Kinetic Boltzmann equations are used to model the ionization and expansion dynamics of xenon clusters irradiated with short intense VUV pulses. This unified model includes predominant interactions that contribute to the cluster dynamics induced by th
is radiation. The dependence of the evolution dynamics on cluster size, $N_{atoms}=20-90000$, and pulse fluence, $F=0.05-1.5$ J/cm$^2$, corresponding to intensities in the range, $10^{12}-10^{14}$ W/cm$^2$ and irradiation times, $leq 50$ fs, is investigated. The predictions obtained with our model are found to be in good agreement with the experimental data. We find that during the exposure the cluster forms a shell structure consisting of a positively charged outer shell and a core of net charge equal to zero. The width of these shells depends on the cluster size. The charged outer shell is large within small clusters ($N_{atoms}=20,70$), and its Coulomb explosion drives the expansion of these clusters. Within the large clusters ($N_{atoms}=2500,90000$) the neutral core is large, and after the Coulomb explosion of the outer shell it expands hydrodynamically. Highly charged ions within the core recombine efficiently with electrons. As a result, we observe a large fraction of neutral atoms created within the core, its magnitude depending on the cluster size.
Non-equilibrium processes following the irradiation of atomic clusters with short pulses of vacuum ultraviolet radiation are modelled using kinetic Boltzmann equations. The dependence of the ionization dynamics on the cluster size is investigated. Th
e predictions on: (i) the maximal and average ion charge created, (ii) ion charge state distribution, (iii) average energy absorbed per atom, (iv) spatial charge distribution, and (v) thermalization scales are obtained for spherical xenon clusters containing: 20, 70, 2500 and 90000 atoms. These clusters were exposed to single rectangular pulses of vacuum ultraviolet radiation of various pulse intensities, I ~ 10^{12}-10^{14} W/cm^2 and durations < 50 fs, at a fixed integrated radiation flux of F=0.4 J/cm^2. The results obtained are found to be in good agreement with the available experimental data, especially the dependence on the cluster size, if it is assumed that the ions from the positively charged outer layer of the cluster constitute the dominant contribution to the experimentally measured ion charge state distribution.
The kinetic Boltzmann equation is used to model the non-equilibrium ionization phase that initiates the evolution of atomic clusters irradiated with single pulses of intense vacuum ultraviolet radiation. The duration of the pulses is < 50 fs and thei
r intensity in the focus is < 10^{14} W/cm^2. This statistical model includes various processes contributing to the sample dynamics at this particular radiation wavelength, and is computationally efficient also for large samples. Two effects are investigated in detail: the impact of the electron heating rate and the effect of the plasma environment on the overall ionization dynamics. Results on the maximal ion charge, the average ion charge and the average energy absorbed per atom estimated with this model are compared to the experimental data obtained at the free-electron-laser facility FLASH at DESY. Our analysis confirms that the dynamics within the irradiated samples is complex, and the total ionization rate is the resultant of various processes. In particular, within the theoretical framework defined in this model the high charge states as observed in experiment cannot be obtained with the standard heating rates derived with Coulomb atomic potentials. Such high charge states can be created with the enhanced heating rates derived with the effective atomic potentials. The modification of ionization potentials by plasma environment is found to have less effect on the ionization dynamics than the electron heating rate. We believe that our results are a step towards better understanding the dynamics within the samples irradiated with intense VUV radiation.
