Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions. II. Circular axis stellarators

TL;DR

This paper extends the near-axis expansion method to construct numerical solutions for circular axis stellarators with anisotropic pressure, overcoming overdetermination issues present in traditional isotropic models.

Contribution

It introduces a second-order near-axis expansion approach for quasisymmetric fields in stellarators with anisotropic pressure, addressing limitations of previous isotropic models.

Findings

Solutions are obtained to second order in the distance from the axis.

A subset of coefficients can avoid overdetermination in the zero anisotropy limit.

The method extends the applicability of near-axis expansions to more general stellarator configurations.

Abstract

We apply the near-axis expansion method for quasisymmetric magnetic fields with anisotropic pressure (developed in the companion paper, Part I [E. Rodriguez, A. Bhattacharjee, arXiv:2008.04715 (2020)]) to construct numerical solutions to circular axis stellarators. The solutions are found to second order in the distance from the axis, not possible in the standard Garren-Boozer construction [D. A. Garren and A. H. Boozer, Physics of Fluids B: Plasma Physics, 2822 (1991)], which assumes magnetostatic equilibria with isotropic pressure. In the limit of zero anisotropy, it is shown that a subset of coefficients can be chosen to avoid the overdetermination problem.