RCM Modeling of Bubble Injections Into the Inner Magnetosphere: Spectral Properties of Plasma Sheet Particles

Collisionless astrophysical plasmas are correlated systems in which particles are often not in thermal equilibrium and can be characterized by power-law distributions. The kappa distribution function, which is a more generalized form of the power-law function, is often used to describe acceleration and production of high-energy particles in different space plasma environments. The spectra of particles in the Earth's plasma sheet constructed using Time History of Events and Mesoscale Interactions during Substorms data show that the kappa index exhibits a strong dawn-dusk asymmetry and a clear dependence on both geocentric distance and magnetic local time. Furthermore, statistics indicate that spectrum hardening, or softening is expected during geomagnetically disturbed periods. To understand how the shape of the particle distribution function evolves and what factors affect the kappa index, we simulate earthward plasma transport using a kinetic drift model. In the simulations, the plasma distribution is initially considered to be a kappa function with k = 6 . However, with time, both protons and electrons' distribution functions evolve and deviate from their initial shapes. We demonstrate that by implementing transient low-entropy plasma injections, the Rice Convection Model average distribution functions can reasonably agree with observations. We also discuss the relative impact of gradient/curvature drift, particle loss, and bubble injections, based on controlled numerical experiments.