Dynamics of low to high (‘‘L’’ to ‘‘H’’) confinement bifurcation: Poloidal flow and ion pressure gradient evolution

A self-consistent model of the low to high (‘‘L’’ to ‘‘H’’) transition is derived from coupled nonlinear envelope equations for the fluctuation level and radial electric field shear, Er′, as determined by ion pressure gradient, ∇Pi, and poloidal flow. These equations extend the phase transition model of the L to H bifurcation by including ∇Pi effects. In this model, the transition occurs when the turbulence drive is large enough to overcome the damping of the total E×B flow. Near the critical power for transition, poloidal flow shear dominates Er′, but at high power, ∇Pi gives the main contribution. The inclusion of ∇Pi also introduces a quenched fluctuation state that is accessible at high power and may be the experimentally observed H-mode state for P≫Pcrit. In this state, the radial electric field is determined only by ∇Pi because no fluctuation energy is available to produce a turbulent Reynolds stress.