A 3D Kinetic Distribution that Yields Observed Plasma Density in the Inner Van Allen Belt

Abstract

A steady-state distribution is obtained that approximately yields the observed plasma density profile of the inner Van Allen radiation belt. The model assumes a collisionless, magnetized plasma with zero electric field present. The inner Van Allen belt consists of a plasma comprising high-energy protons and relativistic electrons. The particle trajectories are obtained from the collisionless Lorentz Force equation for different initial distributions. The resulting steady-state distributions obtained after particles lost to the loss cone are eliminated and are used to generate the density profile. The distribution’s dependence on energy E and magnetic moment $\mu$ is adjusted to make the density profile agree with observations. For a distribution that is a function of energy times a function of magnetic moment, the calculation leads to the desired type of density profile. The kinetic distribution and the type of density profile obtained are presented.