A Nonlinear Theory of Two-Stream Instability

Abstract

The nonlinear development of the two-stream instability in a system of two electron beams with finite temperature is investigated by a perturbation method using macroscopic plasma equations. The equation for the change of amplitude is obtained and shown to be reduced to a nonlinear Schrödinger equation. From this equation it is shown that
(1) a range of wavenumbers exists for which the nonlinearity suppresses the instability before the onset of overtaking and after reaching the limiting amplitude the wave begins to decay.
(2) and that a modulational instability is possible.
The analytical results are compared with direct computer solutions which support the theory.