  Through the process of inward diffusion, a strongly localized clump of plasma
is created in a magnetosphere. The creation of the density gradient, instead of
the usual flattening by a diffusion process, can be explained by the
topological constraints given by the adiabatic invariants of magnetized
particles. After developing a canonical formalism for the standard guiding
center dynamics in a dipole magnetic field, we complete our attempt to build a
statistical mechanics on a constrained phase space by discussing the
construction principles of the associated diffusion operator. We then
investigate the heating mechanism associated with inward diffusion: as
particles move toward regions of higher magnetic field, they experience
preferential heating of the perpendicular (with respect to the magnetic field)
temperature in order to preserve the magnetic moment. A relationship between
conservation of bounce action and temperature isotropy emerged. We further show
that this behavior is scaled by the diffusion parameter of the Fokker-Planck
equation. These results are confirmed by numerical simulations.
