Implementation of Field Error and Resistive Wall Boundary Conditions in Finite Element Codes

Current tokamak experiments depend critically on the boundary conditions of the magnetic fields for effective operation. While non-axisymmetric boundary conditions have been considered deleterious for plasma operation because of locked modes locked modes [J.T. Scoville et.al Nuclear Fusion 31, 875 (1991)], recent experiments show they might be advantageous for ELM control [T.E. Evans et.al. PRL 92, 235003 (2004)]. Instabilities which can arise due to the finite resistivity of the wall have also emerged as a emerged as a problem for advanced tokamak operation. \footnote{A. Garafalo et.al. Phys. Plasmas 9, 1997 (2002)} Implementation of these boundary conditions into finite element codes requires a different formulation of the boundary conditions as compared to the finite difference codes in earlier work [D.J. Ward and A. Bondeson, Phys. Plasmas 2, 1570 (1995)]. Here, we review the proper formulation with particular attention paid to numerical accuracy of the method.