Molecular-dynamics approach for studying the nonequilibrium behavior of x-ray-heated solid-density matter

When matter is exposed to a high-intensity x-ray free-electron-laser pulse, the x rays excite inner-shell electrons leading to the ionization of the electrons through various atomic processes and creating high-energy-density plasma, i.e., warm or hot dense matter. The resulting system consists of atoms in various electronic configurations, thermalizing on subpicosecond to picosecond timescales after photoexcitation. We present a simulation study of x-ray-heated solid-density matter. For this we use XMDYN, a Monte Carlo molecular-dynamics-based code with periodic boundary conditions, which allows one to investigate nonequilibrium dynamics. XMDYN is capable of treating systems containing light and heavy atomic species with full electronic configuration space and three-dimensional spatial inhomogeneity. For the validation of our approach we compare for a model system the electron temperatures and the ion charge-state distribution from XMDYN to results for 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 also compare the average charge evolution of diamond with the predictions of a Boltzmann continuum approach. We demonstrate that XMDYN results are in good quantitative agreement with the above-mentioned approaches, suggesting that the current implementation of XMDYN is a viable approach to simulate the dynamics of x-ray-driven nonequilibrium dynamics in solids. To illustrate the potential of XMDYN for treating complex systems, we present calculations on the triiodo benzene derivative 5-amino-2,4,6-triiodoisophthalic acid (I3C), a compound of relevance of biomolecular imaging, consisting of heavy and light atomic species.

Figure 1

Time evolution of the temperature of the electron plasma within XMDYN simulation during and after x-ray irradiation at different fluences: (a) ${\mathcal{F}}_{\text{low}}=6.7\times {10}^9\mathrm{ph}/\mu {\mathrm{m}}^2$, (b) ${\mathcal{F}}_{\text{med}}=1.9\times {10}^{11}\mathrm{ph}/\mu {\mathrm{m}}^2$ and (c) ${\mathcal{F}}_{\text{high}}=3.8\times {10}^{11}\mathrm{ph}/\mu {\mathrm{m}}^2$. In all three cases, the pulse duration is 10 fs FWHM; the pulse was centered at 20 fs, and the photon energy is 1 keV. The black curve represents the Gaussian temporal envelope. Note that in all cases equilibrium is reached within 100 fs after the pulse.

Figure 2

Relation between plasma temperature and energy absorbed per atom in AA calculations for a carbon system of mass density $0.07\mathrm{g}/{\mathrm{cm}}^3$.

Figure 3

Kinetic-energy distribution of the electron plasma and charge-state distributions from AA and XMDYN simulations (250 fs after the irradiation) for the low fluence (a, b), the medium fluence (c, d), and the high fluence (e, f).

Figure 4

Average energy absorbed per atom within diamond irradiated with a Gaussian pulse of hard and soft x rays of ${\omega }_{\mathrm{ph}}=5000$ eV, $I_{\text{max}}={10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ and ${\omega }_{\mathrm{ph}}=1000$ eV, $I_{\text{max}}={10}^{16}\mathrm{W}/{\mathrm{cm}}^2$, respectively. In both cases, a pulse duration of 10 fs FWHM was used.

Figure 5

Average charge within diamond irradiated with a Gaussian pulse of hard and soft x rays of (a) ${\omega }_{\mathrm{ph}}=5000$ eV, $I_{\text{max}}={10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ and (b) ${\omega }_{\mathrm{ph}}=1000$ eV, $I_{\text{max}}={10}^{16}\mathrm{W}/{\mathrm{cm}}^2$, respectively. In both cases, a pulse duration of 10 fs FWHM was used.

Figure 6

Comparison of impact ionization cross sections for neutral ground-state carbon used in the current work within XMDYN based on the BEB formula [38], and the cross sections used in the continuum approach of Ref. [25] based on experimental data.

Figure 7

Average atomic charge in I3C as a function of time for (a) ${\mathcal{F}}_{\mathrm{med}}=5.0\times {10}^{12}\mathrm{ph}/\mu {\mathrm{m}}^2$ and (b) ${\mathcal{F}}_{\mathrm{high}}=1.0\times {10}^{13}\mathrm{ph}/\mu {\mathrm{m}}^2$, respectively. In both cases, a pulse duration of 10 fs FWHM was used. The black curve represents the Gaussian temporal envelope. The photon energy was 9.7 keV.

Figure 8

Kinetic-energy distribution of the electron plasma in I3C from XMDYN simulations (250 fs after the irradiation) for (a) the medium fluence and (b) the high fluence.