Bulletin of the American Physical Society
51st Annual Meeting of the APS Division of Plasma Physics
Volume 54, Number 15
Monday–Friday, November 2–6, 2009; Atlanta, Georgia
Session DI3: Gyrokinetic Theory and Simulation |
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Chair: Ronald Waltz, General Atomics Room: Centennial II |
Monday, November 2, 2009 3:00PM - 3:30PM |
DI3.00001: Direct multi-scale coupling of a transport code to gyrokinetic turbulence codes, with comparisons to tokamak experiments Invited Speaker: To faithfully simulate ITER and other modern fusion devices, one must resolve electron and ion fluctuation scales in a five-dimensional phase space and time. Simultaneously, one must account for the interaction of this turbulence with the slow evolution of the large-scale plasma profiles. Because of the enormous range of scales involved and the high dimensionality of the problem, resolved first-principles simulations of the full core volume over the confinement time are very challenging using conventional (brute force) techniques. In order to address this problem, we have developed a new approach in which turbulence calculations from multiple gyrokinetic flux tube simulations are coupled together using gyrokinetic transport equations to obtain self-consistent equilibrium profiles and corresponding turbulent fluxes. This multi-scale approach is embodied in a new code, Trinity, which is capable of evolving equilibrium profiles for multiple species, including electromagnetic effects and realistic magnetic geometry, at a fraction of the cost of conventional direct numerical simulations. Key components in the cost reduction are the extreme parallelism enabled by the use of coupled flux tubes and the use of a nonlinear implicit algorithm to take large time steps when evolving the equilibrium. In this talk, we describe the multi-scale model employed in Trinity and present simulation results using nonlinear fluxes calculated with the gyrokinetic turbulence codes GS2 and GENE. We compare the numerical predictions from Trinity simulations with experimental results from a number of fusion devices, including JET and MAST. [Preview Abstract] |
Monday, November 2, 2009 3:30PM - 4:00PM |
DI3.00002: Predictive Gyrokinetic Transport Simulations and Application of Synthetic Diagnostics Invited Speaker: In this work we make use of the gyrokinetic transport solver TGYRO [1] to predict kinetic plasma profiles consistent with energy and particle fluxes in the DIII-D tokamak. TGYRO uses direct nonlinear and neoclassical fluxes calculated by the GYRO and NEO codes, respectively, to solve for global, self-consistent temperature and density profiles via Newton iteration. Previous work has shown that gyrokinetic simulation results for DIII-D discharge 128913 match experimental data rather well in the plasma core, but with a discrepancy in both fluxes and fluctuation levels emerging closer to the edge ($r/a > 0.8$). The present work will expand on previous results by generating model predictions across the entire plasma core, rather than at isolated test radii. We show that TGYRO predicts temperature and density profiles in good agreement with experimental observations which simultaneously yield near-exact (to within experimental uncertainties) agreement with power balance calculations of the particle and energy fluxes for $r/a \leq 0.8$. Moreover, we use recently developed synthetic diagnostic algorithms [2] to show that TGYRO also predicts density and electron temperature fluctuation levels in close agreement with experimental measurements across the simulated plasma volume.\par \vskip8pt \noindent [1] J.~Candy, C.~Holland, R.E.\ Waltz, M.R.\ Fahey, and E.~Belli, ``Tokamak profile prediction using direct gyrokinetic and neoclassical simulation," Phys.\ Plasmas {\bf 16}, 060704 (2009).\par [2] C.~Holland, A.E.\ White, G.R.\ McKee, M.W.\ Shafer, J.~Candy, R.E.\ Waltz, L.~Schmitz, and G.R.\ Tynan, ``Implementation and application of two synthetic diagnostics for validating simulations of core tokamak turbulence," Phys.\ Plasmas {\bf 16}, 052301 (2009). [Preview Abstract] |
Monday, November 2, 2009 4:00PM - 4:30PM |
DI3.00003: Limitations of the gyrokinetic quasineutrality equation Invited Speaker: Traditional electrostatic gyrokinetic treatments consist of a gyrokinetic Fokker-Planck equation and a gyrokinetic quasineutrality equation. The equations implemented in full f codes are typically only consistent through first order in a gyroradius over macroscopic scale length expansion. In axisymmetric configurations such as the tokamak, we will show that these gyrokinetic descriptions are unable to correctly calculate the profile of toroidal rotation and hence the long wavelength radial electric field because even turbulence dominated tokamaks are intrinsically ambipolar. We study the vorticity equation or current conservation equation in the gyrokinetic regime, with wavelengths on the order of the ion gyroradius. We use the momentum conservation equation to determine the perpendicular current density, making explicit the dependence of the current on the transport of toroidal angular momentum. Employing the vorticity equation, it is possible to show that gyrokinetics needs to be calculated to fourth order in the gyroradius expansion if the radial electric field is to be retrieved from quasineutrality. However, existing full f simulations are based on first order gyrokinetic equations that are unreliable for wavelengths longer than the geometric average between the ion gyroradius and the macroscopic scale length. Finally, we replace quasineutrality by the conservation equation for toroidal angular momentum in a form that only requires an ion distribution function correct to second order in ion gyroradius over scale length, and by exploiting an expansion in q $>>$ 1, we propose a scheme in which the first order gyrokinetic Fokker-Planck equation already implemented in codes is enough to find the axisymmetric radial electric field. [Preview Abstract] |
Monday, November 2, 2009 4:30PM - 5:00PM |
DI3.00004: Gyrokinetic Models for Edge Plasmas Invited Speaker: We address two key sets of issues in the development of gyrokinetic equations for magnetic fusion edge simulation codes. Starting with existing second-order gyrokinetic equations [1], we develop a ``minimal'' electromagnetic gyrokinetic model for edge simulations. Large-amplitude perturbations, believed to be present in the edge, result in time evolution of the gyrokinetic Poisson equation operator, and a need to retain second-order terms in the gyrocenter Hamiltonian to satisfy system energy conservation. These aspects have never been implemented in gyrokinetic simulations. We present methods for implementing the second-order terms in the equations of motion, as well as a practical direct finite-element discretization of the evolving gyrokinetic Poisson-equation operator. While tempting, the use of long-wavelength or Pade' approximations for this operator would result in violation of energy conservation. An appropriate model for Coulomb collisions comes from an extension of work on bilinear gyrokinetic collision operators [2,3] to include the first-order terms in the transformation from the gyrocenter- to physical-space distribution function prior to insertion in the Landau-Fokker-Planck operator. We also describe a gyrokinetic theory in an extended ordering in which the small parameter is the ratio of the ExB shearing rate to the gyrofrequency. This theory allows for long wavelength ExB flows of order the thermal velocity instead of the more restrictive standard orderings which require that either the electrostatic potential [1] or the ExB flow velocity [4] be small compared with the thermal levels.\\[4pt] [1] A.J. Brizard, Rev. Mod. Phys. \textbf{79}, 4217 (2007)\\[0pt] [2] A.J. Brizard, Phys. Plasmas \textbf{11}, 4429 (2004)\\[0pt] [3] Z. Xiong et al., J. Comput. Phys. 227, 7192 (2008)\\[0pt] [4] A.M. Dimits et al., Phys Fluids B\textbf{4}, 274 (1992). [Preview Abstract] |
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