Statistical theory of L–H transition in tokamaks*

A statistical model for the bifurcation of the radial electric field E_r is developed in view of describing L–H transitions of tokamak plasmas. Noise in micro-fluctuations is shown to lead to random changes of E_r, if a deterministic approach allows for more than one solution. The probability density function for and the ensemble average of E_r are obtained. The L-to-H and the H-to-L transition probabilities are calculated, and the effective phase limit is derived. Due to the suppression of turbulence by shear in E_r, the limit deviates from Maxwell's rule. The ensemble average of heat flux as well as that of E_r do not show a hysteresis in contrast to the deterministic model. Experimental condition for observing the hysteresis is also addressed.