Bulletin of the American Physical Society
58th Annual Meeting of the APS Division of Plasma Physics
Volume 61, Number 18
Monday–Friday, October 31–November 4 2016; San Jose, California
Session BM9: Mini-Conference: New Developments in Algorithms and Verification of Gyrokinetic Simulations IMini-Conference
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Chair: Robert Hager, Princeton Plasma Physics Laboratory Room: 211 CD |
Monday, October 31, 2016 9:30AM - 9:55AM |
BM9.00001: Comparitive multi-code study of finite-size gyrokinetic electromagnetic instabilities Tobias G\"orler, Natalia Tronko, William A. Hornsby, Alberto Bottino, Ralf Kleiber, Claudia Norscini, Virginie Grandgirard, Frank Jenko, Eric Sonnendr\"ucker Given the recent extensions of global gyrokinetic (GK) codes towards a comprehensive and self-consistent treatment of electromagnetic (EM) effects, corresponding verification tests are necessary steps to be taken. While a number of (semi-)analytic test cases exist in the axisymmetric limit, EM microinstabilities and turbulence are rarely addressed. In order to remedy this problem, a hierarchical linear GK benchmark study is presented starting with electrostatic (adiabatic electron) ion temperature gradient microinstabilities and progressing finally to the characterization of fully EM instabilities as a function of the pressure ratio $\beta$. Results from numerical schemes as different as Eulerian Vlasov, Lagrangian PIC, and Semi-Lagrange codes are shown. The EM microinstability benchmark itself is carried out by various PIC and Vlasov codes, thus confirming a high degree of reliability for the implementation that has never been achieved so far in this context. Insights regarding mode structure characteristics and associated resolution requirements which will be relevant for future global EM studies are highlighted. Finally, extensions into the physically more relevant nonlinear turbulence regime will be discussed. [Preview Abstract] |
Monday, October 31, 2016 9:55AM - 10:20AM |
BM9.00002: Double-weight scheme for gyrokinetic simulation of electromagnetic instabilities in tokamaks Edward Startsev, Wei-li Lee, Weixing Wang, Zhixin Lu An application of recently developed perturbative particle simulation scheme for finite-$\beta $ plasmas in the presence of background inhomogeneities is presented. The scheme uses two delta-f weights carried by each particle to represent particles density and pressure. Use of separate weight to represent particle pressure allows to alleviate cancelation problem in finite-$\beta $ gyrokinetic simulations with fully kinetic electrons. Recently, we have successfully used the new double-weight scheme for simulation of linear tearing and drift-tearing modes, in both collisionless semi-collisional regimes in sheared slab and high-aspect ratio cylindrical cross-section tokamak geometries. Here, we present further development of this scheme which now includes effects of magnetic drifts for the simulation of linear semi-collisional micro-tearing (MTM) and kinetic ballooning (KBM) modes in realistic aspect ratio cylindrical cross-section tokamak using the modified turbulence code GTS. [Preview Abstract] |
Monday, October 31, 2016 10:20AM - 10:35AM |
BM9.00003: The direct method for gyrokinetic simulation with kinetic electrons and magnetic perturbations Yang Chen, Scott Parker Over the past fifteen years we have developed two Particle-in-Cell (PIC) algorithms for gyrokinetic simulation of tokamak plasmas with kinetic electrons and magnetic perturbations. The first, called the Direct Method, uses an adjustable split-weight scheme and a control-variate method to properly handle the "cancellation problem". The second algorithm is the Closure Scheme, which solves the vorticity equation and the generalized Ohm's law, closing with an electron pressure calculated from delta-f PIC electrons. The extention of the Direct Method to handle low-n (long wavelength) fluctuations will be discussed. We will explain the algorithm, describe the low-n geometrical implementation, and present numerical observations in applying the Direct Method to various waves, including shear Alfven waves, ITGs and the $n=1$ tearing mode. These observations suggest that, whereas the cancellation problem appears to be unavoidable and can be solved by the controlled variate method, the split-weight scheme is primarily a technique for numerical stability, and can probably be replaced by other techniques (such as the mixed-variable approach \footnote{Mishchenko et. al. Phys. Plasmas 21, 092110 (2014)}. [Preview Abstract] |
Monday, October 31, 2016 10:35AM - 10:50AM |
BM9.00004: Verification of Pedestal / Edge Gyrokinetics David Hatch, Mike Kotschenreuther, Swadesh Mahajan, Prashant Valanju, Xing Liu, Frank Jenko, Alejandro Banon Navarro, Daniel Told, MJ Pueschel, Tobias Goerler, Craig Michoski There is an increasing imperative to expand the success of gyrokinetics from the core to the edge region, on which the prospects of fusion energy depend, and where both gyrokinetic codes and models are less established. Various groups have used gyrokinetics to explore the role of several MHD and drift-type mechanisms in edge stability and transport. Moreover, recent work predicts a very unfavorable rho* transport scaling associated with the erosion of shear-suppression. The consequences of such a scaling for are profound and therefore must be tested as rigorously as possible. The pedestal / edge system encompasses regions of parameter space foreign to most core parameter regimes and thus demands verification efforts for a range of modeling capabilities including: extreme gradients; electromagnetic effects in regimes close to MHD limits; extreme shaping and geometry; global effects; high levels of ExB shear; and SOL/sheath physics. We will review recent pedestal work with the GENE code and, in this context, discuss some important preliminary targets for verification in the broader community. Specific, simplified benchmark cases will be proposed in order to address some of these important effects. [Preview Abstract] |
Monday, October 31, 2016 10:50AM - 11:15AM |
BM9.00005: Canonicalizable gyrocenter and structure-preserving geometric algorithms for the Vlasov-Maxwell system Hong Qin Littlejohn's introduction of the non-canonical symplectic structure for the gyrocenter dynamics [1] revolutionized plasma kinetic theory. The discovery of the non-canonical symplectic algorithm for gyrocenters [2] initiated the search for symplectic algorithms for the gyrokinetic system. This effort is enforced by the recent discovery of canonical and non-canonical symplectic algorithms for the Vlasov-Maxwell (VM) system [3-5]. However, symplectic algorithms for the gyrokinetic system remain elusive despite intense effort. In retrospect, the success of the symplectic algorithms for the VM system can be attributed to its global canonicalizability. Darboux's theorem ensures that any symplectic structure is locally canonicalizable, but not necessarily globally. Indeed, Littlejohn's gyrocenter is not globally canonicalizable. In this talk, I will show to construct a different gyrocenter that is globally canonicalizable. It should be a good starting point for developing symplectic algorithms for the gyrokinetic system. [1] R. G. Littlejohn, Plasma Phys. 29, 111 (1983). [2] H. Qin {\&} X. Guan, PRL 100, 035006 (2008). [3] H. Qin et al., Nuclear Fusion 56, 014001 (2016). [4] J. Xiao et al, PoP 22, 112504 (2015). [5] Y. He et al., PoP 22,124503 (2015). [Preview Abstract] |
Monday, October 31, 2016 11:15AM - 11:40AM |
BM9.00006: GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods for the Vlasov-Maxwell System and Gyrokinetics Michael Kraus, Katharina Kormann, Eric Sonnendrücker, Philip Morrison In this talk we will describe recent work on the development of geometric particle-in-cell methods for the Vlasov-Maxwell system and gyrokinetics. We present a novel framework for particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive semi-discrete Poisson brackets which satisfy the Jacobi identity and apply Hamiltonian splitting schemes for time integration. Techniques from Finite Element Exterior Calculus and spline differential forms ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge-invariant, feature exact charge conservation show excellent long-time energy behaviour. The talk will be concluded with an outline of how to extend these techniques towards gyrokinetics. [Preview Abstract] |
Monday, October 31, 2016 11:40AM - 12:05PM |
BM9.00007: Reduced Landau collision operator suitable for gyrokinetic particle simulations Alain Brizard Given the importance of the collisionless gyrokinetic formalism [1], the inclusion of self-consistent collisional effects in the neoclassical and collisionless (long-mean-free-path) regimes within the gyrokinetic formalism is of crucial importance in our ability to understand the complex nonlinear dynamics of magnetized fusion plasmas over long time scales. The exact energy-momentum conservation laws of a guiding-center Landau collision operator [2], which play an important role in monitoring the numerical accuracy of gyrokinetic particle simulations, are investigated for arbitrary magnetic-field geometry. \newline [1] A.J. Brizard and T.S. Hahm, Rev. Mod. Phys. 79 (2007) 421. \newline [2] J.W. Burby, A.J. Brizard, and H. Qin, PoP 22 (2015) 100707. [Preview Abstract] |
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