Spatio-temporal evolution of the L → I → H transition

Abstract

We investigate the dynamics of the low(L) → high(H) transition using a time-dependent, one dimensional (in radius) model which self-consistently describes the time evolution of zonal flows (ZFs), mean flows (MFs), poloidal spin-up, and density and pressure profiles. The model represents the physics of ZF and MF competition, turbulence suppression via E×B shearing, and poloidal flows driven by turbulence. Numerical solutions of this model show that the L→H transition can occur via an intermediate phase (I-phase) which involves oscillations of profiles due to ZF and MF competition. The I-phase appears as a nonlinear transition wave originating at the edge boundary and propagates inward. Locally, I-phase exhibits the characteristics of a limit-cycle oscillation. All these observations are consistent with recent experimental results. We examine the trigger of the L→H transition, by defining a ratio of the rate of energy transfer from the turbulence to the zonal flow to the rate of energy input into the turbulence. When the ratio exceeds order unity, ZF shear gains energy, and a net decay of the turbulence is possible, thus triggering the L→H transition. Numerical calculations indicate that the L→H transition is triggered by this peak of the normalized ZF shearing. Zonal flows act as “reservoir,” in which to store increasing fluctuation energy without increasing transport, thus allowing the mean flow shear to increase and lock in the transition. A counterpart of the L → I→H transition, i.e., an L→H transition without I-phase, is obtained in a fast power ramp, for which I-phase is compressed into a single burst of ZF, which triggers the transition. Effects of neutral charge exchange on the L→H transition are studied by varying ZF damping and neoclassical viscosity. Results show that the predicted L→H transition power increases when either ZF damping or viscosity increase, suggesting a link between recycling, ZF damping, and the L→H threshold. Studies of fueling effects on the transition and pedestal structure with an emphasis on the particle pinch are reported.