The goal of this talk is to share some ideas and insights about magnetospheric wave-particle interactions, which the speaker has learned (or been taught) over the past 44 years. Topics to be covered (time permitting) include: response of a single particle to a single electromagnetic wave; conditions for cyclotron resonance under parallel and oblique wave propagation; relationship between duration of resonance and effective frequency bandwidth; quasi-linear diffusion in momentum space; sources of resonance-broadening (e.g., quasi-linear diffusion, wave growth or damping, non-uniformity of the geomagnetic field and magnetospheric plasma); resonance-narrowing (prolonged interaction) caused by phase-trapping of a resonant particle in a narrow-banded wave-form; growth of whistler-mode waves caused by pitch-angle anisotropy of energetic-electron distributions, limit on stably trapped electron fluxes in the magnetosphere for a prescribed pitch-angle anisotropy and energy-spectral shape; and calculation of the limiting energy spectrum for a saturated radiation belt with prescribed anisotropy.
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