Self-organization of plasma in tokamaks

Abstract

A review is given of the main ideas regarding self-organization of a tokamak plasma. The analysis begins with a simple model of canonical profiles that was proposed by Kadomtsev for a plasma column with a circular cross section. Kadomtsev’s model is then generalized to a tokamak plasma with an arbitrary cross section in toroidal geometry. In the generalized model, the canonical profiles are determined by the minimum of the plasma energy functional under the additional condition that the total current is conserved. The Euler equation for the energy functional leads to a second-order differential equation for the canonical profile of the function μ = 1/q. Transport models are constructed on the basis of a concept of critical gradients defined in terms of the canonical profiles. The structures of the heat and particle fluxes in the Ohmic heating regime and in the conventional L-mode are discussed. Examples of plasma self-organization in experiments are presented and are illustrated by the results of calculations based on the transport models developed. The expressions for the heat and particle fluxes are then generalized to regimes with improved confinement and with transport barriers. L-H transitions and approximate formulas for the transport barrier parameters are discussed in detail. Some unresolved problems are also discussed, namely, those concerning a description of the formation of internal transport barriers in terms of the canonical profile model. In the Appendix, the ranges of variations in the plasma parameters within which the temperature profiles remain stiff are considered.