Nonlinear coupling of a modulated wave and a low-frequency mode is shown to produce a resonant interaction and instability when the Cherenkov condition $v_p=v_g$ $cos\theta$ is satisfied for the phase velocity $v_p$ of the low-frequency mode, the group velocity $v_g$ of the modulated wave, and the angle $\theta$ between the two wave vectors. This effect stimulates the self-trapping (modulational instability) or self-focusing of the modulated wave. Examples are shown for the cases of couplings between plasma cyclotron waves and magnetohydrodynamic (MHD) modes.

• Received 23 June 1969

DOI:https://doi.org/10.1103/PhysRevA.1.1746