Field-aligned coordinates for nonlinear simulations of tokamak turbulence

TLDR

Turbulence in tokamaks is characterized by long parallel wavelengths and short perpendicular wavelengths. The authors propose a coordinate system that exploits the elongated nature of tokamak turbulence by resolving a minimal simulation volume—a long, thin twisting flux tube. The method builds on the ballooning representation, incorporating periodicity constraints that enable efficient evaluation of E×B nonlinearities via FFTs, while avoiding artificial correlations by not enforcing periodicity at θ=±π when the parallel correlation length is very long. Applied to high‑resolution 3D simulations of toroidal ion temperature gradient (ITG) driven turbulence, the method predicts fluctuation spectra and ion heat transport similar to experimental measurements.

Abstract

Turbulence in tokamaks is characterized by long parallel wavelengths and short perpendicular wavelengths. A coordinate system for nonlinear fluid, gyrokinetic ‘‘Vlasov,’’ or particle simulations is presented that exploits the elongated nature of the turbulence by resolving the minimum necessary simulation volume: a long thin twisting flux tube. It is very similar to the ballooning representation, although periodicity constraints can be incorporated in a manner that allows E×B nonlinearities to be evaluated efficiently with fast Fourier transforms (FFT’s). If the parallel correlation length is very long, however, enforcing periodicity can introduce artificial correlations, so periodicity should not necessarily be enforced in the poloidal angle at θ=±π. This method is applied to high resolution three-dimensional simulations of toroidal ion temperature gradient (ITG) driven turbulence, which predict fluctuation spectra and ion heat transport similar to experimental measurements.