Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis

Numerical computation of the ideal Magnetohydrodynamic (MHD) equilibrium magneticfield is at the base of stellarator optimisation and provides the starting point for solvingmore sophisticated Partial Differential Equations (PDEs) like transport or turbulencemodels. Conventional approaches solve for a single stationary point of the ideal MHDequations, which is fully defined by three invariants and the numerical scheme employedby the solver. We present the first numerical approach that can solve for a continuousdistribution of equilibria with fixed boundary and rotational transform, varying only thepressure invariant. This approach minimises the force residual by optimising parametersof multilayer perceptrons (MLPs) that map from a scalar pressure multiplier to theFourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.