A simplified model to estimate nonlinear turbulent transport by linear dynamics in plasma turbulence

Abstract

Abstract A simplified model to estimate nonlinear turbulent transport only by linear calculations is proposed, where the turbulent heat diffusivity in tokamak ion temperature gradient(ITG) driven turbulence is reproduced for a wide parameter range including near- and far-marginal ITG stability. The optimal nonlinear functional relation(NFR) between the turbulent diffusivity, the turbulence intensity $$\mathcal{T}$$ T , and the zonal-flow intensity $$\mathcal{Z}$$ Z is determined by means of mathematical optimization methods. Then, an extended modeling for $$\mathcal{T}$$ T and $$\mathcal{Z}$$ Z to incorporate the turbulence suppression effects and the temperature gradient dependence is carried out. The simplified transport model is expressed as a modified nonlinear function composed of the linear growth rate and the linear zonal-flow decay time. Good accuracy and wide applicability of the model are demonstrated, where the regression error of $$\sigma _{\textrm{model}} = 0.157$$ σ model = 0.157 indicates improvement by a factor of about 1/4 in comparison to that in the previous works.