We use numerical simulations to study the resonant interaction of relativistic electrons with rising-frequency EMIC wave packets in the H band. We find that precipitation fluxes are formed by quasi-linear interaction and several nonlinear interaction regimes having opposite effects. In particular, the 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 (can cause pitch angle drift in both directions); phase bunching (slightly increases pitch angle for untrapped particles); directed scattering (strongly decreases pitch angle for untrapped particles) and particle trapping by the wave field (decreases pitch angle). Equatorial pitch angle distribution evolution during several passes of particles through the wave packet is studied. The precipitation 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 precipitated flux. With increasing energy, the precipitated fluxes decrease and become close to the quasi-linear estimates.

We study quasi-periodic VLF emissions observed simultaneously by Van Allen Probes spacecraft and Kannuslehto and Lovozero ground-based stations on 25 December 2015. Both Van Allen Probes A and B detected quasi-periodic emissions, probably originated from a common source, and observed on the ground. In order to locate possible regions of wave generation, we analyze wave normal angles with respect to the geomagnetic field, Poynting flux direction, and cyclotron instability growth rate calculated by using the measured phase space density of energetic electrons. We demonstrate that even parallel wave propagation and proper (downward) Poynting flux direction are not sufficient for claiming observations to be in the source region. Agreement between the growth rate and emission bands was obtained for a restricted part of Van Allen Probe A trajectory corresponding to localized enhancement of plasma density with scale of 700~km. We employ spacecraft density data to build a model plasma profile and to calculate ray trajectories from the point of wave detection in space to the ionosphere, and examine the possibility of their exit to the ground. For the considered event, the wave could exit to the ground in the geomagnetic flux tube with enhanced plasma density, that ensured ducted propagation. The region of wave exit was confirmed by the analysis of wave propagation direction at the ground detection point.