Nonlocal electron kinetics in a weakly ionized plasma

Abstract

Electron dynamics in a time dependent inhomogeneous electric field in a weakly ionized plasma with elastic electron-neutral collisions is analyzed. We consider the most general ordering when the electron mean free path ${v}_{\mathrm{Te}}/{\ensuremath{\nu}}_{e}$ is arbitrary with respect to the characteristic length scale ${k}^{\ensuremath{-}1}$ of the electric field, and frequency $\ensuremath{\omega}$ of the electric field is arbitrary with respect to the electron collisional frequency ${\ensuremath{\nu}}_{e};$ $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\nu}}_{e}\ensuremath{\sim}{\mathrm{kv}}_{t}.$ In this case the standard two-term approximation is not valid and higher order spherical harmonics in the perturbed electron distribution function should be taken into account. This results in an infinite hierarchy of coupled equations for angular harmonics that can be solved in the form of the infinite continued fraction. This method is easily generalized for a wide class of scattering cross sections with angular dependencies. The developed approach uniformly describes both local (strongly collisional) and nonlocal regimes. As an example, a closed form of the perturbed electron distribution function is found for the argon gas with nonmonotic dependence of the collisional cross section as function of energy (Ramsauer effect). The conductivity and surface impedance of a semi-infinite plasma are calculated in different collisionality regimes, and anomalous penetration of the electric field into such plasma is analyzed. The nonmonotonous behavior of the amplitude of the external electric field inside of a plasma has been recovered for the nonlocal case $(\ensuremath{\zeta}>1)$.