Fast computation of three-dimensional fusion plasma equilibria
Antoine Cerfon, MIT

 One of the most promising concepts for the achievement of magnetically confined fusion is the stellarator. It relies on magnetic fields with an inherently three

dimensional structure to confine the hot dense fusion plasma. Such a device presents several desirable features for a fusion reactor, but the lack of a
particular symmetry for the plasma and the fields also represents a major challenge for the computation of equilibrium configurations. If significant
progress in the development of numerical methods for the calculation of 3D equilibria has been made over the last 30 years, with the performance and speed
of present solvers, certain crucial applications remain a goal for the future.
    Our approach to accelerating the calculation of 3D equilibria is to perform an asymptotic analysis based on a few small parameters typically found in modern
stellarator experiments. The end result of our analysis is a set of two surprisingly simple looking coupled partial differential equations for the plasma pressure and the magnetic vector potential, which, once solved, fully determines the equilibrium. A few examples will be given, to illustrate our approach.