Bill Scott

Direct measurement of zonal flows and geodesic acoustic mode oscillations in ASDEX Upgrade using Doppler reflectometry

Zonal flows (ZFs) and associated geodesic oscillations are turbulence-generated time-varying Er × BT rigid poloidal plasma flows with finite radial extent. They are of major interest for tokamak confinement since they are thought to moderate drift-wave turbulence and hence edge transport. However, detection of ZFs (believed to be driven by Reynolds stress) and Geodesic acoustic modes (GAMs) (linked with poloidal pressure asymmetries) is challenging since they appear predominantly as low frequency (few kilohertz) potential or radial electric field Er fluctuations. Presented here are measurements of GAM/ZF properties in ohmic, L-mode and H-mode ASDEX Upgrade tokamak discharges using a new Doppler reflectometry technique to measure Er fluctuations directly.

Three-dimensional computation of drift-alfvén turbulence

A transcollisional, electromagnetic fluid model, incorporating the parallel heat flux as a dependent variable, is constructed to treat electron drift turbulence in the regime of tokamak edge plasmas at the L - H transition. The resulting turbulence is very sensitive to the plasma beta throughout this regime, with the scaling with rising beta produced by the effect of magnetic induction to slow the Alfv?nic parallel electron dynamics and thereby leave the turbulence in a more robust, non-adiabatic state. Magnetic flutter and curvature have a minor qualitative effect on the turbulence mode structure and on the beta scaling, even when their quantitative effect is strong. Transport by magnetic flutter is small compared to that by the flow eddies. Fluctuation statistics show that while the turbulence shows no coherent structure, it is coupled strongly enough so that neither density nor temperature fluctuations behave as passive scalars. Both profile gradients drive the turbulence, with the total thermal energy transport varying only weakly with the gradient ratio, . Scaling with magnetic shear is pronounced, with stronger shear leading to lower drive levels. Scaling with either collision frequency or magnetic curvature is weak, consistent with their weak qualitative effect. The result is that electron drift turbulence at L - H transition edge parameters is drift Alfv?n turbulence, with both ballooning and resistivity in a clear secondary role. The contents of the drift Alfv?n model will form a significant part of any useful first-principles computation of tokamak edge turbulence.

Doppler Reflectometry for the Investigation of Propagating Density Perturbations

Doppler reflectometry is characterized by a finite tilt angle of the probing microwave beam with respect to the normal onto the cutoff surface. According to the Bragg condition the diagnostic selects density perturbations with wave number K⊥ in the reflecting layer. From the Doppler shift of the returning microwave the propagation velocity of these perturbations v⊥ can be obtained directly. The signal intensity contains information about the perturbation amplitude. The diagnostic potential of Doppler reflectometry is demonstrated both numerically by the use of two-dimensional full-wave codes and experimentally by an antenna system with variable tilt angle installed at the W7-AS stellarator. During stationary plasma conditions the measured profile of the propagation velocity v⊥(r) is dominated by the E×B velocity of the plasma, which is obtained from passive spectroscopy. Transient states of the plasma can be followed with a temporal resolution of less than 50 µs. Thus, Doppler reflectometry allows us to investigate the interdependence of sheared flow and turbulence on that timescale.

Frequency scaling and localization of geodesic acoustic modes in ASDEX Upgrade

The frequency behaviour and localization of the geodesic acoustic mode (GAM), believed to be a coherent plasma turbulence-generated Er × B zonal flow (ZF) oscillation, is studied in the ASDEX Upgrade tokamak using Doppler reflectometry. In typical elongated (1.4 < κ < 1.75) plasmas with an X-point divertor configuration the GAM is observed only in the edge density gradient region 0.95 < ρpol < 1.0 between the density pedestal top and the flux surface boundary. The GAM frequency (5–25 kHz) is found to scale linearly as ω = G cs/Ro (sound speed over major radius) but with an inverse dependence on the plasma elongation κ and a weak direct dependence on the safety factor q. The lower the GAM frequency the more important it is expected to become in moderating the turbulence via shear decorrelation. A heuristic scaling law for the frequency scale factor involving κ and finite aspect ratio terms has been obtained from dedicated parameter scans. For circular plasmas κ ~ 1 touching the limiter the density pedestal is weakened and the GAM is seen to reach in radially as far as ρpol ~ 0.75, depending on the q profile, with a frequency scale consistent with theoretical predictions. Radially the GAM frequency is not a smooth function but displays a series of plateaus a few centimetres wide coinciding with peaks in the GAM amplitude, suggesting several ZF layers. At the plateau edges the GAM spectral peak splits into two frequency branches.

E x B Shear Flows and Electromagnetic Gyrofluid Turbulence

Low frequency tokamak edge turbulence is modelled numerically using gyrofluid equations for electrons and ions on an equal footing. The electrons are electromagnetic, and arbitrarily strong finite gyroradius effects are included for the ions. Computations are in a globally consistent truncation of flux surface geometry arising from ideal tokamak equilibria. The turbulence is similar to that in the fluid model in steep gradient regimes, for which the electron transit frequency is comparable to that of the turbulence. The nonlinear drift wave instability is shown to be caused by E×B self-advection, and is similar for both two-and three-dimensional models. The turbulence always has drift wave mode character for the parameter regime of interest, except when the ideal ballooning threshold is reached. Turbulence interacts strongly with E×B shear flows, but does not build the flow shear to significant levels by itself. On the other hand, an imposed shear layer arising from the neoclassical equilibrium of the edg...

Three-dimensional computation of collisional drift wave turbulence and transport in tokamak geometry

Three-dimensional computations of turbulence arising from the nonlinear collisional drift wave equations are carried out. The flux-surface-based coordinate system is aligned with the magnetic field, and the geometry is that of an actual model tokamak with arbitrary poloidal cross section. The physical periodicity constraint is rigorously respected. The results show that the dominant process arising from this system is the three-dimensional version of the collisional drift wave nonlinear instability, in which fluctuation free energy transfer among parallel wavelengths plays an enhanced role. Poloidal asymmetry in the fluctuations and associated transport are found to result primarily from the poloidal variation in the ion polarization drift and not the more traditional ballooning (magnetic curvature) effects. Magnetic curvature is found to be very important only in the case of reversed magnetic shear: with it, reversing the shear causes a drop in the thermal energy flux by a factor of three. The contrast with concurrent work on ballooning is suggested to result from the latters neglect of the electron temperature dynamics. As in previous results of two-dimensional slab computations, the electron temperature gradient is the principal free energy source. The turbulence appears to be non-local over the radial range of the 4 cm covered by the computations; the non-locality is a form of weighted averaging of the free energy sources and sinks by the turbulence, and is sufficient to explain the rise in relative amplitude with increasing radius since the absolute amplitude is relatively constant. Initial tests with an isothermal ion pressure suggest that the ion dynamics could make up the quantitative difference between these results and the experimental observations, once the ion temperature is properly incorporated.

Shifted metric procedure for flux tube treatments of toroidal geometry: Avoiding grid deformation

Recent treatments of flute-mode-type turbulence in closed magnetic flux surface geometry align the coordinates to the magnetic field, leaving the field with one nonvanishing contravariant component. Magnetic shear leads to strong deformation of coordinate cells in the plane perpendicular to the field, impacting the results. To remedy this one can apply shifts in the drift angle coordinate, the one which remains purely periodic. All operations involving polarization and nonlinear advection are then performed locally on an orthogonal grid, allowing arbitrarily sheared and shaped magnetic geometries in computations.

Global consistency for thin flux tube treatments of toroidal geometry

In order to avoid a self-mapping problem due to a very long correlation length along a field line, present treatments of magnetized plasma turbulence in flux tube geometry often extend the computational domain to several times the field line connection length. This is shown to result in the admission of nonphysical parallel wavelengths, possibly corrupting the solution even if it is converged. Also shown is that if a flux tube domain is constructed by thinning the full spectrum of allowed wavelengths, the same boundary condition results as if the domain were the entire flux surface. The only consistent remedy is therefore to extend the domain in the perpendicular coordinate within the flux surface, possibly all the way back to the entire flux surface, remaining consistent with the global boundary conditions.

The Isotope Effect in ASDEX

The paper describes the effect of the isotopic mass on plasma parameters as observed in the ASDEX tokamak. The paper comprises Ohmic as well as L mode, H mode and H* mode scenarios. The measurements reveal that the ion mass is a substantial and robust parameter, which affects all the confinement times (energy, particle and momentum) in the whole operational window. Both core properties such as the sawtooth repetition time and edge properties such as the separatrix density change with the isotopic mass. Specific emphasis is given to the edge parameters and changes of the edge plasma due to different types of wall conditioning, such as carbonization and boronization. The pronounced isotope dependences of the edge and divertor parameters are explained by the secondary effect of different power fluxes into the scrape-off layer plasma and onto the divertor plates. Finally, the observations serve to test different transport theories. With respect to the ion temperature gradient driven turbulence, the isotope effect is also studied in pellet refuelled discharges with peaked density profiles. The results from ASDEX are compared with the results from other experiments

Comparison of scrape-off layer turbulence in Alcator C-Mod with three dimensional gyrofluid computations

This paper describes quantitative comparisons between turbulence measured in the scrape-off layer (SOL) of Alcator C-Mod [S. Scott, A. Bader, M. Bakhtiari et al., Nucl. Fusion 47, S598 (2007)] and three dimensional computations using electromagnetic gyrofluid equations in a two-dimensional tokamak geometry. These comparisons were made for the outer midplane SOL for a set of inner-wall limited, near-circular Ohmic plasmas. The B field and plasma density were varied to assess gyroradius and collisionality scaling. The poloidal and radial correlation lengths in the experiment and computation agreed to within a factor of 2 and did not vary significantly with either B or density. The radial and poloidal propagation speeds and the frequency spectra and poloidal k-spectra also agreed fairly well. However, the autocorrelation times and relative Da fluctuation levels were higher in the experiment by more than a factor of 2. Possible causes for these disagreements are discussed. 2009 American Institute of Physics.