Transport theory of phase space zonal structures

Abstract

We adopt gyrokinetic theory to extract the phase space zonal structure from the flux surface averaged particle response, that is, the nonlinear response that is undamped by collisionless processes. We argue that phase space zonal structures are a proper definition for the nonlinear distortion of the plasma reference state and, thus, of the generally non-Maxwellian neighboring nonlinear equilibria consistent with toroidal symmetry breaking fluctuations. Evolution equations for phase space zonal structures are derived and discussed, along with the corresponding density and energy transport equations. It is shown that this approach is consistent with the usual evolution of macroscopic plasma profiles under the action of fluctuation induced fluxes, when the deviation of the reference state from local Maxwellian response is small. In particular, the present results recover those of a previous article [M. V. Falessi and F. Zonca, Phys. Plasmas 25, 032306 (2018)], where transport equations holding on the reference state length scale have been derived using the moment approach introduced in the classical review work by Hinton and Hazeltine.