Self-organization and heating by inward diffusion in magnetospheric plasmas

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 [ Z. Yoshida and S.M. Mahajan, Prog. Theor. Exp. Phys. 2014, 073J01 (2014). N. Sato and Z. Yoshida, J. Phys. A: Math. Theor. 48, 205501 (2015).]. 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.