Field-aligned coordinates for nonlinear simulations of tokamak turbulence

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.