On the validity of the guiding-center approximation in a magnetic dipole field

TL;DR

This paper evaluates the accuracy of the guiding-center approximation for charged particles in a magnetic dipole field, emphasizing the importance of polarization effects for regular, magnetically confined orbits.

Contribution

It demonstrates that the guiding-center approximation remains valid when higher-order polarization corrections are included in axisymmetric magnetic dipole fields.

Findings

Guiding-center approximation conserves energy and angular momentum.

Polarization effects are crucial for accurate orbit description.

Approximation fidelity depends on orbit regularity.

Abstract

The problem of the charged-particle motion in an axisymmetric magnetic-dipole geometry is used to assess the validity of Hamiltonian guiding-center theory, which includes higher-order corrections associated with guiding-center polarization induced by magnetic-field nonuniformity. When a magnetically-confined charged-particle orbit is regular (i.e., its guiding-center magnetic moment is adiabatically invariant), the guiding-center approximation, which conserves both energy and azimuthal canonical angular momentum, is shown to be faithful to the particle orbit when guiding-center polarization effects are taken into account.