Combined plasma-coil optimization algorithms

Abstract

Combined plasma-coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi free-boundary optimization, and the free-boundary (coil) optimization. These are described using the multi-region relaxed magnetohydrodynmics (MRxMHD) energy functional, the Biot-Savart integral, the coil-penalty functional and the virtual casing integral, and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma-coil optimization algorithms, we emphasize the importance of the stability matrix.

arXiv commentto be submitted to JPP

References in corpus (14)

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• Stellarators with permanent magnets
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Cited by in corpus (10)

• Constructing precisely quasi-isodynamic magnetic fields
• Single-Stage Stellarator Optimization: Combining Coils with Fixed Boundary Equilibria
• Direct construction of stellarator-symmetric quasi-isodynamic magnetic configurations
• Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry
• Robust stellarator optimization via flat mirror magnetic fields
• A compact stellarator-tokamak hybrid
• Existence of an optimized stellarator with simple coils
• Stellarator optimization for nested magnetic surfaces at finite $\beta$ and toroidal current
• On the relationship between the multi-region relaxed variational principle and resistive inner layer theory
• Including the vacuum energy in stellarator coil design