Resistive modes in the edge and scrape-off layer of diverted tokamaks

The linear behavior of resistive ballooning modes in the edge and scrape-off layer of diverted tokamaks is explored in the context of a collisional fluid model. It is shown that the large magnetic shear and small poloidal field in the X-point region act to increase the wave number, and hence the importance of resistivity, near the X point. The resulting “disconnection” of the eigenmodes across the X point profoundly influences the unstable spectrum. A new class of modes called resistive X-point (RX) modes exploits this synergism between resistivity and the X-point geometry, giving rise to robust growth rates at moderate-to-low mode numbers. Relative to an equivalent limited plasma, the diverted plasma is shown to be more unstable in the edge (inside the separatrix), and more stable in the scrape-off layer.