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

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Abstract
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.

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