Effective potential energy in St\ormer's problem for an inclined rotating magnetic dipole

TL;DR

This paper analyzes the motion of charged particles around a rotating magnetic celestial body, deriving equations, defining effective potential energy, and identifying regions accessible for particle motion based on constants of motion.

Contribution

It introduces a new approach to define effective potential energy in Störmer's problem for inclined rotating magnetic dipoles and studies particle motion regions.

Findings

Regions of accessible and inaccessible particle motion are mapped.

Effective potential energy is formulated based on the first constant of motion.

Particular solutions to the equations of motion are identified.

Abstract

We discuss the dynamics of a charged nonrelativistic particle in electromagnetic field of a rotating magnetized celestial body. The equations of motion of the particle are obtained and some particular solutions are found. Effective potential energy is defined on the base of the first constant of motion. Regions accessible and inaccessible for a charged particle motion are studied and depicted for different values of a constant of motion.