Constrained Optimization Methods in DESC

Stellarators require careful optimization of their three-dimensional fields to achieve desirable properties for the magnetic equilibrium and coils. Traditionally, this problem is solved using unconstrained optimization methods where both the desired properties and equilibrium constraints are combined into a single objective function. In this work, we implement constrained optimization methods into the new DESC stellarator code [1-4]. This allows the optimizer to simultaneously decrease the objective function while further satisfying the equilibrium constraints at each successive step. This procedure is more computationally efficient, robust, and may avoid some local minima. In contrast, in an unconstrained, multi-objective approach, the optimizer must satisfy the equilibrium constraints at each step, which can slow convergence and may lead to the Maratos effect. Finally, using constrained optimization methods prevents the optimizer from over-penalizing inequality constraints, and can lead to discovering new optimized equilibria. Example equilibria from both methods are presented, with objectives including quasisymmetry, magnetic well, and turbulent heat flux.

[1] D.W. Dudt, and E. Kolemen, “DESC: A stellarator equilibrium solver”, Physics of Plasmas, 27, 102513 (2020) doi:10.1063/1.5109160

[2] D. Panici, et al. “The DESC Stellarator Code Suite Part I: Quick and accurate equilibria computations.” pre-print. doi:10.48550/arXiv.2203.17173

[3] R. Conlin, et al. “The DESC Stellarator Code Suite Part II: Perturbation and continuation methods.” pre-print. doi:10.48550/arXiv.2203.15927

[4] D.W. Dudt, et al. “The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization.” pre-print. doi:10.48550/arXiv.2204.00078.