The Way to Prove the Correctness of Nonlinear Equations of Magnetron Devices

Abstract

Two methods are currently used for description of a nonlinear electron beam – travelling wave interaction in the crossed-field microwave devices. They both pursue the same object – to obtain the equation of electron’s motion in an interaction space of the device and equation of excitation of slow-wave structure by prebunched electron stream. The first method deals with a high frequency field of slow-wave structure as a field of “cold” slow-wave structure with real amplitudes and phases slowly changing along the interaction space. The second one – with slowly changing complex amplitudes in a plane of static trajectory of electron motion. One of the ways to prove the correctness of the method for description of a nonlinear electron beam – travelling wave interaction in crossed field devices is linearisation of the equations of motion and excitation of input and output cascades of the two cascade magnetron frequency multipliers. The characteristic equations of the linearised equations coincide with the widely known equation of dispersion, which is obtained from the linear theory. This proves the correctness of the nonlinear equations.