Edge instability regimes with applications to blob transport and the quasicoherent mode

An analytic theory of the resistive X-point (RX) mode in the edge region of a diverted tokamak is developed by employing an outgoing-evanescent wave boundary condition along the field lines. This result is employed to deduce a new categorization of edge instabilities in the presence of X points. A regime diagram shows the relationship of the RX mode to the ideal and conventional resistive ballooning modes. In addition to describing growth rates of linear instabilities, the analysis also yields regimes and scalings for nonlinear convective "blob" propagation velocities. The regime diagram and a knowledge of experimental and BOUT code simulation results suggest that the quasicoherent mode seen in the Alcator C-Mod tokamak [M. Greenwald, R. Boivin, P. Bonoli et al., [Phys. Plasmas 6, 1943 (1999)] can be classified as an electromagnetic RX mode. Analytical scalings for the existence of this mode compare well with experimental trends, as does the solution of a model radial eigenvalue problem. Finally, using a finite Larmor radius assumption to eliminate the perpendicular wave number, the instability regime diagram can be converted to an edge phase space diagram. X-point physics adds a new region to this edge parameter space that is postulated to be the enhanced D-alpha regime.