The Geometry of Flux Surfaces with Quasi-Poloidal Symmetry

TL;DR

This paper introduces a new 2D framework for understanding and finding quasi-poloidal flux surfaces in magnetic confinement, simplifying the analysis and enabling efficient optimization of plasma confinement configurations.

Contribution

It presents a novel 2D simplification for analyzing QP flux surfaces, facilitating theoretical insights and computational optimization, which was previously hindered by the 3D complexity.

Findings

Validated the reduced model against numerical equilibria.

Identified classes of QP flux surfaces as flat mirrors.

Explained features like cusps and high mirror ratios in equilibria.

Abstract

Quasi-poloidal (QP) magnetic fields have desirable properties for confining plasma: no radial drift of guiding centres (with positive implications for neoclassical transport), zero Pfirsch-Schl\"uter current, a lower level of damping for poloidal flows, leading to reduced anomalous transport, and possible stability benefits. Despite their attractive properties, QP fields are not amenable to the near-axis expansion, a major theoretical tool for understanding toroidal fields. In this paper, we provide a novel framework for defining and understanding QP flux surfaces. This framework relies on a simplification that transforms the task of finding a quasi-poloidal flux surface from a 3D problem to a 2D problem. This simplification also applies to asymmetric magnetic mirrors with desirable properties. We sketch how this 2D problem can form the basis of an efficient optimisation problem for finding QP flux surfaces. We leverage this 2D problem for theoretical understanding: for instance, we identify one class of QP flux surfaces that are naturally flat mirrors (Velasco et al. 2023). The reduced model is validated against numerically optimised QP equilibria. We further utilise the reduced model to explain the prevalence of cusps, high mirror ratios, and narrow pinch points in these numerical equilibria.