Zonal flow generation from trapped electron mode turbulence

Most existing zonal flow generation theory [1,2] has been developed with a usual assumption of $q_r \rho _{i\theta } <<1$ ($q_r $ is the radial wave number of zonal flow, and $\rho _{i\theta } $ is the ion poloidal gyroradius). However, recent nonlinear gyrokinetic simulations of trapped electron mode (TEM) turbulence exhibit a relatively short radial scale of the zonal flows with $q_r \rho _{i\theta } \sim 1$ [3,4,5]. This work reports an extension of zonal flow growth calculation to this short wavelength regime via the wave kinetics approach. A generalized expression for the polarization shielding for arbitrary radial wavelength [6] which extends the Rosenbluth-Hinton formula in the long wavelength limit [7] is applied. The electron nonlinearity effects on zonal flow are investigated by using GTC simulation. This work was supported by the China Scholarship Council (LW), U.S. DoE Contract No. DE--AC02--09CH11466 (TSH, LW), the U. S. DOE SciDAC center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas, and the U. S. DOE SciDAC-FSP Center for Plasma Edge Simulation (TSH). [1] P. H. Diamond et al., IAEA-CN-69/TH3/1 (1998). [2] L. Chen, Z. Lin, and R. White, Phys. Plasmas \textbf{7}, 3129 (2000). [3] Z. Lin et al., IAEA-CN-138/TH/P2-8 (2006). [4] D. Ernst et al., Phys. Plasmas \textbf{16}, 055906 (2009). [5] Y. Xiao and Z. Lin, ``Turbulent transport of trapped electron modes in collisionless plasmas'', submitted to Phys. Rev. Lett. (2009). [6] Lu Wang and T.S. Hahm, Phys. Plasmas \textbf{16}, 062309 (2009). [7] M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. \textbf{80}, 724 (1998).