Neoclassical generation of toroidal zonal flow by drift wave turbulence

Abstract

Zonal-flow instabilities due to drift-wave turbulence in the presence of toroidicity-induced parallel (neoclassical) viscosity and allowing for the toroidal flow are studied. It is shown that, as a result of the neoclassical viscosity a new type of zonal-flow instability is possible, leading to the generation of the considerable toroidal zonal flow. The toroidal instability is complementary to the previously studied instability resulting in the poloidal flow generation and occurs as a second branch of the general dispersion relation describing the evolution of the poloidal and toroidal flow. Nonlinear saturation of the new instability is studied. It is shown that saturated zonal toroidal velocity, generated in this instability, is large compared to the mean cross-field drift velocity as the ratio q∕ϵ, where q is the safety factor and ϵ is the inverse aspect ratio. In addition to the broad turbulent spectrum of drift waves, a monochromatic wave packet is considered. It is revealed that for the case of sufficiently strong neoclassical viscosity such a wave packet is subjected to generation of the toroidal zonal flow due to instability of hydrodynamic type.