Asymptotic expansion for stellarator equilibria with a non-planar magnetic axis

We perform an asymptotic analysis to reduce the complexity of the MHD equilibrium equations in stellarators. In our new formulation, stellarator equilibria are fully determined by the solution of a set of two simple looking coupled partial differential equations for the plasma pressure and the magnetic vector potential. As in the classic work by Greene and Johnson [1], the asymptotic expansion relies on the ratio of the helical magnetic field to the vacuum toroidal field. However, our ordering for the equilibrium quantities generalizes that of [1] in order to provide a better match with modern stellarator experiments. In particular, toroidal effects enter the analysis in the same order as helical effects, allowing the calculation of equilibria with multiple helicities and a non-planar magnetic axis. To illustrate the simplicity and the versatility of our approach, we construct semi-analytic solutions to the system of equations for the pressure and the vector potential. With these solutions, we compute stellarator equilibria for several special cases. \\[4pt] [1] J.M. Greene and J.L. Johnson, Phys. Fluids 4, 875 (1961)