Electron Heating and Landau Damping in Intense Localized Electric Fields

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 Schrödinger equation includes nonlinear Landau-damping effects which prevent soliton collapse. An analytic calculation predicts a heated-electron distribution behaving asymptotically as $\exp (-\frac{v}{v_0})$ ($v_0=\frac{e{\mathcal{E}}_0}{4m{\omega }_0}$) and modulated in the region near the localized field to form streamers in phase space.