Neoclassical Toroidal Viscosity Calculations in Tokamaks using a $\delta f$ Monte Carlo Simulation and Their Verifications

Effect of magnetic perturbation on plasma rotation is an important issue in tokamaks, since recent studies have shown that perturbation as small as $\delta B/B_0\sim 10^{-4}$ can induce significant rotation damping. A new simulation to calculate neoclassical toroidal viscosity (NTV) in tokamaks with weak non-axisymmetric perturbation has been developed by adopting the $\delta f$ Monte Carlo method [1]. Previous benchmark has proven that in $\mathbf{E}\times\mathbf{B}\rightarrow 0$ limit the simulation result agrees well with the combined analytic formula by Park [2] in wide range of collision frequency [3]. In the presentation, further benchmark results of NTV calculation will be reported for the cases with finite $\mathbf{E}\times \mathbf{B}$ rotation and toroidal flow. Non-local (finite-orbit-width) effects on NTV, which may appear only in the $\delta f$ simulation, will also be investigated.\\[4pt] [1] S. Satake et al., Plasma Phys. Controlled Fusion {\bf 53}, 054018 (2011).\\[0pt] [2] J.-K. Park et al., Phys. Plasmas {\bf 16}, 056115 (2009).\\[0pt] [3] S. Satake et al., accepted to Phys. Rev. Lett.