Theory of ion-temperature-gradient-driven turbulence in tokamaks

An analytic theory of ion-temperature-gradient-driven turbulence in tokamaks is presented. Energy-conserving, renormalized spectrum equations are derived and solved in order to obtain the spectra of stationary ion-temperature-gradient-driven turbulence. Corrections to mixing-length estimates are calculated explicitly. The resulting anomalous ion thermal diffusivity χi=0.4[(π/2)ln(1+ηi)]2[(1+ηi)/τ]2 ρ2pcs/Ls is derived and is found to be consistent with experimentally deduced thermal diffusivities. The associated electron thermal and particle diffusivity, and particle and heat-pinch velocities are also calculated. The effect of impurity gradients on saturated ion-temperature-gradient-driven turbulence is discussed and a related explanation of density profile steepening during Z-mode operation is proposed.