Nonlinear Plasma Waves. III. Nonlinear Temperature Effects in the Electron—Ion Two-Stream Instability

The nonlinear interaction of two warm interpenetrating electron and ion streams is treated by investigating the traveling wave solutions to the two fluid macroscopic plasma equations. These equations are reduced to the form of a nonlinear differential equation with an additional small nonlinear term. Application of the perturbation procedure, described previous by [J.P. Freidberg, Phys. Fluids 10, 171 (1967)], leads to (1) conditions on the maximum amplitudes for which traveling wave solutions exist and (2) a nonlinear amplitude dependent dispersion relation. An examination of this dispersion relation indicates that below a certain critical temperature there is a range of wavenumbers where the two stream instability may level off before the amplitude reaches the maximum amplitude for existence of traveling wave solutions. This range of wavenumbers decreases with increasing temperture and therefore is largest when the temperature is zero.