Gyrokinetic Studies of Ion Temperature Gradient Turbulence and Zonal Flows in Helical Systems

Gyrokinetic theory and simulation results are presented to investigate regulation of ion temperature gradient (ITG) turbulence due to E × B zonal flows in helical systems. In order to examine effects of changes in helical magnetic configuration on anomalous transport and zonal flows, magnetic field parameters representing the standard and inward-shifted configurations of the Large Helical Device (LHD) [O. Motojima, N. Ohyabu, A. Komori, et al., Nucl. Fusion 43, 1674 (2003)] are used. The linear gyrokinetic analyses show that the largest growth rate of the linear ITG instability for the inward-shifted configuration is slightly higher than that in the standard one while, as theoretically predicted, zonal flows generated by given sources keep larger values for longer time for the inward-shifted case because of a smaller safety factor, a lower aspect ratio, and slower radial drift velocities of helical-ripple-trapped particles. It is shown from the gyrokinetic Vlasov simulation of the ITG turbulence that, in spite of the higher ITG-mode growth rate, the inward-shifted plasma takes a smaller average value of the ion thermal diffusivity in the steady turbulent state with a higher zonal-flow level. These results imply that neoclassical optimization contributes to reduction of the anomalous transport by enhancing the zonal-flow level and give a physical explanation for the confinement improvement observed in the LHD experiments with the inward plasma shift. When equilibrium radial electric fields produce poloidal E × B rotation of helically-trapped particles with reduced radial displacements, further enhancement of zonal flows and resultant transport reduction are theoretically expected