Particle Motions in Earth's Inner Magnetosphere: A Test Particle Simulation Approach

This article aims to understand the dynamics of charged particles trapped in Earth's dipolar magnetic field. The emphasis is on numerical simulation to characterize the trajectories of the charged particles of solar origin that enter the Earth's magnetosphere and get trapped. These particles perform three different periodic motions namely: gyration, bounce and azimuthal drift. We developed a test particle simulation model in which the relativistic equation of motion is solved numerically using Runge-Kutta sixth-order method. The stability of simulation model is verified by checking the adiabatic invariants linked with each type of motion. We found that bounce and drift periods of particles obtained from simulations are in good agreement with their theoretical estimates when adiabatic invariants are conserved. However, the energy ranges for which adiabatic invariants are violated, the theoretical estimates of the bounce/drift periods are not valid. This situation is successfully demonstrated through the present simulation, which arises due to larger gyro-radius (few Earth radii) of particles, over which the ambient magnetic field is not constant. In addition, we have examined the pitch angle distributions of the trapped particles. It is noted that the pitch angle distribution tends to follow $90^o$-peaked distribution when the adiabatic invariants are not conserved. This information is useful to understand charged particle pitch angle distributions observed from some recent spacecrafts in the Earth's magnetosphere.