The DESC Stellarator Code Suite Part II: Perturbation and continuation methods

TL;DR

This paper introduces a novel perturbation and continuation method integrated into the DESC stellarator code, enabling efficient computation and analysis of complex stellarator equilibria through series expansion and automatic differentiation.

Contribution

It presents a new perturbation and continuation approach for stellarator equilibria, with an efficient algorithm for higher-order solutions implemented in DESC.

Findings

Efficient computation of complex equilibria

Perturbation of tokamaks into stellarators

Rapid parameter scans in plasma properties

Abstract

A new perturbation and continuation method is presented for computing and analyzing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $F \equiv J \times B - \nabla p = 0$, and an efficient algorithm for computing solutions to 2nd and 3rd order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator, and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.