Bounce-averaged approach to radial diffusion modeling: From a new derivation of the instantaneous rate of change of the third adiabatic invariant to the characterization of the radial diffusion process

摘要

In this paper, a new approach for the derivation of the instantaneous rate of change of the third adiabatic invariant is introduced. It is based on the tracking of the bounce-averaged motion of guiding centers with assumptions that are only kept to the necessary conditions for definition and conservation of the first two adiabatic invariants. The derivation is first given in the case of trapped equatorial particles drifting in a time varying magnetic field in the absence of electrostatic potential. It is then extended to more general cases including time varying electric potentials and non-equatorial particles. Finally, the general formulation of the third adiabatic invariant time derivative is related to the description of the radial diffusion process occurring in the radiation belts. It highlights the links that exist between previous theoretical works with the objective of a better understanding of the radial diffusion process. A theoretical validation in the specific case of equatorial particles drifting in a magnetic field model whose disturbed part is limited to the first terms of a spherical expansion is also presented.