Non-linear incompressible poloidal viscosity and its implications for H mode in stellarator/heliotron plasmas

Non-linear incompressible poloidal viscosity is an important ingredient in understanding the L-H transition in both tokamaks and stellarators. Usually two or more local maxima in poloidal viscosity corresponding to this transition may appear in stellarator/heliotron devices. Depending on the relative magnitudes of the toroidal and helical components of the magnetic spectrum, the local maxima can occur at a poloidal E*B Mach number M_p somewhat larger than mod m-nq mod /m, where E (B) is the electric (magnetic) field strength, m(n) is the poloidal (toroidal) mode number of the components of the mod B mod spectrum and q is the safety factor. Non-linear incompressible viscosities for the plateau Pfirsch-Schluter regime are calculated for present and next generation stellarator/heliotron devices (Heliotron-E, CHS, LHD, W7-AS and W7-X) by using a magnetic spectrum near the edge region under the assumption of negligibly small parallel flow. The possibility of the occurrence of the L-H transition and the limitation due to the effect of the charge exchange momentum loss are discussed. When the ion-ion collision frequency and neutrals are reduced sufficiently, all these devices show a local maximum of poloidal viscosity at M_p approximately 1. However, the reduction of the poloidal viscosity in the region beyond this maximum is not large compared with the tokamak case.