Modification of the Coulomb Logarithm due to Electron-Neutral Collisions

We demonstrate that in partially ionized plasmas, Coulomb scattering can be significantly perturbed by electron collisions with neutral gas particles, and that this effect can be incorporated in the Coulomb collision terms of the Boltzmann equation by a modification of the classical Coulomb logarithm. We show that Boltzmann transport calculations using this modified Coulomb logarithm are in excellent agreement, for a sensitive model problem and a wide range of conditions, with particle simulations describing the many-body Coulomb interactions from first principles.

Figure 1

Electron drift velocity in xenon as a function of reduced electric field strength $E/N$ (units $\mathrm{Td}={10}^{-21}\mathrm{V}{\mathrm{m}}^2$) for different ionization degrees $n_e/N$ (colors) and different gas pressures (left- and right-hand panels), calculated by different methods: first-principles particle simulation (symbols), Boltzmann equation (BE) with full electron-electron collision terms (solid lines), and Boltzmann equation with isotropic electron-electron collision term only (dashed lines).

Figure 2

Electron energy probability function (top) and anisotropy $|F_1/F_0|$ (bottom) in xenon with $n_e/N={10}^{-6}$, for different $E/N$, obtained from first-principles particle simulations (black curves) and from the Boltzmann equation with classical (green curves) and modified (red curves) Coulomb logarithm.

Figure 3

Comparison between the effective Coulomb logarithm ${\sigma }_m^{\mathrm{eff}}/(4\pi {\rho }^2)$ from Eq. (14) and from the approximate Eq. (13) with $\alpha =3$.

Figure 4

Same as Fig. 1 but using the modified Coulomb logarithm of Eq. (16) in the Boltzmann calculations (solid lines), with full electron-electron collision terms.