Gradient-based optimization of 3D MHD equilibria

Abstract

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on MHD equilibria (Antonsen et al. 2019; Paul et al. 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well, and quasisymmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ($\sim 50-500$) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

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Cited by in corpus (7)

• The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization
• Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function
• Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary
• Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation
• Adjoint methods for quasisymmetry of vacuum fields on a surface
• Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations
• Spectrally accurate, reverse-mode differentiable bounce-averaging algorithm and its applications