An oscillator model representative of electron interactions with EMIC waves

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Abstract
Nonlinear interactions of relativistic electrons with a monochromatic electromagnetic ion cyclotron (EMIC) wave were investigated in previous studies by solving the Lorentz equation for test particles. In the present study, we simplify the Lorentz equation to a set of oscillator equations, which capture the key features of the wave‐particle interaction. These reduced oscillator equations confirm that the inhomogeneity ratio plays an important role in determining the nonlinear nature of the interaction with a monochromatic wave. When considering the case of two discrete wave elements, three general regimes were identified in the nonlinear interactions, depending on the separation of the two wave numbers: There were (1) a decoupled regime in which electrons pass only one of the two distant resonance points, (2) a coupled regime in which electrons pass both of the two moderately separated resonance points, and (3) a degenerate regime in which electrons pass two closely situated resonance points. The decoupled and degenerate regimes in the nonlinear interaction are characterized by phase bunching. However, the electrons experience alternate trapping and detrapping near the separatrix in the coupled regime, leading to chaotic nature of electrons' motion. The linear interaction region is also considered, where the linear superposition principle is tested. The linear approximation results generally agree with the two‐wave simulation except in the coupled regime.

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