D. R. Ernst

Massachusetts Institute of Technology, Cambridge, Massachusetts, United States

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Publications (89)89.38 Total impact

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    ABSTRACT: We present inboard (HFS) and outboard (LFS) radial electric field (Er) and impurity temperature (Tz) measurements in the I-mode and H-mode pedestal of Alcator C-Mod. These measurements reveal strong Er wells at the HFS and the LFS midplane in both regimes and clear pedestals in Tz, which are of similar shape and height for the HFS and LFS. While the H-mode Er well has a radially symmetric structure, the Er well in I-mode is asymmetric, with a stronger ExB shear layer at the outer edge of the Er well, near the separatrix. Comparison of HFS and LFS profiles indicates that impurity temperature and plasma potential are not simultaneously flux functions. Uncertainties in radial alignment after mapping HFS measurements along flux surfaces to the LFS do not, however, allow direct determination as to which quantity varies poloidally and to what extent. Radially aligning HFS and LFS measurements based on the Tz profiles would result in substantial inboard-outboard variations of plasma potential and electron density. Aligning HFS and LFS Er wells instead also approximately aligns the impurity poloidal flow profiles, while resulting in a LFS impurity temperature exceeding the HFS values in the region of steepest gradients by up to 70%. Considerations based on a simplified form of total parallel momentum balance and estimates of parallel and perpendicular heat transport time scales seem to favor an approximate alignment of the Er wells and a substantial poloidal asymmetry in impurity temperature.
    Nuclear Fusion. 06/2014; 54:083017.
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    ABSTRACT: Conventional radially-local neoclassical calculations become inadequate if the radial gradient scale lengths of the H-mode pedestal become as small as the poloidal ion gyroradius. Here, we describe a radially global $\delta f$ continuum code that generalizes neoclassical calculations to allow stronger gradients. As with conventional neoclassical calculations, the formulation is time-independent and requires only the solution of a single sparse linear system. We demonstrate precise agreement with an asymptotic analytic solution of the radially global kinetic equation in the appropriate limits of aspect ratio and collisionality. This agreement depends crucially on accurate treatment of finite orbit width effects.
    Plasma Physics and Controlled Fusion 12/2013; 56(4). · 2.37 Impact Factor
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    ABSTRACT: Joint experiment/theory/modelling research has led to increased confidence in predictions of the pedestal height in ITER. This work was performed as part of a US Department of Energy Joint Research Target in FY11 to identify physics processes that control the H-mode pedestal structure. The study included experiments on C-Mod, DIII-D and NSTX as well as interpretation of experimental data with theory-based modelling codes. This work provides increased confidence in the ability of models for peeling–ballooning stability, bootstrap current, pedestal width and pedestal height scaling to make correct predictions, with some areas needing further work also being identified. A model for pedestal pressure height has made good predictions in existing machines for a range in pressure of a factor of 20. This provides a solid basis for predicting the maximum pedestal pressure height in ITER, which is found to be an extrapolation of a factor of 3 beyond the existing data set. Models were studied for a number of processes that are proposed to play a role in the pedestal ne and Te profiles. These processes include neoclassical transport, paleoclassical transport, electron temperature gradient turbulence and neutral fuelling. All of these processes may be important, with the importance being dependent on the plasma regime. Studies with several electromagnetic gyrokinetic codes show that the gradients in and on top of the pedestal can drive a number of instabilities.
    Nuclear Fusion 08/2013; 53(9):093024. · 2.73 Impact Factor
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    Matt Landreman, Darin R. Ernst
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    ABSTRACT: Numerical techniques for discretization of velocity space in continuum kinetic calculations are described. An efficient spectral collocation method is developed for the speed coordinate - the radius in velocity space - employing a novel set of non-classical orthogonal polynomials. For problems in which Fokker-Planck collisions are included, a common situation in plasma physics, a procedure is detailed to accurately and efficiently treat the field term in the collision operator (in the absence of gyrokinetic corrections). When species with disparate masses are included simultaneously, a careful extrapolation of the Rosenbluth potentials is performed. The techniques are demonstrated in neoclassical calculations of the bootstrap current and plasma flows in a tokamak.
    Journal of Computational Physics 10/2012; 243. · 2.14 Impact Factor
  • Matt Landreman, Darin Ernst
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    ABSTRACT: In a tokamak pedestal, radial scale lengths can become comparable to the ion orbit width, invalidating conventional neoclassical calculations of flow and current. Here, we generalize neoclassical calculations to allow radial density and electron temperature scale lengths as small as the ion orbit width [1], considering a relatively weak ion temperature gradient so the distribution remains nearly Maxwellian. In this ordering, non-local effects alter the magnitude and poloidal variation of the flow and current. The approach is implemented in a new global δf continuum code using the full linearized Fokker-Planck collision operator. Arbitrary collisionality and aspect ratio are allowed as long as the poloidal magnetic field is small compared to the total magnetic field. Strong radial electric fields, sufficient to electrostatically confine the ions, are also included. In contrast to conventional neoclassical theory, we find analytically and numerically that a steep density gradient causes the parallel and poloidal flow coefficients to differ from each other, acquire poloidal variation, and possibly change sign.[4pt] [1] Landreman and Ernst, arXiv:1207.1795v1.
    10/2012;
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    ABSTRACT: Previous studies of turbulence using the reduced gyro-landau fluid code TGLF, and the gyrokinetic code GYRO, have predicted that in C-Mod ohmic plasmas a dilution of the main ions by a significant amount causes a reduction of turbulent transport in the ion channel [1]. This could be a factor in the LOC-SOC transition. To test this effect, experiments were performed where nitrogen was puffed into ohmic target plasmas with the density kept constant. This seeding reduced the turbulence in the ion diamagnetic direction as measured by phase contrast imaging. To determine impurity concentrations in the plasma, line brightnesses for the relevant impurity species (N, O, Ar, and Mo) were compared to Zeff from neoclassical conductivity and from continuum measurements. The turbulence and transport simulated with GYRO and TGLF were compared to that measured experimentally. Work supported by US DOE awards DE-FG02-94-ER54235 and DE-FC02-99-ER54512.[4pt] [1] M. Porkolab, et al, Bull. Am Phys. Soc. 56, no 12 139 (2011).
    10/2012;
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    ABSTRACT: Internal Transport Barriers (ITBs) in C-Mod feature highly peaked density and pressure profiles and are typically induced by the introduction of radio frequency power in the ion cyclotron range of frequencies (ICRF) with the second harmonic of the resonance for minority hydrogen ions positioned off-axis at the plasma half radius on either the low or high field side of the plasma. These ITBs are formed in the absence of particle or momentum injection, and with monotonic q profiles with qmin< 1. Thus they allow exploration of ITB dynamics in a reactor relevant regime. Recently, linear and non-linear gyrokinetic simulations have demonstrated that changes in the ion temperature and plasma rotation profiles, coincident with the application of off-axis ICRF heating, contribute to greater stability to ion temperature gradient driven fluctuation in the plasma. This results in reduced turbulent driven outgoing heat flux. To date, ITB formation in C-Mod has only been observed in EDA H-mode plasmas with moderate (2-3 MW) ICRF power. Experiments to explore the formation of ITBs in other operating regimes such as I-mode and also with high ICRF power are being undertaken to understand further the process of ITB formation and sustainment, especially with regard to turbulent driven transport.
    10/2012;
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    Matt Landreman, Darin R. Ernst
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    ABSTRACT: In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow and current are examined both analytically and numerically. Steep density gradients are considered, with scale lengths comparable to the poloidal ion gyroradius, together with strong radial electric fields sufficient to electrostatically confine the ions. Attention is restricted to relatively weak ion temperature gradients (but permitting arbitrary electron temperature gradients), since in this limit a delta-f (small departures from a Maxwellian distribution) rather than full-f approach is justified. This assumption is in fact consistent with measured inter-ELM H-Mode edge pedestal density and ion temperature profiles in many present experiments, and is expected to be increasingly valid in future lower collisionality experiments. In the numerical analysis, the distribution function and Rosenbluth potentials are solved for simultaneously, allowing use of the exact field term in the linearized Fokker-Planck collision operator. In the pedestal, the parallel and poloidal flows are found to deviate strongly from the best available conventional neoclassical prediction, with large poloidal variation of a different form than in the local theory. These predicted effects may be observable experimentally. In the local limit, the Sauter bootstrap current formulae appear accurate at low collisionality, but they can overestimate the bootstrap current near the plateau regime. In the pedestal ordering, ion contributions to the bootstrap and Pfirsch-Schluter currents are also modified.
    Plasma Physics and Controlled Fusion 07/2012; 54(11). · 2.37 Impact Factor
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    Matt Landreman, Darin R. Ernst
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    ABSTRACT: In a tokamak pedestal, radial scale lengths can become comparable to the ion orbit width, invalidating conventional neoclassical calculations of flow and bootstrap current. In this work we illustrate a non-local approach that allows strong radial density variation while maintaining small departures from a Maxwellian distribution. Non-local effects alter the magnitude and poloidal variation of the flow and current. The approach is implemented in a new global delta-f continuum code using the full linearized Fokker-Planck collision operator. Arbitrary collisionality and aspect ratio are allowed as long as the poloidal magnetic field is small compared to the total magnetic field. Strong radial electric fields, sufficient to electrostatically confine the ions, are also included. These effects may be important to consider in any comparison between experimental pedestal flow measurements and theory.
    06/2012;
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    ABSTRACT: New results suggest that changes observed in the intrinsic toroidal rotation influence the internal transport barrier (ITB) formation in the Alcator C-Mod tokamak [E. S. Marmar and Alcator C-Mod group, Fusion Sci. Technol. 51, 261 (2007)]. These arise when the resonance for ion cyclotron range of frequencies (ICRF) minority heating is positioned off-axis at or outside of the plasma half-radius. These ITBs form in a reactor relevant regime, without particle or momentum injection, with Ti Almost-Equal-To Te, and with monotonic q profiles (q{sub min} < 1). C-Mod H-mode plasmas exhibit strong intrinsic co-current rotation that increases with increasing stored energy without external drive. When the resonance position is moved off-axis, the rotation decreases in the center of the plasma resulting in a radial toroidal rotation profile with a central well which deepens and moves farther off-axis when the ICRF resonance location reaches the plasma half-radius. This profile results in strong E Multiplication-Sign B shear (>1.5 Multiplication-Sign 10{sup 5} rad/s) in the region where the ITB foot is observed. Gyrokinetic analyses indicate that this spontaneous shearing rate is comparable to the linear ion temperature gradient (ITG) growth rate at the ITB location and is sufficient to reduce the turbulent particle and energy transport. New and detailed measurement of the ion temperature demonstrates that the radial profile flattens as the ICRF resonance position moves off axis, decreasing the drive for the ITG the instability as well. These results are the first evidence that intrinsic rotation can affect confinement in ITB plasmas.
    Physics of Plasmas 01/2012; 19(5). · 2.38 Impact Factor
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    ABSTRACT: Lower Hybrid Current Drive (LHCD) induced rotation has been observed in Alcator C-Mod plasmas as well as in other devices. Recent experiments at Alcator C-Mod have for the first time identified the plasma conditions that determine the LHCD driven rotation direction, co- or counter-current, of the main ion species. This effect is found to depend strongly on the plasma current: low current plasmas have co-current rotation and higher current plasmas exhibit counter-current rotation. Experiments were performed to explore this dependence and changes in rotation were observed to approach 40 km/s at < e =0.66e20 m-3; the LHCD rotation reversal point, δv=0, was also identified. There appears to be a magnetic field configuration effect with the favorable (unfavorable) ∇B configuration having a rotation reversal point around ˜400 kA (˜550 kA). In both co- and counter- current cases, rotation profiles show that the momentum originates near the core of the plasma. Analyses of plasma behavior and gyrokinetic simulations were performed and results are shown.
    11/2011;
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    ABSTRACT: We have modulated on-axis ICRF minority heating to trigger fluctuations and core electron transport in Alcator C-Mod Internal Transport Barriers (ITB's). Temperature swings of 50% produced strong bursts of density fluctuations, measured by phase contrast imaging (PCI), while edge fluctuations from reflectometry, Mirnov coils, and gas puff imaging (GPI) simultaneously diminished. The PCI fluctuations are in phase with sawteeth, further evidence that they originate within the ITB foot. Linear gyrokinetic analysis with GS2 shows TEMs are driven unstable in the ITB by the on-axis heating, as in Refs. [1,2]. Nonlinear gyrokinetic simulations of turbulence in the ITB are compared with fluctuation data using a synthetic diagnostic [1]. Strong ITB's were produced with high quality ion and electron profile data. [4pt] [1] D. R. Ernst et al., 20th IAEA Fusion Energy Conference (2006), Chengdu, China, paper IAEA-CN-149/TH/1-3. [2] D. R. Ernst et al., Phys. Plasmas 11 (2004) 2637.
    11/2011;
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    ABSTRACT: ITBs in Alcator C-Mod featuring highly peaked density and pressure profiles are induced by injecting ICRF power with the second harmonic of the resonant frequency for minority hydrogen off-axis at the plasma half radius. These ITBs are formed in the absence of particle or momentum injection, and with monotonic q profiles with qmin < 1. In C-Mod a strong co-current toroidal rotation, peaked on axis, develops after the transition to H-mode. If an ITB forms, this rotation decreases in the center of the plasma and forms a well, and often reverses direction in the core. This indicates that there is a strong EXB shearing rate in the region where the foot in the ITB density profile is observed. Preliminary gyrokinetic analyses indicate that this shearing rate is comparable to the ion temperature gradient mode (ITG) growth rate at this location and may be responsible for stabilizing the turbulence. Gyrokinetic analyses of recent experimental data obtained from a complete scan of the ICRF resonance position across the entire C-Mod plasma will be presented.
    11/2010;
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    ABSTRACT: These recent experiments demonstrate apparent success in modulating core transport and fluctuations in an internal transport barrier (ITB) with ICRF heating, serving to localize phase contrast imaging measurements of density fluctuations. With well-resolved profile measurements for both ions and electrons, including flows, this provides a validation testbed for gyrokinetic simulations of electron transport. Modulated electron temperature swings of 40% were accompanied by strong bursts of density fluctuations on phase contrast imaging (PCI), while edge fluctuations from reflectometry and Mirnov coils diminished. Previously, we observed strong density fluctuations during steady on-axis heating of C-Mod ITB's. Nonlinear gyrokinetic simulations of TEM turbulence [1] in the ITB reproduced the shape of the measured fluctuation wavelength spectrum during on-axis heating, using a synthetic PCI diagnostic in GS2, while matching the particle flux [2]. [1] D. R. Ernst et al., 20th IAEA Fusion Energy Conference (2006), Chengdu, China, paper IAEA-CN-149/TH/1-3, http://www-pub.iaea.org/MTCD/Meetings/FEC2006/th1-3.pdf [2] D. R. Ernst et al., Phys. Plasmas 11 (2004) 2637.
    11/2010;
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    ABSTRACT: This work explores the beta dependence of trapped electron mode turbulence and associated electron thermal energy and particle transport, using the GS2 (continuum), GEM (particle), and GYRO (continuum) codes. Leadership class computing facilities enable us to extend to shorter wavelengths that contribute significantly to electron thermal transport, which can increase with beta in ITG dominated cases.footnotetextJ. Candy, Phys. Plasmas 12, 072307 (2005). See posters by R. Waltz and W. Nevins, this conference. Analytic work on zonal flow modulational instabilities with finite beta suggests interesting and non-monotonic beta dependence, arising from competition between drift wave and drift-Alfv'en wave pumps.footnotetext P. N. Guzdar et al., Phys. Plasmas 8(9) 3907 (2001). Finally, our previous TEM zonal flow studiesfootnotetextD. R. Ernst, J. Lang, W. M. Nevins et al., Phys. Plasmas 16, 055906 (2009). found that convergence was poor for etae> 3, despite including wavenumbers kalpharhos
    11/2009;
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    ABSTRACT: The Core Thomson scattering (TS) diagnostic on Alcator C-Mod has been upgraded to provide ne and Te measurements with improved radial spatial resolution up to 1cm (r/a˜0.05) in the range of r/a
    11/2009;
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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. · 2.38 Impact Factor
  • Peter J. Catto, Darin R. Ernst
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    ABSTRACT: A self-adjoint velocity space divergence form for a new model like particle collision operator is shown to exist that preserves all the conservation properties of the full linearized Fökker-Planck collision operator and from which the entropy can be easily seen to not decrease. A Monte Carlo prescription is developed for particle-in-cell codes.
    Plasma Physics and Controlled Fusion 01/2009; 51. · 2.37 Impact Factor
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    ABSTRACT: A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-Theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2 is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.
    Physics of Plasmas 10/2008; · 2.38 Impact Factor
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    ABSTRACT: Understanding anomalous transport in plasmas at pressures approaching the ideal MHD balloon limit is of great importance to projections of ITER operations. Past efforts to simulate plasma microturbulence as beta is increased toward the ideal limit have met with mixed success. We investigate this problem by comparing results from the GYRO, GS2, GEM, and GENE codes over a sequence of runs in which beta is increased toward the ideal ballooning limit. We will also comment on finite-beta effects to trapped electron modes. see, e.g., J. Candy et al, Phys. Plasmas 12, 072307 (2005), and references therein.
    01/2008;

Publication Stats

366 Citations
89.38 Total Impact Points

Institutions

  • 1998–2013
    • Massachusetts Institute of Technology
      • Plasma Science and Fusion Center (PSFC)
      Cambridge, Massachusetts, United States
  • 1995–2006
    • Princeton University
      • Princeton Plasma Physics Laboratory
      Princeton, NJ, United States
  • 2004
    • University of Maryland, College Park
      Maryland, United States