Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

Zonal flow helps reduce and regulate the turbulent transport level in tokamaks. Rosenbluth and Hinton have shown that zonal flow damps to a nonvanishing residual level in collisionless [M. Rosenbluth and F. Hinton, Phys. Rev. Lett. 80, 724 (1998)] and collisional [F. Hinton and M. Rosenbluth, Plasma Phys. Control. Fusion 41, A653 (1999)] banana regime plasmas. Recent zonal flow advances are summarized including the evaluation of the effects on the zonal flow residual by plasma cross-section shaping, shorter wavelengths including those less than an electron gyroradius, and arbitrary ion collisionality relative to the zonal low frequency. In addition to giving a brief summary of these new developments, the analytic results are compared with GS2 numerical simulations [M. Kotschenreuther, G. Rewoldt, and W. Tang, Comput. Phys. Commun. 88, 128 (1991)] to demonstrate their value as benchmarks for turbulence codes. (C) 2007 American Institute of Physics.