Shear-induced Reynolds stress at the edge of L-mode tokamak plasmas

The turbulent flux of momentum—or Reynolds stress—is a mechanism responsible for the generation of sheared flow by turbulence. The structure of the flux-surface-averaged stress is investigated in the edge region of an L-mode tokamak plasma. The stress induced by the perpendicular tilting of ballooning modes is considered. In addition to the tilting by the E × B flow shear, which is a negative viscosity effect, a magnetic-shear-induced Reynolds stress—called -residual stress—arises as a consequence of a residual spatial tilting of ballooning modes by the magnetic shear in a poloidally up–down asymmetric magnetic geometry. A model is derived in the weak flow shear regime under the approximation of circular flux surfaces. The amplitude of this residual stress is of the order of the square of the radial velocity fluctuations in the scrape-off layer (SOL), and in the immediate radial vicinity of the separatrix if an X-point exists. Its amplitude drops rapidly to zero towards the plasma core, thus appearing as a source of transverse rotation at the interface. Its non-linear dependence on the electric shear is discussed in the context of the weak electric shear effect on the poloidal shape of the ballooning envelope. The local -residual stress is non-uniform poloidally and changes sign according to the up/down position of SOL end-plates with respect to the ∇B × B direction. The electric- and magnetic-shear-induced stresses are then included in a flux-surface-averaged 1D model of mean flow conservation at the plasma edge, including the SOL volume. In L-mode weak shear regimes, it is shown that changing the plasma geometry from ∇B × B away from the divertor to ∇B × B towards the divertor approximately doubles the electric shear strength inside the separatrix, as reported in experiments. This shear-induced stress also enters the toroidal momentum balance, where it appears as a significant source of momentum in the immediate vicinity of the separatrix. Balanced by the toroidal viscosity only, it can sustain toroidal flow gradients of the order of a km s−1 cm−1 at the separatrix, with a sign also dependent on the plasma geometry. These momentum sources arising from symmetry breaking at the boundary of the confined region may explain why low to high mode power thresholds are lower in favourable than unfavourable configurations, and may be important for the issue of optimal plasma shapes with respect to edge intrinsic shear.