Probability of Statistical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>L</mml:mi><mml:mo>–</mml:mo><mml:mi>H</mml:mi></mml:math>Transition in Tokamaks

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