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

arXiv: https://arxiv.org/abs/2203.15927 · HTML: https://mlsanity.com/paper/2203.15927/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2022.

## Built on by (most cited first, 4 of 4)

- [Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function](https://mlsanity.com/paper/2206.01637/) (2022)
- [Improving ideal MHD equilibrium accuracy with physics-informed neural networks](https://mlsanity.com/paper/2507.03119/) (2025)
- [Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis](https://mlsanity.com/paper/2510.13521/) (2025)
- [A proof-of-concept for automated AI-driven stellarator coil optimization with in-the-loop finite-element calculations](https://mlsanity.com/paper/2603.15240/) (2026)

## Abstract (arXiv)

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 × 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.