Electron-relocalization dynamics in xenon clusters in intense soft-x-ray fields

Intense and temporally structured x-ray laser fields enable the controlled generation of strongly coupled nonequilibrium cluster nanoplasmas and the time-resolved investigation of their dynamics. Recent femtosecond pump-probe experiments on xenon clusters revealed subpicosecond relaxation dynamics in the cluster nanoplasma via delay-dependent charge states of emitted atomic ions [M. Krikunova et al., J. Phys. B: At. Mol. Opt. Phys. 45, 105101 (2012)]. Here we report a scheme based on local electron single-particle energy spectra that enables microscopic tracing of the underlying electron-relocalization processes in molecular dynamics simulations up to the strong-coupling regime. We find more efficient recombination in the cluster core and delay-dependent ion charge states, in good agreement with experiments. Our method is applicable to any particle-based plasma simulation and expected to offer insights into correlated relaxation processes in inhomogenous, strongly coupled plasmas.

Figure 1

Time-dependent pathways of Xe${}_{923}$ in the density-temperature plane for pump (black) and pump-probe excitation (colored, delays as indicated). Crosses show respective snapshots in time, measured relative to the peak of the pump pulse; the temperature $T$ is estimated classically from the mean kinetic energy $k_{\mathrm{B}}T=\frac{2}{3}\langle E_{\mathrm{e}}^{\mathrm{kin}}\rangle$ of delocalized cluster electrons; the density $n$ is derived from the number of delocalized electrons and the cluster radius $R=\sqrt{\frac{5}{3N}{\sum }_{i=0}^N{r}_i^2}$ with the radial atomic positions $r_i$. Arrows indicate the evolution and serve as guide to the eyes. Colored areas indicate different plasma regimes, with the degeneracy parameter $\Theta =k_{B}T/E_F<1$ (Fermi energy $E_F$) for the quantum regime (reddish area) and the Debye number $N_D=4/3\pi n{\lambda }_D^3>1$ (Debye length ${\lambda }_D$) for the weakly coupled regime (bluish area), where $N_D=1$ corresponds to the plasma coupling parameter $\Gamma =1/3$ with $\Gamma =\frac{e^2}{4\pi {\epsilon }_0{k}_{B}T}{\left(\frac{4\pi n}{3}\right)}^{1/3}$. Thus the white area illustrates the strongly coupled regime.

Figure 2

Time-resolved cluster dynamics of a pump-probe excited Xe${}_{923}$ with 100 fs delay, $I_{\mathrm{pump}}=1\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and $I_{\mathrm{probe}}=2I_{\mathrm{pump}}$. (a) Ionization dynamics during and shortly after laser excitation; the time axis is centered to the maximum of the pump pulse; dashed lines refer to the pump-only scenario. (b) Correlation between the average kinetic energy of delocalized electrons (red line) and the increasing cluster radius. (c)–(e) Nanoplasma dynamics in terms of single-particle energy spectra of the electrons with respect to either the continuum threshold [(c) and (e)] or the local quasicontinuum [(d)], see text for details. The evolution of the relocalization as well as the main ionization parameters $Q_{\mathrm{inner}}$, $Q_{\mathrm{outer}}$, and $Q_{\mathrm{eff}}$ are displayed in (f) together with a shell-resolved analysis of the latter. Solid symbols at $t=3$ ps indicate converged values, used for the delay-dependent analysis in Fig. 3.

Figure 3

Delay dependence of inner, outer, and effective charge states, evaluated 3 ps after the probe pulse [see solid symbols in Fig. 2]. $Q_{\mathrm{eff}}^1$ and $Q_{\mathrm{eff}}^2$ denote the effective charge states before and right after the probe pulse. The bluish area illustrates relocalization after probe excitation. Note that $Q_{\mathrm{eff}}^1$ is not fully saturated due to the slower cluster expansion.