The presence of open magnetic surfaces in contact with a conductor maylead to the development of a mixed-circuit instability, providing anexplanation of asymmetric halo currents in tokamaks. It is explainedwhy the open magnetic surfaces of the scrape-off layer can be thoughtof as effectively rational. The particular difficulties that themixed-circuit geometry presents to analysis are identified. Theyconcern the radial and poloidal discontinuities in the currentdensity, the matching between the plasma core and the scrape-offlayer, and the layer physics. To overcome the first, a simpleapproximation of `phase smoothing' is introduced. The others areaddressed by an ad hoc matching of the core and the layer, whichallows numerical simulation in toroidal geometry. The results areconsistent with expectations from the smoothing approximation.