Resonant interaction of relativistic electrons with realistic electromagnetic ion-cyclotron wave packets

We study the influence of real structure of electromagnetic ion-cyclotron wave packets in the Earth's radiation belts on precipitation of relativistic electrons. Automatic algorithm is used to distinguish isolated elements (wave packets) and obtain their amplitude and frequency profiles from satellite observations by Van Allen Probe B. We focus on rising-tone EMIC wave packets in the proton band, with a maximum amplitude of 1.2-1.6 nT. The resonant interaction of the considered wave packets with relativistic electrons 1.5-9 MeV is studied by numerical simulations. The precipitating fluxes are formed as a result of both linear and nonlinear interaction; for energies 2-5 MeV precipitating fluxes are close to the strong diffusion limit. The evolution of precipitating fluxes is influenced by generation of higher-frequency waves at the packet trailing edge near the equator and dissipation of lower-frequency waves in the He+ cyclotron resonance region at the leading edge. The wave packet amplitude modulation leads to a significant change of precipitated particles energy spectrum during short intervals of less than 1 minute. For short time intervals about 10-15 s, the approximation of each local amplitude maximum of the wave packet by a Gaussian amplitude profile and a linear frequency drift gives a satisfactory description of the resonant interaction.