Saturation of collisionless driftwave turbulence via symmetric dynamics

In ion temperature gradient (ITG) driven turbulence, the manner in which zonal flows saturate in the absence of collisionality remains an outstanding question. In this work, collisionless zonal flow saturation is analytically investigated using a reduced two field fluid model for ITG driven turbulence subject to a 3-wavevector, 5-mode truncation. Using weak turbulence closure theory, wave kinetic equations (WKE) are derived describing how the zonal flow and eigenmode energy spectra of this system will fluctuate with time according to linear and nonlinear dynamics. In the collisionless limit, the time evolution operators in these equations reduce to combinations of centro- and skew-centrosymmetric matrices, and conditions are found for spectral saturation in this regime. One set of such stationary solutions to the WKEs suggests a state of turbulent fluid in which down- and up-gradient thermal energy transport (from stable and unstable modes, respectively) at each fluctuation length scale are perfectly balanced, implying ideal confinement despite the ITG instability. These predictions are confirmed by numerical simulations of the system. Generalization to the non-truncated system is also briefly discussed.

This work was supported by the US DOE grant DE-FG02-89ER53291.