Dynamic database generation for efficient calculation of stellarator plasma equilibria

A numerical scheme has been developed and tested that significantly reduces (by a factor of 30, typically) both the computation time and storage requirements for external magnetic field calculations embedded in a three-dimensional iterative magnetohydrodynamic equilibrium calculation. The equilibrium is computed from external magnetic fields that are calculated numerically using the Biot-Savart law applied to a complex set of coils. These fields must be evaluated on the plasma boundary, which evolves as the equilibrium converges. The improved efficiency of the present method results from dynamically building and storing a database of magnetic field components on a grid that is determined by the changing plasma boundary itself. When possible, field values on the plasma boundary for a particular iteration are interpolated from these grid values, thus eliminating the need for further time-consuming Biot-Savart calculations. New grid points are added to the database only when the boundary moves outside the spatial range of previously computed interpolation values. This dynamical method is particularly efficient when the equilibrium calculation is embedded in an optimization loop, where evolution of the coil set requires many reevaluations of the database.