W. Guttenfelder

Princeton University, Princeton, New Jersey, United States

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Publications (73)103.3 Total impact

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    ABSTRACT: This paper describes the enhanced pedestal (EP) H-mode observed in the National Spherical Torus Experiment (NSTX). The defining characteristics of EP H-mode are given, namely (i) transition after the L- to H-mode transition, (ii) region of very steep ion temperature gradient, and (iii) associated region of strong rotational shear. A newly observed long-pulse EP H-mode example shows quiescent behaviour for as long as the heating and current drive sources are maintained. Cases are shown where the region of steep ion temperature gradient is located at the very edge, and cases where it is shifted up to 10 cm inward from the plasma edge; these cases are united by a common dependence of the ion temperature gradient on the toroidal rotation frequency shear. EP H-mode examples have been observed across a wide range of q95 and pedestal collisionality. No strong changes in the fluctuation amplitudes have been observed following the EP H-mode transition, and transport analysis indicates that the ion thermal transport is comparable to or less than anticipated from a simple neoclassical transport model. Cases are shown where EP H-modes were reliably generated, though these low-q95 examples were difficult to sustain. A case where an externally triggered edge localized mode (ELM) precipitates the transition to EP H-mode is also shown, though an initial experiment designed to trigger EP H-modes in this fashion was unsuccessful.
    Nuclear Fusion 06/2014; 54(8):083021. · 2.73 Impact Factor
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    ABSTRACT: Previous pedestal turbulence measurements in the National Spherical Torus Experiment assessed the spatial and temporal properties of turbulence in the steep gradient region of H-mode pedestals during edge localized mode (ELM)-free, MHD-quiescent periods. Here, we extend the analysis to fluctuation amplitudes and compare observations to pedestal turbulence simulations. Measurements indicate normalized fluctuation amplitudes are about 1-5% in the steep gradient region. Regression analysis indicates fluctuation amplitudes scale positively with electron density gradient, collisionality, and poloidal beta, and scale negatively with magnetic shear, electron density, ion temperature gradient (ITG), toroidal flow and radial electric field. The scalings are most consistent with trapped electron mode, kinetic ballooning mode, or microtearing instabilities, but, notably, least consistent with ITG turbulence. Gyrokinetic simulations of pedestal turbulence with realistic pedestal profiles show collisional instabilities with growth rates that increase at higher density gradient and decrease at higher ITG, in qualitative agreement with observed scalings. Finally, Braginskii fluid simulations of pedestal turbulence do not reproduce scalings from measurements and gyrokinetic simulations, and suggest electron dynamics can be a critical factor for accurate pedestal turbulence simulations.
    Nuclear Fusion 11/2013; 53(11):3029-. · 2.73 Impact Factor
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    ABSTRACT: The pedestal structure in NSTX is strongly affected by lithium coatings applied to the PFCs. In discharges with lithium, the density pedestal widens, and the electron temperature (Te) gradient increases inside a radius of ψN ∼ 0.95, but is unchanged for ψN > 0.95. The inferred effective electron thermal (\chi_{e}^{eff} ) and particle (D_{e}^{eff} ) profiles reflect the profile changes: \chi_{e}^{eff} is slightly increased in the near-separatrix region, and is reduced in the region ψN < 0.95 in the with-lithium case. The D_{e}^{eff} profile shows a broadening of the region with low diffusivity with lithium, while the minimum value within the steep-gradient region is comparable in the two cases. The linear microstability properties of the edge plasma without and with lithium have been analysed. At the pedestal top microtearing modes are unstable without lithium. These are stabilized by the stronger density gradient with lithium, becoming TEM-like with growth rates reduced and comparable to E × B shearing rates. In the region ψN > 0.95, both the pre- and with-lithium cases are calculated to be unstable to ETG modes, with higher growth rates with lithium. Both cases are also found to lie near the onset for kinetic ballooning modes, but in the second-stable region where growth rates decrease with increasing pressure gradient.
    Nuclear Fusion 11/2013; 53(11):3016-. · 2.73 Impact Factor
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    ABSTRACT: Nonlinear simulations based on multiple NSTX discharge scenarios have progressed to help differentiate unique instability mechanisms and to validate with experimental turbulence and transport data. First nonlinear gyrokinetic simulations of microtearing turbulence in a high-beta NSTX H-mode discharge predict experimental levels of electron thermal transport that are dominated by magnetic flutter and increase with collisionality, roughly consistent with energy confinement times in dimensionless collisionality scaling experiments. Electron temperature gradient (ETG) simulations predict significant electron thermal transport in some low- and high-beta discharges when ion scales are suppressed by E × B shear. Although the predicted transport in H-modes is insensitive to variation in collisionality (inconsistent with confinement scaling), it is sensitive to variations in other parameters, particularly density gradient stabilization. In reversed shear L-mode discharges that exhibit electron internal transport barriers, ETG transport has also been shown to be suppressed nonlinearly by strong negative magnetic shear, s 0. In many high-beta plasmas, instabilities which exhibit a stiff beta dependence characteristic of kinetic ballooning modes (KBMs) are sometimes found in the core region. However, they do not have a distinct finite beta threshold, instead transitioning gradually to a trapped electron mode (TEM) as beta is reduced to zero. Nonlinear simulations of this 'hybrid' TEM/KBM predict significant transport in all channels, with substantial contributions from compressional magnetic perturbations. As multiple instabilities are often unstable simultaneously in the same plasma discharge, even on the same flux surface, unique parametric dependencies are discussed which may be useful for distinguishing the different mechanisms experimentally.
    Nuclear Fusion 08/2013; 53(9):093022. · 2.73 Impact Factor
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    ABSTRACT: Progress in characterizing the edge stability and properties of the microinstabilities responsible for enhanced transport in the pedestal region is reported. The stability of the pedestal is characterized in high performance discharges on National Spherical Torus Experiment. These high performance plasmas are found to be ideal kink-peeling and ideal infinite-n ballooning unstable prior to the onset of edge-localized modes (ELM). The spatial structure of turbulence present during an ELM cycle in the pedestal region indicates poloidal spatial scales propagating in the ion diamagnetic drift direction at the pedestal top, and radial spatial scales . These propagating spatial scales are found to be poloidally elongated and consistent with ion-scale microturbulence. Both global and local gyrokinetic simulations have been performed to identify the microturbulence structure. The local gyrokinetic analysis indicates the presence of a linearly unstable hybrid kinetic ballooning mode and trapped electron mode with spatial scale and propagation direction consistent with experimental observations. In the global gyrokinetic analysis, the nonlinearly saturated potential fluctuations show radial and poloidal correlation lengths in agreement with experimental density fluctuation correlation length measurements.
    Nuclear Fusion 08/2013; 53(9):093026. · 2.73 Impact Factor
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    ABSTRACT: Microturbulence is considered to be a major candidate in driving anomalous transport in fusion plasmas, and the equilibrium E × B shear generated by externally driven flow can be a powerful tool to control microturbulence in future fusion devices such as FNSF and ITER. Here we present the first observation of the change in electron-scale turbulence wavenumber spectrum (measured by a high-k scattering system) and thermal transport responding to continuous E × B shear ramp-up in an NSTX centre-stack limited and neutral beam injection-heated L-mode plasma. It is found that while linear stability analysis shows that the maximum electron temperature gradient mode linear growth rate far exceeds the observed E × B shearing rate in the measurement region of the high-k scattering system, the unstable ion temperature gradient (ITG) modes are susceptible to E × B shear stabilization. We observed that as the E × B shearing rate is continuously ramped up in the high-k measurement region, the ratio between the E × B shearing rate and maximum ITG mode growth rate continuously increases (from about 0.2 to 0.7) and the maximum power of the measured electron-scale turbulence wavenumber spectra decreases. Meanwhile, electron and ion thermal transport is also reduced in the outer half of the plasmas as long as magnetohydrodynamic activities are not important and the L-mode plasmas eventually reach H-mode-like confinement. Linear and nonlinear gyrokinetic simulations are presented to address the experimental observations.
    Nuclear Fusion 07/2013; 53(8):083007. · 2.73 Impact Factor
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    ABSTRACT: The spherical torus edge region is among the most challenging regimes for plasma turbulence simulations. Here, we measure the spatial and temporal properties of ion-scale turbulence in the steep gradient region of H-mode pedestals during edge localized mode-free, MHD quiescent periods in the National Spherical Torus Experiment. Poloidal correlation lengths are about 10 ρi, and decorrelation times are about 5 a/cs. Next, we introduce a model aggregation technique to identify parametric dependencies among turbulence quantities and transport-relevant plasma parameters. The parametric dependencies show the most agreement with transport driven by trapped-electron mode, kinetic ballooning mode, and microtearing mode turbulence, and the least agreement with ion temperature gradient turbulence. In addition, the parametric dependencies are consistent with turbulence regulation by flow shear and the empirical relationship between wider pedestals and larger turbulent structures.
    Physics of Plasmas 05/2013; 20(5). · 2.38 Impact Factor
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    ABSTRACT: Understanding the dependence of confinement on collisionality in tokamaks is important for the design of next-step devices, which will operate at collisionalities at least one order of magnitude lower than in the present generation. A wide range of collisionality has been obtained in the National Spherical Torus Experiment (NSTX) by employing two different wall conditioning techniques, one with boronization and between-shot helium glow discharge conditioning (HeGDC+B), and one using lithium evaporation (Li EVAP). Previous studies of HeGDC+B plasmas indicated a strong increase of normalized confinement with decreasing collisionality. Discharges with lithium conditioning discussed in the present study generally achieved lower collisionality, extending the accessible range of collisionality by a factor of two. While the confinement dependences on dimensional, engineering variables of the HeGDC+B and Li EVAP datasets differed, collisionality was found to unify the trends, with the lower collisionality lithium conditioned discharges extending the trend of increasing normalized confinement time, BTτE, with decreasing collisionality when other dimensionless variables were held as fixed as possible. This increase of confinement with decreasing collisionality was driven by a large reduction in electron transport in the outer region of the plasma. This result is consistent with gyrokinetic calculations that show microtearing and electron temperature gradient (ETG) modes to be more stable for the lower collisionality discharges. Ion transport, near neoclassical at high collisionality, became more anomalous at lower collisionality, possibly due to the growth of hybrid TEM/KBM modes in the outer regions of the plasma.
    Nuclear Fusion 04/2013; 53(6):063005. · 2.73 Impact Factor
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    ABSTRACT: Characterization of the spatial structure of turbulence fluctuations during the edge localized mode cycle in the pedestal region is reported. Using the beam emission spectroscopy and the correlation reflectometry systems, measurements show spatial structure—k⊥ρiped—ranging from 0.2 to 0.7 propagating in the ion diamagnetic drift direction at the pedestal top. These propagating spatial scales are found to be anisotropic and consistent with ion-scale microturbulence of the type ion temperature gradient and/or kinetic ballooning modes.
    Physics of Plasmas 01/2013; 20(1). · 2.38 Impact Factor
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    ABSTRACT: The onset and characteristics of Micro-Tearing Modes (MTM) in the core of spherical (NSTX) and conventional tokamaks (ASDEX-UG and JET) are studied through local linear gyrokinetic simulations with gyro [J. Candy and E. Belli, General Atomics Report GA-A26818 (2011)]. For experimentally relevant core plasma parameters in the NSTX and ASDEX-UG tokamaks, in agreement with previous works, we find MTMs as the dominant linear instability. Also, for JET-like core parameters considered in our study an MTM is found as the most unstable mode. In all these plasmas, finite collisionality is needed for MTMs to become unstable and the electron temperature gradient is found to be the fundamental drive. However, a significant difference is observed in the dependence of linear growth rate of MTMs on electron temperature gradient. While it varies weakly and non-monotonically in JET and ASDEX-UG plasmas, in NSTX it increases with the electron temperature gradient.
    Nuclear Fusion 01/2013; 53(6). · 2.73 Impact Factor
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    ABSTRACT: Recent nonlinear gyrokinetic calculations have indicated that microtearing modes are driven unstable in NSTX (National Spherical Torus experiment) and may account for the observed anomalous electron thermal transport (Guttenfelder et al 2011 Phys. Rev. Lett. 106 155004). In order to study magnetic fluctuations of both coherent and incoherent modes, a 288 GHz (λ ≈ 1 mm) polarimeter is under development (Zhang et al 2012 Rev. Sci. Instrum. 83 10E321) for NSTX-U (NSTX-Upgrade) (Menard et al 2012 Nucl. Fusion 52 083015). The system will utilize a retro-reflective geometry and view the plasma along the major radius close to the midplane. In order to assess whether the system will have sufficient sensitivity to observe microtearing modes in NSTX-U, a synthetic diagnostic code is developed and utilized to determine the expected phase fluctuation level. The fluctuating profiles for density and magnetic field generated by the non-linear gyrokinetic simulation are used as input to the code. Results indicate that the polarimeter phase fluctuation level due to the modeled microtearing modes is 2°. Utilizing the same model, it was also established that the calculated phase fluctuations are dominated by magnetic, not density fluctuations. This was especially true when the horizontal viewing chord was close (within ±5 cm) to the plasma midplane. These results indicate that the polarimeter planned for NSTX-U should have sufficient sensitivity to observe magnetic fluctuations associated with microtearing modes.
    Plasma Physics and Controlled Fusion 01/2013; · 2.37 Impact Factor
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    ABSTRACT: Here we present the first observation of the change in electron-scale turbulence wavenumber spectrum (measured by a high-k scattering system) and thermal transport responding to continuous ExB shear ramping-up at the edge of a set of NSTX NBI-heated L-mode plasmas (r/a ˜ 0.66-0.78). We observed that as the ExB shearing rate is continuously ramped up, the ratio between the ExB shearing rate and the maximum ITG mode growth rate continuously increases and the maximum power of the measured electron-scale turbulence wavenumber spectra decreases. Meanwhile, both the electron and ion thermal transports are also reduced as long as MHD activities are not important. These observations are consistent with that some of the observed electron-scale turbulence is nonlinearly driven by ITG turbulence and its power decreases as ITG turbulence is progressively suppressed by ExB shear. Heat fluxes predicted by local nonlinear ITG simulations at different radial locations can be larger or significantly smaller than the corresponding local experimental heat fluxes depending on the local ExB shearing rate, which indicates that global effects may have to be included in future simulations. Comparison with gyrokinetic simulations of L-mode plasmas of conventional tokamaks will be also presented.
    10/2012;
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    ABSTRACT: Early experimental work on NSTX has reported measurements of the spatial structure of turbulence fluctuations during an ELM cycle in the pedestal region. These measurements showed spatial structures with scales kθρi^ped ranging from 0.1 to 0.2 propagating in the ion diamagnetic drift direction. These propagating spatial scales structures are found to have a large poloidal extent (˜ 18ρi^ped) and are found to be consistent with ion-scale microturbulence of the type ion temperature gradient (ITG), hybrid ITG and trapped electron mode, and/or kinetic ballooning modes (KBM). Motivated by these experimental observations, we seek to identify the role of pedestal transport between type I ELMs and compare it with microturbulence-induced transport in the pedestal region. Using TRANSP, we show that both the ion and electrons heat diffusivities at the pedestal top remains unchanged between ELMs. Preliminary simulations during the last part of the ELM cycle, using XGC1 code in a delta-f mode shows localized fluctuations consistent with experimental level radial and poloidal correlation lengths. Extension of these simulations to full-f mode will be presented. In addition, other gyrokinetics simulations (e.g., GS2, GYRO) will be performed to identify the unstable modes in the pedestal top and associated heat fluxes The turbulence and neoclassical contributions to these fluxes will also be discussed. Work supported by US DOE contracts DE-AC02-09CH11466.
    10/2012;
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    ABSTRACT: Lithium wall coating techniques have been experimentally explored on National Spherical Torus Experiment (NSTX) for the last six years. The lithium experimentation on NSTX started with a few milligrams of lithium injected into the plasma as pellets and it has evolved to a dual lithium evaporation system which can evaporate up to ∼160 g of lithium onto the lower divertor plates between re-loadings. The unique feature of the NSTX lithium research program is that it can investigate the effects of lithium coated plasma-facing components in H-mode divertor plasmas. This lithium evaporation system has produced many intriguing and potentially important results. In 2010, the NSTX lithium program has focused on the effects of liquid lithium divertor (LLD) surfaces including the divertor heat load, deuterium pumping, impurity control, electron thermal confinement, H-mode pedestal physics, and enhanced plasma performance. To fill the LLD with lithium, 1300 g of lithium was evaporated into the NSTX vacuum vessel during the 2010 operations. The routine use of lithium in 2010 has significantly improved the plasma shot availability resulting in a record number of plasma shots in any given year. In this paper, as a follow-on paper from the 1st lithium symposium [1], we review the recent progress toward developing fundamental understanding of the NSTX lithium experimental observations as well as the opportunities and associated R&D required for use of lithium in future magnetic fusion facilities including ITER.
    Fusion Engineering and Design. 10/2012; 87(10):1770–1776.
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    ABSTRACT: The gyrokinetic turbulence code, GS2, has been adapted to handle stellarator geometry. Herein a new computational grid generator and upgrades to GS2 itself are described and benchmarked with GENE and GKV-X. Additionally, detailed linear studies using the National Compact Stellarator Experiment (NCSX) geometry are discussed, in particular those comparing stability in two equilibria with different β and those comparing NCSX linear stability to a tokamak case. Finally, a comparison of linear stability of two locations in a Wendelstein 7-AS (W7-AS) plasma is presented. The experimentally-measured parameters used were from a W7-AS shot in which measured heat fluxes were too large for neoclassical predictions at both radii. Results from GS2 linear simulations show that the outer location has higher gyrokinetic instability growth rates than the inner one. Mixing-length estimates of the heat flux are within a factor of 3 of the experimental measurements, indicating that gyrokinetic turbulence may be responsible for the higher transport measured by the experiment in the outer regions. This work was supported by the SciDAC Center for the Study of Plasma Microturbulence and Department of Energy Contract DE-AC02-09CH11466.
    10/2012;
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    ABSTRACT: Linear gyrokinetic simulations demonstrate a large variety of microinstabilities are possible in NSTX. Microtearing modes are often unstable in the core region (r/a=0.5-0.8) of NBI heated H-modes. In cases without Lithium wall conditioning, the local ExB shearing rates are larger than linear growth rates (r/a=0.5-0.6). Instead, the ETG instability (at electron scales) is unstable; nonlinear simulations in this region will be presented. Farther out (r/a=0.7-0.8), and in plasmas with Lithium wall conditioning, other ion scale instabilities can co-exist with, or dominate, microtearing modes. The nature of these ballooning modes is complicated and can exhibit ITG/TEM or KBM behavior depending on the MHD alpha parameter (αMHD=-q^2R∇β). In limited cases tearing-parity ITG modes have also been identified. While non-linear simulations of these ``mixed-mode'' conditions are challenging, first attempts are underway. This work is supported by US DOE contract DE-AC02-09CH11466.
    10/2012;
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    ABSTRACT: The National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] can achieve high electron plasma confinement regimes that are super-critically unstable to the electron temperature gradient driven (ETG) instability. These plasmas, dubbed electron internal transport barriers (e-ITBs), occur when the magnetic shear becomes strongly negative. Using the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], the first nonlinear ETG simulations of NSTX e-ITB plasmas reinforce this observation. Local simulations identify a strongly upshifted nonlinear critical gradient for thermal transport that depends on magnetic shear. Global simulations show e-ITB formation can occur when the magnetic shear becomes strongly negative. While the ETG-driven thermal flux at the outer edge of the barrier is large enough to be experimentally relevant, the turbulence cannot propagate past the barrier into the plasma interior.
    Physics of Plasmas 05/2012; 19(5). · 2.38 Impact Factor
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    ABSTRACT: Electron-scale turbulence is predicted to drive anomalous electron thermal transport. However, experimental study of its relation with transport is still in its early stage. On the National Spherical Tokamak Experiment (NSTX), electron-scale density fluctuations are studied with a novel tangential microwave scattering system with high radial resolution of {+-}2 cm. Here, we report a study of parametric dependence of electron-scale turbulence in NSTX H-mode plasmas. The dependence on density gradient is studied through the observation of a large density gradient variation in the core induced by an edge localized mode (ELM) event, where we found the first clear experimental evidence of density gradient stabilization of electron-gyro scale turbulence in a fusion plasma. This observation, coupled with linear gyro-kinetic calculations, leads to the identification of the observed instability as toroidal electron temperature gradient (ETG) modes. It is observed that longer wavelength ETG modes, k{sub Up-Tack }{rho}{sub s} Less-Than-Or-Equivalent-To 10 ({rho}{sub s} is the ion gyroradius at electron temperature and k{sub Up-Tack} is the wavenumber perpendicular to local equilibrium magnetic field), are most stabilized by density gradient, and the stabilization is accompanied by about a factor of two decrease in electron thermal diffusivity. Comparisons with nonlinear ETG gyrokinetic simulations show ETG turbulence may be able to explain the experimental electron heat flux observed before the ELM event. The collisionality dependence of electron-scale turbulence is also studied by systematically varying plasma current and toroidal field, so that electron gyroradius ({rho}{sub e}), electron beta ({beta}{sub e}), and safety factor (q{sub 95}) are kept approximately constant. More than a factor of two change in electron collisionality, {nu}{sub e}{sup *}, was achieved, and we found that the spectral power of electron-scale turbulence appears to increase as {nu}{sub e}{sup *} is decreased in this collisonality scan. However, both linear and nonlinear simulations show no or weak dependence with the electron-ion collision frequency, {nu}{sup e/i}. Instead, other equilibrium parameters (safety factor, electron density gradient, for example) affect ETG linear growth rate and electron thermal transport more than {nu}{sup e/i} does. Furthermore, electron heat flux predicted by the simulations is found to have an order-of-magnitude spatial variation in the experimental measurement region and is also found to be much smaller than experimental levels except at one radial location we evaluated. The predicted electron heat flux is shown to be strongly anti-correlated with density gradient, which varies for a factor of three in the measurement region, which is in agreement with the density gradient dependence study reported in this paper.
    Physics of Plasmas 05/2012; 19(5). · 2.38 Impact Factor
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    ABSTRACT: Thermal energy confinement times in National Spherical Torus Experiment (NSTX) dimensionless parameter scans increase with decreasing collisionality. While ion thermal transport is neoclassical, the source of anomalous electron thermal transport in these discharges remains unclear, leading to considerable uncertainty when extrapolating to future spherical tokamak (ST) devices at much lower collisionality. Linear gyrokinetic simulations find microtearing modes to be unstable in high collisionality discharges. First non-linear gyrokinetic simulations of microtearing turbulence in NSTX show they can yield experimental levels of transport. Magnetic flutter is responsible for almost all the transport (??8%), perturbed field line trajectories are globally stochastic, and a test particle stochastic transport model agrees to within 25% of the simulated transport. Most significantly, microtearing transport is predicted to increase with electron collisionality, consistent with the observed NSTX confinement scaling. While this suggests microtearing modes may be the source of electron thermal transport, the predictions are also very sensitive to electron temperature gradient, indicating the scaling of the instability threshold is important. In addition, microtearing turbulence is susceptible to suppression via sheared E????B flows as experimental values of E????B shear (comparable to the linear growth rates) dramatically reduce the transport below experimental values. Refinements in numerical resolution and physics model assumptions are expected to minimize the apparent discrepancy. In cases where the predicted transport is strong, calculations suggest that a proposed polarimetry diagnostic may be sensitive to the magnetic perturbations associated with the unique structure of microtearing turbulence.
    Phys. Plasmas. 04/2012; 19(5):056119-056119-10.
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    ABSTRACT: The GS2 gyrokinetic code is being used to study microinstabilities and turbulence in non-axisymmetric flux-tube geometries. Non-axisymmetric systems, such as stellarators, have a number of interesting features, like natural reversed magnetic shear and a large number of shaping parameters. These offer possibilities for reducing microturbulence and improving performance. The NCSX, W7-AS, and W7-X designs were partially optimized for neoclassical transport; however, the turbulent transport has not been studied in detail. We will present studies of gyrokinetic instabilities in NCSX and W7-X equilibria, including important geometry and linear benchmarks between GS2 and GENE, a gyrokinetic code from IPP. Specifically, we have investigated effects of plasma beta and magnetic shear on linear instabilities in NCSX geometry. In addition, we have conducted studies of the microstability of realistic W7-AS plasmas. Finally, we will discuss improvements to the GS2 trapped particle treatment and a new computational grid generator for GS2. This work was supported by the SciDAC Center for the Study of Plasma Microturbulence and Department of Energy Contract DE-AC02-09CH11466.
    03/2012;

Publication Stats

143 Citations
103.30 Total Impact Points

Institutions

  • 2011–2014
    • Princeton University
      • Princeton Plasma Physics Laboratory
      Princeton, New Jersey, United States
  • 2013
    • Massachusetts Institute of Technology
      • Plasma Science and Fusion Center (PSFC)
      Cambridge, Massachusetts, United States
  • 2009–2011
    • The University of Warwick
      • Department of Physics
      Coventry, England, United Kingdom
    • University of California, Los Angeles
      • Department of Physics and Astronomy
      Los Angeles, CA, United States
  • 2003–2010
    • University of Wisconsin, Madison
      • Department of Electrical and Computer Engineering
      Madison, MS, United States