Scaling Of Impurity Fractions For Divertor Detachment In High-Density High-Power Operation Scenarios

For future reactor designs and for planning of operational scenarios in the present and future machines, impurity fractions in the tokamak divertor plasma, c(Z), is an essential input for predictive scalings of divertor detachment. A new quantitative scaling law for c(Z), averaged over the scrape-off layer (SOL), required to attain detachment is developed for high power H-mode plasmas operated at high densities close to the density limit. It is based on a simple SOL radiation model which uses the combination of the empirical scaling laws for the H-mode power threshold and the separatrix density limit imposed by MHD instabilities. Additionally, it assumes, in agreement with experimental observations that the width of the power conducting layer outside of the separatrix scales approximately with the ion poloidal gyro-radius. The derived expression for c(Z) scales strongly with toroidal magnetic field, B, major radius R, the factor of access of the power flow through the separatrix over that required for the L-H transition, f(LH), and isotope mass A: c(Z) proportional to B(1.47)R(1.59)f(LH)(1.38)/A(1.38). Estimates of required impurity fractions for divertor detachment for an number of impurity species (N-2, Ne and Ar) in future tokamak reactors ITER and DEMO are made in the paper.