Faithful guiding-center orbits in an axisymmetric magnetic field

TL;DR

This paper evaluates the accuracy of higher-order guiding-center theory in axisymmetric magnetic fields, demonstrating its effectiveness in modeling regular charged-particle orbits in magnetic mirror and tokamak geometries.

Contribution

It assesses the validity of advanced guiding-center Hamiltonian theory with higher-order corrections for axisymmetric magnetic fields, including gyrogauge invariance and polarization effects.

Findings

Guiding-center approximation accurately models regular particle orbits with higher-order corrections.

Conservation of energy and azimuthal angular momentum ensures fidelity of the guiding-center approach.

Higher-order Hamiltonian corrections improve the agreement between particle and guiding-center trajectories.

Abstract

The problem of the charged-particle motion in an axisymmetric magnetic geometry is used to assess the validity of higher-order Hamiltonian guiding-center theory, which includes higher-order corrections associated with gyrogauge invariance as well as guiding-center polarization induced by magnetic-field non-uniformity. Two axisymmetric magnetic geometries are considered: a magnetic mirror geometry and a simple tokamak geometry. 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 higher-order corrections are taken into account.