Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions: I. Generalised force balance

TL;DR

This paper introduces a new near-axis expansion method that overcomes overdetermination issues in constructing quasisymmetric magnetic fields, suggesting such fields may exist with anisotropic pressure.

Contribution

It develops a general near-axis expansion technique that does not assume isotropic pressure, allowing higher-order solutions and challenging the belief that global quasisymmetric fields cannot exist.

Findings

Overdetermination in isotropic pressure equilibria can be circumvented with anisotropic pressure.

Higher-order power-series solutions are possible in anisotropic pressure equilibria.

Existence of global quasisymmetric fields is likely if isotropic pressure assumption is relaxed.

Abstract

It is well known that the process of construction of quasisymmetric magnetic fields in magnetostatic equilibrium with isotropic pressure suffers from the problem of overdetermination. This has led to the widespread belief that global quasisymmetric solutions are likely not to exist. We develop a general near-axis expansion procedure that does not rely on the assumption of magnetostatic equilibria with isotropic pressure. We then demonstrate that in equilibria with anisotropic pressure, it is possible to circumvent the problem of overdetermination and carry out the power-series solutions to higher order. This suggests, contrary to current belief, that the existence of globally quasisymmetric fields is likely if one relaxes the assumption of magnetostatic equilibria with isotropic pressure.