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

Abstract

Residual turbulence from velocity shear stabilized interchange instabilities Phys. Plasmas 20, 012301 (2013); 10.1063/1.4775082 Spatiotemporal temperature fluctuation measurements by means of a fast swept Langmuir probe array Rev. Sci. Instrum. 78, 053505 (2007);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 Â 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. V C 2012 American Institute of Physics.

Interchange Turbulence Model for the Edge Plasma in SOLEDGE2D‐EIRENE

“…For instance, prey-predator models have been derived to describe the complex interplay between large scales and small scales in tokamak plasma turbulence. The model by Miki [14] shows in fact some similarities with the k − model. In this 1D radial model, equations are solved for the mean field plasma quantities (density n, pressure (energy) p, poloidal velocity v θ ).…”

“…The mean flow shearing is given by E V = v E 2 where v E is provided by a force balance detailed in [14]. From a dimensional analysis, the turbulent diffusion is given by…”

“…The second term in the equation describes turbulence self-saturation. The diffusive term in the left hand side describes turbulence intensity transport (expression for χ N can be found in [14]). Finally, the two turbulence predators remain, E 0 being zonal flow shearing and E V being mean flow shearing.…”

“…The radial transport due to turbulence is modeled using a diffusion coefficient D which is computed with the following predator-prey 3-equations turbulence model. Like in the k − ε model, the first equation describes the evolution of turbulence intensity [normalized to c 2 s ] (denoted I in [14]):…”

Bifurcation theory of a one-dimensional transport model for the L-H transition

“…36, would be a relevant extension. Recently, a paper was published 37 which proposes such a combination of the 1-D transport equations with the evolution of the turbulence and zonal flows, and is probably suitable for investigation with our bifurcation analysis.…”