Constructing nested coordinates inside strongly shaped toroids using an action principle

TL;DR

This paper introduces a variational method to construct boundary-conforming coordinates inside strongly shaped toroids, enabling accurate 3D MHD equilibrium computations where traditional methods fail.

Contribution

A novel variational approach using an action principle for constructing nested coordinates inside complex toroidal geometries.

Findings

Successfully constructs coordinates for strongly shaped toroids.

Enables accurate 3D MHD equilibrium calculations.

Outperforms traditional boundary interpolation methods.

Abstract

A new approach for constructing polar-like boundary-conforming coordinates inside a toroid with strongly shaped cross-sections is presented. A coordinate mapping is obtained through a variational approach, which involves identifying extremal points of a proposed action in the mapping space from [0, 2{\pi}] x [0, 2{\pi}] x [0, 1] to a toroidal domain in R3. This approach employs an action built on the squared Jacobian and radial length. Extensive testing is conducted on general toroidal boundaries using a global Fourier-Zernike basis via action minimization. The results demonstrate successful coordinate construction capable of accurately describing strongly shaped toroidal domains. The coordinate construction is successfully applied to the computation of 3D MHD equilibria in the GVEC code where the use of traditional coordinate construction by interpolation from the boundary failed.