Isodrastic magnetic fields for suppressing transitions in guiding-centre motion

• Published in: Nonlinearity Vol. 36; no. 11; pp. 5884 - 5954
• Main Authors: Burby, J W, MacKay, R S, Naik, S
• Format: Journal Article
• Language: English
• Published: United States IOP Publishing 01.11.2023; IOP Science
• Subjects: 37J46; 37N99; dynamical systems; Hamiltonian dynamics; invariant submanifolds; isodrastic magnetic fields; magnetic confinement of plasma; MATHEMATICS AND COMPUTING; Melnikov function
• ISSN: 0951-7715; 1361-6544
• DOI: 10.1088/1361-6544/acf26a

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. 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 with some simple examples.