Nonstationary self-effect of wave fields in beat accelerators

Abstract

The nonstationary self-effect of wave fields in the excitation of plasma oscillations is studied analytically and numerically. It is assumed that the self-effect is determined by the dependence of the relativistic electron mass on oscillation amplitude in the plasma wave excited at the beat frequency. The dynamics of the wave field self-effect are analyzed for a medium with the corresponding type of nonlinear response relaxation. It is shown that there are exact self-similar solutions of nonstationary equations in the form of compressible filaments (homogeneous wave ducts). The maximum amplitudes of electromagnetic and plasma waves are estimated on the basis of those solutions. Qualitative relationships and conclusions have been confirmed numerically. The cascade processes, by which the electromagnetic wave is scattered by plasma oscillations, are also taken into account. It is shown that cascading does not affect the estimate for the maximum amplitude of the plasma wave.