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Current potential patches
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A novel form of the current potential, a mathematical tool for the design of stellarators and stellarator coils, is developed. Specifically, these are current potentials with a finite-element-like basis, called \textit{current potential patches}. Current potential patches leverage the relationship between distributions of magnetic dipoles and current potentials to explore limits of the access properties of stellarator coil sets. An example calculation is shown using the Helically Symmetric Experiment (HSX) equilibrium, demonstrating the method's use in coil design and understanding the limits of the access properties of coil sets. Current potential patches have additional desirable properties such as of promoting sparse current sheet solutions and identifying crucial locations of shaping current placement. A result is found for the HSX equilibrium that shaping currents covering only 25\% of the winding surface is sufficient to produce the equilibrium to a good accuracy, provided a toroidal field is pre-supplied.
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Cited by 1 Pith paper
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Surface Current Optimization and Coil-Cutting Algorithms for Stage-Two Stellarator Optimization
Explicit derivations and a documented, DESC-implemented algorithm for optimizing a surface current on a toroidal surface and cutting it into modular or helical stellarator coils.
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