Energetics of the interaction between electromagnetic ExB turbulence and zonal flows

A detailed analysis of the energy transfer system between ExB turbulence and zonal flows is given. Zonal flows, driven by the ExB Reynolds stress of the turbulence, are coupled to pressure disturbances with sinusoidal poloidal structure in toroidal geometry through the geodesic curvature. These pressure 'sidebands' are nonlinearly coupled not only back to the turbulence, but also to the global Alfven oscillation whose rest state is the Pfirsch-Schlueter current in balance with the pressure gradient. The result is a statistical equilibration between turbulence, zonal flows and sidebands, and additionally the various poloidally asymmetric parallel dynamical subsystems. Computations in three-dimensional flux surface geometry show this geodesic transfer effect to be the principal mechanism which limits the growth of zonal flows in tokamak edge turbulence in its usual parameter regime, by means of both control tests and statistical analysis. As the transition to the magnetohydrodynamic (MHD) ballooning regime is reached, the Maxwell stress takes over as the main drive, forcing the Reynolds stress to become a sink