A comparative Study Electron Tracking in Magnetic Field by Ordinary Differential Equation and Euler Method

Abstract

Two electron tracking methods were developed and compared to determine the trajectory and conserved energy of an electron. The trajectory integrators include: the Euler electron tracking method and Ordinary Differential Equations (ODE) Solvers method. The goal of this study is to compare the Euler electron tracking method with the Ordinary Differential Equations method. The Euler method was found inadequate for tracking electrons in a dipole magnetic field because it was not able to maintain the correct orbit of the electron, conserve bounce period and electron kinetic energy. The Ordinary Differential Equations method is shown to conserve energy and maintain the correct orbit of the electron. The Ordinary Differential Equations is quite adequate to describe the trajectory of electrons in the Earth’s magnetic field. Key words: Particle trajectory computations; the dynamics of electrons in magnetosphere model; three adiabatic invariants associated with three types of periodic motions.