W. Dorland

Publications (73)158.31 Total impact

• Article: An Oscillating Langevin Antenna for Driving Plasma Turbulence Simulations

  J. M. TenBarge, G. G. Howes, W. Dorland, G. W. Hammett
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  ABSTRACT: A unique method of driving Alfvenic turbulence via an oscillating Langevin antenna is presented. This method of driving is motivated by a desire to inject energy into a finite domain numerical simulation in a manner that models the nonlinear transfer of energy from fluctuations in the turbulent cascade at scales larger than the simulation domain.. The oscillating Langevin antenna is shown to capture the essential features of the larger scale turbulence and efficiently couple to the plasma, generating steady-state turbulence within one characteristic turnaround time. The antenna is also sufficiently flexible to explore both strong and weak regimes of Alfvenic plasma turbulence.
  05/2013;
• Article: Zero-Turbulence Manifold in a Toroidal Plasma.

  E G Highcock, A A Schekochihin, S C Cowley, M Barnes, F I Parra, C M Roach, W Dorland
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  ABSTRACT: Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/ϵ (magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/ϵ, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the zero-magnetic-shear limit, over the parameter space (γ_{E}, q/ϵ, R/L_{T}), where γ_{E} is the perpendicular flow shear and R/L_{T} is the normalized inverse temperature gradient scale. The extent to which it can be constructed from linear theory is discussed.
  Physical Review Letters 12/2012; 109(26):265001. · 7.37 Impact Factor
• Article: Turbulent Transport and Heating of Trace Heavy Ions in Hot Magnetized Plasmas.

  M Barnes, F I Parra, W Dorland
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  ABSTRACT: Scaling laws for the transport and heating of trace heavy ions in low-frequency magnetized plasma turbulence are derived and compared with direct numerical simulations. The predicted dependences of turbulent fluxes and heating on ion charge and mass number are found to agree with numerical results for both stationary and differentially rotating plasmas. Heavy ion momentum transport is found to increase with mass, and heavy ions are found to be preferentially heated, implying a mass-dependent ion temperature for very weakly collisional plasmas and for partially ionized heavy ions in strongly rotating plasmas.
  Physical Review Letters 11/2012; 109(18):185003. · 7.37 Impact Factor
• Article: Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows

  I. G. Abel, G. G. Plunk, E. Wang, M. Barnes, S. C. Cowley, W. Dorland, A. A. Schekochihin
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  ABSTRACT: This paper presents a complete theoretical framework for plasma turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by-order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equillibrium is obtained from the Grad-Shafranov equation for a rotating plasma and the slow (resistive) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the high-flow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived. Total energy is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating, and the equilibration of mean temperatures. Finally, this framework is condensed, in the low-Mach-number limit, to a concise set of equations suitable for numerical implementation.
  09/2012;
• Article: Freely decaying turbulence in two-dimensional electrostatic gyrokinetics

  T. Tatsuno, G. G. Plunk, M. Barnes, W. Dorland, G. G. Howes, R. Numata
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  ABSTRACT: In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ("sub-Larmor scales") [Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a time-asymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number D*, a quantity analogous to the Reynolds number. The marginal state is marked by a critical number D* = D0 that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger D*; turbulence initialized below D0 become more and more collisional, decaying to progressively smaller D*.
  08/2012;
• Article: Considering Fluctuation Energy as a Measure of Gyrokinetic Turbulence

  G. G. Plunk, T. Tatsuno, W. Dorland
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  ABSTRACT: In gyrokinetic theory there are two quadratic measures of fluctuation energy, left invariant under nonlinear interactions, that constrain the turbulence. The recent work of Plunk and Tatsuno [Phys. Rev. Lett. 106, 165003 (2011)] reported on the novel consequences that this constraint has on the direction and locality of spectral energy transfer. This paper builds on that work. We provide detailed analysis in support of the results of Plunk and Tatsuno but also significantly broaden the scope and use additional methods to address the problem of energy transfer. The perspective taken here is that the fluctuation energies are not merely formal invariants of an idealized model (two-dimensional gyrokinetics) but are general measures of gyrokinetic turbulence, i.e. quantities that can be used to predict the behavior of the turbulence. Though many open questions remain, this paper collects evidence in favor of this perspective by demonstrating in several contexts that constrained spectral energy transfer governs the dynamics.
  06/2012;
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  Available from: ArXiv

  Article: Simulating Gyrokinetic Microinstabilities in Stellarator Geometry with GS2

  J. A. Baumgaertel, E. A. Belli, W. Dorland, W. Guttenfelder, G. W. Hammett, D. R. Mikkelsen, G. Rewoldt, W. M. Tang, P. Xanthopoulos
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  ABSTRACT: The nonlinear gyrokinetic code GS2 has been extended to treat non-axisymmetric stellarator geometry. Electromagnetic perturbations and multiple trapped particle regions are allowed. Here, linear, collisionless, electrostatic simulations of the quasi-axisymmetric, three-field period National Compact Stellarator Experiment (NCSX) design QAS3-C82 have been successfully benchmarked against the eigenvalue code FULL. Quantitatively, the linear stability calculations of GS2 and FULL agree to within ~10%.
  09/2011;
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  Available from: ArXiv

  Article: A Weakened Cascade Model for Turbulence in Astrophysical Plasmas

  G. G. Howes, J. M. TenBarge, W. Dorland
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  ABSTRACT: A refined cascade model for kinetic turbulence in weakly collisional astrophysical plasmas is presented that includes both the transition between weak and strong turbulence and the effect of nonlocal interactions on the nonlinear transfer of energy. The model describes the transition between weak and strong MHD turbulence and the complementary transition from strong kinetic Alfven wave (KAW) turbulence to weak dissipating KAW turbulence, a new regime of weak turbulence in which the effects of shearing by large scale motions and kinetic dissipation play an important role. The inclusion of the effect of nonlocal motions on the nonlinear energy cascade rate in the dissipation range, specifically the shearing by large-scale motions, is proposed to explain the nearly power-law energy spectra observed in the dissipation range of both kinetic numerical simulations and solar wind observations.
  09/2011;
• Article: Overview of physics results from NSTX

  R. Raman, J-W. Ahn, J.P. Allain, R. Andre, R. Bastasz, D. Battaglia, P. Beiersdorfer, M. Bell, R. Bell, E. Belova, [......], K.L. Wong, J. Wright, Z. Xia, D. Youchison, G. Yu, H. Yuh, L. Zakharov, D. Zemlyanov, G. Zimmer, S.J. Zweben
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  ABSTRACT: In the last two experimental campaigns, the low aspect ratio NSTX has explored physics issues critical to both toroidal confinement physics and ITER. Experiments have made extensive use of lithium coatings for wall conditioning, correction of non-axisymmetric field errors and control of n = 1 resistive wall modes (RWMs) to produce high-performance neutral-beam heated discharges extending to 1.7 s in duration with non-inductive current fractions up to 0.7. The RWM control coils have been used to trigger repetitive ELMs with high reliability, and they have also contributed to an improved understanding of both neoclassical tearing mode and RWM stabilization physics, including the interplay between rotation and kinetic effects on stability. High harmonic fast wave (HHFW) heating has produced plasmas with central electron temperatures exceeding 6 keV. The HHFW heating was used to show that there was a 20–40% higher power threshold for the L–H transition for helium than for deuterium plasmas. A new diagnostic showed a depletion of the fast-ion density profile over a broad spatial region as a result of toroidicity-induced Alfvén eigenmodes (TAEs) and energetic-particle modes (EPMs) bursts. In addition, it was observed that other modes (e.g. global Alfvén eigenmodes) can trigger TAE and EPM bursts, suggesting that fast ions are redistributed by high-frequency AEs. The momentum pinch velocity determined by a perturbative technique decreased as the collisionality was reduced, although the pinch to diffusion ratio, Vpinch/χ, remained approximately constant. The mechanisms of deuterium retention by graphite and lithium-coated graphite plasma-facing components have been investigated. To reduce divertor heat flux, a novel divertor configuration, the 'snowflake' divertor, was tested in NSTX and many beneficial aspects were found. A reduction in the required central solenoid flux has been realized in NSTX when discharges initiated by coaxial helicity injection were ramped in current using induction. The resulting plasmas have characteristics needed to meet the objectives of the non-inductive start-up and ramp-up program of NSTX.
  Nuclear Fusion 08/2011; 51(9):094011. · 4.09 Impact Factor
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  Available from: ArXiv

  Article: Gyrokinetic simulations of the tearing instability

  R. Numata, W. Dorland, G. G. Howes, N. F. Loureiro, B. N. Rogers, T. Tatsuno
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  ABSTRACT: Linear gyrokinetic simulations covering the collisional -- collisionless transitional regime of the tearing instability are performed. It is shown that the growth rate scaling with collisionality agrees well with that predicted by a two-fluid theory for a low plasma beta case in which ion kinetic dynamics are negligible. Electron wave-particle interactions (Landau damping), finite Larmor radius, and other kinetic effects invalidate the fluid theory in the collisionless regime, in which a general non-polytropic equation of state for pressure (temperature) perturbations should be considered. We also vary the ratio of the background ion to electron temperatures, and show that the scalings expected from existing calculations can be recovered, but only in the limit of very low beta.
  07/2011;
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  Available from: ArXiv

  Article: Gyrokinetic simulations of solar wind turbulence from ion to electron scales.

  G G Howes, J M TenBarge, W Dorland, E Quataert, A A Schekochihin, R Numata, T Tatsuno
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  ABSTRACT: A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.
  Physical Review Letters 07/2011; 107(3):035004. · 7.37 Impact Factor
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  Available from: 144.206.159.178

  Article: Parallel magnetic field perturbations in gyrokinetic simulations

  N. Joiner, A. Hirose, W. Dorland
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  ABSTRACT: At low β it is common to neglect parallel magnetic field perturbations on the basis that they are of order β2. This is only true if effects of order β are canceled by a term in the ∇B drift also of order β [ H. L. Berk and R. R. Dominguez, J. Plasma Phys. 18, 31 (1977) ]. To our knowledge this has not been rigorously tested with modern gyrokinetic codes. In this work we use the gyrokinetic code GS2 [ Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995) ] to investigate whether the compressional magnetic field perturbation B∥ is required for accurate gyrokinetic simulations at low β for microinstabilities commonly found in tokamaks. The kinetic ballooning mode (KBM) demonstrates the principle described by Berk and Dominguez strongly, as does the trapped electron mode, in a less dramatic way. The ion and electron temperature gradient (ETG) driven modes do not typically exhibit this behavior; the effects of B∥ are found to depend on the pressure gradients. The terms which are seen to cancel at long wavelength in KBM calculations can be cumulative in the ion temperature gradient case and increase with ηe. The effect of B∥ on the ETG instability is shown to depend on the normalized pressure gradient β′ at constant β.
  Physics of Plasmas 07/2010; 17(7):072104-072104-9. · 2.15 Impact Factor
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  Available from: ArXiv

  Article: Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence

  T. Tatsuno, M. Barnes, S. C. Cowley, W. Dorland, G. G. Howes, R. Numata, G. G. Plunk, A. A. Schekochihin
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  ABSTRACT: Two-dimensional electrostatic turbulence in magnetized weakly-collisional plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103, 015003 (2009)]. At scales smaller than the gyroradius, this cascade is characterized by the dimensionless ratio D of the collision time to the eddy turnover time measured at the scale of the thermal Larmor radius. When D >> 1, a broad spectrum of fluctuations at sub-Larmor scales is found in both position and velocity space. The distribution function develops structure as a function of v_{perp}, the velocity coordinate perpendicular to the local magnetic field. The cascade shows a local-scale nonlinear interaction in both position and velocity spaces, and Kolmogorov's scaling theory can be extended into phase space. Comment: 8 pages, 10 figures, Conference paper presented at 2009 Asia-Pacific Plasma Theory Conference. Ver.2 includes corrected typos & updated references
  03/2010;
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  Available from: ArXiv

  Article: Resolving velocity space dynamics in continuum gyrokinetics

  M. Barnes, W. Dorland, T. Tatsuno
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  ABSTRACT: Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent fluxes. Consequently, it is necessary to monitor velocity space resolution in gyrokinetic simulations. In this paper, we present a set of computationally efficient diagnostics for measuring velocity space resolution in gyrokinetic simulations and apply them to a range of plasma physics phenomena using the continuum gyrokinetic code GS2. For the cases considered here, it is found that the use of a collisionality at or below experimental values allows for the resolution of plasma dynamics with relatively few velocity space grid points. Additionally, we describe the implementation of an adaptive collision frequency, which can be used to improve velocity space resolution in the collisionless regime, where results are expected to be independent of collision frequency.
  Physics of Plasmas 03/2010; 17(3):032106-032106-13. · 2.15 Impact Factor
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  Available from: ArXiv

  Article: Direct multiscale coupling of a transport code to gyrokinetic turbulence codes

  M. Barnes, I. G. Abel, W. Dorland, T. Goerler, G. W. Hammett, F. Jenko
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  ABSTRACT: Direct coupling between a transport solver and local, nonlinear gyrokinetic calculations using the multiscale gyrokinetic code TRINITY [M. Barnes, Ph.D. thesis, arxiv:0901.2868] is described. The coupling of the microscopic and macroscopic physics is done within the framework of multiscale gyrokinetic theory, of which we present the assumptions and key results. An assumption of scale separation in space and time allows for the simulation of turbulence in small regions of the space-time grid, which are embedded in a coarse grid on which the transport equations are implicitly evolved. This leads to a reduction in computational expense of several orders of magnitude, making first-principles simulations of the full fusion device volume over the confinement time feasible on current computing resources. Numerical results from TRINITY simulations are presented and compared with experimental data from JET and ASDEX Upgrade plasmas. Comment: 12 pages, 13 figures, invited paper for 2009 APS-DPP meeting, submitted to Phys. Plasmas
  12/2009;
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  Available from: Colin Malcolm Roach

  Article: Gyrokinetic simulations of spherical tokamaks

  C M Roach, I G Abel, R J Akers, W Arter, M Barnes, Y Camenen, F J Casson, G Colyer, J W Connor, S C Cowley, [......], G W Hammett, R J Hastie, E Highcock, N F Loureiro, A G Peeters, M Reshko, S Saarelma, A A Schekochihin, M Valovic, H R Wilson
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  ABSTRACT: This paper reviews transport and confinement in spherical tokamaks (STs) and our current physics understanding of this that is partly based on gyrokinetic simulations. Equilibrium flow shear plays an important role, and we show how this is consistently included in the gyrokinetic framework for flows that greatly exceed the diamagnetic velocity. The key geometry factors that influence the effectiveness of turbulence suppression by flow shear are discussed, and we show that toroidal equilibrium flow shear can sometimes entirely suppress ion scale turbulence in today's STs. Advanced nonlinear simulations of electron temperature gradient (ETG) driven turbulence, including kinetic ion physics, collisions and equilibrium flow shear, support the model that ETG turbulence can explain electron heat transport in many ST discharges.
  Plasma Physics and Controlled Fusion 11/2009; 51(12):124020. · 2.42 Impact Factor
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  Available from: arxiv.org

  Article: Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence.

  T Tatsuno, W Dorland, A A Schekochihin, G G Plunk, M Barnes, S C Cowley, G G Howes
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  ABSTRACT: Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.
  Physical Review Letters 08/2009; 103(1):015003. · 7.37 Impact Factor
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  Available from: psfc.mit.edu

  Article: Role of zonal flows in trapped electron mode turbulence through nonlinear gyrokinetic particle and continuum simulation

  D. R. Ernst, J. Lang, W. M. Nevins, M. Hoffman, Y. Chen, W. Dorland, S. Parker
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  ABSTRACT: Trapped electron mode (TEM) turbulence exhibits a rich variety of collisional and zonal flow physics. This work explores the parametric variation of zonal flows and underlying mechanisms through a series of linear and nonlinear gyrokinetic simulations, using both particle-in-cell and continuum methods. A new stability diagram for electron modes is presented, identifying a critical boundary at ηe = 1, separating long and short wavelength TEMs. A novel parity test is used to separate TEMs from electron temperature gradient driven modes. A nonlinear scan of ηe reveals fine scale structure for ηe≳1, consistent with linear expectation. For ηe<1, zonal flows are the dominant saturation mechanism, and TEM transport is insensitive to ηe. For ηe>1, zonal flows are weak, and TEM transport falls inversely with a power law in ηe. The role of zonal flows appears to be connected to linear stability properties. Particle and continuum methods are compared in detail over a range of ηe = d ln Te/d ln ne values from zero to five. Linear growth rate spectra, transport fluxes, fluctuation wavelength spectra, zonal flow shearing spectra, and correlation lengths and times are in close agreement. In addition to identifying the critical parameter ηe for TEM zonal flows, this paper takes a challenging step in code verification, directly comparing very different methods of simulating simultaneous kinetic electron and ion dynamics in TEM turbulence.
  Physics of Plasmas 05/2009; 16(5):055906-055906-7. · 2.15 Impact Factor
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  Available from: umd.edu

  Article: Using Graphics Processors for High-Performance Computation and Visualization of Plasma Turbulence

  G. Stantchev, D. Juba, W. Dorland, A. Varshney
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  ABSTRACT: Direct numerical simulation (DNS) of turbulence is computationally intensive and typically relies on some form of parallel processing. The authors present techniques to map DNS computations to modern graphics processing units (GPUs), which are characterized by very high memory bandwidth and hundreds of SPMD (single-program-multiple-data) processors.
  Computing in Science and Engineering 05/2009; · 1.42 Impact Factor
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  Available from: plasma.physics.wisc.edu

  Article: Role of stable eigenmodes in gyrokinetic models of ion temperature gradient turbulence

  D. R. Hatch, P. W. Terry, W. M. Nevins, W. Dorland
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  ABSTRACT: Investigation of ion temperature gradient turbulence in gyrokinetic models shows that some of the key features of reduced models associated with saturation by nonlinearly excited damped eigenmodes carry over to gyrokinetics. For nonzonal wavenumbers the frequency spectrum in gyrokinetics is broader by a factor of 10 than simple nonlinear broadening of the most unstable eigenmode. The width, including its variations with wavenumber and temperature gradient scale length, closely tracks accessible stable eigenmodes as approximated by a gyro-Landau fluid model for the same parameters. Cross-phase probability distribution functions (pdfs) and fluxes show nonlinear behavior consistent with stable eigenmodes in nonzonal wavenumbers contributing to 30% of the fluctuation energy. Phase pdfs and cross-phase time histories show that multiple eigenmodes [in addition to high frequency geodesic acoustic modes (GAMs)] are a significant part of the ky = 0 spectrum. Two possible roles of zonal modes in saturation are proposed. First, known nonlinearly accessible stable zonal eigenmodes (in addition to zonal flows and GAMs) are discussed and it is suggested that if these eigenmodes are excited they may be the primary arbiter of saturation. Second, zonal modes may facilitate energy transfer from unstable eigenmodes to stable eigenmodes at finite ky.
  Physics of Plasmas 02/2009; 16(2):022311-022311-15. · 2.15 Impact Factor