Pressure Balance in the Presence of Zonal Flows

The presence of equilibrium zonal flows in the gyrokinetic particle simulation of the gradient-driven microinstablities was first observed in 1983 [1]. It was caused by the difference of the second-order finite Larmor radius effects between the electrons and the ions, which, in the presence of background spatial inhomogeneity, gave rise to a zeroth-order radial mode, $\phi_{00}(x)$. Recently, a more complete formulation taking into account both the density and temperature gradients has been derived [2]. The question concerning its relationship with the usual diamagnetic current was raised by Bolton [3]. For this presentation, we will explore the pressure balance, \[ \sum_\alpha n_\alpha q_\alpha {\bf E} + {1 \over c} \sum_\alpha q_\alpha n_\alpha {\bf V}_\alpha \times {\bf B} = \nabla \sum_\alpha p_\alpha, \] in the presence of the equilibrium zonal flows as well as the global zonal flows, $\phi_{00}(x)$, generated nonlinearly due to the ITG turbulence [4]. \\[4pt] [1] W. W. Lee, Phys. Fluids {\bf 26}, 556 (1983).\\[0pt] [2] W. W. Lee, R. A. Kolesnikov, Phys. Plasmas {\bf 16}, 044506 (2009).\\[0pt] [3] C. Bolton, private communication.\\[0pt] [4] W. W. Lee et al. Comp. Sci. \& Disc. {\bf 1}, 015010 (2008).