Numerical investigation of nonequilibrium electron effects on the collisional ionization rate in the collisional-radiative model

The interplay of kinetic electron physics and atomic processes in ultrashort laser-plasma interactions provides a comprehensive understanding of the impact of the electron energy distribution on plasma properties. Notably, nonequilibrium electrons play a vital role in collisional ionization, influencing ionization degrees and spectra. This paper introduces a computational model that integrates the physics of kinetic electrons and atomic processes, utilizing a Boltzmann equation for nonequilibrium electrons and a collisional-radiative model for atomic state populations. The model is used to investigate the influence of nonequilibrium electrons on collisional ionization rates and its effect on the population distribution, as observed in a widely known experiment [Young et al., Nature (London) 466, 56 (2010)]. The study reveals a significant nonequilibrium electron presence during XFEL-matter interactions, profoundly affecting collisional ionization rates in the gas plasma, thereby necessitating careful consideration of the Collisional-Radiative model applied to such systems.

Figure 1

(a) The calculated electron energy distribution function in ${\text{cm}}^{-3}{\text{eV}}^{-1}$ as a function of electron energy (eV) in time during irradiation by $2.5\times {10}^{18}\text{W}/{\text{cm}}^2$ XFEL laser pulse with the pulse duration of 230 fs. The pulse center is in 300 fs and the density of neon plasma is $2\times {10}^{19}{\text{cm}}^{-3}$. (b) The representative electron energy distribution for four different time steps. Two major peaks from KLL Auger decay ($\sim 770\text{eV}$) and photoionization ($\sim 1130\text{eV}$) process are observed first early, followed by other satellite peaks associated with those processes. (c) The evolution of EEDF in a longer timescale. Eventually it ends up with the Maxwell-Boltzmann (MB) distribution with Te $\sim$ 100 eV, which is the same value estimated by the population kinetic calculation part. Modeling beyond the collisional-radiative model, such as the hydrodynamic expansion, conductive energy loss, etc., must be incorporated to accurately describe EEDF in this region, so simulations are conducted to test whether the approach is limited solely to equilibrium conditions.

Figure 2

Experimental and simulated charge state populations for neon plasma heated by a 2000 eV XFEL pulse. The experimental data are depicted in the black bar [20], and the simulation results are represented by the various color bars. The red bar corresponds to a simulation that includes nonequilibrium electrons, and the blue bar reflects the same calculation assuming instant thermalization of free electrons. This instant thermalization scenario closely aligns with the theoretical estimations presented by Young et al. (purple) [20] and Ciricosta et al. (green) [12] as expected.

Figure 3

Comparison of collisional ionization rate between without (a) and with (b) nonequilibrium electron contributions during the XFEL pulse for charge states $+1$ to $+10$. The dotted line represents the photoionization rate for each ion, and it is consistent in both graphs. These plots are presented side by side to facilitate a comparison of collisional ionization rates. The XFEL pulse has the pulse duration of 230 fs whose pulse center is on 300 fs.