Gradient-based optimization of 3D MHD equilibria

TL;DR

This paper introduces a gradient-based optimization approach for 3D MHD stellarator equilibria using adjoint methods, enabling efficient design of magnetic configurations with desired properties.

Contribution

It presents the first analytic gradient-based optimization of fixed-boundary stellarator equilibria utilizing adjoint methods, significantly reducing computational effort.

Findings

Optimized stellarator equilibria with improved figures of merit.

Reduced equilibrium evaluations by a factor of 50-500.

Developed a regularization method to prevent plasma boundary self-intersection.

Abstract

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on MHD equilibria (Antonsen et al. 2019; Paul et al. 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well, and quasisymmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ($\sim 50-500$) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.