Numerical asymptotics of near-axis expansions of quasisymmetric magnetohydrostatic equilibria with anisotropic pressure

TL;DR

This paper introduces pyAQSC, a novel computational tool for analyzing near-axis expansions of anisotropic-pressure quasisymmetric magnetohydrostatic equilibria, enabling higher-order studies and potential stellarator design improvements.

Contribution

The paper presents the first code for solving near-axis expansions of anisotropic-pressure QS equilibria to any order, advancing the understanding of global QS solutions.

Findings

Demonstration of a 6th order QA near-axis equilibrium with anisotropic pressure.

Convergence analysis of the pyAQSC code.

Comparison of RB method with DESC equilibria with anisotropic pressure.

Abstract

Quasisymmetry (QS) is a property of special magnetic configurations, where the magnetic field strength, but not necessarily the full vector field, has a direction of symmetry. QS leads to reduced neoclassical transport and thus can be a desirable property in stellarator design. The Garren-Boozer (GB) conundrum has been interpreted to mean that globally quasisymmetric magnetohydrostatic (MHS) equilibria, other than axisymmetric solutions, with isotropic pressure do not exist. When expanded as power series of an effective minor radius, the governing equations become overdetermined at the 3rd order. Despite this, recent optimization efforts have found numerical isotropic-pressure equilibria with nearly exact global QS. To reconcile these two perspectives, Rodriguez and Bhattacharjee (RB) showed that by introducing pressure anisotropy into the problem, one can overcome the GB conundrum. This formally enables the study of equilibria with exact, global QS. Building on RB's work, we present pyAQSC, the first code for solving the near-axis expansion (NAE) of anisotropic-pressure quasisymmetric equilibria to any order. As a demonstration, we present a 6th order, QA near-axis equilibrium with anisotropic pressure, and a convergence analysis. PyAQSC opens the door to the study of higher-order properties of equilibria with exact global QS. Like existing isotropic-pressure NAE codes, PyAQSC can accelerate stellarator optimization as an initial state tool. However, by optimizing for low pressure anisotropy in a space that allows anisotropy, pyAQSC may discover practical QS stellarator designs previously hard to access. We give results comparing the RB method with DESC equilibria with anisotropic pressure.