A Unified theory of transport barriers (TBs) in magnetically confined systems

Abstract

A thermodynamic model of a plasma boundary layer, characterized by enhanced temperature contrasts is proposed. The theory is constructed to determine the inner boundary temperature $T_1$ for a specified outer (colder) boundary temperature $T_0$, the heat flux $F$ entering the inner boundary, and the parameters defining the layer. The system shows bifurcation and switches to a stable high gradient state if the heat flux $F$ entering through the inner boundary exceeds a critical value $F_c$. However there is an additional stringent condition for the transition to occur; the edge temperature $T_0$ must exceed a critical value $T_c$- no transition is possible if $T_0<T_c$ even for arbitrary large $F$. Equally important is the finding that $F_c$ is not a monotonic function of $T_0$ but has a minimum at $T_{optimum}$ (= $4T_c$ )in the model calculation. The confinement peaks at $T_{optimum}$. The basic conceptual physics is obviously simple: The high contrast state becomes the preferred state when the incoming power into the layer is preferentially converted into coherent motions like the fluid flows and currents (undermining the standard diffusive processes that keep the lower temperature contrast). The purely macroscopic thermodynamic model bears excellent comparison with experimental and detailed microscopic investigations of the H-mode. Deeper plausibility reasons for the workability of this heat engine, creating the simultaneous existence of an ordered state and large entropy production, are suggested.