Kinetic Nonlinear Buneman's Instability in Field‐Free Isothermal Collisonal Plasma

Abstract

A nonlinear dispersion relation is derived and solved for a 1-D electron-ion two-stream (Buneman) instability excited in an isothermal field-free plasma. The major nonlinear mechanism is the qualilinear modification of the background distribution function. We take into consideration the effect of Coulomb collisions which describes the broadening of the Cherenkov interaction of waves with particles. Nonlinear effects seem to lead, in field-free plasma, to the increase in the current velocity and consequently, to the growth of the instability and a rapid turbulent heating of plasma electrons. The methods used here to solve the Vlasov's kinetic equation may also be used to investigate other types of current micro-instabilities in plasmas.Since the pioneering work of BUNEMAN [l], there has been a revival interest in BUNEMAN'S (or electron-ion two-stream) instability due its connection with the thermal conductivity of laser-heated plasma, plasma heating by relativistic electron beam return currents, and ion acceleration in the nonlinear stage of this instability.This type of instability is excited hydrodynamically [2, 31 when the relative streaming velocity between electrons and ions is much exceeds the electron thermal velocity (u B V,,, u = u, -ui), as in early stages of various pulsed heating experiments (0 -pinch, turbulent heating). The excitation of BUNEMAN'S instability leads to a strong turbulence state of the plasma. Accordingly a strong turbulent heating of the plasma leads to a rapid increase of the threshold current velocity (ut,,) of the instability up to a valaue u. Therefore, it will be of great interest to investigate this instability at a current velocities close to the threshold values, i.e., at Au = u -uCh G u,,,. Besides, at u N VTe the instability is excited kinetically [4-81.In the present work, the development of the kinetic electron-ion two-stream instability (BUNEMAN'S instability) excited in an isothermal (17; = K), field-free plasma is investigated in the nonlinear approximation by considering the quasilinear modification of the background distribution function.Generalizing previous investigations [4 -61, we consider the effect of pair Coulomb collisions.We start by considering the influence of the quasilinear effects near the threshold of the instability and by taking into consideration the pair Coulomb collisions, the field-free Vlasov's kinetic equation is: