Simulation of Resistive Wall Modes using NIMROD

The resistive wall mode (RWM) is an external, or free boundary, MHD kink instability in the presence of a wall with finite conductivity. It leads to beta limits and is also considered as one of the significant reasons for the triggering of disruptions in the tokamak. In this study, RWMs are modeled with the high-order spectral finite element code NIMROD, which has been verified with the analytic linear theory for RWM in cylindrical geometry for a range of wall positions and wall resistivities. New linear results for toroidal geometry compare two different numerical approaches for the resistive wall, a Green’s function approach and a Lagrange multiplier approach with a meshed external vacuum region. The code is used to study the nonlinear evolution of a RWM in a tokamak with a large aspect ratio and nearly circular cross-section, where the most unstable n=1 ideal kink mode is found to couple with the high-order modes and drive them to finite amplitude. The nonlinear phase of the RWM is important for understanding the triggering of disruptions due to the destructive RWM fluctuations.