Collisionless Electrostatic Shocks

Abstract

A one-dimensional computational model of counter-streaming plasmas exhibits enhanced dynamic friction created by electrostatic instabilities. Buneman and Dawson previously demonstrated the validity of the sheet charge model, and using this model, the collective electrostatic interactions of two contra-streaming plasmas were calculated for mass ratios mi/me = 1, 10, and 100. For initially cold plasma streams KTe = 7.5 × 10−3 (½mev02), KTi = 2.78 × 10−3 (½miv02) (where v0 is the stream velocity), electron oscillations grow to saturation in several electron plasma periods, creating a thermal electron distribution. Ion-electron oscillations then grow to saturation in several ion plasma periods (1/fpi) with mean potentials of approximately (½3miv02) (me/mi)½. These oscillations heat the electrons and thermalize the two ion streams in a time 13 (mi/me)½/fpi. Two nonlinear effects occur (adiabatic electron modulation heating and electron trapping) that maintain the ion-electron instability. A larger mass ratio problem was not calculated because of computational time limitations, but an extrapolation of these results predicts the existence of electrostatic shocks for mi/me = 1836.