References and related work¶
This project is inspired by and designed to interoperate with common stellarator/toroidal workflows.
Coil design and current potential methods¶
Current potential representation: \(\mathbf K = \hat{\mathbf n}\times \nabla_s \Phi\) on a surface (used by many winding-surface / inverse magnetostatics approaches).
NESCOIL (Merkel): an influential “inverse magnetostatics” approach for representing coils via a current potential on a coil surface (Nucl. Fusion 27 (1987) 867).
REGCOIL (Landreman): adds Tikhonov-style regularization to avoid pathological growth with resolution and provides a tunable tradeoff between field quality and current magnitude (Nucl. Fusion 57 (2017) 046003, DOI: 10.1088/1741-4326/aa57d4). (See
regcoil-master/in this workspace.)
Related open-source toolchains in the community include:
SIMSOPT: Python optimization framework for stellarator design workflows (coils, equilibria, objectives). Landreman et al. (JOSS 2021), DOI: 10.21105/joss.03525.
FOCUS / FOCUSADD: direct coil-shape optimization using gradient-based methods. See e.g. Zhu et al. (PPCF 2018), DOI: 10.1088/1361-6587/aab8c2.
QUADCOIL: quadratic-constraint / convex-relaxation coil optimization formulations to enforce engineering constraints more directly. See e.g. Fu et al. (Nucl. Fusion 2025), DOI: 10.1088/1741-4326/ada810.
MHD equilibrium and target surfaces¶
VMEC: a widely-used 3D MHD equilibrium code that represents plasma boundaries by Fourier series in \((\theta,\phi)\).
Near-axis / quasisymmetry tools (e.g. “Garren–Boozer” constructions): used to generate quasisymmetric target surfaces and magnetic-axis parameterizations.
JAX ecosystem¶
JAX: composable transformations (JIT, vmap, grad) for high-performance differentiable computing.
Optax: gradient-based optimization (Adam, etc).
JAXopt: classical optimization methods (L-BFGS, etc).
Equinox: neural network / PyTree utilities for JAX.
Note
This documentation intentionally emphasizes the mapping between physics equations and code structure. For publication-quality scientific references, consult the upstream projects (REGCOIL, VMEC, pyQSC) and their associated papers.