Quantum Kinetics of Fast-Electron Inelastic Collisions in Partially-Ionized Plasmas

Abstract

Fast electrons in partially ionized plasmas lose energy through inelastic collisions with bound electrons. While the mean energy loss is well described by stopping-power theory, fluctuations associated with discrete excitation and ionization events produce energy straggling and an additional longitudinal diffusion in momentum space. We incorporate this effect into fast-electron kinetics through a derived Fokker-Planck operator whose coefficients are obtained from ab initio quantum many-body simulations. We demonstrate that neglecting inelastic energy diffusion in partially ionized D-Ar plasmas can underestimate primary runaway-electron generation by several orders of magnitude.

Figures (4)

• Figure 1: Particle density distribution of an electron beam undergoing collisional slowing down from initial energy $1\,\mathrm{keV}$ (blue solid) in neutral Ne gas ($n_{Ne}=10^{20}\,\mathrm{m^{-3}}$). For inelastic energy loss: red dashed dotted---convective slowing-down only; green dotted---convective-diffusive (Gaussian) approximation; orange dashed---probabilistic energy transfers for $\Delta t = 0.66 \, \mathrm{\mu s}$, corresponding to about five inelastic collision times. Initial beam width is $5 \, \%$ of the final energy spreading.
• Figure 2: The TDDFT results of (a,b) $T_0$ in keV, (c,d) $\ln I$ and $\ln I_1$ in eV for Ne (a,c) and Ar (b,d), respectively. The HF calculation in (a,b) is the averaged kinetic energy of orbital electrons. Reference results, identified by author names in the legend, are included for comparison Inokuti1978PRACummings1975JCPKumar2010JCPKoga2002JCPSauer2015AQCSauer2018JCP.
• Figure 3: The net energy diffusion frequency $\nu_\parallel$ in pure impurity gases (a,b) and mixture plasmas (c,d). Impurity species are Ne for (a,c) and Ar for (b,d).
• Figure 4: (a), (b) $\frac{dn_{RE}}{dt}$ in $m^{-3}s^{-1}$ as a function of $n_{Ar}$ with $n_D = 2\times10^{19}\,m^{-3}$. (c), (d) The corresponding distribution function $F_0$ yielding steady-state $\frac{dn_{RE}}{dt}$ when $n_{Ar} = 3.31\times 10^{19}\,\mathrm{m^{-3}}$. $T_e = 2 \, \mathrm{eV}, \, E=230 \, \mathrm{V \, m^{-1}}$ for (a), (c) and $T_e = 5 \, \mathrm{eV}, \, E=90 \, \mathrm{V\, m^{-1}}$ for (b), (d), respectively. Blue solid curve neglects free-bound inelastic collisions. Orange dashed and green dotted curves use Eq. \ref{['eq:linearFP']} with the CL and SD asymptotes, respectively. Red dashed dotted curve merely takes $T_b=0$ in all phase space regions. Gray-shaded areas show the region where the collisionless asymptote (Eq. \ref{['eq:const_cl']}) is applied.