Self-Regulating Shear Flow Turbulence: A Paradigm for the<i>L</i>to<i>H</i>Transition

A self-consistent model of the L to H transition is derived from coupled nonlinear envelope equations for the fluctuation level and radial electric field shear ${\mathrm{E}}_{\mathrm{r}}^{\ensuremath{'}}$. These equations exhibit a supercritical bifurcation between dual L-mode and H-mode fixed points. The transition occurs when the turbulence level is large enough for the Reynolds stress drive to overcome the damping of the E\ifmmode\times\else\texttimes\fi{}B flow. This defines a power threshold for the transition, which is calculated and found to be consistent with experimental findings.