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 exp(-vv₀) (v₀=eE₀4mω₀) and modulated in the region near the localized field to form streamers in phase space.
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Bezzerides et al. (1975) studied this question.
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