Nusselt number scaling in tokamak plasma turbulence

Anomalous heat transport caused by ion temperature gradient (ITG) driven turbulence in tokamak plasmas is evaluated from numerical simulations of the two-dimensional (2D) partial-differential equations of the ITG model and of a reduced 1D version derived from a quasilinear approximation. In the strongly turbulent state, intermittent bursts of thermal transport are observed in both cases. In the strongly turbulent regime, the reduced model as well as the direct numerical simulation show that the Nusselt number Nu (normalized heat flux) scales with the normalized ion pressure gradient Ki as Nu∝Ki1/3. Since the Rayleigh number for ITG turbulence is proportional to Ki, the Nusselt number scaling for ITG turbulence is thus similar to the classical thermal transport scaling for Rayleigh-Benard convections in neutral fluids