Nonlinear theory of a quasi-monochromatic whistler mode packet in inhomogeneous plasma

A nonlinear theory is developed for a quasi-monochromatic whistler wave packet interacting with the resonant particles in an inhomogeneous plasma. Expressions for the distribution functions for the trapped and untrapped particles are obtained on the basis of generalized theorems of phase volume conservation. A nonlinear equation is derived which describes the space-time evolution of the wave amplitude. The nonlinear growth (damping) rate at large distances from the front edge of the packet is shown to be determined by the difference between the average distribution functions of the trapped and untrapped resonant particles. Qualitative features of the nonlinear evolution of a wave packet in inhomogeneous plasma are investigated.