VMEC Convergence Near the Magnetic Axis: Issues, Diagnosis, and Repair

The VMEC (Variational Moments Equilibrium Code) code is a non-axisymmetric MHD equilibrium code. It can compute both free-boundary and fixed-boundary equilibria, and is widely used for equilibrium reconstruction, stellarator design, and experimental planning and interpretation. Recent comparison of free-boundary zero-beta toroidal current-free equilibria with Biot-Savart field-line following have shown that some VMEC-computed physics properties near the magnetic axis converge slower than expected (with exponent ~ -1 instead of the expected -2) as the radial resolution is increased. Possible causes of this slow convergence, along with potential algorithm improvements will be explored.