The DESC stellarator code suite Part 3: 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.

Single-stage stellarator optimization: combining coils with fixed boundary equilibria

“…Nevertheless, further exploration of different quasisymmetry forms (e.g. [30]), might contribute to the refinement of the optimization method applied in the current work quasi-isodynamic magnetic fields are fields that are omnigeneous with poloidally closed contours of the magnetic field strength B. To achieve a quasi-isodynamic magnetic field, we follow the approach in [31] and…”

Magnetic fields with general omnigenity

“…Accessing this larger design space would unlock new possibilities for stellarators and is worthwhile to consider despite its increased computational complexity. This article presents an approach to achieve this goal, which is made possible through the DESC stellarator optimization code suite (Dudt & Kolemen 2020;Conlin et al 2023;Dudt et al 2023;Panici et al 2023;Dudt et al 2024). It is similar to the original idea of Cary & Shasharina (1997a), in the sense that a perfectly omnigenous magnetic field is constructed to have the same form on every field line in terms of some new coordinate.…”

The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations

“…The efficiency and utility of the method are shown in the computation of complicated equilibria, highlighting the benefits of automatic differentiation. Part 3 (Dudt et al 2023) presents DESC's unique stellarator optimization capabilities made possible by the efficient equilibrium solver and the perturbation method described in the earlier parts, resulting in a speed-up in optimization by orders of magnitude. These advantages are shown in the context of quasi-symmetry optimization, where results are compared with conventional tools (Spong et al 1998;Lazerson et al 2020).…”

“…While a relatively robust and widely used code, VMEC still suffers from shortcomings stemming from its issues at the axis and its radial discretization, as well as its legacy design. A new 3-D stellarator equilibrium code, DESC (Dudt & Kolemen 2020;Dudt et al 2022), has been developed which can overcome these issues.…”

“…Additionally, an updated version of VMEC, GVEC, is currently being developed (Bañón Navarro et al 2020;Hudson et al 2020). DESC (Dudt & Kolemen 2020;Dudt et al 2022) is a recent pseudospectral code which employs a spectral Fourier-Zernike basis in all three coordinates, and finds equilibria by satisfying the MHD force balance (1.1a) directly at collocation nodes. This choice of spectral basis automatically satisfies the necessary constraints at the axis for analytic functions, and the code is explained more in section 3.2.…”