Profile consistency based on the magnetic entropy concept: theory and observation

The relevance of the magnetic entropy concept for the description of relaxed current density, temperature and pressure profiles has been recently demonstrated in Ohmic TCV discharges. In this paper the parameter space characterizing the tokamak states with stationary magnetic entropy (SME) is extended to sawtoothing auxiliarly heated discharges. The condition of stationary entropy determines the current density profile and the temperature profile through Ohmic relaxation. The compatibility of SME Ohmically relaxed current density profiles with the toroidal force balance (Grad–Shafranov–Schl¨uter (GSS)) and the power balance basically restricts the profiles of the pressure and of the effective thermal diffusivity. Furthermore, the ‘ansatz’ on the density profile, introduced successfully in the Ohmic case and supported by theoretical considerations on approximate conservation of adiabatic invariants in particle transport (TEP), imposes a final definite form on the pressure profile, consistently with SME and GSS. It is shown that the magnetic configuration of the SME states is invariant with respect to a certain family of transformations involving the auxiliary power PA, the toroidal magnetic field, the loop voltage, the average density and the major and minor radius. The invariance under the admissible transformations is then the appropriate definition of the concept of profile consistency in the presence of auxiliary heating. It will follow that, on the one hand, the insensitivity of the relaxed profiles to external variation of PA is a particular aspect of this invariance. On the other hand, when the value of PA is fixed by some process internal to the plasma, as the threshold of the L–H transition, and the L-state just before the transition is identified as a SME state, PA should scale with the parameters above consistently with the invariant identification of the state, irrespective of the details of the underlying dynamical process. It is shown that this scaling is precisely that observed for the power threshold of the L–H transition, provided that the confinement time of the L- (and SME) state is given by the ITER89-P scaling law. In the rest of the paper the SME point of view is exemplified by comparing the theory with the profiles observed in Ohmic and ECRH discharges in FTU and with the observed critical gradient-dependence of the thermal diffusivity.