Turbulent Generation of Flows and Magnetic Field at the Rational Magnetic Surfaces of a Tokamak

Full text: Comparative analysis of generation of large-scale structures, zonal flows and streamers, by drift wave turbulence is conducted for periodic systems with magnetic shear such as a tokamak. In a strong magnetic field dynamics of quasi two-dimensional perturbations strongly depends on the value of the wave vector along the magnetic field. When the parallel wave vector is significantly large, so that the parallel phase velocity of perturbation is small compared to electron thermal velocity, the parallel electron motion results in a finite electron density perturbation. It follows the Boltzmann distribution. However, for large-scale structures with poloidal and toroidal symmetry m = n = 0, and the parallel wave vector is zero. This results in strong reduction of density perturbation for m = n = 0. This difference has profound consequences for generation of large-scale zonal flows and streamers due to different structure of the nonlinear interaction matrix. The interaction term has a structure similar to the standard convective nonlinearity for zonal flows, while for streamers it has the structure of the Hasegawa-Mima nonlinearity (which is the higher order due to a small parameter associated with a finite ion Larmor radius). Respectively, zonal flows have the larger growth rate gamma(ZF) compared to that of the streamers. It is shown that 3D electromagnetic helical perturbations will have the growth rate comparable to that of zonal flows if their symmetry coincides with the symmetry of rational magnetic surface, m = nq. The field line bending provides a stabilizing effect and thus determines the radial localization of such structures. Therefore, it is expected that three-dimensional structures of flows and magnetic field will be preferentially generated at the rational magnetic surfaces of a tokamak with a growth rate of order gamma(ZF). This theoretical result may corroborate existing experimental correlations of large-scale shear flow structures with rational magnetic surfaces of a tokamak. (author)