Low to high confinement transition theory of finite-beta drift-wave driven shear flow and its comparison with data from DIII-D

Abstract

Shear flow stabilization of edge turbulence in tokamaks has been the accepted paradigm for the improvement in confinement observed in high (H) confinement mode plasmas. Results on the generation of zonal flow and fields in finite β plasmas are presented. This theory yields a criterion for bifurcation from low to high (L–H) confinement mode, proportional to Te/Ln, where Te is the electron temperature and Ln is the density scale-length at the steepest part of the density gradient. When this parameter exceeds a critical value (mostly determined by the strength of the toroidal magnetic field), the transition occurs. The predicted threshold based on this parameter shows good agreement with edge measurements on discharges undergoing L–H transitions in DIII-D [J. L. Luxon, R. Anderson, F. Batty et al., in Proceedings of the 11th Conference on Plasma Physics and Controlled Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159]. The observed differences in the transitions with the reversal of the toroidal magnetic field are reconciled in terms of this critical parameter due to the differences in the density gradient scale-lengths in the edge. The theory also provides a possible explanation for lowered threshold power, pellet injection H modes in DIII-D, thereby providing a unified picture of the varied observations on the L–H transition.

Edge Turbulence and its Interaction with the Equilibrium

“…The dominant linear instabilities in this parameter regime are resistive [34] even when the steeper temperature gradients give them an ITG character. Turbulence at the same parameters is often assumed without diagnosis to follow not only the linear mechanism but also the linear scales, whether in interpreting a computation [32,33] or in forming transport models based upon edge turbulence [35,36]. By contrast, it is known via control tests and in-context diagnosis that edge turbulence is viable in the absence of linear instabilities [6,7], and can eliminate the linear destabilisation mechanism [5,25].…”

Simulations of drift resistive ballooning L-mode turbulence in the edge plasma of the DIII-D tokamak

“…((1)-(4)) and does not includeb Á r terms. However, these equations support the drift-resistive ballooning mode physics, [5][6][7][8][9][10][11][15][16][17]27 which is enough to capture the main features of instability growth and resulting turbulence. Case 6 is the most complete system: it includes all terms in Eqs.…”

“…The reduction of the Braginskii equations in the drift ordering to the simpler set of equations used here is somewhat arbitrary but illustrates various physics terms and shares the philosophy of earlier published work exploring model equations for edge turbulence. [5][6][7][8][9][10][11] For example, the evolution equations for the temperature fluctuations are much simplified and include only E Â B convection and parallel thermal conduction.…”

“…4 There are strong gradients in the edge region that provide drive mechanisms for collective modes of instability that can lead to the observed anomalous transport. Antecedents for the work presented here are the earlier studies by Carreras and co-workers, 5,6 and by Guzdar, Drake and co-workers [7][8][9][10][11] wherein resistive interchange, resistive ballooning, and drift-resistive ballooning modes were considered. The theory of resistive interchange modes traces back to the earlier classic papers of Furth et al 12 and Coppi.…”

Integrated ELM Modelling

“…The modelling described above can be contrasted with other studies, which have similar elements, but are based on different physics considerations [41][42][43][44]. Most of these studies are broad approaches attempting to describe the L-H transition, the H-mode and the characteristics of the pedestal, but do not deal extensively with ELM modelling.…”