Probability of Statistical [Formula presented] Transition in Tokamaks

A statistical model for the bifurcation of the radial electric field [Formula presented] is analyzed in view of describing [Formula presented] transitions of tokamak plasmas. Noise in microfluctuations is shown to lead to random changes of [Formula presented] if a deterministic approach allows for more than one solution. The probability density function for and the ensemble average of [Formula presented] are obtained. The [Formula presented]-to-[Formula presented] and the [Formula presented]-to-[Formula presented] transition probabilities are calculated, and the effective phase limit is derived. Because of the suppression of turbulence by shear in [Formula presented], the limit deviates from Maxwell’s rule.