Phase space structures in gyrokinetic simulations of fusion plasma turbulence

Abstract

Gyrokinetic simulations of fusion plasmas give extensive information in 5D on turbulence and transport. This paper highlights a few of these challenging physics in global, flux driven simulations using experimental inputs from Tore Supra shot TS45511. The electrostatic gyrokinetic code GYSELA is used for these simulations. The 3D structure of avalanches indicates that these structures propagate radially at localised toroidal angles and then expand along the field line at sound speed to form the filaments. Analysing the poloidal mode structure of the potential fluctuations (at a given toroidal location), one finds that the low modes m = 0 and m = 1 exhibit a global structure; the magnitude of the m = 0 mode is much larger than that of the m = 1 mode. The shear layers of the corrugation structures are thus found to be dominated by the m = 0 contribution, that are comparable to that of the zonal flows. This global mode seems to localise the m = 2 mode but has little effect on the localisation of the higher mode numbers. However when analysing the pulsation of the latter modes one finds that all modes exhibit a similar phase velocity, comparable to the local zonal flow velocity. The consequent dispersion like relation between the modes pulsation and the mode numbers provides a means to measure the zonal flow. Temperature fluctuations and the turbulent heat flux are localised between the corrugation structures. Temperature fluctuations are found to exhibit two scales, small fluctuations that are localised by the corrugation shear layers, and appear to bounce back and forth radially, and large fluctuations, also readily observed on the flux, which are associated to the disruption of the corrugations. The radial ballistic velocity of both avalanche events if of the order of 0.5ρ _∗ c ₀ where ρ _∗ = ρ ₀/a, a being the tokamak minor radius and ρ ₀ being the characteristic Larmor radius, ρ ₀ = c ₀/Ω ₀. c ₀ is the reference ion thermal velocity and Ω ₀ = q _i B ₀/m _i the reference ion Larmor frequency for the characteristic amplitude of the magnetic field B ₀, q _i and m _i being, respectively, the ion charge and mass. The electric drift velocity is also found to exhibit a poloidal pattern, with maximum amplitude of the fluctuations either in the top or in the bottom regions of the machine depending on the sign of the zonal flow shear. This effect is found to be correlated to the stopping capability of the corrugation structures. The neoclassical properties stemming from the trapped particle drifts lead to large distortion of the distribution function. As expected, these prevail at the outer part of the simulation region despite the large collisionality. The distribution function fluctuations appear to be aligned along the v _∥ = const. lines at constant poloidal angle. A specific symmetry is observed regarding the interplay of turbulence with the trapped-passing region.