Resonance Interaction of Relativistic Electrons with Ion-Cyclotron Waves. I. Specific Features of the Nonlinear Interaction Regimes
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We analyze the resonant interaction of relativistic electrons with ion-cyclotron waves in the Earth radiation belts. Finite-length wave packets with variable frequencies and different amplitude profiles are considered. Specific features of the nonlinear interaction regimes are analyzed on the basis of solving numerically a system of equations of the particle motion along with the efficiency of this interaction for a single pass of the particle through the wave packet. In the first part of this work, the peculiarities of the trajectories of individual particles are analyzed. The influence of the shape of the wave packet on the well-known regimes, such as particle trapping by the wave field and particle phase bunching, which leads to a non-zero average variation in the pitch angle in an inhomogeneous medium, are considered. It is shown that a long stay of a particle near the separatrix on the phase plane in the region far from the saddle leads to a strong decrease in the pitch angle of the particle in the absence of the trapping as well. This nonlinear regime (directed scattering) is possible for comparatively low initial pitch angles. In this case, the value of the pitch angle decrease depends on the initial phase of the particle. It is shown that the trajectories corresponding to the directed scattering can be regarded as a transitional type of trajectories, between the trajectories of the untrapped and trapped particles. Quantitative estimates of variations in the pitch angle are obtained, and it is confirmed that the directed scattering and trapping of particles by the wave field can lead to electron precipitation into the loss cone.
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