Quasi-linear diffusion coefficients for field-aligned electromagnetic waves with applications to the magnetosphere

[1] Much current research in magnetospheric physics is directed toward understanding the dramatic variations in relativistic (> 1 MeV) electron fluxes that can take place in the Earth's outer zone during magnetic storms. The behavior of outer-zone energetic electrons is partly controlled by the competing mechanisms of acceleration and loss that result from wave-particle interactions, in particular electron gyroresonance with ELF, VLF, and electromagnetic ion cyclotron (EMIC) waves. Powerful techniques for treating gyroresonant wave-particle interactions are provided by quasi-linear diffusion theory. In this paper, we derive formulae for the quasi-linear ( momentum, mixed, and pitch-angle) diffusion coefficients for cyclotron resonance with field-aligned electromagnetic waves of any mode and general spectral density. The formulae are fully exact, expressed in closed analytical form, and easily computable. Our results can therefore be readily used to determine accurate diffusion rates for many forms of wave-particle interaction in the magnetosphere and other space plasmas. We find that momentum diffusion rates for MeV electrons in gyroresonance with VLF chorus can be less than a day in the lower-density regions outside the plasmasphere. The mechanism of stochastic acceleration by VLF chorus could therefore be instrumental in generating relativistic electrons during the recovery phase of a magnetic storm. Pitch-angle diffusion rates of MeV electrons scattered by EMIC waves along the plasmapause can approach the limit of strong diffusion. EMIC wave scattering could hence contribute significantly to electron precipitation loss over the course of a storm. Codes designed to model electron dynamics in the radiation belts need to incorporate, in addition to radial ( cross-L) diffusion, resonant diffusion due to electron gyroresonance with ELF, VLF, and EMIC waves. In order to determine the quasi-linear diffusion coefficients for such codes, observational data are required on the power spectral density, spatial distribution, and temporal variation of these wave modes. Currently, only limited wave data sets are available. In addition, problems of numerical instability associated with diffusion codes need to be solved. The development of fully comprehensive models of radiation belt electron dynamics remains a considerable scientific challenge.