Effects of zonal flows on transport crossphase in dissipative trapped-electron mode turbulence in edge plasmas

Abstract

Confinement regimes with edge transport barriers occur through the suppression of turbulent (convective) fluxes in the particle and/or thermal channels, i.e. , and , respectively, for drift-wave turbulence. The quantity is the turbulence intensity, while and are the crossphases. For H-mode, standard decorrelation theory predicts that it is the turbulence intensity that is mainly affected via flow-induced shearing of turbulent eddies. However, for other regimes (e.g. I-mode, characterized by high energy confinement but low particle confinement), this decrease of turbulence amplitude cannot explain the decoupling of particle versus thermal flux, since a suppression of turbulence intensity would necessarily affect both fluxes the same way. Here, we explore a possible new stabilizing mechanism: zonal flows may directly affect the transport crossphase. We show the effect of this novel mechanism on the turbulent particle flux, by using a simple fluid model (Baver et al 2002 Phys. Plasmas 9 3318) for dissipative trapped-electron mode (DTEM), including zonal flows. We first derive the evolution equation for the transport crossphase δk between density and potential fluctuations, including contributions from the E × B nonlinearity. By using a parametric interaction analysis including the back-reaction on the pump, we obtain a predator–prey like system of equations for the pump amplitude ϕp, the pump crossphase δp, the zonal amplitude ϕz and the triad phase-mismatch Δδ. The system displays limit-cycle oscillations where the instantaneous DTEM growth rate—proportional to the crossphase—shows quasi-periodic relaxations where it departs from that predicted by linear theory.