Nonlinear Wave-Particle Interactions in Radiation Belt Physics

Earth's radiation belts have undergone considerable theoretical and experimental investigation since their discovery in 1958 by James Van Allen and colleagues.Much of our understanding of wave-particle interactions in the radiation belts has been based on the linear theory of plasma waves and quasi-linear diffusion.There is recent evidence ,however,that fully nonlinear aspects of wave-particle interactions may play an essential role in radiation belt physics.This evidence is in the form of increasingly refined wave and particle data,and,in parallel,recently developed nonlinear wave growth theory supported by self-consistent particle simulations.We examine the nonlinear spatio-temporal evolution of whistler-mode chorus emissions in the Earth's inner magnetosphere.Chorus waves with rising frequency are generated at the magnetic equator,and propagate to higher latitudes.During propagation,nonlinear wave evolution occurs due to interaction with resonant electrons.From model equations we reproduce the time evolution of the chorus wave at the equator.By taking into account the adiabatic variation of the off-equatorial energetic particle distribution,we determine the resonant current.Then by solving general wave equations numerically we obtain the time evolution of the chorus wave frequency and amplitude along the static dipole magnetic field.Further,we incorporate the effects of nonlinear wave growth into the calculation of the Kennel-Petschek limit for the stably-trapped particle flux in a planetary magnetosphere.Using the model chorus equations we estimate nonlinear growth rates for a range of input parameters.By calculating the resulting total wave gain,we are able to estimate the self-limiting particle flux.We compare our new theoretical results for the limiting flux with particle observations at Earth and Saturn.