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The theory of the L-H transition in tokamaks is discussed. A transport bifurcation model is presented, which predicts reasonably well several properties of the L-H transition in the DIII-D tokamak, including the evolution in time of the density and temperature profiles. A bifurcation in the radial transport occurs because of a nonlinear feedback mechanism involving the radial electric field. A spontaneous transition is predicted when certain conditions are met; no trigger mechanism is necessary. The predicted profile evolution in H-mode can include a transition to VH-mode, with its characteristically wider transport barrier at the plasma edge. Trigger mechanisms are discussed, as well as the idea of considering the L-H transition as a phase transition.
A technique of fitting a modified hyperbolic tangent to the edge profiles has improved the localization of plasma edge parameters. Non-dimensional edge parameters are broadly consistent with several theories of the L-H transition that use edge gradients in their formulation of a critical threshold parameter. The ion (nabla)B drift direction has only a small effect on the edge plasma conditions measured near the plasma midplane but a large effect on the divertor plasma. The dramatic change of power threshold with the direction of the ion (nabla)B drift implies that phenomena in the divertor region may be critical for the L-H transition.
Edge profiles during the L-H transition and pedestal evolution on the Alcator C-Mod tokamak have been measured with high spatial and time resolution. For input power near the threshold, periodic 'dithering' cycles are seen, and the sustained transition occurs in a series of steps which appear related to this oscillatory behaviour. Even at higher power, there is evidence of non-smooth Te evolution and pedestal Te shows a double break-in-slope at the transition. Calculations with a fluctuation-shear flow model, for parameters typical of this experiment, reproduce much of the observed behaviour. Profiles just before the L-H transition, averaged over steady or dithering periods, are compared with an analytic criterion based on shear suppression by zonal flows [Guzdar P N et al, Phys. Rev. Lett. 89, 265004 (2002).]. Experimental values of ... are about 50% below the theoretical threshold, for a range of BT.