Constructing Integrable Full-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibria

Abstract

For the (non‐axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands are guaranteed to exist. Magnetic islands break the smooth topology of nested flux surfaces and chaotic field lines result when magnetic islands overlap. An analogous case occurs with 112‐dimension Hamiltonian systems where resonant perturbations cause singularities in the transformation to action‐angle coordinates and destroy integrability. The suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Techniques for ‘healing’ vacuum fields and fixed‐boundary plasma equilibria have been developed, but what is ultimately required is a procedure for designing stellarators such that the self‐consistent plasma equilibrium currents and the coil currents combine to produce an integrable magnetic field, and such a procedure is presented here for the first time. Magnetic islands in free‐boundary full‐pressure full‐current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver [A.H.Reiman & H.S.Greenside, Comp. Phys. Comm., 43:157, 1986.] which iterates the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible. The method is applied to a candidate plasma and coil design for the National Compact Stellarator eXperiment [G.H.Neilson et.al., Phys. Plas., 7:1911, 2000.].