamburg) [19]
They then go into a long undulator, made of periodically spaced magnets, which produce
magnetic fields of alternating direction as can be seen in Figure 5. The Lorentz force
F!"= qv"!B!"(+ qE!") (10)
causes the (relativistic) electrons to wiggle – i.e. to be accelerated – and emit radiation in a
cone of
�
1
! N opening angle, illustrated in Figure 6, given the relativistic Doppler effect [19].
17
Figure 5: Scheme of an undulator. The electron beam, accelerated to relativistic velocities, radiates
coherently when passing inside the undulator. At the end, a bending magnet deviates the electron
beam, and the emitted radiation alone goes into the experimental hall. (Source: DESY, Hamburg)
Figure 6: Radiation from a non-relativistic (left) and relativistic (right) accelerated electron. In the
first case the radiation is isotropic while in the second case it is emitted in a cone, because of the
relativistic Doppler effect.
The interaction between electron kinematics, which both creates and is affected by
the electromagnetic field, and the overall electromagnetic field, which has contributions from
the motion of the electrons and from the undulator magnets, results in a density modulation
and a microbunching of the electron beam (see Figure 7), with the same spatial period as the
undulator.
In this situation the electron microbunches have a longitudinal dimension shorter than
the wavelength of the radiation they emit, and can thus be described as a point-like electron
distribution, which radiates coherently, with a radiation power
�
P! given by [19]:
�
P! =N
2e
2
6"#0c
3! 4
˙ v 2, (11)
18
where N is the number of electrons,
�
! the relativistic factor
�
! =1
1"# 2
=1
1" v c( )2
, and
�
˙ v the acceleration of the electrons.
This value is proportional to
�
N2, which is a large improvement compared to the case
of incoherent radiation from a spread bunch of electrons, where the radiated power scales
only with N [19]. The increase in the power radiated by the electron bunch, due to the
microbunching inside the undulator, is shown in Figure 7.
Figure 7: Microbunching process. The electron bunch experiences a spatial density modulation when
passing through the XFEL undulator. The power of the radiation emitted by the electrons increases
during the microbunching process (Source: DESY, Hamburg).
Finally, the electron beam is deflected into a dump (Figure 5), and the
electromagnetic radiation alone is directed to the beamlines, in the experimental hall. The
wavelength of the radiation depends on the electron beam energy and on the magnetic field
strength. An XFEL can therefore be tuned to a given frequency, depending on the application.
3.2 Experiments on solids
Experiments on solids were performed in September 2006, at FLASH.
The samples used are shown in Figure 8. They consisted of niobium rods, doped with
different amounts of hydrogen and deuterium, a tantalum plate doped with hydrogen, and a
PMMA (Polymethyl methacrylate, C5H8O2) plate. Niobium and tantalum samples were
prepared at the Material Physics group of the Physics Department, at Uppsala University, by
Gunnar Pálsson and Björgvin Hjörvarsson [20] (cf. Appendix A). The niobium samples have a
19
concentration of dopants given by cH +D
= 0.86(mol!1) , with different relative amounts of
the two isotopes: cH= 0 and c
D= 0 ; c
H= c
D; c
H= 3c
D; c
D= 3c
H. The tantalum
sample has a concentration of H given by cH= 0.86(mol
!1) . The PMMA sample was
provided by the laboratory of Prof. Libor Juha, from Prague. All samples were kept in air
before entering the chamber, and therefore contain some extra amount of hydrogen, namely
in the case of “pure” Nb.
Figure 8: Picture of the sample holder, with the samples used in September 2006. The numbers
correspond to the order in which the samples were exposed to the FEL; A and B were not shot at.
In order to optimize the detection of emitted ions, the samples were mounted
perpendicularly to the detector. The sample mount was therefore bent by an angle of 35º ,
and rotated 20º away from the FEL beam direction, as shown in Figure 9.
Figure 9: Left: Picture of the inside of the chamber, with the sample holder mounted, although
not in the final position (cf. scheme on the right). Right: Scheme of the geometry of the
interaction. The TOF is mounted perpendicular to the samples, in order to maximize the detection
efficiency: the sample holder is bent by an angle of 35º relative to the vertical; the XFEL beam makes an
angle of 20º with the vertical plane, which contains the TOF direction.
20
Both the chamber and the detector used for these experiments belong to Ryszard
Sobierajski’s team, in Warsaw. The detector consisted of an ion time-of-flight detector (TOF),
with the geometry presented in Figure 10.
Figure 10: Picture (left) and scheme (right) of the Warsaw TOF detector, used during the
September 2006 experiments at FLASH. For the experiments described here only the drift tube and
the MCP had some voltage applied.
The cones are used for ion acceleration, at the entrance of the TOF. They are
followed by a diaphragm and a tube diaphragm, used for beam focusing and direction
selection. The ions then travel inside a drift tube, at a constant potential, until they reach a
LED (“Low Energy Discriminator”), consisting of three golden grid electrodes, which cut out
ions that have a lower energy than the one applied to the grids. Finally, a microchannel plate
(MCP) detector, situated after the grids, records the signal.
In our case, neither the cones or the grids of the LED had any voltage applied to
them. As a consequence, no energy discrimination was possible for the ions reaching the
MCP detector.
A measure of the beam intensity could be obtained through the output of the GMD
(Gas Monitor Detector), located just before the XFEL shutter, at the entrance of the
experimental hall. This value had to be calibrated by an average value, obtained after
processing by the DOOCS software, at DESY.
As for the characteristics of the XFEL, during the experiment itself, a wavelength of
21nm , corresponding to 51.9eV photons, was used. The beam energy varied between 1
and 20µJ , and the pulse length between 10 and 20 fs . The focal spot had a 20µm
diameter (FWHM), i.e. a 314µm2 area. As a consequence, the beam intensity attained was
at the most 1014W cm
!2s!1
.
21
The pressure measured in the chamber, during the experiment, was of about
10!6mbar = 10
!4Pa . For such vacuum conditions, there could be deposition of water on the
samples at a rate of approximately one monolayer per second [21].
The experiments were performed in single bunch mode, two consecutive shots being
about 2 s apart from each other. Each sample was shot at least 90 times, on at least 3
different spots. Only some of the available samples were used, namely Nb, NbD, NbH, NbDH
(relative concentration of 1, for H and D), TaH and PMMA. Data for TaH were later discarded,
since the output was mostly noise, and no clear peaks could be observed.
3.3 Experiments on gas clusters
Experiments on gas clusters were realized in March 2007, at DESY.
Two gases were used, for forming clusters: argon, in a first step, since rare gases
behavior is well known; and methane, the object under study, in a second step.
The chamber, the cluster generator, and the ion TOF detector were provided by the
cluster group at the Technischen Universität Berlin. The TOF has the geometry presented in
Figure 11.
Figure 11: Left: setup of the March 2007 gas experiments at FLASH; Right: scheme of the Berlin
TOF detector used. The XFEL and the cluster beam are parallel to the plates; the outgoing ions pass
through a small aperture in the grounded plate.
22
The interaction between the XFEL and the clusters takes place between the two
plates. The ions then go through the energy discrimination grids, and finally reach the MCP
detector. In our case, no voltage was applied to the grids and therefore no energy
discrimination was possible for the ions.
Beam intensity measurements were made as for the solids experiments, by means of
the GMD located before the XFEL shutter of the experimental hall, whose signal was later
calibrated by other values, as explained for the case of the solids.
During these experiments, the XFEL was operating at a 13.5nm wavelength ( 92eV
photons). The pulse energy was on average 20µJ , but could go up to 40µJ , and its
duration was of about 10 fs ; the focusing achieved corresponded to an area of around
5µm2 (FWHM). The pulse intensity was therefore of about 4.10
16Wcm
!2s!1
.The pressure
inside the chamber was different from place to place: the minimum value was of about
10!5mbar , at the valve where the XFEL beam goes into the chamber; the highest was in the
interaction region, when gas clusters were injected in the chamber.
In order to study the influence of the gas backing pressure – the pressure in the gas
reservoir, before the cluster generating nozzle – in the cluster formation, it was set to both
300mbar and 7bar , in the case of Ar, and both 1bar and 10bar , in the case of methane.
A few thousand shots were recorded in each case, while the XFEL beam was operating in
multibunch mode, with a shooting frequency of 100Hz . Several hundreds of bunches were
sent every time, and data were recorded for the second one. At 10ms separation, it is
expected that all interactions are totally independent, i.e. the collected data should not have
any remnants from previous explosions.
23
4 Results and analysis
4.1 Experiments on solids
Experimental data from solid samples clearly show the presence of light ions –
hydrogen, in all samples, and deuterium, in deuterated ones – leaving the interaction region
with very short times-of-flight. H+ ions always account for the most intense peak, together with
D+, but other species, with varying ionization levels, can also be observed and identified.
Typical TOF data for each solid sample are shown in Figure 12.
The first part of the analysis will deal with the identification of the observed ion peaks,
assuming constant energy among the species. In a second phase light ions will be studied in
more detail.
In the analysis only a part of the collected data were taken into account, in order to
create a homogeneous data set: three spots, shot 30 or 50 times, were kept for each sample.
The value of the intensity of the pulse, for each shot, was obtained from the GMD signal and
calibrated to the maximum value, for each spot. The data were then classified according to
their corresponding intensity, which made it possible to study the general evolution of the TOF
output with the pulse intensity.
Figure 12a: TOF spectra for NbH. Nb and NbH spectra present the same characteristics,
since Nb samples also contained hydrogen. A typical spectrum for Nb, with a split H+ peak, is
shown on the top of Figure 15. The H+ peak can also be split in NbH.
24
Figure 12b: TOF spectra for NbDH. Typical spectra for NbD are shown on Figure 13 and on
the top of Figure 16. NbD and NbDH spectra present the same characteristics, since NbD
samples also contained hydrogen.
Figure 12c: TOF spectra for PMMA.
4.1.1 General analysis
The analysis of the experimental data regarding solid samples was made using a
program developed by Florian Burmeister et al. [22], based on IgorPro, a widely used data
analysis and signal processing software [23]. This program was first developed for TOF data
acquisition and analysis. For our purposes only a small part of it is required, where direct
output data from the TOF (intensity vs. time) are converted to intensity vs. mass/charge plot.
25
One needs to assume constant energy among the ions – which makes sense in a Coulomb
explosion, and for this time scale ( ! 10
!5s ) – and to know the mass/charge ratio for two
peaks, as shown in Figure 13.
Figure 13: First step in the determination of the present ion species. We assume the nature of two
peaks, which serve as an input to the fitting formula.
The mass/charge ratio for the other peaks, and thus a good guess about their nature,
is then obtained, by fitting the data to the following formula [22]:
t = ! +"m
q, (14)
where
�
! and
�
! are fitting parameters.
Before the analysis the origin of the plots has to be fixed so that the photon peak,
which appears together with the ion peaks, corresponds to
�
t = 0. The detected photons are
emitted during the interaction and can be used as a triggering signal for the time
measurements, since their flight time is negligible.
This analysis method carries a drawback, since it requires at least three reference
points. Two of those points are used for the time to charge/mass conversion, and the third
one for testing the validity of the initial assumption. Therefore, plots with only one or two
peaks could not be analyzed (this is a problem for Nb, for instance).
Although this analysis is not limited to the H+ and D
+ ions alone, which constitute the
main targets of this project, it is relevant when trying to define the best environment for future
experiments: it helps determining conditions for acceleration of light ions, and finding out how
the output features vary with different experimental parameters (sample composition, beam
intensity, etc.).
26
It is observed that, in general, pulse intensity does not appear to have a very big
influence on the level of ionization of the heavy ions, in the studied energy range. Increasing
the intensity leads to a higher ion yield rather than create new ionization states, i.e., the ratio
between the intensity of the H+ peak – the highest – and the others decreases with increasing
pulse intensity.
In Nb containing samples, ionized states of Nb up to 5+ can be found (see Figure
12b). A comparison of the samples shows that Nb3+
and Nb2+
ions are quite rare, when
compared to Nb4+
and Nb5+
ions.
Furthermore, species with a mass/charge ratio of 2 in deuterium containing samples
(NbD and NbDH) are D+, and not H2
+. Otherwise, they would also show up in the Nb and NbH
data, which they do not (Figure 12a vs. Figure 12b or Figure 16).
A species with a mass/charge ratio of 4 is also observed in deuterium containing
samples. In the absence of more experimental diagnostics we assumed it to be D2+, created
during the flight time by recombination of two D+ ions. However, it is surprising not to see a
more enhanced HD+ yield, with a mass/charge ratio of 3, given the similar recombination
energies for D2 and HD. Also, since there was no energy discrimination between the ions
(Figure 10), the whole analysis was made assuming constant energy: would the energy be
different from peak to peak, what appear to be ions with a mass/charge ratio of 4 could be H+
or D+ ions with a different energy. Drawing a conclusion on the nature of the ions requires
further diagnostics.
Apart from these features, some peaks remain unassigned, which could be due to
impurities, located on or inside the samples used, in the vacuum chamber itself, or even on
the sample holder (supposing some shot might have been misplaced). Given the
mass/charge ratio of the unassigned peaks, and the experiment’s environment, both Si and
Fe seem to be “good candidates” for impurities.
After their exposure to the FEL beam, the samples were analyzed using a Nomarski
differential interference contrast microscope. Figure 14 shows craters, both on PMMA and
NbDH, which correspond to the areas exposed to the FEL beam. The diameter of the craters
is about 50µm , which is consistent to the diameter of 20µm (FWHM) assumed for the
focal spot, since the damaged area is always bigger than the beam itself, and each spot in the
pictures was shot at least 30 times. No further crater analysis has yet been pursued on the
samples used in our experiments, partially because they were not polished enough;
nevertheless, studies on ablation and crater formation have been successfully performed at
FLASH [24], and could be later used as a model.
27
Figure 14: Nomarski differential interference contrast microscope (x100) pictures taken from
PMMA (left) and NbDH (right) samples. Craters are visible in both cases, with a diameter of about 50
!m. This is consistent with the size of the FEL beam focal spot, which was assumed to have a diameter
of 20 !m (FWHM).
4.1.2 Light ions energy analysis
The main interest of the current project lies on the behavior of light ions, and a
detailed analysis was therefore made on the hydrogen and deuterium peaks. Given the TOF
dimensions presented in Figure 10, it is possible to convert time-of-flight measurements, t, to
energy, En, for a given ion species, characterized by its mass m and charge q, through the
following calibration:
t = 106
m 2
c
d1+ d
4+ d
5
1000E+
d2+ d
3
1000 E + qVDrift( )
!
"##
$
%&&+
2m
c
d61000 E + qVMCP( )
1000qVMCP
'
(
)))
*
+
,,,
, (15)
where En is in eV and t in seconds.
This allows one to follow the evolution of, mainly, the H+ or D
+ ions’ energy, and of the
corresponding peaks inner structure – when there is any – with the pulse intensity.
Having converted the time-of-flight of the ions to kinetic energy, the most exciting
result is the fact that there are H+ ions with energies up to hundreds of eV and even 1keV ,
in all samples. Results for the H+ peak in Nb are presented in Figure 15.
28
Figure 15: Top: Direct TOF output for a single FEL shot on an Nb sample. Bottom:
Corresponding energy distribution for H+ ions (from three different origins), fitted by three
gaussians. Three different contributions can thus be identified, for the H+ yield, which might account for
different chemical origins or ejection mechanisms.
The hydrogen peak is often split into several superimposed subpeaks, as seen in
Figure 15, which might correspond to several chemical origins or ejection mechanisms of the
H+ ions. This phenomenon is observed in all samples, but easier to identify in deuterium free
ones, since no other peak is present in that region of the time-of-flight axis. A first approach in
the description and understanding of these peaks’ nature is to fit three gaussians to the
multiple peak, in order to isolate the two or three possibly different hydrogen contributions.
The gaussians are later converted to an energy dependency, using Equation 15. It is then
possible to identify the energy range characteristic of each H+ ion kind, which spreads from a
few hundreds of eV , for the lowest energy one, until up to 1keV , for the most energetic.
29
For deuterium containing samples, four light ion peaks were converted to an energy
dependency, in the way described above for the H+ peak in an Nb sample. As seen in Figure
16, light ions – H+, D
+ and D2
+ - all have the same energy distribution, centered on a few
hundreds of eV , and going up to 1keV for H+ ions. The D
+ ions are generally limited to
lower energies, corresponding to the main contribution in the split hydrogen peak. However,
deuterium ions in the tail of the energy distribution can reach energies up to 1keV .
Nb+ ions seem to have a different energy distribution than the lighter ions, in Figure
16. This might be due to the fact that the Nb peak contains several ionization states, while
only one was considered for the current time-of-flight to energy conversion.
Figure 16: Top: Direct TOF output for a single FEL shot on an NbD sample, with a gaussian fit to
the H+, D
+, D2
+ and Nb
+ peaks. Bottom: Corresponding energy distribution of the H
+, D
+, D2
+ and
Nb+ peaks. All light species have the same energy distribution, centered on hundreds of eV, but
reaching up to 1 keV. Nb+ ions have an energy shifted towards higher energy when compared to light
ions, which might indicate that several ionization states of Nb are present.
30
A beam intensity dependence analysis was also made, based on data from the GMD,
as described above. Figures 17 and 18 depict one of the main conclusions of the present
study: there is an energy increase for the three H+ ions kinds – corresponding to the three
subpeaks –, which follows the increase in pulse intensity. The energy increase is obvious in
Figure 17. As for Figure 18a, there is a diminishing of the time-of-flight (i.e. an increase in
kinetic energy) in all plots, which correspond to the three H+ ions kinds, both in Nb and NbDH.
Furthermore, Figure 17 illustrates the different behavior of the H+ ions kinds with the
increase in pulse intensity, namely that some of them only become relevant after a given
intensity threshold. The existence of an intensity threshold is confirmed by Figure 18a, in
which data for the second and third hydrogen peaks are only present after a given intensity.
The different behavior of the H+ ions kinds with the increase in pulse intensity supports the
hypothesis of a different chemical origin or ejection mechanism for the hydrogen ions.
Figure 17: Intensity dependence of the three hydrogen subpeaks, in Nb, based on three FEL
shots. The three kinds of H+ ions experience an increase in kinetic energy with increasing pulse
intensity. The energy increase is different for each kind of ion, suggesting several distinct ejection
mechanisms or chemical origins.
31
Figure 18a: Intensity dependence of the time-of-flight for the three kinds of H+ ions (illustrated in
Figure 17) in NbH (green) and Nb (red). The ions energy increases (the tof decreases) with the pulse
intensity, for all kinds of H+ ions. Furthermore, there are thresholds in the intensity, corresponding to the
onset of the second and third H+ kind contribution.
32
Figure 18b: Intensity dependence of the time-of-flight for the H+, D
+ and D2
+ ions in NbDH. An
increase in the kinetics energy (a decrease in the tof) of the ions follows the increase in beam intensity.
While Figures 15 to 17 correspond to single shot results, Figure 18 is built on data coming from many
shots. It therefore proves the consistency of the collected data among each other.
Figure 18b shows a similar evolution for the three independent peaks featured in the
NbDH sample, corresponding to H+, D
+, and D2
+. The three ions are accelerated with
increasing beam intensity, which can be deducted from the clear decrease – at least for H+
and D+ data – in the time-of-flight measurements.
Figure 19 shows data from a PMMA sample where the hydrogen, carbon and oxygen
peaks can be easily identified. It is clear that the beam intensity increase is followed by an
33
energy increase, for all three kinds of ions. It must be noted that Nb+ ions in Nb-containing
samples also present an increase in energy for increasing beam intensity, although that is not
so striking in the plots, since the peak is always rather small.
Figure 19: Intensity dependence of the three peaks (from left to right: H, C and O) of the PMMA,
based on three FEL shots. The kinetic energy of all three species increases (the flight time diminishes)
with the beam intensity. Also, higher ionization states become more relevant, for higher beam intensity,
and contribute for a broadening of the carbon and oxygen peaks (since H+ cannot be ionized more).
Furthermore, higher ionization states become more relevant for higher beam
intensity: the highly ionized states change the shape of the carbon and oxygen peaks, as can
be seen in Figure 19. The hydrogen ions cannot be further ionized, thus their lower time-of-
flight, for higher intensities, is only due to a kinetic energy increase.
4.2 Simulations
The plasma simulation software package Cretin [16] was used for simulating the
initial plasma heating after an XFEL-solid interaction, which lasts for about 1ps and is
characterized by Te! Ti , where Te is the electron temperature and Ti the ion
temperature. Each simulation describes the 50 fs period right after the interaction, during
which the hydrodynamics expansion is governed by the electron thermal energy, due to a
high Te , and by the ions mass, which behaves like an inertial break. Given this information,
one can calculate the approximate expansion velocity of the system
�
vexp , assuming it to be
equal for all ions, by [25]:
34
vexp =Z! K
BTe
M, (16)
where
�
! =3
5 is the adiabatic coefficient and
�
KB
the Boltzmann’s constant. M and Z are the
average mass and ionization of the ions, calculated by weighting the mass and ionization of
each atom by its stoichiometric coefficient in the material. This approach is no longer valid
once the plasma reaches an equilibrium between electrons and ions, about 1ps after the
interaction has occurred.
The expansion kinetic energy of the system can be calculated as well, making use of
the average ionization of the ions, which is an output of the simulation.
Eexp =1
2Mvexp
2=1
2Z! K
BTe
. (17)
This expansion energy is, however, characteristic of the system as a whole, and
cannot be applied to the individual ions. Very fast ions are therefore not modeled in this initial
thermal heating stage.
Both 0d and 1d simulations were made for the materials (Nb, NbD, NbH, NbDH,
PMMA) used during the solid-XFEL interaction experiments, in September 2006, at DESY.
The input parameters used were kept as close as possible to the experimental ones,
meaning a wavelength of 21nm (i.e. 59.1eV photons), a pulse duration of 15 fs , and a
focal area of 314µm2 (focal spot with D = 20µm ). The beam energy was varied from
1µJ to 100µJ , which corresponds to a variation in beam intensity between
2.12.1013W cm
!2s!1
and 2.12.1015W cm
!2s!1
. The aim here was not only to reproduce
the experimental conditions (1! 20µJ range), but also to study the effect of an increase in
the beam intensity. This increase was achieved increasing the beam energy ( 20 !100µJ
range), but it could also have been done by decreasing the focal spot area or the pulse
duration, given the formula below:
�
BeamIntensity =BeamPower
FocalArea=BeamEnergy PulseDuration
FocalArea. (18)
4.2.1 Interaction of the FEL pulse with solid samples
In a first approach, 0d simulations were made, which are expected to model the
heating at the surface of the sample, since no depth information is included.
The main conclusion of this calculation is the fact that the highest achieved energy is
around 0.1keV , for the Nb sample, at 100µJ beam energy, when continuum lowering is
taken into account, as can be seen in Figure 20. This energy corresponds to the final thermal
35
energy of the ions, and is about an order of magnitude lower than the experimental values
described in the previous section.
Figure 20: Simulated beam intensity dependence for Nb, at 21nm, with (bottom) and without (top)
taking the continuum lowering effect into account. It is clear that an increase in the beam intensity
corresponds to an increase in the kinetic energy of the ions ejected from the sample. Furthermore,
taking the continuum lowering effect into account leads to higher kinetic energies of the ions, especially
in the early plasma heating phase.
Kinetic energy values are always higher for the case with continuum lowering, which
is as expected since the effect of the continuum lowering is to speed up ionization, and
therefore ions leave the sample sooner, and with larger kinetic energy. Figure 20 shows that
the simulations appear to be somehow unstable for some beam energies/intensities.
The top of Figure 21 shows the ion kinetic energy evolution with time, for all the
intensities considered, in the case of PMMA. It is clear that the ions kinetic energy increases
36
with the beam intensity. This result can be very relevant and useful for later experiments,
although it only concerns the initial thermal expansion phase of the explosion process. Similar
plots, for the other samples, can be found in Figure B1, in Appendix B. They all present the
same kind of increase in the kinetic energy, following the increase of pulse intensity, which
shows that this behavior is independent of the material considered.
Figure 21: Top: Simulated beam intensity dependence of the kinetic energy in PMMA. Bottom:
Simulated dependence of the kinetic energy on the sample used, for fixed beam energy of 75!J.
Doing a similar kind of plot, but this time for a fixed intensity – 75µJ was chosen as
an example, and is shown in the bottom part of Figure 21 –, and for all materials, one can see
that the lowest ion kinetic energies are achieved for PMMA, then NbDH, NbD, NbH and finally
Nb. A complete set of results can be found in Figure B2, in Appendix B, which confirms the
generality of the conclusion. It is interesting to note that the NbD and NbH curves overlap (for
37
higher intensities), as is to be expected given the similarity between hydrogen and deuterium
masses.
Ionization E (eV) 1st 2nd 3rd 4th 5th 6th
H 13.6
D 13.6
C 11.3 24.4 47.9 64.5 (392.1)
O 13.6 35.1 55.0 77.4 (113.9)
Nb 6.76 14.0 25.0 38.3 50.6 (102.2)
Table 2: Ionization values for the ions relevant in the context of this experiment. The incoming
photons have an energy of 59.1eV, meaning that ionization states with energies higher than that cannot
be achieved through direct photoionization (since multiphoton ionization and inverse Bremstrahlung
have a small effect, at these wavelengths, the ionization state is limited by the ionization potential and
the photon energy).
As can be seen in Table 2, Nb is ionizable up to 5 times, by 59.1eV photons. 0d
simulations were run for the Nb sample, at beam energies of 20µJ and 100µJ , to test
how much the ions would be ionized, in the initial plasma heating process. The results
obtained are shown in Figure 22.
The situation closest to the experiment is the 20µJ case, and there is a larger
fraction of Nb3+
, Nb4+
, and even Nb2+
, than of the others, whereas in the experiments Nb2+
and Nb3+
are rather rare. Nb2+
and Nb3+
could recombine during the flight time, to become
Nb+, more than Nb
4+ and Nb
5+ do. On the other hand, results for simulations made for a beam
energy of 100µJ are closest to the experimental ones, with more Nb4+
and Nb5+
than other
kinds of ions. The change is most likely due to the fact that a higher beam intensity enhances
higher ionization levels, as noticed in the experimental results. However, both simulations
show a small contribution of the Nb+ ion yield, which does not seem to be the case in the
experiments.
38
Figure 22: Simulated ionization levels for Nb, at 21 nm, as calculated by Cretin, for a beam
energy of 20!J (top) or 100!J (bottom). Ionization states of Nb up to 5+ are formed during the
interaction, while the Nb atoms disappear almost entirely.
In a second stage results were obtained for 1d simulations that allow one to draw
conclusions on the depth evolution of the ion kinetic energy by running the simulation in
several zones, at different depths.
Comparing the results obtained for these simulations to the ones obtained above, for
0d simulations, one sees that the single zone considered in the 0d simulations corresponds to
the surface of the material, in 1d simulations. The results are even improved in the 1d case
since the instabilities in the output disappear, when continuum lowering is included.
Figure 23: Simulated dependence of the ion kinetic energy as a function of depth, for several
beam intensities, on Nb.
39
As shown in Figure 23, the kinetic energy increase with the beam intensity,, for the
Nb sample, is not to restricted to the surface layer alone, rather it is common to all zones,
independently of how deep they are situated in the material. Furthermore, deeper lying zones
contribute with lower kinetic energy ions. In conclusion, higher beam intensity is translated
into energetic ions in deeper zones within the sample.
It is worth noticing, from Figure 24, that the PMMA contributes with lower energy ions
from zones close to the surface, but that this behavior changes when one goes deeper inside
the sample. Ion energies in niobium-containing samples are relevant until about 20nm inside
the sample, whereas in PMMA they stay relatively high until a depth of about 70nm .
Also shown in Figure 24 are the electron temperature, whose evolution with depth is
equivalent within Nb-containing samples, although rather different when compared to PMMA,
and the average ionization level of the ions, which differs even among Nb-containing
samples.
40
Figure 24: Simulated electron temperature (top), average ionization (center) and ion kinetic
energy (bottom) for Nb, NbD, NbDH, NbH and PMMA, at 21nm, with a beam energy of 100!J. The
energy is higher at the surface for Nb-containing samples compared to PMMA. When going deeper
inside the material, the energy drops quickly for Nb samples, but stays high for a longer depth, for
PMMA.
The different behavior of PMMA and Nb-containing samples with increasing depth is
reflected in the absorption of the material, as can be seen in Figure 25.
Figure 25: Simulated absorption for Nb, NbD, NbDH, NbH and PMMA, at 21nm, with a beam
energy of 100 !J. The absorption presents the same behavior with respect to Nb-containing samples
and PMMA, as was described for the kinetic energy.
Comparing the results with data from the Center for x-ray optics of Lawrence
Berkeley National Labs [26], one sees that the characteristic depths in both kinds of samples
correspond to the attenuation length of the material at 21nm , which is 18nm for Nb – with
very little variation when H or D is added – and 75nm for PMMA. Figure 26 shows the
41
attenuation length for Nb and PMMA over a range of wavelengths. To have a similar xray
penetration strength for both materials, a wavelength of about 12 nm would be required.
Figure 26: Attenuation length for Nb (top) and PMMA (bottom) between 1 and 40 nm. For our
experiments a wavelength of 21 nm was used, corresponding to an 18 nm attenuation length for Nb and
a 75 nm attenuation length for PMMA. [26]
4.3 Preliminary results on gas clusters
The near-solid density of gas clusters makes them a very interesting object to study.
One would expect clusters to have a behavior similar to that of solids, namely to present signs
of light ions acceleration, as was reported in [14].
42
Figure 27: Methane data for a backing pressure of 1.2 bar (top) and 10 bar (bottom). Only the
higher backing pressure leads to cluster formation. There is no significant difference in the spectra
arising from the presence of clusters rather than gas.
Experimental results are presented in Figure 27, for two values of the backing
pressure. Only the higher backing pressure leads to cluster formation. Figure 27 shows no
significant difference between the gas and the cluster spectra, namely regarding the light ions
(H+ and H2
+) yield.
43
Figure 28: Intensity dependence of the H+ ions energy, for a 10 bar backing pressure.
Figure 28 shows no decrease in the H+ ions time-of-flight, i.e. no increase in their
energy, for higher beam intensity. The result is surprising, since an ion energy increase was
observed to follow the beam intensity increase for all ions, in the case of solid samples,
Gas experiments results do not show any visible light ions energy increase due to the
presence of clusters or to an increase in the beam intensity, which would be expected given
the results obtained for solids, and those presented for clusters in the literature [14]. However,
the absence of fast ions in the spectra could be explained by a poor adaptation of the TOF to
energies of the order of 1KeV or higher, or by its geometry, namely the size of the slit the
ions have to go through to reach the MCP detector (shown in Figure 11).
44
5 Discussion
The present study describes the first measurements of light ions acceleration during
an XFEL-solid interaction, performed at the only SASE-based XFEL available at this point,
FLASH.
During the interaction of the XFEL beam with solid samples, H+, D
+, and what was
assumed to be D2+ ions were detected, with energies of up to 1KeV . It was noticed that
there are three different contributions to the H+ ions yield, reflected in the spectra as a split
hydrogen peak. Furthermore, the energy of the ions was seen to increase for increasing
beam intensity. The energy increase occurs differently for different ions, and also for each
kind of H+ ions. The beam intensity increase also contributes to a larger yield of higher
charged ion species. Measurements of the methane clusters interaction with the XFEL beam
have shown no light ions acceleration compared to the case when methane gas was used.
No light ions energy increase was observed for increasing beam intensity.
Simulations made for solids, with the radiation transfer plasma code Cretin, estimate
the ion energy after the initial heating phase to be ten times lower than the experimental one.
The ion energy increase, following an increase in the beam intensity, is also modeled.
The ions energy increase with the beam intensity was predicted by MD simulations
[5]. Higher beam intensity means larger number of photons per unit time and per unit area on
the sample; this leads to an easier ionization of the samples, up to a higher ionization level. At
soft x-ray energies, photoelectric effect is one of the main ionization processes, which makes
the number of photons a very relevant parameter. Increasing the ionization efficiency can be
achieved by decreasing the focal spot area or the pulse duration, i.e. concentrating the
photons in time or space, or by increasing the beam energy, i.e. increasing the number of
photons in the beam.
We also measured that the energy distribution of the ejected protons has a complex
structure. This led to the hypothesis that these ions could have different origins, namely they
could come from different chemical environments, or be accelerated by different ejection
mechanisms. Several such mechanisms are discussed below.
As all the samples contain hydrogen, this constitutes the main origin for H+ ions
ejected after the interaction with the XFEL beam. The hydrogen in the samples is either
located in the interstitials of the lattice structure of the niobium, or as a part of the molecule
itself, for PMMA. The pure Nb sample, although not injected with hydrogen, still contains
some, absorbed in the sample from the atmosphere.
On the other hand, some water molecules might be present on the sample, not only
during the first shot in a given spot, but also in subsequent shots: the water layer could rebuild
to up to 2 monolayers between each shot, given the pressure conditions (10!6mbar ) and the
45
2 s shooting time delay [21]. However, the sample heats up during the interaction, and it is
unclear at this point how much the water molecules contribute to the observed H+ signal.
With the aim of understanding the mechanisms responsible for the ejection of these
energetic ions, simulations were made with a plasma code, which calculates the thermal
contribution of the initial plasma heating phase for the final energy of the ions. This
contribution is found to be smaller than the values observed experimentally. In our
experiments, the faster hydrogen ions have kinetic energies of up to 1keV (Figure 16),
whereas the simulations report ions of 0.1keV at the most (Figure 20). Only 10% of the
energy of the ions can thus be explained by thermal heating in the initial phase of the
interaction. The remaining acceleration must be explained by other mechanisms, such as
Coulomb acceleration, in which the ions are further accelerated by charge repulsion from the
positively charged core of the sample.
Furthermore, one should notice the difference in the ionization states of Nb ions,
between the experiments and the simulations. A probable explanation could come from
processes such as ion recombination, which occur after the initial thermal heating described
by Cretin, and have an influence in the ionization state of the ions.
It is difficult to have a good estimate of the contribution of the Coulomb explosion,
through simulations. Cretin does not include this kind of mechanism, and MD simulations,
performed for hard x-rays interactions, might not be entirely accurate in this energy range.
Other simulation methods, namely particle-in-cell [11], would be required, in order to have a
good estimate of the Coulomb acceleration contribution to the final energy of the ions. This
would confirm whether this is the only effect that should be considered, or if other acceleration
mechanisms should be taken into account – such as space charge effects, as described by
Mora in [27] – which should be relevant in ionized materials.
Another considered hypothesis was a possible contribution of the water layer, present
at the surface of the samples, in the acceleration of the ions. The result of simulations
including few water zones on the surface of the solid sample, show no increase of the kinetic
energy of the ions due to the presence of the water.
The results from preliminary experiments performed on methane are surprising when
compared to data from the solids experiment or from the literature [14]. The incapacity of the
TOF to measure energies of the order of 1KeV , or the small size of the slit the ions have to
go through to reach the MCP detector (see Figure 11) could come as explanations for the
discrepancy among the results.
46
6 Conclusions and outlook
This study represents the beginning of a larger project, whose aim is to analyze and
define conditions for achieving fusion through the interaction of an XFEL beam with both solid
samples and gas clusters. The first experiments performed at FLASH in this context have
yielded very exciting results, in respect to solid samples, through the observation of H+ – and
some D+ – ions with energies up to 1KeV .
We have observed considerable proton emissions in which the energy of the emitted
protons is very high (many hundreds of eV to KeV), namely higher than expected from
simulations made with an atomic physics code, Cretin. Furthermore, theoretical models
grounded on Molecular Dynamics predict different energies for protons coming from different
chemical environments (including protons originating from adsorbed waters or hydrogens on
the surface). We, therefore, expected to see split or multiple proton peaks in the TOF signals,
and they were indeed present in the results. The models also predict that the energy of
protons coming from different chemical environments will change differently with the FEL
pulse energy. We have observed this and have seen a larger proportion of faster protons at
higher beam intensities, in solid samples. Moreover, we expected to see more than one
mechanism behind proton ejection, and the gaussians fitted to the data from solid samples
confirmed such an expectation. Finally, methane cluster studies are an ongoing project,
where experimental details need to be worked out.
These promising results led to the allocation of dedicated beamtime for this project
during the next run at FLASH, starting in the end of 2007, and to the development of
collaborations, necessary to cover the broadness of the experiments and of the analysis
required. Several improvements are necessary, namely regarding the solid and gas samples
– chosen materials, amount of hydrogen and deuterium, polishing of the surface, in the case
of the solids –, the available diagnostics – type of detectors and their adaptation to the
experiment –, and the overall characteristics of the beam – focusing, wavelength, stability –,
some of which can, and will, be addressed in the next experiments. Apart from these
improvements in the experiments, one must both develop tools for analyzing the data, and
compare the outcoming results with simulation models (based on Molecular Dynamics or
particle-in-cell) that are better adapted to this particular matter.
Eventually, XFELs will start operating at hard x-rays wavelengths, opening new
possibilities for all kinds of research, among which fusion related projects.
47
References
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[7] X-ray induced Coulomb Explosion and nuclear fusion - experimental proposal II-
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from a free-electron laser Nature 420 482-485
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[13] http://www.physik.tu-berlin.de/cluster, for the expression “nano-labs”
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heteronuclear clusters Physical Review Letters 87 033401
Grillon G. et al. (2002) Deuterium-Deuterium fusion dynamics in low-density
molecular cluster jets irradiated by intense ultrafast laser pulses Physical Review Letters 89
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Madison K. W. et al. (2004) Fusion neutron and ion emission from deuterium and
deuterated methane cluster plasmas Physics of Plasmas 11 270-277
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Van der Spoel et al. (2005) GROMACS: fast, flexible and free Journal of
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[17] Langer S. H. et al. (2003) Comparisons of line emission from 2- and 3-dimensional
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Radiative Transfer 81 275-286
[18] Castro P. et al (2000) Overview of SASE experiments XX International Linac
Conference, Monterey, California
[19] Rossbach J. (2004) Linac based free-electron laser – TESLA-FEL Report 2004-08
[20] Pálsson G. K. (2006) Reportlet on hydrogen concentration determination of NbHx and
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[21] http://en.wikipedia.org/wiki/Monolayer
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49
Appendix A
Nb and Ta containing samples used during the September experiment at FLASH
were analyzed at the Material Physics group of the Physics Department, at Uppsala
University, using High Resolution X-Ray Diffraction (HRXRD) [20]. This method, combined
with precision density measurements, gives the concentration of both H and D isotopes in the
sample. HRXRD results consist of shifts in Bragg reflection peaks, which can be translated
into a measure of the variation of the lattice parameter
�
!a , and, therefore, of the volume of
expansion of the sample, through
�
!V
V=a0
3" (a
0+ !a)
3
a0
3. (12)
Density measurements determine the specific volume change
�
!v
". The H (or D)
concentration
�
cH
(or
�
cD
) then follows:
�
!V
V= c
H
!v
". (13)
50
Appendix B
Detailed simulation plots showing the dependence of ion kinetic energy with sample
composition and beam intensity are presented below. All of them assume continuum
lowering.
Figure B1 shows the dependence of the ion kinetic energy time evolution with the
beam intensity, for all samples. The kinetic energy increases with the pulse intensity, for all
materials.
Figure B1: Variation of the ion kinetic energy with the beam intensity, for each of the five
samples (Nb, NbD, NbDH, NbH, PMMA, from left to right, and top to bottom).
51
Figure B2 shows the dependence of the ion kinetic energy time evolution with the
sample, for all the intensities considered in the simulation. The lowest ion kinetic energies are
achieved for PMMA, then NbDH, NbD, NbH and finally Nb, for all intensities.
It is interesting to note that the NbD and NbH curves sometimes overlap (for higher
intensities), which makes sense given the similarity between hydrogen and deuterium
masses.
52
Figure B2: Variation of the ion kinetic energy with the sample, for each of the ten beam
intensities considered (1 !J, 2 !J, 5 !J, 10 !J, 15 !J, 20 !J, 25 !J, 50 !J, 75 !J, 100 !J, from left to
right, and top to bottom).