Physics of intrinsic rotation in flux-driven ITG turbulence

Abstract

Abstract. Global, heat flux-driven ITG gyrokinetic simulations which manifest the formation of macroscopic, mean toroidal flow profiles with peak thermal Mach number 0.05, are reported. Both a particle-in-cell (XGC1p) and a semi-Lagrangian (Gysela) approach are utilized without a priori assumptions of scale-separation between turbulence and mean fields. Flux-driven ITG simulations with different edge flow boundary conditions show in both approaches the development of net unidirectional intrinsic rotation in the co-current direction. Intrinsic torque is shown to scale approximately linearly with the inverse scale length of the ion temperature gradient. External momentum input is shown to effectively cancel the intrinsic rotation profile, thus confirming the existence of a local residual stress and intrinsic torque. Fluctuation intensity, intrinsic torque and mean flow are demonstrated to develop inwards from the boundary. The measured correlations between residual stress and two fluctuation spectrum symmetry breakers, namely E × B shear and intensity gradient, are similar. Avalanches of (positive) heat flux, which propagate either outwards or inwards, are correlated with avalanches of (negative) parallel momentum flux, so that outward transport of heat and inward transport of parallel momentum are correlated and mediated by avalanches. The probability distribution functions of the outward heat flux and the inward momentum flux show strong structural similarity.

Momentum transport in the vicinity of qmin in reverse shear tokamaks due to ion temperature gradient turbulence

“…(20). It indicates that a turbulence intensity gradient naturally arises because A 1 and A 2 contain mean plasma profiles.…”

“…The process of hk k i symmetry breaking by E Â B shear and/or intensity gradient implies a coupling between intrinsic rotation and transport barrier dynamics, such as internal transport barrier (ITB) formation, which involves steep temperature and/or density gradients (i.e., strong radial inhomogeneity) and the strong E Â B shear and/or the fluctuation intensity gradient (i.e., hk k i symmetry breaking). Gyrokinetic simulations have shown the generation of intrinsic rotation from the hk k i symmetry breaking by mean E Â B shear [20][21][22][23] and turbulence intensity gradient 20 and up-down asymmetry of equilibrium magnetic topology. 24,25 Gyrokinetic simulations have also shown residual stress from profile shearing effects.…”

Neoclassical physics in full distribution function gyrokinetics

“…(3) and (18) are required; a dedicated study of intrinsic rotation with both GYSELA and XGC1 is to be reported elsewhere. 79,80 A careful accounting of collisions is also important to correctly describe the residual level of the low frequency turbulence-induced axisymmetric sheared E Â B mean and zonal flows. The importance of such flows, linearly damped through collisions alone and which dynamically participate in turbulence self-regulation has long been emphasised.…”

How turbulence fronts induce plasma spin-up

“…In contrast, here we show that edge and core flows are coupled via the propagation of fluctuation momentum from the edge region into the core region, via a nonlocal process such as turbulence spreading, avalanches, etc. [10][11][12]. Typically, tokamak plasmas become more turbulent towards the edge with increasing turbulence amplitude [13].…”