Shock formation in a poloidally rotating tokamak plasma

When the Mach number Mp of the poloidal rotation in a tokamak approaches unity, the poloidal variations of plasma density and potential appear to have the characteristics of a shock whose front lies on a plane (ribbon) of a fixed poloidal angle η0. The shock first appears, when 1−Mp≲(ε)1/2 (ε is the inverse aspect ratio), on the inside of the torus at a shock angle η0≥π if the plasma rotates counterclockwise poloidally. As Mp increases, η0 moves in the direction of the poloidal rotation. At Mp=1, η0=2π. When Mp −1≲(ε)1/2, the shock angle is at η0≲π. The parallel viscosity associated with the shock is collisionality independent, in contrast to the conventional neoclassical viscosity. The viscosity reaches its maximum at Mp=1, which is the barrier that must be overcome to have a poloidal supersonic flow. Strong up–down asymmetric components of poloidal variations of plasma density and potential develop at Mp ≂1. In the edge region, the convective poloidal momentum transport weakens the parallel viscosity and facilitates the L–H transition.