A unified physical scaling law for tokamak energy confinement

Abstract

From the equations which describe local transport in a turbulent plasma the scaling of the local diffusivity with the plasma parameters can be established. It is shown that, by appropriate choices of time and length scales for the turbulence, the scaling of the global energy confinement can be cast in two limiting forms: a short and a long wavelength scaling. The scaling laws consist of a leading term and a function F whose arguments are the dimensionless normalized plasma collisionality and beta. The scaling of the leading term in the short wavelength expression for global confinement is shown to fit both L-mode and H-mode confinement data from JET. The function F which describes the precise physical mechanism of the turbulence is found to increase with collisionality, but its dependence on the plasma beta remains uncertain. Several theoretical models are found to be a reasonable fit to the JET confinement data; others, however, such as that for the dissipative trapped electron mode, can be discarded. The short wavelength confinement scaling is shown to unify a multiplicity of existing theoretical/empirical scaling laws by suitable choices of the function F. These scaling laws all exhibit a similar dependence of F upon collisionality but have different dependences upon the plasma beta. It is shown that for the JET data it is very difficult to determine the beta dependence and this explains why so many apparently different scaling laws produce reasonable fits to the data. Using the leading term of the scaling, the fusion product can be extrapolated to reactor conditions (ITER) with an uncertainty factor of four. This uncertainty can be reduced to ±30% by the use of a similarity technique in which F is determined directly from the JET data.