Oblique Whistler-Mode Waves in the Inhomogeneous Magnetospheric Plasma: Resonant Interactions with Energetic Charged Particles

A consistent account is given of the theory of resonant interactions between energetic charged particles and a whistler-mode wave propagating obliquely to the non-uniform geomagnetic field in the inhomogeneous magnetospheric plasma. The basic equations for the wave field and charged particle dynamics are presented, with the emphasis being placed on the parameters governing the problem. A Hamiltonian approach is consistently used in the analysis of the particle equations of motion which are discussed in detail and solved analytically in various cases. Two applications of the theory are considered. First, we calculate the growth (or damping) rate for a whistler-mode wave propagating obliquely to geomagnetic field in the magnetosphere. Secondly, we estimate the proton precipitation into the upper atmosphere induced by a VLF transmitter signal.