The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization

Abstract

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss-Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

Mapping the space of quasisymmetric stellarators using optimized near-axis expansion

“…To confirm the correctness of the near-axis method, each example below is checked using a fixed-boundary MHD equilibrium calculation that does not make a near-axis expansion, as follows. Given the constructed boundary, the field inside is computed and converted to Boozer coordinates with the DESC code (Dudt & Kolemen 2020;Conlin et al 2022;Dudt et al 2022;Panici et al 2022). Similar checks of near-axis solutions were done using the VMEC code (Hirshman & Whitson 1983) previously in , Plunk et al (2019), and .…”

Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations

“…These methods have been used to perform optimization of stellarator design (Paul, Landreman & Antonsen 2021). Other work uses gradients obtained from analytic (Zhu et al 2017) and automatic differentiation 1 (AD) (McGreivy, Hudson & Zhu 2021;Conlin et al 2022;Dudt et al 2022;) towards similar device optimization goals. Here, we propose the application of gradient-based optimization towards understanding the nonlinear, kinetic plasma dynamics using differentiable kinetic simulations.…”