Relativistic transverse modulational instability of two electron cyclotron waves

The transverse modulational instabilities of two finite-amplitude electron-cyclotron waves due to the ponderomotive force and relativistic mass variation of electrons are considered using the coupled nonlinear Schrödinger equation model. The waves are modulationally unstable, with maximum growth rate larger than that of a single wave. The stable waves can be unstable by the effect of coupling. The instability is caused only by the mass variation of electrons, and the contribution of the ponderomotive force is negligibly small. The instability of copropagating waves has a convective nature and that due to the counterpropagating waves has an absolute nature, no matter how large the pump intensities are. The threshold of modulational instability is also considered for finite-length plasmas.