(The) nonlinear effects by the ponderomotive wave in free electron laser

Abstract

We investigate the nonlinear effects due to the interactions between the reaivistic beam electrons and the ponderomotive potential wave in free electron laser. This ponderomotive potential wave comes from the beating of the wiggler magnetic field($B_w$) and the scattered electromagnetic waves($E_s,\;B_s$). We calculate the growth rate of the scattered electromagnetic waves in the relativistic electron beam frame, and again reduce the result to that in the laboratory frame. Firstly, we show that the linear growth rate($\gamma$L) obtained from the energy conservation law is same as that exactly calculated from the Vlasov-Maxwell equations. Therefore we can apply the energy conservation law to obtaining the nonlinear growth rate($\gamma$NL). In early stages(t/$\gamma\ll$1), $\gamma$NL reduced to $\gamma$L. As t/ goes to infinity the equilibrium BGK are formed in which the beam electrons, the wiggler magnetic field and a finite amplitude primary electromagnetic wave coexist in quasi-steady equilibrium.