Guiding-center dynamics in a screw-pinch magnetic field

TL;DR

This paper investigates guiding-center dynamics in a screw-pinch magnetic field, verifying the consistency of adiabatic invariants and providing a non-perturbative expression for the magnetic moment.

Contribution

It demonstrates the match between Kruskal's adiabatic-invariant expansion and perturbation expansion, offering a new integral expression for the magnetic moment.

Findings

Kruskal's adiabatic-invariant series matches the perturbation expansion up to first order.

Radial action integral is an exact invariant of full-orbit dynamics.

Magnetic moment expressed as a non-perturbative integral for testing guiding-center approximation.

Abstract

The guiding-center dynamics of charged particles moving in a doubly-symmetric screw-pinch magnetic field is investigated. In particular, we verify that Kruskal's adiabatic-invariant series expansion of the radial action integral associated with the reduced full-orbit radial motion matches the perturbation expansion of the magnetic-moment gyroaction up to first order in magnetic-field non-uniformity. Because the radial action integral is an exact invariant of the full-orbit dynamics, the magnetic moment is therefore represented as non-perturbative integral expression, which can be used to test the validity of the guiding-center approximation.