We use numerical simulations to study the resonant interaction of relativistic electrons with rising‐frequency electromagnetic ion cyclotron (EMIC) wave packets in the normalH+ band. We find that precipitating fluxes are formed by quasi‐linear interaction and several nonlinear interaction regimes having opposite effects. In particular, the direct influence of Lorentz force on the particle phase (force bunching) decreases precipitation for particles with low equatorial pitch angles (up to 15–25°) and can even block it completely. Four other nonlinear regimes are possible: nonlinear shift of the resonance point, which can cause pitch angle drift in both directions; phase bunching that slightly increases pitch angle for untrapped particles; directed scattering that strongly decreases pitch angle for untrapped particles; and particle trapping by the wave field that decreases pitch angle. The evolution of the equatorial pitch angle distribution during several passes of particles through the wave packet is studied. The precipitating fluxes are evaluated and compared with theoretical estimates. We show that strong diffusion limit is maintained for a certain range of energies by a wave packet with realistic amplitude and frequency drift. In this case, the quasi‐linear theory strongly underestimates the precipitating flux. With increasing energy, the precipitating fluxes decrease and become close to the quasi‐linear estimates.

Dynamics of relativistic electron fluxes in the Earth's inner magnetosphere is largely controlled by the competition of acceleration processes (due to resonances with whistler-mode waves and/or radial transport, see, e.g.,Millan &

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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 $$\text {He}^+$$ 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.

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