Entropy production, scaling laws and state transitions in Tokamaks

The requirement of vanishing production of the magnetic entropy in the confinement zone of Ohmically relaxed auxiliary heated Tokamaks imposes a definite relation or "state law" between the characteristic global parameters of the discharge. The conditions under which an isoentropic state can exist are expressed in this paper in a form comparable with the experiment. The Goldston scaling of the confinement time with respect to current, auxiliary power and toroidal magnetic field is contained in the isoentropic state law. An isoentropic state is susceptible to evolving spontaneously toward a bifurcating equilibrium with higher entropy. We calculate explicitly the transition thresholds in terms of global parameters of the auxiliary power, magnetic field, current and temperature pedestal and the plasma detachment. The results are compared with the experimental observations on the H-transitions. It is finally shown that the sustenance of the current and temperature pedestals, generally required for the occurrence of the higher entropy state, could be the result of a purely neoclassical thermal conductivity of the ions in the outer neighbourhood of the confinement zone. The theory leads to definite predictions on the magnitude and on the parametric dependence of the radial electric field, the poloidal velocity and the thickness of the stabilizing layer at the edge.