A molecular-dynamics approach for studying the non-equilibrium behavior of x-ray-heated solid-density matter
Malik Muhammad Abdullah, Anurag, Zoltan Jurek, Sang-Kil Son, Robin Santra
aa r X i v : . [ phy s i c s . a t m - c l u s ] A ug A molecular-dynamics approach for studying the non-equilibriumbehavior of x-ray-heated solid-density matter
Malik Muhammad Abdullah,
1, 2, 3
Anurag,
4, 1
ZoltanJurek,
1, 2
Sang-Kil Son,
1, 2 and Robin Santra
1, 2, 31
Center for Free-Electron Laser Science, DESY,Notkestrasse 85, 22607 Hamburg, Germany The Hamburg Centre for Ultrafast Imaging,Luruper Chaussee 149, 22761 Hamburg, Germany Department of Physics, University of Hamburg,Jungiusstrasse 9, 20355 Hamburg, Germany Department of Physics, Indian Insitute of Technology, Kharagpur, West Bengal, India (Dated: October 17, 2018) bstract When matter is exposed to a high-intensity x-ray free-electron-laser pulse, the x rays exciteinner-shell electrons leading to the ionization of the electrons through various atomic processesand creating high-energy-density plasma, i.e., warm or hot dense matter. The resulting systemconsists of atoms in various electronic configurations, thermalizing on sub-picosecond to picosec-ond timescales after photoexcitation. We present a simulation study of x-ray-heated solid-densitymatter. For this we use XMDYN, a Monte-Carlo molecular-dynamics-based code with periodicboundary conditions, which allows one to investigate non-equilibrium dynamics. XMDYN is capa-ble of treating systems containing light and heavy atomic species with full electronic configurationspace and 3D spatial inhomogeneity. For the validation of our approach we compare for a modelsystem the electron temperatures and the ion charge-state distribution from XMDYN to resultsfor the thermalized system based on the average-atom model implemented in XATOM, an ab-initio x-ray atomic physics toolkit extended to include a plasma environment. Further, we alsocompare the average charge evolution of diamond with the predictions of a Boltzmann continuumapproach. We demonstrate that XMDYN results are in good quantitative agreement with theabove mentioned approaches, suggesting that the current implementation of XMDYN is a viableapproach to simulate the dynamics of x-ray-driven non-equilibrium dynamics in solids. In orderto illustrate the potential of XMDYN for treating complex systems we present calculations on thetriiodo benzene derivative 5-amino-2,4,6-triiodoisophthalic acid (I3C), a compound of relevance ofbiomolecular imaging, consisting of heavy and light atomic species. . INTRODUCTION X-ray free-electron lasers (XFELs) [1, 2] provide intense radiation with a pulse durationdown to only tens of femtoseconds. The cross sections for the elementary atomic processesduring x-ray–matter interactions are small. Delivering high x-ray fluence can increase theprobabilities of photoionization processes to saturation [3]. Nonlinear phenomena arise be-cause of the complex multiphoton ionization pathways within molecular or dense plasmaenvironment [4–8]. Theory has a key role in revealing the importance of different mech-anisms in the dynamics. Many models have been developed for this purpose using bothparticle and continuum approaches [9–17]. In order to give a complete description of theevolution of the atomic states in the plasma, one needs to account for the possible occurrenceof all electronic configurations of the atoms/ions. A computationally demanding situationarises when a plasma consists of heavy atomic species [18, 19]. For example, at a photonenergy of 5.5 keV, the number of electronic configurations accessible in a heavy atom such asxenon ( Z =54) is about 20 million [19]. If one wants to describe the accessible configurationspace of two such atoms, one must deal with (2 × ) = 4 × electronic configurations.It is clear that following the populations of all electronic configurations in a polyatomic sys-tem as a function of time is a formidable task. To avoid this problem, the approximation ofusing superconfigurations has long been used [20–22]. Moreover, the approach of using a setof average configurations [23, 24] and the approach of limiting the available configurationsby using a pre-selected subset of configurations in predominant relaxation paths [25] hasbeen applied.The most promising approach to address this challenge is to sample the most impor-tant pathways in the unrestricted polyatomic electronic configuration space. This can berealized by using a Monte-Carlo strategy, which is straightforward to implement in a par-ticle approach. In the present study we simulate the effect of individual ultrafast XFELpulses of different intensities incident on a model system of carbon atoms placed on a latticeand analyze the quasi-equilibrium plasma state of the material reached through ionizationand electron plasma thermalization. In order to have a comprehensive description duringelectron plasma thermalization we include all possible atomic electronic configurations forMonte-Carlo sampling, and no pre-selection of transitions and configurations is introduced.To this end, we use XMDYN [7, 8, 26], a Monte-Carlo molecular-dynamics based code.3MDYN gives a microscopic description of a polyatomic system, and phenomena suchas sequential multiphoton ionization [3, 18], nanoplasma formation [8], thermalization ofelectrons through collisions and thermal emission [8] emerge as an outcome of a simulation.Probabilities of transitions between atomic states are determined by cross-section and ratedata that are calculated by XATOM [26–28], a toolkit for x-ray atomic physics. In XMDYNindividual ionization and relaxation paths are generated via a Monte-Carlo algorithm. Arecent extension of XMDYN to periodic boundary conditions allows us to investigate bulksystems [29, 30].To validate the XMDYN approach towards a free-electron thermal equilibrium, we use anaverage-atom (AA) extension of XATOM [31], which is based on concepts of average-atommodels used in plasma physics [32–36]. AA gives a statistical description of the behaviorof atoms immersed in a plasma environment. It calculates plasma properties such as ioncharge-state populations and plasma electron densities for a system with a given temper-ature. We compare the electron temperatures and ion charge-state distributions providedby XMDYN and AA. We also make a comparison between predictions for the ionizationdynamics in irradiated diamond obtained by the XMDYN particle approach and resultsfrom a Boltzmann continuum approach published recently [25]. With these comparisons, wedemonstrate the potential of the XMDYN code for the description of high-energy-densitybulk systems in and out of equilibrium.Finally, we consider a complex system of 5-amino-2,4,6-triiodoisophthalic acid (I3C incrystalline form) consisting of heavy and light atomic species. We show the evolution of av-erage atomic charge states and free electron thermalization. We demonstrate that XMDYNcan simulate the dynamics of x-ray-driven complex matter with all the possible electronicconfigurations without pre-selecting any pathways in the electronic configuration space. II. THEORETICAL BACKGROUNDA. XMDYN: Molecular dynamics with super-cell approach
XMDYN [26] is a computational tool to simulate the dynamics of matter exposed tohigh-intensity x rays. A hybrid atomistic approach [14, 26] is applied where neutral atoms,atomic ions and ionized (free) electrons are treated as classical particles, with defined po-4ition and velocity vectors, charge and mass. The molecular-dynamics (MD) technique isapplied to calculate the real-space dynamics of these particles by solving the classical equa-tions of motion numerically. XMDYN treats only those orbitals as being quantized that areoccupied in the ground state of the neutral atom. It keeps track of the electronic config-uration of all the atoms and atomic ions. XMDYN calls the XATOM toolkit on the fly,which provides rate and cross-section data of x-ray-induced processes such as photoioniza-tion, Auger decay, and x-ray fluorescence, for all possible electronic configurations accessibleduring intense x-ray exposure. Probabilities derived from these parameters are then usedin a Monte-Carlo algorithm to generate a realization of the stochastic inner-shell dynamics.XMDYN includes secondary (collisional) ionization and recombination, the two most impor-tant processes occurring due to an environment. XMDYN has been validated quantitativelyagainst experimental data on finite samples calculated within open boundary conditions[7, 8].Our focus here is the bulk properties of highly excited matter. XMDYN uses the conceptof periodic boundary condition (PBC) to simulate bulk behavior [29, 30]. In the PBCconcept, we calculate the irradiation-induced dynamics of a smaller unit, called a super-cell. A hypothetical, infinitely extended system is constructed as a periodic extension ofthe super-cell. The Coulomb interaction is calculated for all the charged particles insidethe super-cell within the minimum image convention [37]. Therefore, the total Coulombforce acting on a charge is given by the interaction with other charges within its well-definedneighborhood containing also particles of the surrounding copies of the super-cell.
B. Impact ionization and recombination
While core excited states of atoms decay typically within ten or less femtoseconds, elec-tron impact ionization and recombination events occur throughout the thermalization pro-cess and are in dynamical balance in thermal equilibrium. The models used in this studyconsider these processes on different footing that we overview in this section. Within theXMDYN particle approach, electron impact ionization is not a stochastic process (i.e., norandom number is needed in the algorithm), but it depends solely on the real space dynamics(spatial location and velocity) of the particles and on the cross section. When a classical freeelectron is close to an atom/ion, its trajectory is extrapolated back to an infinite distance5n the potential of the target ion by using energy and angular momentum conservation.Impact ionization occurs only if the impact parameter at infinity is smaller than the radiusassociated with the total electron impact ionization cross section. The total cross sectionis a sum of partial cross sections evaluated for the occupied orbitals, using the asymptotickinetic energy of the impact electron. In the case of an ionization event the orbital to beionized is chosen randomly, according to probabilities proportional to the subshell partialcross sections. XMDYN uses the binary-encounter-Bethe (BEB) cross sections [38] suppliedwith atomic parameters calculated with XATOM. Similarly, in XMDYN recombination is aprocess that evolves through the classical dynamics of the particles. XMDYN identifies forthe ion that has the strongest Coulomb potential for each electron and calculates for howlong this condition is fulfilled. Recombination occurs when an electron remains around thesame ion for n full periods (e.g., n = 1) [26, 39]. While recombination can be identifiedbased on this definition, the electron is still kept classical if its classical orbital energy ishigher than the orbital energy of the highest considered orbital i containing a vacancy. Whenthe classical binding becomes stronger, the classical electron is removed and the occupationnumber of the corresponding orbital is incremented by one. Although treating recombi-nation the above way is somewhat phenomenological (e.g., no cross section derived frominverse processes is used), in particle simulations similar treatments are common [39–41].This process corresponds to three-body (or many-body) recombination as energy of electronsis transferred to other plasma electrons leading to the recombination event. The three-bodyrecombination is the predominant recombination channel in a warm-dense environment. C. Electron plasma analysis
Electron plasma is formed when electrons are ejected from atoms in ionization eventsand stay among the ions through an extensive period as, e.g., in bulk matter. The plasmadynamics are governed not only by the Coulomb interaction between the particles but also bycollisional ionization, recombination, and so on. XMDYN follows the system from the veryfirst photoionization event through non-equilibrium states until free electron thermalizationis reached asymptotically. In order to quantify the equilibrium properties reached, we fit6he plasma electron velocity distribution using a Maxwell-Boltzmann distribution, f ( v ) = s(cid:18) πT (cid:19) πv e − v T , (1)where T represents the temperature (in units of energy), and v is the electron speed. Atomicunits are used unless specified. With the function defined in Eq. (1) we fit the temperature,which is used later to compare with equilibrium-state calculations. III. VALIDATION OF THE METHODOLOGY
In order to validate how well XMDYN can simulate free electron thermalization dynamics,we compare AA, where full thermalization is assumed, and XMDYN after reaching a thermalequlibrium. We first consider a model system consisting of carbon atoms. For a reasonablecomparison of the results from XMDYN and AA, one should choose a system that can beaddressed using both tools. AA does not consider any motion of atomic nuclei. Therefore wehad to restrict the translational motion of atoms and atomic ions in XMDYN simulations aswell. In order to do so, we set the carbon mass artificially so large that atomic movementswere negligible throughout the calculations. Further, we increased the carbon-carbon dis-tances to reduce the effect of the neighboring ions on the atomic electron binding energies.In XMDYN simulations, we chose a super-cell of 512 carbon atoms arranged in a diamondstructure, but with a 13.16 ˚A lattice constant (in case of diamond it is 3.567 ˚A). The numberdensity of the carbon atoms is ρ = 3 . × − ˚A − , which corresponds to a mass densityof 0 . / cm . Plasma was generated by choosing different irradiation conditions typical atXFELs. Three different fluences, F low = 6.7 × ph /µ m , F med = 1.9 × ph /µ m , and F high = 3.8 × ph /µ m , were considered. In all three cases the photon energy and pulseduration were 1 keV and 10 fs (full width at half maximum), respectively. From XMDYNplasma simulations shown in Fig. 1, the time evolution of the temperature of the electronplasma is analyzed by fitting to Eq. (1). Counterintuitively, right after photon absorptionhas finished, the temperature is still low, and then it gradually increases although no moreenergy is pumped into the system. The reason is that during the few tens of femtosecondsirradiation the fast photoelectrons are not yet part of the free electron thermal distribu-tion; initially only the low-energy secondary electrons and Auger electrons that have lost7 arameters Low fluence Medium fluence High fluence Fluence (ph/ µ m ) 6 . × . × . × Energy absorbed per atom (eV) 29 665 1170XMDYN temperature (eV) 7 57 91AA temperature (eV) 6 60 83TABLE I. Final temperatures obtained from XMDYN runs after 250 fs propagation and from AAcalculations. XMDYN temperatures are obtained from fitting using Eq. (1), while AA temperaturesare obtained from the absorbed energy–temperature relation (Fig. 2). a significant part of their energy in collisions determine the temperature. The fast elec-trons thermalize on longer timescales as shown in Figs. 1(b) and (c), contributing to theequilibrated subset of electrons. In all cases equilibrium is reached within 100 fs after thepulse.AA calculates only the equilibrium properties of the system, which means that it doesnot consider the history of the system’s evolution through non-equilibrium states. We firstcalculate the total energy per atom, E ( T ), as a function of temperature T within a carbonsystem of density ρ . E ( T ) = X p ε p ˜ n p ( µ, T ) Z r ≤ r s d r | ψ p ( r ) | , (2)where p is a one-particle state index, ε p and ψ p are corresponding orbital energy and orbital,and ˜ n p stands for the fractional occupation numbers at chemical potential µ . Details arefound in Ref. [31]. In this way we obtain a relation between the average energy absorbed peratom, ∆ E = E ( T ) − E (0), and the electron temperature (see Fig. 2). From XMDYN theaverage number of photoionization events per atom, n ph , is available for each fluence point,and therefore the energy absorbed on average by an atom is known (= n ph × ω ph , where ω ph is the photon energy). Using this value we can select the corresponding temperature thatAA yields. This temperature is compared with that fitted from XMDYN simulation. Allthese results are in reasonable agreement, as shown in Table I. Later we use this temperaturefor calculating the charge-state distributions.Figure 3 shows the kinetic-energy distribution of the electron plasma (in the left panels)and the charge-state distributions (in the right panels) for the three different fluences. Thecharge-state distributions obtained from XMDYN at the final timestep (250 fs) are compared8
50 100 150 200 250
Time [fs] T e m p e r a t u r e [ e V ] Low Fluence
Time [fs] T e m p e r a t u r e [ e V ] MediumFluence
Time [fs] T e m p e r a t u r e [ e V ] High Fluence (a)(b)(c)
FIG. 1. Time evolution of the temperature of the electron plasma within XMDYN simulationduring and after x-ray irradiation at different fluences: (a) F low = 6.7 × ph /µ m , (b) F med =1.9 × ph /µ m and (c) F high = 3.8 × ph /µ m . In all three cases, the pulse duration is 10 fsFWHM; the pulse was centered at 20 fs, and the photon energy is 1 keV. The black curve representsthe Gaussian temporal envelope. Note that in all cases equilibrium is reached within 100 fs afterthe pulse. to those obtained from AA at the temperatures specified in Table I. Although similar chargestates are populated using the two approaches, differences can be observed: AA yieldsconsistently higher ionic charges than XMDYN (20%–30% higher average charges) for thecases investigated. 9
250 500 750 1000
Temperature [eV] E n e r g y a b s o r b e dp e r a t o m [ e V ] FIG. 2. Relation between plasma temperature and energy absorbed per atom in AA calculationsfor a carbon system of mass density 0 . / cm . This is probably for the following reasons. XMDYN calls XATOM on the fly to calculatere-optimized orbitals for each electronic configuration. In this way XMDYN accounts forthe fact that ionizing an ion of charge Q costs less energy than ionizing an ion of charge Q +1. However, in the current implementation of AA, this effect is not considered. At agiven temperature, AA uses the same orbitals (and, therefore, the same orbital energies)irrespective of the charge state. A likely consequence is that AA gives more populationto higher charge states, simply because their binding energies are underestimated. Thatcould also be the reason why AA produces wider charge-state distributions and predicts asomewhat higher average charge than XMDYN does. The other reason for the discrepan-cies could be the fact that XMDYN treats only those orbitals as being quantized that areoccupied in the ground state of the neutral atom. For carbon, these are the 1 s, s , and 2 p or-bitals. All states above are treated classically in XMDYN, resulting in a continuum of boundstates. As a consequence, the density of states is different and it may yield different orbitalpopulations and therefore different charge-state distributions. Moreover, while free-electronthermalization has been ensured the bound electrons are not necessarily fully thermalizedin XMDYN. In spite of the discrepancies observed, XMDYN and AA equilibrium propertiesare in reasonably good agreement.We also performed simulations under the conditions that had been used in a recentpublication using a continuum approach [25]. In these simulations, we do not restrict nuclearmotions. A Gaussian x-ray pulse of 10 fs FWHM was used. The intensities considered liewithin the regime typically used for high-energy-density experiments : I max = 10 W / cm
20 40 60 80 100
Energy [eV] P r o b a b ili t y d e n s i t y [ a r b . un i t s ] Low Fluence
Charge F r a c t i o n a li o n y i e l d Low Fluence
XMDYNAA
Energy [eV] P r o b a b ili t y d e n s i t y [ a r b . un i t s ] Medium Fluence
Charge F r a c t i o n a li o n y i e l d Medium Fluence
Energy [eV] P r o b a b ili t y d e n s i t y [ a r b . un i t s ] High Fluence
Charge F r a c t i o n a li o n y i e l d High Fluence (a) (b)(c) (d)(e) (f)
FIG. 3. Kinetic-energy distribution of the electron plasma and charge-state distributions fromAA and XMDYN simulations (250 fs after the irradiation) for the low fluence (a,b), the mediumfluence (c,d), and the high fluence (e,f).
Time [fs] A v e r ag ee n e r g y p e r a t o m Photon energy 5000 eVPhoton energy 1000 eV
FIG. 4. Average energy absorbed per atom within diamond irradiated with a Gaussian pulse ofhard and soft x rays of ω ph = 5000 eV, I max = 10 W / cm and ω ph = 1000 eV, I max = 10 W / cm ,respectively. In both cases, a pulse duration of 10 fs FWHM was used.
50 100 150 200 250
Time [fs] A v e r ag ec h a r g e XMDYNContinuum approach
Photon energy = 5000 eV
Time [fs] A v e r ag ec h a r g e XMDYNContinuum approach
Photon energy = 1000 eV (a) (b)
FIG. 5. Average charge within diamond irradiated with a Gaussian pulse of hard and soft x rays of(a) ω ph = 5000 eV, I max = 10 W / cm and (b) ω ph = 1000 eV, I max = 10 W / cm , respectively.In both cases, a pulse duration of 10 fs FWHM was used. for ω ph = 1000 eV, and I max = 10 W / cm for ω ph = 5000 eV. We employed a super-cell of diamond (mass density = 3 .
51 g / cm ) containing 1000 carbon atoms within the PBCframework. In this study, 25 different Monte-Carlo realizations were calculated and averagedfor each irradiation case in order to improve the statistics of the results. For a system of1000 carbon atoms each XMDYN trajectory takes 45 minutes of runtime. The averageenergy absorbed per atom [Fig. 4] is ∼
28 eV and ∼
26 eV, respectively, for the 1000-eVand 5000-eV photon-energy cases, in agreement with Ref. [25]. Figure 5 shows the timeevolution of the average charge for the two different photon energies. Average atomic chargestates of +1.1 and +0.9, respectively, were obtained long after the pulse was over. Althoughthe rapid increase of the average ion charge is happening on very similar times, the chargevalues at the end of the calculation are 30% and 40% higher than those in Ref. [25] for the1000-eV and 5000-eV cases, respectively [Fig. 5(a,b)].We can name two reasons that can cause such differences in the final charge states. Oneis that two different formulas for the total impact ionization cross section were used in thetwo approaches. In Ref. [25] the cross sections are approximated from experimental groundstate atomic and ionic data [42], while XMDYN employs the semi-empirical BEB formulataking into account state-specific properties. Figure 6 compares these cross sections forneutral carbon atom. It can be seen that the cross section and, therefore, the rate of theionization used by XMDYN are larger, which can shift the final average charge state higher12 Energy [eV] C r o ss - s ec t i o n [ m ] × -20 XMDYNContinuum approach
FIG. 6. Comparison of impact ionization cross sections for neutral ground-state carbon used inthe current work within XMDYN based on the BEB formula [38], and the cross sections used inthe continuum approach of Ref. [25] based on experimental data. as well. The second reason is the evaluation of the three-body recombination cross section.In Ref. [25] recombination is defined using the principle of microscopic reversibility whichstates that the cross section of impact ionization can be used to calculate the recombinationrate [43]. In the current implementation of the Boltzmann code the two-body distributionfunction is approximated using one-body distribution functions in the evaluation of the ratefor three-body recombination, whereas in XMDYN correlations at all levels are naturallycaptured within the classical framework due to the explicit calculation of the microscopicelectronic fields.
IV. APPLICATION
In order to demonstrate the capabilities of XMDYN we investigate the complex systemof crystalline form I3C (chemical composition: C H I NO · H O) [44] irradiated by intensex rays. I3C contains the heavy atomic species iodine, which makes it a good prototype forinvestigations of experimental phasing methods based on anomalous scattering [45–50]. Weconsidered pulse parameters used at an imaging experiment recently performed at the LinacCoherent Light Source (LCLS) free-electron laser [51]. The photon energy was 9.7 keVand the pulse duration was 10 fs FWHM. Two different fluences were considered in thesimulations, F high = 1.0 × ph /µ m (estimated to be in the center of the focus) and its13alf value F med = 5.0 × ph /µ m . In these simulations, we do not restrict nuclear motions.The computational cell used in the simulations contained 8 molecules of I3C (184 atomsin total). The time propagation ends 250 fs after the pulse. For the analysis 50 XMDYNtrajectories are calculated for both fluence cases. These trajectories sample the stochasticdynamics of the system without any restriction of the electronic configuration space thatpossesses (2 . × ) possible configurations considering the subsystem of the 24 iodineatoms only. The calculation of such an XMDYN trajectory takes approximately 150 minuteson a Tesla M2090 GPU while the same calculation takes 48 hours on Intel Xenon X56602.80GHz CPU (single core).Figure 7 shows the average charge for the different atomic species in I3C as a functionof time. Both fluences pump enormous energy in the system predominantly through thephotoionization of the iodine atoms due to their large photoionization cross section. Inboth cases almost all the atomic electrons are removed from the light atoms, but mainly viasecondary ionization. The ionization of iodine is very efficient: already when applying theweaker fluence F med , the iodine atoms lose on average roughly half of their electrons, whereasfor the high fluence case the average atomic charge goes even above +40. Further, we alsoinvestigate the free electron thermalization. The plasma electrons reach thermalization vianon-equilibrium evolution within approximately 200 fs. The Maxwellian distribution of thekinetic energy of these electrons corresponds to very high temperatures: 365 eV for F med and 1 keV for F high (see Fig. 8). Hence, we have shown that XMDYN is a tool that can treatsystems with 3D spatial inhomogeneity, whereas the continuum models usually deal withuniform or spherically symmetric samples. If the sample includes heavy atomic species, pre-selecting electronic configurations can affect the dynamics of the system. XMDYN allows fora flexible treatment of the atomic composition of the sample and, particularly, easy accessto the electronic structure of heavy atoms with large electronic configuration space. V. CONCLUSIONS
We have investigated the electron plasma thermalization dynamics of x-ray-heated carbonsystems using the simulation tool XMDYN and compared its predictions to two other con-ceptually different simulation methods, the average-atom model (AA) and the Boltzmanncontinuum approach. Both XMDYN and AA are naturally capable to address ions with14
20 40 60 80 100
Time [fs] A v e r ag ec h a r g e Time [fs] A v e r ag ec h a r g e Gaussian beamHydrogenCarbonNitrogenOxygenIodine (a) (b)
FIG. 7. Average atomic charge in I3C as a function of time for (a) F med = 5.0 × ph /µ m and(b) F high = 1.0 × ph /µ m , respectively. In both cases, a pulse duration of 10 fs FWHM wasused. The black curve represents the Gaussian temporal envelope. The photon energy was 9.7 keV. Energy [eV] P r o b a b ili t y d e n s i t y [ a r b i t r a r y un i t s ] Medium Fluence
Energy [eV] P r o b a b ili t y d e n s i t y [ a r b i t r a r y un i t s ] High Fluence (a) (b)
FIG. 8. Kinetic-energy distribution of the electron plasma in I3C from XMDYN simulations (250 fsafter the irradiation) for (a) the medium fluence and (b) the high fluence. arbitrary electronic configurations, a very common situation in high-energy-density mattergenerated by, e.g., high-intensity x-ray irradiation. We found very similar quasi-equilibriumtemperatures for the two methods. Qualitative agreement can be observed between the pre-dicted ion charge-state distributions, although AA tends to yield somewhat higher charges.The reason could be that, in the current implementation, AA uses fixed atomic bindingenergies irrespective of the atomic electron configuration. We have also compared resultsfrom XMDYN and the Boltzmann continuum approach for free electron thermalization dy-namics of XFEL-irradiated diamond as a validation of our approach. Thermal equilibrium15f the electron plasma is reached within similar times in the two descriptions, althoughthe asymptotic average ion charge states are somewhat different. The discrepancy couldbe attributed to the different approaches for impact ionization and recombination processesin the two models and to different parametrizations used in the simulation. Moreover, wehave considered a complex system, crystalline I3C, containing the heavy atomic speciesiodine. We calculated the dynamics and evolution of the system from an x-ray-inducednon-equilibrium state to a state where the plasma electrons are thermalized and hot densematter is formed. The atomic electronic configurations for iodine are taken into accountin full detail. Therefore, with XMDYN the treatment of systems including heavy atomicspecies (exhibiting complex inner-shell relaxation pathways) is comprehensive and expectedto be reliable. Finally, we note that, in contrast to a Boltzmann continuum approach, itis straightforward within XMDYN to treat spatially inhomogeneous systems consisting ofseveral or even many atomic species.
ACKNOWLEDGEMENT
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