RELATIVISTIC LONGITUDINAL MODULATIONAL INSTABILITY OF COUPLED ELECTRON-CYCLOTRON WAVES

The longitudinal modulational instabilities of two finite-amplitude el ectron cyclotron waves due to the ponderomotive force and the relativi stic mass variation of the electron are considered using the coupled n onlinear Schrodinger equations. The waves are modulationally unstable with a maximum growth rate larger than that of single wave. The result s show that the instability is caused by the relativistic mass variati on and it can be enhanced by the ponderomotive force. The relativistic modulational instability of two copropagating waves has a convective nature, and it can give a serious damage to the beat-wave particle acc elerator. The instabilities of counterpropagating waves have an absolu te nature. The modulational instability of counterpropagating waves wi th a very small amplitude backward wave has a considerably large growt h rate. Thus, the stimulated Brillouin backward scattered wave is rega rded as a backward pump, and the modulational instability of a single wave can be absolute.