Multistream Instability in Two and Three-Species Plasmas

Abstract

A detailed parametric investigation of the linear dispersion relation of electron-ion (e-i) and electron-electron-ion (e-e-i) in the hydrogen plasma fluid is carried out in order to determine the different current driven instabilities that can exist in each case. Equations governing the two-stream (e-i) and three-stream (e-e-i) instabilities in cold plasmas are solved numerically and solutions are thoroughly investigated. For the two-stream instability, numerical solutions of the corresponding dispersion relation show the appearance of an
unstable mode for kv_e > 0 , where k is the wave number and v_e is the electron drift speed. Results reported in some references in literature on the peak value of the instability growth rate, when compared with the numerical result, have been found to overestimate the instability maximum growth rate by 17%, while others' estimates coincide with our numerically obtained value. A three-stream instability regime, with two oppositely drifting electron streams with respect to a static ion stream, is also studied; the presence of the third stream has been found to modify the mode spectra by giving rise to a highly unstable mode compared to that observed in the two-stream case. By increasing the number of electrons in the third stream (and keeping a zero net current in the plasma), a red shift in the instability peak value of the growth rate has been observed with an insignificant change in its peak value.

Keywords: Multistream instabilities; Three-species plasma; Kinetic theory.