Effect of turbulence on electron cyclotron current drive and heating in ITER

Non-linear local electromagnetic gyrokinetic turbulence simulations of the ITER standard scenario H-mode are presented for the q=3/2 and q=2 surfaces. The turbulent transport is examined in regions of velocity space characteristic of electrons heated by electron cyclotron waves. Electromagnetic fluctuations and sub-dominant micro-tearing modes are found to contribute significantly to the transport of the accelerated electrons, even though they have only a small impact on the transport of the bulk species. The particle diffusivity for resonant passing electrons is found to be less than 0.15 m^2/s, and their heat conductivity is found to be less than 2 m^2/s. Implications for the broadening of the current drive and energy deposition in ITER are discussed.Comment: Letter, 5 pages, 5 figures, for submission to Nuclear Fusio

Angular momentum transport modeling: achievements of a gyrokinetic quasi-linear approach

QuaLiKiz, a model based on a local gyrokinetic eigenvalue solver is expanded to include momentum flux modeling in addition to heat and particle fluxes. Essential for accurate momentum flux predictions, the parallel asymmetrization of the eigenfunctions is successfully recovered by an analytical fluid model. This is tested against self-consistent gyrokinetic calculations and allows for a correct prediction of the ExB shear impact on the saturated potential amplitude by means of a mixing length rule. Hence, the effect of the ExB shear is recovered on all the transport channels including the induced residual stress. Including these additions, QuaLiKiz remains ~10 000 faster than non-linear gyrokinetic codes allowing for comparisons with experiments without resorting to high performance computing. The example is given of momentum pinch calculations in NBI modulation experiments

Charge dependence of neoclassical and turbulent transport of light impurities on MAST

Carbon and nitrogen impurity transport coefficients are determined from gas puff experiments carried out during repeat L-mode discharges on the Mega-Amp Spherical Tokamak (MAST) and compared against a previous analysis of helium impurity transport on MAST. The impurity density profiles are measured on the low-field side of the plasma, therefore this paper focuses on light impurities where the impact of poloidal asymmetries on impurity transport is predicted to be negligible. A weak screening of carbon and nitrogen is found in the plasma core, whereas the helium density profile is peaked over the entire plasma radius.Comment: 17 pages, 7 figure

Validation of gyrokinetic modelling of light impurity transport including rotation in ASDEX Upgrade

Upgraded spectroscopic hardware and an improved impurity concentration calculation allow accurate determination of boron density in the ASDEX Upgrade tokamak. A database of boron measurements is compared to quasilinear and nonlinear gyrokinetic simulations including Coriolis and centrifugal rotational effects over a range of H-mode plasma regimes. The peaking of the measured boron profiles shows a strong anti-correlation with the plasma rotation gradient, via a relationship explained and reproduced by the theory. It is demonstrated that the rotodiffusive impurity flux driven by the rotation gradient is required for the modelling to reproduce the hollow boron profiles at higher rotation gradients. The nonlinear simulations validate the quasilinear approach, and, with the addition of perpendicular flow shear, demonstrate that each symmetry breaking mechanism that causes momentum transport also couples to rotodiffusion. At lower rotation gradients, the parallel compressive convection is required to match the most peaked boron profiles. The sensitivities of both datasets to possible errors is investigated, and quantitative agreement is found within the estimated uncertainties. The approach used can be considered a template for mitigating uncertainty in quantitative comparisons between simulation and experiment.Comment: 19 pages, 11 figures, accepted in Nuclear Fusio

The linear tearing instability in three dimensional, toroidal gyrokinetic simulations

Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro kinetic turbulence code, GKW . The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate and frequency of the mode were investigated by varying the current profile, collisionality and the pressure gradients. Both collision-less and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absense of a pressure gradient is observed which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However the island rotation reverses direction at high collisionality. The growth rate is found to follow a $\eta^{1/7}$ scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability using resistive MHD theory, however a modification due to toroidal coupling and pressure effects is seen

On three-manifolds dominated by circle bundles

We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. We also determine which three-manifolds are dominated by non-trivial circle bundles, and which three-manifold groups are presentable by products.Comment: 12 pages; to appear in Math. Zeitschrift; ISSN 1103-467

3-manifolds which are spacelike slices of flat spacetimes

We continue work initiated in a 1990 preprint of Mess giving a geometric parameterization of the moduli space of classical solutions to Einstein's equations in 2+1 dimensions with cosmological constant 0 or -1 (the case +1 has been worked out in the interim by the present author). In this paper we make a first step toward the 3+1-dimensional case by determining exactly which closed 3-manifolds M^3 arise as spacelike slices of flat spacetimes, and by finding all possible holonomy homomorphisms pi_1(M^3) to ISO(3,1).Comment: 10 page