Mixed-circuit modes and halo current asymmetry

The presence of open magnetic surfaces in contact with a conductor may lead to the development of a mixed-circuit instability, providing an explanation of asymmetric halo currents in tokamaks. It is explained why the open magnetic surfaces of the scrape-off layer can be thought of as effectively rational. The particular difficulties that the mixed-circuit geometry presents to analysis are identified. They concern the radial and poloidal discontinuities in the current density, the matching between the plasma core and the scrape-off layer, and the layer physics. To overcome the first, a simple approximation of `phase smoothing' is introduced. The others are addressed by an ad hoc matching of the core and the layer, which allows numerical simulation in toroidal geometry. The results are consistent with expectations from the smoothing approximation.