Isodrastic Magnetic fields for suppressing transitions in guiding-centre motion

TL;DR

This paper introduces the concept of isodrastic magnetic fields, which prevent guiding-centre motion transitions to improve plasma confinement, generalizing previous notions like omnigenity and enabling better magnetic field design.

Contribution

It develops both weak and strong formulations of isodrasticity, demonstrating its broader applicability beyond omnigenity, and provides a framework for optimizing magnetic fields to suppress guiding-centre transitions.

Findings

Weakly isodrastic mirror fields are not necessarily omnigenous.

The strong formulation recovers the weak version via a Melnikov function.

Deviations from isodrasticity can be quantified for optimal design.

Abstract

In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres make no transitions between classes of motion. Therefore, this is an important ideal for enhancing confinement. First, we present a weak formulation, based on the longitudinal adiabatic invariant, generalising omnigenity. To demonstrate that isodrasticity is strictly more general than omnigenity, we construct weakly isodrastic mirror fields that are not omnigenous. Then we present a strong formulation that is exact for guiding-centre motion. We develop a first-order treatment of the strong version via a Melnikov function and show that it recovers the weak version. The theory provides quantification of deviations from isodrasticity that can be used as objective functions in optimal design. The theory is illustrated on some simple examples.