Theory and Computer Experiment on Self-Trapping Instability of Plasma Cyclotron Waves

A theory explaining the self‐trapping instability (modulational instability) of plasma cyclotron waves is developed and the results are compared with computer experiments using a sheet current model. The observed growth rate at an initial phase of the instability is in rough agreement with that given by perturbation theory. However, as the level of the modulation increases, the rate of the growth of the modulation increases due to excitation of additional side bands, and finally, the carrier wave is found to collapse suddenly leading to rapid thermalization. The cause of the sudden collapse of the wave is attributed to the crossing of particles which are accelerated in the direction parallel to the ambient magnetic field by a large pressure gradient force, ${\mathrm{\nabla (B\perp }}^2{\text{/2μ}}_0)$ , developed by the instability, where $\mathrm{B\perp }$ is the transverse magnetic field associated with the wave.