Computational boundary specification in 3D fixed-boundary magnetohydrodynamic equilibrium modeling

Outside the core of the plasma, the plasma current and pressure rapidly transition to zero in a scrape-off or edge region or plasma-vacuum interface. However, existing tools for fixed-boundary magnetohydrodynamic equilibria in 2D and 3D domains $\Omega$ typically prescribe the computational boundary $\partial\Omega$ interior to this transition layer. We (1) argue that a more realistic and robust assumption is to define the computational boundary exterior to this transition layer, in a vacuum-like region where $J|_{\partial\Omega} \sim p|_{\partial\Omega} \sim 0$, (2) show that, without this boundary change, existing coil optimization routines for 3D toroidal equilibria (stellarators) should be changed to match free-boundary equilibrium requirements, and (3) derive an algorithm for a fixed-boundary 3D equilibrium solver compatible with a very general computational boundary, with conditions $B \cdot n|_{\partial\Omega} \neq 0$ (not necessarily a flux surface), $p|_{\partial\Omega} \neq \text{const.}$ (not necessarily an isobar), and $J \times n|_{\partial\Omega} \neq 0$.