Trajectories of charged particles trapped in Earth’s magnetic field

This article presents the theory of relativistic charged-particle motion in Earth’s magnetosphere, at a level suitable for undergraduate courses. I discuss particle and guiding center motion and derive the three adiabatic invariants associated with the three periodic motions in a dipolar field. I provide 12 computational exercises that can be used as classroom assignments or for self-study. Two of the exercises, drift-shell bifurcation and Speiser orbits, are adapted from active magnetospheric research. The PYTHON code provided in the supplement can be used to replicate the trajectories and can be easily extended for different field geometries.