This paper analyses the properties of a critical gradient transport model based on a few assumptions: electrostatic gyroBohm scaling law, existence of an instability threshold and finite background transport below the threshold. A quantitative criterion of stiffness is proposed, which provides the means for a quantitative assessment and inter-machine comparison. It is also shown that this transport model is compatible with a two-term scaling law of global confinement, as proposed recently by the International Tokamak Physics Activity-Confinement Data Base and Modelling Topical Group. This model has also been applied to analyse a variety of experiments mostly using electron heat modulation on JET, ASDEX-Upgrade, TORE SUPRA and FTU. The thresholds are found to be in the expected domain for micro-instabilities in tokamaks. However, the stiffness factor is found to cover a broad range of variation.

This paper is an overview of recent results relating to turbulent particle and heat transport, and to the triggering of internal transport barriers (ITBs). The dependence of the turbulent particle pinch velocity on plasma parameters has been clarified and compared with experiment. Magnetic shear and collisionality are found to play a central role. Analysis of heat transport has made progress along two directions: dimensionless scaling laws, which are found to agree with the prediction for electrostatic turbulence, and analysis of modulation experiments, which provide a stringent test of transport models. Finally the formation of ITBs has been addressed by analysing electron transport barriers. It is confirmed that negative magnetic shear, combined with the Shafranov shift, is a robust stabilizing mechanism. However, some well established features of internal barriers are not explained by theory.

The entropy production rate is calculated for an interchange driven turbulence both in fluid and kinetic regimes. This calculation provides a rigorous way to define thermodynamical forces and fluxes. It is found that the forces are the gradients of density and temperature normalized to their “canonical” values, which are Lagrangian invariants of the flow. This formulation is equivalent to expressing the fluxes in terms of “curvature pinches,” where the curvature pinches are proportional to the logarithmic gradient of canonical profiles. Off diagonal terms in the transport matrix are found, which correspond to thermodiffusion and its Onsager symmetrical contribution to the heat flux. Hence, if thermodiffusion is significant, a heat pinch due to the density gradient also exists. The entropy production rate is found to be minimum when the profiles are equal to their canonical values. This property yields a generalized form of profile stiffness. However, a state where all profiles match their canonical values is not attainable because it is linearly stable.