Stiffness and rigidity of the temperature profile in a tokamak

The notions of “stiffness” and “rigidity” of the temperature profile in a tokamak are introduced and formalized. By stiffness is meant the consistency of the profile when the plasma density, boundary temperature, and heating power change. By rigidity is meant the strong dependence of the central temperature on the boundary temperature. Analytical and numerical estimates carried out in a transport model with critical temperature gradients show that, at a low boundary temperature (the L-mode), the profiles are, as a rule, stiff but are not rigid. For a sufficiently high temperature pedestal in the H-mode, there exists a parameter range in which the profiles are stiff and at the same time rigid. However, when the pedestal temperature is too high and the deposited power profile is flat, the temperature profile may be neither stiff nor rigid. This behavior of the electron temperature profile was observed in a number of H-mode discharges with high plasma densities in the DIII-D and JET tokamaks. An analysis is also made of the stiffness and rigidity of the temperature profiles in the MAST and T-10 tokamaks.