Trajectories of charged particles trapped in Earth's magnetic field

TL;DR

This paper explains the theory of relativistic charged-particle motion in Earth's magnetosphere, including guiding center motion and adiabatic invariants, with computational exercises and Python code for educational purposes.

Contribution

It provides an accessible derivation of particle trajectories and adiabatic invariants in Earth's magnetic field, integrating research-adapted exercises and extendable Python code for teaching and self-study.

Findings

Derivation of guiding center motion and adiabatic invariants.

Illustration of particle trajectories in a dipolar field.

Inclusion of computational exercises and Python code for educational use.

Abstract

I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and present particle trajectories in a dipolar field. I provide twelve 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.