Growing transverse waves in a plasma in a magnetic field

Abstract

Instabilities in uniform collisionless plasmas may be relevant to the under-standing of several astrophysical and geophysical problems and to the confinement of plasmas in the laboratory. This paper presents a practicable method for ascertaining the instability of such plasmas in a uniform steady magnetic field with respect to disturbances propagating along the direction of that field. The method is applied to two examples of plasmas having anisotropic pressure, that is, having the pressure p ‖ along the steady magnetic field not equal to the pressure p ⊥ perpendicular to the field. The examples given are those of an electron plasma (with fixed neutralizing background) and of a plasma with two species having equal masses and opposite but equally large charges. The latter example is treated because it is mathematically simpler than an electron-ion plasma, and is referred to as an “electron-positron” plasma. In both examples when p ⊥ > p ‖ unstable electromagnetic type waves occur for all values of the dc magnetic field strength. When p ⊥ > p ‖ a new family of unstable hydromagnetic waves is found in the “electron-positron” plasma. Steady waves with frequency Ω(p ⊥ − p ‖) p ⊥ , where Ω is the electron gyrofrequency, are found in both examples for p ⊥ > p ‖. When p ‖ > p ⊥, classical results for the “hose” instability are recovered and are extended outside the guiding center limit in the case of the plasma with two oppositely charged species. The electron gas with fixed neutralizing background is found to be stable for p ‖ > p ⊥. Most of the results are found to be applicable to real (electron-ion) plasmas. Growth rates of unstable waves are treated in some detail.