Modeling the effect of toroidal plasma rotation on drift-magnetohydrodynamic modes in tokamaks

A new code, MISHKA-F (Flow), has been developed as an extension of the ideal magneto-hydrodynamic (MHD) code MISHKA-1 [Mikhailovskii et al., Plasma Phys. Rep. 23, 844 (1997)] in order to investigate the linear MHD stability of ideal and resistive eigenmodes with respect to the effects of toroidal rotation in tokamaks in general toroidal geometry with the ion diamagnetic drift effect taken into account. Benchmark test results of the MISHKA-F code show good agreement with analytic theory [A. B. Mikhailovskii and S. E. Sharapov, Plasma Phys. Controlled Fusion 42, 57 (2000)] for the stability limits of the ideal n /m=1/1 internal kink mode. The combined stabilizing effects of the ion diamagnetic drift frequency, ω*i, and the toroidal flow shear are also studied. The ω*i stabilization of the internal kink mode is found to be more effective at finite flow shear. Finite-n ballooning modes are studied in plasmas with the toroidal flow shear effect included. The stabilization of the ballooning modes by toroidal rotation is found to agree well with earlier predictions [Webster et al., Phys. Plasmas 11, 2135 (2004)]. The effect of high flow shear is analyzed for a sawtoothing discharge typical in the Mega Ampère Spherical Tokamak (MAST) [Sykes et al., Nucl. Fusion 41, 1423 (2001)]. It is found that the ideal n =1 internal kink mode can be stabilized by toroidal rotation at values observed experimentally.