Two-dimensional self-modulation of a whistler wave propagating along the magnetic field in a plasma

Two-dimensional nonlinear self-modulations of a high-frequency whistler wave propagating along an applied magnetic field in a plasma are investigated. We derive new, fairly broad, regions of modulational instabilities in directions oblique to the initial wave propagation with growth rates much greater than in the case of ‘parallel’ self-modulation. The largest growth rate appears to be for the angles corresponding to the parametric instabilities. Nonlinear solutions describing the envelope solitons propagating obliquely to the initial wave are also discussed. Our results are in qualitative agreement with recent experiments.