Modeling the pitch angle distribution on the nightside of the Earth’s magnetosphere

Abstract

A mathematical model has been proposed for the diffusion pitch angle distribution in the magnetosphere. It makes it possible to calculate theoretically the phase space density (or the pitch angle distribution) of charged particles depending on the particle mass and energy, McIlwain parameter, magnetic local time, initial perpendicular value of the particle pitch angle distribution parameter (γ⊥0), variable parameter k characterizing the wave-particle interaction time, and magnetic activity index Kp. The model describes all four main types of pitch angle distributions, together with their variations, and simultaneously takes into account the possible physical mechanisms by which “butterfly” pitch angle distributions are formed as a wave-particle interaction, particle injection and drift, and splitting of the electric field drift shell. The potential of the proposed pitch angle diffusion model in the Earth’s magnetosphere has been demonstrated, as exemplified by the pitch angle distribution evolution over the last 68 hours of the magnetic storm that occurred on May 1–7, 1998. The model was quantitatively tested by a comparison of the calculated proton fluxes with the Polar/MICS spacecraft measurements during the magnetic storm of October 21–22, 1999. Good agreement between the calculated pitch angle distribution and the experimental data was obtained.