Plasma transport in tokamaks

The mechanism of high-power island pumping recently proposed by Kadomtsev, combined with the constraint that the plasma magnetic configuration of the tokamak is associated, under ohmic relaxation, with a stationary magnetic entropy (isoentropic state), allows the derivation of the ITER89-P scaling of the confinement time with considerable precision, particularly with respect to power, density and current. An equation for the thermal transport consistent with the requirements above is formulated and solved for a simple example of inhomogeneous heat deposition. In this formulation the thermal conductivity depends on the space derivatives of the temperature. The profile resiliency of the temperature follows from a certain idealized condition discussed in the paper (uniform magnetic braiding), which when combined with ohmic relaxation is characteristic of the isoentropic states. The formalism also implies a relation between the density profile and the space derivatives of the temperature. The implications of the Kadomtsev scaling of the diffusivity on the dependence of the bifurcation thresholds between the isoentropic state and H-mode, with respect to power, density and magnetic field, are also discussed.