A NONLINEAR THEORY OF 2-STREAM INSTABILITY

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. © 1969, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.