We present analyses of mechanisms which convert radial inhomogeneity to broken k||-symmetry and thus produce turbulence driven intrinsic rotation in tokamak plasmas. By performing gyrokinetic simulations of ITG turbulence, we explore the many origins of broken k||-symmetry in the fluctuation spectrum and identify both E × B shear and the radial gradient of turbulence intensity—a ubiquitous radial inhomogeneity in tokamak plasmas—as important k||-symmetry breaking mechanisms. By studying and comparing the correlations between residual stress, E × B shearing, fluctuation intensity and its radial gradient, we investigate the dynamics of residual stress generation by various symmetry breaking mechanisms and explore the implication of the self-regulating dynamics of fluctuation intensity and E × B shearing for intrinsic rotation generation. Several scalings for intrinsic rotation are reported and are linked to investigations of underlying local dynamics. It is found that stronger intrinsic rotation is generated for higher values of ion temperature gradient, safety factor and weaker magnetic shear. These trends are broadly consistent with the intrinsic rotation scaling found from experiment—the so-called Rice scaling.
Intrinsic rotation in tokamaks: theory