Surface currents on the plasma-vacuum interface in MHD equilibria

The VMEC$^{1}$ non-axisymmetric MHD equilibrium code can compute free-boundary equilibria$^{2}$. Since VMEC assumes that magnetic fields within the plasma form closed and nested flux surfaces, the plasma-vacuum interface is a flux surface, and the total magnetic field there has no normal component. VMEC imposes this condition of zero normal field using the potential formulation of Merkel$^{3}$, and solves a Neumann problem for the magnetic potential in the exterior region. This boundary condition necessarily admits the possibility of a surface current on the plasma-vacuum interface. While this current may be small in MHD equilibrium, this current may be readily computed in terms of a magnetic potential in both the interior and exterior regions. Examples of the surface current for VMEC equilibria will be shown. $^{1}$ Hirshman S P and Whitson J, Phys. Fluids \textbf{26} 3553 (1983) $^{2}$ Hirshman S P, Van Rij W I and Merkel P, Comp. Phys. Comm. \textbf{43} 143--55 (1986) $^{3}$ Merkel P, J. Comp. Phys. \textbf{66} 83--98 (1986)