Particle Scattering in the Presence of Moderate to Strong Adiabatic Focusing

Abstract

Starting from the Vlasov‐Boltzmann equation, we derive corrections to the quasi linear Fokker‐Planck pitch angle scattering coefficient caused by a non‐uniformity of the background magnetic field. Integration of the perturbed particle distribution function is performed along a modified unperturbed trajectory that takes into account the effects of focusing and mirroring on pitch angle and gyrophase. We calculate the changes to the quasi‐linear scattering rate owing to a variations in the field strength and the gyrophase drift that affects the resonance between particles and magnetic fluctuations. It is shown that the scattering coefficient has an oscillating behavior in pitch angle when the focusing lengthscale is comparable to the correlation length of the turbulence and the particle's Larmor radius. The applicability of analytic results are demonstrated with a simple model of charged particles trapped in a magnetic field of a planet. It is suggested that the pitch angle diffusion coefficient could become negative for the case of very strong focusing.