Renormalized theory of ion temperature gradient instability of the magnetic-field-aligned plasma shear flow with hot ions

The developed kinetic theory for the stability of a magnetic-field-aligned (parallel) shear flow with inhomogeneous ion temperature [Mikhailenko et al., Phys. Plasmas 21, 072117 (2014)] predicted that a kinetic instability arises from the coupled reinforcing action of the flow velocity shear and ion temperature gradient in the cases where comparable ion and electron temperatures exist. In the present paper, the nonlinear theory was developed for the instability caused by the combined effects of ion-temperature-gradient and shear-flow (ITG-SF). The level of the electrostatic turbulence is determined for the saturation state of the instability on the basis of the nonlinear dispersion equation, which accounts for a nonlinear scattering of ions by the developed turbulence in a sheared flow. The renormalized quasilinear equation for the ion distribution function, which accounts for the turbulent scattering of ions by ITG-SF driven turbulence, was derived and employed for the estimation of the turbulent ion viscosity, the anomalous ion thermal conductivity, and anomalous ion heating rate at the saturation state of the instability. (C) 2015 AIP Publishing LLC.