A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a BEC described by the Gross-Pitaevskii equation on grids up to 5760^3. For the first time, an accurate power law scaling for the quantum Kelvin wave cascade is determined: k^{-3}. The incompressible kinetic energy spectrum exhibits very distinct power law spectra in 3 ranges of k-space: a classical Kolmogorov k^{-5/3} spectrum at scales much greater than the individual quantum vortex cores, and a quantum Kelvin wave cascade spectrum k^{-3} on scales of order the vortex cores. In the semiclassical regime between these two spectra there is a pronounced steeper spectral decay, with non-universal exponent. The Kelvin k^{-3} spectrum is very robust, even on small grids, while the Kolmogorov k^{-5/3} spectrum becomes more and more apparent as the grids increase from 2048^3 grids to 5760^3.
Spherical tokamaks (STs), which feature relatively high neutron flux and good economy, operate generally in high‐ß regimes, in which the usual EC O‐ and X‐ modes are cut‐off. In this case, electron Bernstein waves (EBWs) seem to be the only option that can provide features similar to the EC waves—controllable localized heating and current drive (H&) that can be utilized for core plasma heating as well as for accurate plasma stabilization. We first derive an analytical expression for Gaussian beam OXB conversion efficiency. Then, an extensive numerical study of EBW H&CD performance in four typical ST plasmas (NSTX L‐ and H‐mode, MAST Upgrade, NHTX) is performed. Coupled ray‐tracing (AMR) and Fokker‐Planck (LUKE) codes are employed to simulate EBWs of varying frequencies and launch conditions. Our results indicate that an efficient and universal EBW H&CD system is indeed viable. In particular, power can be deposited and current reasonably efficiently driven across the whole plasma radius. Such a system could be controlled by a suitably chosen launching antenna vertical position and would also be sufficiently robust.
Heat loads to the target plate in reactor tokamaks are estimated to be orders of magnitude higher than those that can be withstood by known materials. In regimes of plasma detachment, there is strong evidence that plasma recombination occurs near the divertor plate, leading to a cold neutral gas blanket. Because of the strong coupling between the plasma and the neutrals within the divertor region, there is significant neutral flows along field lines up to Mach 1.2 and Reynolds numbers over 1000. Here the effects of three dimensional (3D) neutral turbulence within the gas blanket on heat deposition to the toroidal wall are examined. Both two dimensional (2D) mean shear flows over toroidal cavities as well as a fully 3D initial value problem of heat pulse propagation are considered. The results for algebraic stress model, K-ε and laminar flows are compared. It is found that 3D velocity shear turbulence has profound effects on the heat loads, indicating that simple (linear) Reynolds stress closure schemes are inadequate.
Magnetohydrodynamic Turbulence Simulations on the Earth Simulator Using the Lattice Boltzmann Method Jonathan Carter 1 , Min Soe 2 , Leonid Oliker 1 , Yoshinori Tsuda 3 , George Vahala 4 , Linda Vahala 5 , and Angus Macnab 6 Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Rogers State University, OK 74017, USA Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan College of William & Mary, Williamsburg, VA 23187, USA Old Dominion University, Norfolk, VA 23529, USA CSCAMM, University of Maryland, 20742, MD Highly optimized large-scale lattice Boltzmann simulations of 3D magnetohydrodynamic turbulence are performed on the Earth Simulator. We discuss code optimization schemes for both single processor and parallel performance, and present performance data at various concurrencies and grid sizes. A production run on a 1440 grid using 4800 processors achieved a total aggregate performance of over 26 Tflop/s, making this study one of the largest yet undertaken and allowing access to an unprecedented level of detail. While a full analysis will require much more work, representative features of some 3D MHD turbulence are presented. Introduction Magnetohydrodynamics (or MHD) describes self-consistently the macroscopic behavior of an electrically conducting fluid by combining the Navier-Stokes equations with Maxwell’s equations. MHD turbulence plays an important role in many branches of physics [1]: from astrophysical phenomena in stars, accretion discs, interstellar and intergalactic media to plasma instabilities in magnetic fusion devices. It is well known that the simulation of turbulent flows in complex geometries places great strain on computational algorithms designed for the direct solution of the MHD equations. Sophisticated schemes must be developed to handle the singular matrices that crop up in accurately resolving the nonlinear convective derivatives, e.g., high order finite elements or Newton-Krylov algorithms. Lattice Boltzmann (LB) schemes are an alternate approach that circumvent the resolution problems with the macroscopic nonlinear convective derivatives by embedding into a higher dimensional (kinetic) phase space. While this appears to be an inverse- Statistical mechanical approach, the resulting kinetic equations can be discretized on a phase space lattice that has a minimal number of (discrete) velocities sufficient that the long-time, long-wavelength (Chapman-Enskog) limit reproduces the desired macroscopic nonlinear equations. With simple linear advective terms the difficult macroscopic non-local nonlinearities are recovered by simple polynomial (local) nonlinearities in the collision operator of the kinetic equation. For Navier-Stokes turbulence, one needs to introduce only a scalar distribution whose discrete moments yield the fluid density and mean velocity. While this LB algorithm has been used extensively over the past ten years for simulating Navier-Stokes flows [2], its application to MHD has not been as vigorously pursued presumably because of the difficulty of introducing the magnetic field at a kinetic level. The first attempts introduced a complex double velocity lattice-streaming algorithm on a scalar distribution function. Recently for 2D MHD, Dellar [3] introduced a separate vector distribution function for the magnetic field whose zero (vector discrete) moment yielded the magnetic field. These sets of
The electron Bernstein wave (EBW) is typically the only wave in the electron cyclotron (EC) range that can be applied in spherical tokamaks for heating and current drive (H&CD). Spherical tokamaks (STs) operate generally in high-β regimes, in which the usual EC O- and X-modes are cut off. In this case, EBWs seem to be the only option that can provide features similar to the EC waves—controllable localized H&CD that can be used for core plasma heating as well as for accurate plasma stabilization. The EBW is a quasi-electrostatic wave that can be excited by mode conversion from a suitably launched O- or X-mode; its propagation further inside the plasma is strongly influenced by the plasma parameters. These rather awkward properties make its application somewhat more difficult. In this paper we perform an extensive numerical study of EBW H&CD performance in four typical ST plasmas (NSTX L- and H-mode, MAST Upgrade, NHTX). Coupled ray-tracing (AMR) and Fokker–Planck (LUKE) codes are employed to simulate EBWs of varying frequencies and launch conditions, which are the fundamental EBW parameters that can be chosen and controlled. Our results indicate that an efficient and universal EBW H&CD system is indeed viable. In particular, power can be deposited and current reasonably efficiently driven across the whole plasma radius. Such a system could be controlled by a suitably chosen launching antenna vertical position and would also be sufficiently robust.
A three-dimensional quantum lattice algorithm (QLA) for electromagnetic wave propagation is being developed by stitching together the individual QLAs for 1D wave propagation in the three orthogonal Cartesian directions.
The progress and challenges in thermal lattice-Boltzmann modeling are discussed. In particular, momentum and energy closures schemes are contrasted. Higher order symmetric (but no longer space filling) velocity lattices are constructed for both 2D and 3D flows and shown to have superior stability properties to the standard (but lower) symmetry lattices. While this decouples the velocity lattice from the spatial grid, the interpolation required following free-streaming is just 1D. The connection between fixed lattice vectors and temperature-dependent lattice vectors (obtained in the Gauss–Hermite quadrature approach) is discussed. Some (compressible) Rayleigh–Benard simulations on the 2D octagonal lattice are presented for extended BGK collision operators that allow for arbitrary Prandtl numbers.
