Influence of atomic kinetics on inverse bremsstrahlung heating and nonlocal thermal transport

This paper describes a computational model that self-consistently combines physics of kinetic electrons and atomic processes in a single framework. The formulation consists of a kinetic Vlasov-Boltzmann-Fokker-Planck equation for free electrons and a non-Maxwellian collisional-radiative model for atomic state populations. We utilize this model to examine the influence of atomic kinetics on inverse bremsstrahlung (IB) heating and nonlocal thermal transport. We show that atomic kinetics affects nonlinear IB absorption rates by further modifying the electron distribution in addition to laser heating. We also show that accurate modeling of nonlocal heat flow requires a self-consistent treatment of atomic kinetics, because the effective thermal conductivity strongly depends on the ionization balance of the plasma.

Figure 1

Simulation of IB heating and ionization of Al at $n_i={10}^{19}{\mathrm{cm}}^{-3}$. The plasma is initially in LTE at 2 ev. (a) Electron temperature, (b) charge state densities, (c) ionization state, and (d) IB absorption coefficient are shown as functions of time. In panel (d), the solid line refers to the absorption coefficient from the simulation, while the dashed line is calculated from Eq. (4) using $\alpha$ from the simulation.

Figure 2

Electron distribution function at 1.3 ps. The solid line is the distribution from simulation, and the dashed and dash-dotted lines are Maxwellian and Langdon distributions, respectively. The Langdon distribution is a super Gaussian distribution of order $m=2.96$, where $m$ is determined from Eq. (5) using $\alpha$ from the simulation. The two analytical distributions are normalized to have the same density and temperature as the actual distribution.

Figure 3

Simulations of IB heating and ionization of (a) Cu and (b) Mo at $n_i={10}^{19}{\mathrm{cm}}^{-3}$. The plasma is initially in LTE at 5 ev. In both plots, the black solid and dashed lines are IB absorption coefficients $R$ and the red dash-dotted lines are the ionization state $Z$. Solid lines refer to the absorption coefficients from the simulation, while dashed lines are calculated from Eq. (4) using $\alpha$ from the simulation.

Figure 4

(a) Temperature and (b) ionization state from both VFBP (solid) and VFP (dashed) simulations at four times: 10, 40, 80 and 140 ps (thermal wave moves from left to right). VBFP simulation includes self-consistent atomic kinetics, while VFP simulation assumes $Z=18$. The crosses mark spatial locations used in Fig. 6

Figure 5

Heat fluxes at 140 ps from VFBP and VFP simulations. Different values of flux-limited SH heat flux are also shown for comparison purpose.

Figure 6

Electron distribution functions at 140 ps and at five different locations as marked in Fig. 4. All distributions are normalized to have same density and energy. The dashed line is the equivalent Maxwellian distribution.