Exact expressions for nonperturbative guiding center theory in symmetric fields

TL;DR

This paper develops exact nonperturbative guiding center expressions for charged particles in symmetric fields, providing a precise theoretical framework that extends beyond traditional perturbative approaches and matches known invariants.

Contribution

It introduces a nonperturbative guiding center formalism that yields exact constants of motion in symmetric fields, aligning with adiabatic invariants to all orders.

Findings

Exact constants of motion are derived for symmetric fields.

The formalism matches Kruskal's adiabatic invariants in the perturbative limit.

The model predicts particle dynamics accurately without relying on the cyclotron timescale.

Abstract

We apply a recently-developed nonperturbative guiding center formalism to charged particle dynamics in fields with two-parameter continuous symmetry groups. This entails finding exact constants of motion, valid in the nonperturbative regime, that agree with Kruskal's adiabatic invariant series to all orders in the perturbative regime, when the field scale length is large compared with a typical gyroradius. We demonstrate that the nonperturbative guiding center model makes exact predictions in these cases, even though it eliminates the cyclotron timescale, thereby establishing a theoretical baseline for performance of the nonperturbative formalism.