Combined plasma-coil optimization approaches *

Approaches for combined plasma–coil optimization for designing stellarators are investigated and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics is proposed (Henneberg, et al., (2021). JPP, 87(2), 905870226). Stellarators exploit three-dimensional magnetic fields to generate external rotational transform -- rotational transform solely generated by the coils’ magnetic field.  This reduces or even eliminates the need for generating toroidal plasma currents, which can lead to instabilities such as disruptions. However, the three-dimensionality can involve some drawbacks, e.g., more complicated coils are typically needed compared to the axisymmetric case. Achieving favorable plasma and coil properties simultaneously is a major challenge in stellarator design.  Nonetheless, with careful exploitation of the large design space, the apparent disadvantages can be diminished. With this work we investigate the mathematical structure of the various inter-related calculations that underpin the integrated stellarator optimization problem to better understand how the equilibrium calculation, the coil calculation, and the optimization calculation communicate with each other. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed and will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation.