Electron Heating and Landau Damping in Intense Localized Electric Fields

Abstract

A systematic kinetic-theory treatment of the interaction of electrons and ions with intense high-frequency localized electrostatic fields is formulated. A generalization of the familiar nonlinear Schr\"odinger equation includes nonlinear Landau-damping effects which prevent soliton collapse. An analytic calculation predicts a heated-electron distribution behaving asymptotically as $\mathrm{exp}(\ensuremath{-}\frac{v}{{v}_{0}})$ (${v}_{0}=\frac{e{\mathcal{E}}_{0}}{4m{\ensuremath{\omega}}_{0}}$) and modulated in the region near the localized field to form streamers in phase space.