A model for generating relativistic electrons in the Earth's inner magnetosphere based on gyroresonant wave-particle interactions

During the recovery phase of a magnetic storm, fluxes of relativistic (>1 MeV) electrons in the inner magnetosphere (3 less than or equal to L less than or equal to 6) increase to beyond prestorm levels, reaching a peak similar to 4 days after the initiation of the storm. In order to account for the generation of these killer electrons a model is presented primarily on the basis of the stochastic acceleration of electrons by enhanced whistler mode chorus. In terms of a quasi-linear formulation a kinetic (Fokker-Planck) equation for the electron energy distribution is derived comprising an energy diffusion coefficient based on gyroresonant electron-whistler mode wave interaction and parallel wave propagation, a source term representing substorm-produced (lower-energy) seed electrons, and a loss term representing electron precipitation due to pitch angle scattering by whistler mode waves and electromagnetic ion cyclotron (EMIC) waves. Steady state solutions for the, electron energy distribution are constructed and fitted to an empirically derived relativistic Maxwellian distribution for the high-energy hard electron population at geosynchronous orbit. If the average whistler amplitude is sufficiently large, for instance, 75-400 pT, dependent on the values of the other model parameters, and assuming a background plasma density of N-0 = 10 cm(-3) outside the plasmasphere, then a good fit to the empirical distribution is obtained and corresponds to a timescale for the formation of the high-energy steady state distribution of 3-5 days. For a lower representative value of the background plasma density, No 1 cm(-3), smaller whistler amplitudes, in the range 13-72 pT, can produce the high-energy distribution in the required time frame of several days. It is concluded from the model calculations that the process of stochastic acceleration by gyroresonant electron-whistler mode wave interaction in conjunction with pitch angle scattering by EMIC waves constitutes a viable mechanism for generating killer electrons during geomagnetic storms. The mechanism is expected to be particularly effective for the class of small and moderate storms possessing a long-lasting recovery phase during which many substorms occur.