On modeling of nonlinear dynamics of an electron beam in a plasma microwave amplifier

The problem of signal amplification in a plasma microwave amplifier is considered in the linear approximation and with allowance for nonlinear effects leading to saturation of instability. The solutions of the exact dispersion equation and an approximate dispersion equation used in calculation of parameters of plasma microwave amplifiers are compared. It is shown that the solutions of these equations in the region of high frequencies are significantly different. Nonlinear dynamics of beam–plasma instability in plasma microwave amplifiers is described by a system of differential equations which is obtained by the slowly varying amplitude method and yields an approximate dispersion equation when it is linearized. A method for modifying parameters of a nonlinear system of differential equations to make it consistent with the exact dispersion equation is proposed and the calculation results are demonstrated.