NONLINEAR EFFECTS INVOLVING WHISTLER WAVE-PROPAGATION IN THE MAGNETOSPHERE

We consider nonlinear effects associated with the propagation of a quasi monochromatic whistler wave packet along the inhomogeneous geomagnetic field. We show that under the specific conditions of the Siple experiment the whistler packet is subject to the modulational instability, resulting in longitudinal and transverse modulation of the envelope amplitude and the excitation of quasi-neutral density perturbations akin to ion acoustic waves. In particular, we examine the behavior of the wave packet in the vicinity of the region where the group velocity of the packet is a maximum. In general, the wave packet is subject to the competing effects of dispersive broadening and the nonlinear tendency to steepen. In the vicinity of the region of interest the dispersive broadening is small, and the tendency for steepening prevails. This results in the creation of anomolously narrow solitary waves. We analyze the situation analytically using a modification of the nonlinear Schrodinger equation. We evaluate the conditions required for the onset of the modulational instability and find its typical growth rate. We then construct nonlinear traveling wave solutions. These take the form of solitons, which move toward the rear edge of the wave packet. Because the dispersive effects are small, these solitons are narrow structures with steep boundaries. We then analyze the possibility that these solitons act as drivers for triggered emission. The interaction of resonant particles with the wave at the soliton leads to particle bunching in velocity. The resulting current serves as a source term for monochromatic radiation, the frequency of which changes with time as the bunches move in the inhomogeneous geomagnetic field.