The present work addresses the issue of identifying the major non-linear physics processes which may regulate drift and drift-Alfvén turbulence using a weak turbulence approach. Within this framework, on the basis of the non-linear gyrokinetic equation for both electrons and ions, an analytic theory is presented for non-linear zonal dynamics described in terms of two axisymmetric potentials, δϕz and δA|| z, which spatially depend only on a (magnetic) flux co-ordinate. Spontaneous excitation of zonal flows by electrostatic drift microinstabilities is demonstrated both analytically and by direct 3-D gyrokinetic simulations. Direct comparisons indicate good agreement between analytic expressions of the zonal flow growth rate and numerical simulation results for ion temperature gradientdriven modes. Analogously, it is shown that zonal flows may bespontaneously excited by drift-Alfvén turbulence, in the form of modulational instability of the radial envelope of the mode as well, whereas in general, excitations of zonal currents are possible but have little feedback on the turbulence itself.
Overview of gyrokinetic studies of finite-β microturbulence