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Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E ×B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.

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Nondiffusive anomalous momentum transport in toroidal plasmas occurs through symmetry breaking mechanisms. In this paper the contribution of sheared E×B flows to parallel momentum transport [R. R. Dominguez and G. M. Staebler, Phys Fluids B 5, 3876 (1993)] is investigated with nonlinear gyrokinetic simulations in toroidal geometry. The background perpendicular shear is treated independently from the parallel velocity shear to isolate a nondiffusive, nonpinch contribution to the parallel momentum flux. It is found that the size of the term depends strongly on the magnetic shear, with the sign reversing for negative magnetic shear. Perpendicular shear flows are responsible for both symmetry breaking and suppression of turbulence, resulting in a shearing rate at which there is a maximum contribution to the momentum transport. The E×B momentum transport is shown to be quenched by increasing flow shear more strongly than the standard linear quench rule for turbulent heat diffusivity.

Quasilinear turbulent transport models are a successful tool for prediction of core tokamak plasma profiles in many regimes. Their success hinges on the reproduction of local nonlinear gyrokinetic fluxes. We focus on significant progress in the quasilinear gyrokinetic transport model QuaLiKiz [C. Bourdelle et al. 2016 Plasma Phys. Control. Fusion 58 014036], which employs an approximated solution of the mode structures to significantly speed up computation time compared to full linear gyrokinetic solvers. Optimization of the dispersion relation solution algorithm within integrated modelling applications leads to flux calculations ×10 6−7 faster than local nonlinear simulations. This allows tractable simulation of flux-driven dynamic profile evolution including all transport channels: ion and electron heat, main particles, impurities, and momentum. Furthermore, QuaLiKiz now includes the impact of rotation and temperature anisotropy induced poloidal asymmetry on heavy impurity transport, important for W-transport applications. Application within the JETTO arXiv:1708.01224v2 [physics.plasm-ph] 7 Aug 2017Tractable flux-driven temperature, density, and rotation profile evolution with the quasilinear gyrokinetic tran integrated modelling code results in 1 s of JET plasma simulation within 10 hours using 10 CPUs. Simultaneous predictions of core density, temperature, and toroidal rotation profiles for both JET hybrid and baseline experiments are presented, covering both ion and electron turbulence scales. The simulations are successfully compared to measured profiles, with agreement mostly in the 5-25% range according to standard figures of merit. QuaLiKiz is now open source and available at www.qualikiz.com.Tractable flux-driven temperature, density, and rotation profile evolution with the quasilinear gyrokinetic tran

Tokamak experiments operate with a rotating plasma, with toroidal velocity which can be driven externally but can also arise spontaneously. In the frame that corotates with the plasma, the effects of the centrifugal force are felt through a centrifugal drift and an enhanced mirror force [Peeters et al., Phys. Plasmas 16, 042310 (2009)]. These inertial terms become important in the case of strong rotation, as is common in spherical devices, and are also important for heavy impurity ions even at small toroidal velocities. In this work, the first gyrokinetic simulations including the centrifugal force in a strongly rotating plasma are presented. The enhanced mirror force redistributes density over a flux surface and modifies the trapping condition, destabilizing trapped electron modes. At intermediate scales this can result in promotion of the trapped electron mode over the ion temperature gradient (ITG) mode as the dominant instability, which under marginal conditions could result in an enhanced electron heat flux. The centrifugal drift acts to damp the residual zonal flow of the geoacoustic mode, while its frequency is increased. For nonlinear ITG dominated turbulence, increased trapped electron drive and reduced zonal flow lead to an increase in ion heat diffusivity if the increased rotation is not accompanied by rotational shear stabilization. An increased fraction of slow trapped electrons enhances the convective particle pinch, leading to an increase in the steady state density gradient with strong rotation. Linear ITG mode results show an increased pinch of heavy trace impurities due to their strong centrifugal trapping. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3491110

The interaction between small scale turbulence (of the order of the ion Larmor radius) and meso-scale magnetic islands is investigated within the gyrokinetic framework. Turbulence, driven by background temperature and density gradients, over nonlinear mode coupling, pumps energy into long wavelength modes, and can result in an electrostatic vortex mode that coincides with the magnetic island. The strength of the vortex is strongly enhanced by the modified plasma flow response connected with the change in topology, and the transport it generates can compete with the parallel motion along the perturbed magnetic field. Despite the stabilizing effect of sheared plasma flows in and around the island, the net effect of the island is a degradation of the confinement. When density and temperature gradients inside the island are below the threshold for turbulence generation, turbulent fluctuations still persist through turbulence convection and spreading. The latter mechanisms then generate a finite transport flux and, consequently, a finite pressure gradient in the island. A finite radial temperature gradient inside the island is also shown to persist due to the trapped particles, which do not move along the field around the island. In the low collisionality regime, the finite gradient in the trapped population leads to the generation of a bootstrap current, which reduces the neo-classical drive.

We present an ultrafast neural network (NN) model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 300 million flux calculations of the quasilinear gyrokinetic transport model QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modelling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order 1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study of density buildup following the L-H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modelling is a promising route towards enabling accurate and fast tokamak scenario optimization, Uncertainty Quantification, and control applications.