Modeling Flow Suppression of Error-field-induced Magnetic Islands in Tokamaks

Small deviations from axisymmetry in applied tokamak magnetic fields can induce island formation at magnetic surfaces whose rotational transform resonates with the perturbation. These islands have a braking effect on plasma rotation that can destabilize resistive wall modes. The IPEC code\footnote{J.K. Park, et al., \textit{Phys. Plasmas} \textbf{14}, 052110 (2007).} is useful for computing plasma response to harmonic perturbations in the infinite-conducting limit, assuming perfect shielding at the resonant surface, but cannot predict the nonlinear effects of finite-sized islands. Using the nonlinear extended MHD code M3D,\footnote{W. Park, \textit{et al}., \textit{Phys. Plasmas} \textbf{6}, 1796 (1999).} we explore the effects of a 2,1 perturbation on the nonlinear evolution of a family of equilibria with finite resistivity. Particular attention is paid to the effects of toroidal flow on suppressing island formation, making contact with the analytic theory of Fitzpatrick.\footnote{R. Fitzpatrick, \textit{Phys. Plasmas} \textbf{5}, 3325 (1998).} Island suppression is shown to depend strongly on the tearing mode stability properties of the equilibrium.