Ion Oscillations in Multistream Plasmas

Abstract

Longitudinal ion oscillations (including ion-ion oscillations) in two-stream and multistream plasmas are discussed using first the fluid equations and then the Vlasov equations. Ion oscillations occur when the electron inertia is small compared with the electron pressure, or, stated in an alternative way, when the magnitude of the phase velocity of the wave relative to the electrons is less than the electron thermal speed. The fluid approach to the subject fails to treat in an adequate way the damping effect of the ion thermal motions and therefore cannot provide precise criteria for stability. Furthermore, in a collisionfree plasma it is not clear from the fluid treatment whether the electrons fluctuate isothermally or adiabatically, and to this extent there is some doubt whether ion oscillations are possible in the absence of electron-electron collisions. On the assumption that collisions are of negligible effect, the Vlasov equations are then used to derive an ion oscillation dispersion relation in which, for wavelengths greater than the electron Debye length, the ion plasma frequencies are reduced by the screening effect of the electrons. This equation shows that the electron gas fluctuates isothermally and the electron density therefore varies according to the Boltzmann law. The stability of ion-ion oscillations in multistream plasmas is then considered. It is shown, for example, that the sufficient condition for stability for all possible velocities of the ion streams is that -1/Te >or= 0.2847, where Te is the electron temperature and is the mean reciprocal of the ion temperatures. This result is for singly-charged ions and is readily generalized for multiply-charged ions. When the multistream medium consists of two identical counterstreaming plasmas the condition that there are no exponentially time growing ion oscillations is determined in terms of the plasma velocities.