A geometric approach to constructing quasi-isodynamic fields

TL;DR

This paper introduces a geometric reformulation of near-axis theory for quasi-isodynamic stellarator equilibria, enabling more direct construction and control of magnetic configurations with diverse topologies and properties.

Contribution

It presents a new geometric method for constructing magnetic axes and controlling surface shaping, enhancing the design process for quasi-isodynamic stellarators.

Findings

Constructed magnetic axes using Frenet-Serret equations.

Controlled plasma elongation at first order without extensive optimization.

Demonstrated a scaling symmetry in configurations with specific axis helicity.

Abstract

The near-axis theory for quasi-isodynamic stellarator equilibria is reformulated in terms of geometric inputs, to allow greater control of the ``direct construction'' of quasi-isodynamic configurations, and to facilitate understanding of the space of such equilibria. This includes a method to construct suitable magnetic axis curves by solving Frenet-Serret equations, and an approach to controlling magnetic surface shaping at first order (plasma elongation), which previously has required careful parameter selection or additional optimization steps. The approach is suitable for studying different classes of quasi-isodynamic stellarators including different axis ``helicities'' and topologies (e.g. knotted solutions), and as the basis for future systematic surveys using higher order near-axis theory. As an example application, we explore a family of configurations with per-field-period axis helicity equal to one half, demonstrating an approximate scaling symmetry relating different field period numbers.