Effect of Beam Deceleration in the Two-Stream Instability

Abstract

Two-stream instability induced by the interaction between a proton beam and a plasma is investigated analytically in consideration of the beam deceleration by the nonlinear effect. Expression of beam deceleration is derived from a modification of the orbit of the beam particle due to the wave potential. Nonlinear dispersion relation is obtained from a set of equations which includes the term of the beam deceleration in addition to the perturbation of the beam velocity. Saturation level of the wave potential is determined from the nonlinear growth rate. Result indicates that the beam deceleration due to the nonlinear interaction provides the saturation level which is almost equal to one obtained by the analyses based on the trapping of beam particles.