Study of ion turbulent transport and profile formations using global gyrokinetic full-f Vlasov simulation

Abstract

A global gyrokinetic toroidal full-f five-dimensional Vlasov simulation GT5D (Idomura et al 2008 Comput. Phys. Commun. 179 391)is extended including sources and collisions. Long time tokamak micro-turbulence simulations in open system tokamak plasmas are enabled for the first time based on a full-f gyrokinetic approach with self-consistent evolutions of turbulent transport and equilibrium profiles. The neoclassical physics is implemented using the linear Fokker-Planck collision operator, and the equilibrium radial electric field E r is determined self-consistently by evolving equilibrium profiles. In ion temperature gradient driven turbulence simulations in a normal shear tokamak with on-axis heating, key features of ion turbulent transport are clarified. It is found that stiff ion temperature T i profiles are sustained with globally constant L ti ≡ |T i /T i | near a critical value, and a significant part of the heat flux is carried by avalanches with 1/f type spectra, which suggest a self-organized criticality. The E r shear strongly affects the directions of avalanche propagation and the momentum flux. Non-diffusive momentum transport due to the E r shear stress is observed and a non-zero (intrinsic) toroidal rotation is formed without momentum input near the axis.

Benchmark test of drift-kinetic and gyrokinetic codes through neoclassical transport simulations

“…(9a) either in Vlasov code with a finite velocity grids or in Monte Carlo code with a finite number of simulation markers. Then an iterative operation of the field-particle operator is usually taken in simulation codes [8,20] to reduce the numerical error, but it is time consuming. In FORTEC-3D, the accuracy of collision operator is improved by solving the factors (a, b, c) as functionals of (δn, δP, δE) instead of using their theoretical values given by Eq.…”

“…Recent progress in theory and simulation studies of plasma transport processes now turn their attention to the combination of these two models that can treat multi-scale transport phenomena ranging from O(ρ i ) to O(L T,n ). Idomura et al [8] has developed a gyrokinetic simulation code GT5D which includes neoclassical physics by adopting the full-f approach and introducing a conserved form linear Fokker-Planck collision operator [9,10]. In the simulation study of ion-temperature-gradient (ITG) turbulence transport by GT5D, it is found that the shear of the equilibrium radial electric field dE r /dr plays a critical role in dictating the directions of avalanche propagation and non-diffusive momentum transport.…”

“…[8], a benchmark test of GT5D for the neoclassical transport calculation has been carried out, in which neoclassical heat diffusivity and the parallel force balance equation were tested against analytic formulae derived by neoclassical transport theories [1,12]. Though it has shown qualitatively good agreements, more strict, quantitative test requires a strict drift-kinetic calculation as a counterpart, since analytic formulae use many conventional assumptions such as large-aspect-ratio expansion (assumption a/R ≪ 1, where a and R are plasma minor and major radius, respectively) and zero-orbit-width limit (neglect of guiding-center radial excursion).…”

“…Neoclassical heat transport and parallel momentum balance are checked in the same way as shown in Ref. [8]. Not only the comparison of steady state transport feature, transient phase of radial electric field towards steady state is also compared between two codes.…”

Parallel filtering in global gyrokinetic simulations

“…Unfortunately, the field equation is in that case solved with an iterative solver whose convergence is not guaranteed and depends on the physical problem. For these reasons, many of the global gyrokinetic codes [23,11,12,13] still solve the field equation on the poloidal plane with direct solvers. The GT3D code [23] uses a ballooning phase factor to extract analytically the k = 0 structure at a given magnetic surface: the grid resolution of the field equation can be strongly reduced.…”