An approximate analytic description of plasma bulk parameters, and pitch angle anisotropy under adiabatic flow, in a dipolar magnetospheric field

Abstract

An approximate expression for the variation with L of the equatorial pitch angle of a particle undergoing adiabatic convection in a dipole magnetic field is obtained. The additional assumptions of no particle loss and the other usual conservation laws then are invoked to describe the variation of such bulk parameters as pressure and density for any assumed initial distribution function. Explicit solutions are obtained for initial distributions separable in energy and pitch angle with sink α0 dependence on pitch angle and are shown to be weakly dependent on k. The expressions obtained are compared with the results predicted for the case of strong pitch angle diffusion to obtain bounds on the variation. The approximation for the L dependence of the equatorial pitch angle is also used to show how pitch angle anisotropy is modified during inward convection, and the rapid development of anisotropy for sharply falling initial spectra is noted.