Driving toroidally asymmetric current through the tokamak scrape-off layer. II. Magnetic field structure and spectrum

The structure of the magnetic field perturbations due to nonaxisymmetric field-aligned currents in the tokamak scrape-off layer (SOL) are analytically calculated near the X-point. Paper I [I. Joseph , Phys. Plasmas 16, 052510 (2009)] demonstrated that biasing divertor target plates in a toroidally asymmetric fashion can generate an appreciable toroidally asymmetric parallel current density in the SOL along the separatrix. Here, the magnetic field perturbation caused by a SOL current channel of finite width and stepwise constant amplitude at the target plate is derived. Flux expansion amplifies the magnetic perturbation near the X-point, while phase interference causes the SOL amplitude to be reduced at large toroidal mode number. Far enough from the current channel, the magnetic field can be approximated as arising from a surface current near the separatrix with differing amplitudes in the SOL and the divertor leg. The perturbation spectrum and resonant components of this field are computed analytically asymptotically close to the separatrix in magnetic flux coordinates. The size of the stochastic layer due to the applied perturbation that would result without self-consistent plasma shielding is also estimated. If enough resonant field is generated, control of the edge pressure gradient may allow stabilization of edge localized modes.