The effects of applied 3-D magnetic fields and resistive wall boundary conditions on nonlinear MHD simulations

Two applications of a resistive wall boundary condition are implemented in \textsc{nimrod}: the periodic cylinder with external resonant magnetic fields, and a toroidal resistive wall condition. The resonant 3-D magnetic fields are used to study the shielding of error-fields by axial flow and error-field penetration leading to locked magnetic islands. These studies employ stable, zero-$\beta $ equilibria, and the effects of the degree of stability (measured by the parameter $\Delta $') are investigated. A toroidal resistive wall boundary condition is also developed for \textsc{nimrod} by matching the magnetic fields inside the domain with the external fields found using a vacuum-field solver. The toroidal boundary condition is tested in the large aspect ratio, circular cross-section limit, and compared to the results from the periodic cylinder boundary condition.