Physics of pitch angle scattering and velocity diffusion, 1. Theory

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Abstract
We present a general theory for the pitch angle scattering and velocity diffusion of particles in the field of a spectrum of waves in a magnetized plasma. We use the test particle theory to analyze the particle motion. We examine the form of diffusion surfaces and give analytical expressions for the resonance width and bounce frequency. The resonance widths are found to vary strongly as a function of harmonic number. The resulting diffusion can be quite asymmetric with respect to pitch angle of 90°. The conditions for the onset of pitch angle scattering and energy diffusion are explained in detail. We also address some of the known shortcomings of the standard quasi‐linear theory and show ways to overcome them. In particular, we find the often stated quasi‐linear gap at 90° to exist only under very special cases. For instance, oblique wave propagation can easily remove the gap. The conditions for the existence of the gap is described in great detail. A new diffusion equation which takes into account the finite resonance widths is also discussed. The differences between this new theory and the standard resonance broadening theory is explained. The emphasis is on the simplicity of the theory and its power in making quantitative predictions.