D. R. Ernst

Massachusetts Institute of Technology, Cambridge, Massachusetts, United States

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Publications (145)185.24 Total impact

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    ABSTRACT: Measurements of impurities in Alcator C-Mod indicate that in the pedestal region, significant poloidal asymmetries can exist in the impurity density, ion temperature, and main ion density. In light of the observation that ion temperature and electrostatic potential are not constant on a flux surface [Theiler et al., Nucl. Fusion 54, 083017 (2014)], a technique based on total pressure conservation to align profiles measured at separate poloidal locations is presented and applied. Gyrokinetic neoclassical simulations with XGCa support the observed large poloidal variations in ion temperature and density, and that the total pressure is approximately constant on a flux surface. With the updated alignment technique, the observed in-out asymmetry in impurity density is reduced from previous publishing [Churchill et al., Nucl. Fusion 53, 122002 (2013)], but remains substantial ( n z , H / n z , L ∼ 6 ). Candidate asymmetry drivers are explored, showing that neither non-uniform impurity sources nor localized fluctuation-driven transport are able to explain satisfactorily the impurity density asymmetry. Since impurity density asymmetries are only present in plasmas with strong electron density gradients, and radial transport timescales become comparable to parallel transport timescales in the pedestal region, it is suggested that global transport effects relating to the strong electron density gradients in the pedestal are the main driver for the pedestal in-out impurity density asymmetry.
    Physics of Plasmas 05/2015; 22(5):056104. DOI:10.1063/1.4918353 · 2.25 Impact Factor
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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. DOI:10.1088/0029-5515/54/8/083017 · 3.24 Impact Factor
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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). DOI:10.1088/0741-3335/56/4/045005 · 2.39 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. DOI:10.1088/0029-5515/53/9/093024 · 3.24 Impact Factor
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    ABSTRACT: The first measurements of long wavelength (k(y)rho(s) < 0.3) electron temperature fluctuations in Alcator C-Mod made with a new correlation electron cyclotron emission diagnostic support a long-standing hypothesis regarding the confinement transition from linear ohmic confinement (LOC) to saturated ohmic confinement (SOC). Electron temperature fluctuations decrease significantly (similar to 40%) crossing from LOC to SOC, consistent with a change from trapped electron mode (TEM) turbulence domination to ion temperature gradient (ITG) turbulence as the density is increased. Linear stability analysis performed with the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) shows that TEMs are dominant for long wavelength turbulence in the LOC regime and ITG modes are dominant in the SOC regime at the radial location (rho similar to 0.8) where the changes in electron temperature fluctuations are measured. In contrast, deeper in the core (rho < 0.8), linear stability analysis indicates that ITG modes remain dominant across the LOC/SOC transition. This radial variation suggests that the robust global changes in confinement of energy and momentum occurring across the LOC/SOC transition are correlated to local changes in the dominant turbulent mode near the edge.
    Nuclear Fusion 08/2013; 53(8):083010. DOI:10.1088/0029-5515/53/8/083010 · 3.24 Impact Factor
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    ABSTRACT: Several seemingly unrelated effects in Alcator C-Mod ohmic L-mode plasmas are shown to be closely connected: non-local heat transport, core toroidal rotation reversals, energy confinement saturation and up/down impurity density asymmetries. These phenomena all abruptly transform at a critical value of the collisionality. At low densities in the linear ohmic confinement regime, with collisionality ν* ≤ 0.35 (evaluated inside of the q = 3/2 surface), heat transport exhibits non-local behaviour, core toroidal rotation is directed co-current, edge impurity density profiles are up/down symmetric and a turbulent feature in core density fluctuations with kθ up to 15 cm−1 (kθρs ~ 1) is present. At high density/collisionality with saturated ohmic confinement, electron thermal transport is diffusive, core rotation is in the counter-current direction, edge impurity density profiles are up/down asymmetric and the high kθ turbulent feature is absent. The rotation reversal stagnation point (just inside of the q = 3/2 surface) coincides with the non-local electron temperature profile inversion radius. All of these observations suggest a possible unification in a model with trapped electron mode prevalence at low collisionality and ion temperature gradient mode domination at high collisionality.
    Nuclear Fusion 02/2013; 53(3):033004. DOI:10.1088/0029-5515/53/3/033004 · 3.24 Impact Factor
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    ABSTRACT: In the absence of an internal particle source, plasma turbulence will impose an intrinsic relationship between an inwards pinch and an outwards diffusion resulting in a stationary density profile. The Alcator C-mod tokamak utilizes RF heating and current drive so that fueling only occurs in the vicinity of the separatrix. Discharges that transition from L-mode to I-mode are seen to maintain a self-similar stationary density profile as measured by Thomson scattering. For discharges with negative magnetic shear, an observed rise of the safety factor in the vicinity of the magnetic axis appears to be accompanied by a decrease of electron density, qualitatively consistent with the theoretical expectations.
    Physics of Plasmas 12/2012; 19(12). DOI:10.1063/1.4773215 · 2.25 Impact Factor
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    ABSTRACT: Transport in ohmically heated plasmas in Alcator C-Mod was studied in both the linear (LOC) and saturated (SOC) ohmic L-mode confinement regimes and the importance of turbulent transport in the region r/a = 0.5–0.8 was established. After an extensive analysis with TGLF and GYRO, it is found that using an effective impurity ion species with Zi = 8, and moderately high Zeff (2.0–5.6), in the LOC regime electron transport becomes dominant due to TEM turbulence. The key ingredient in the present results is the observation that dilution of the main ion species (deuterium) by impurity species of moderate charge state reduces dominant ITG turbulence, in contrast to the SOC regime with little, if any dilution. The turbulent spectrum measured with the phase contrast imaging (PCI) diagnostic is in qualitative agreement with predictions of a synthetic PCI diagnostic adopted to Global GYRO. The toroidal rotation in the low-density LOC regime is in the co-current direction but as the density is raised in the SOC regime the rotation reverses to the counter current drive direction. The impurity content of the plasma was measured recently and an effective Zi of 9 was deduced.
    Plasma Physics and Controlled Fusion 11/2012; 54(12):124029. DOI:10.1088/0741-3335/54/12/124029 · 2.39 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. DOI:10.1016/j.jcp.2013.02.041 · 2.49 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.
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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.
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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).
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    ABSTRACT: Previous investigations of ITG and TEM/ETG turbulence using the reduced gyro-landau fluid code TGLF, and gyrokinetic code GYRO have predicted that in the linear ohmic confinement (LOC) regime in Alcator C-Mod the dilution of the main D ion species by low-Z impurities reduces the ion transport to experimentally observed levels. This analysis assumed an average impurity ion charge Zi= 8. Recent spectroscopic measurements of the impurity ion species in the LOC regime in C-Mod have shown that the average Zi is approximately 9, which at the measured Zeff values (2-4) results in a significant dilution (>10%) of the majority D ion species. By puffing in nitrogen while using a cryopump to keep the density constant, new experiments enabled us to lower Zi to values near 8, thus further increasing dilution. To account for the sensitivity of the turbulent transport on the density (Lne) and temperature (LTe) gradient scale lengths, recently we used TGYRO to improve the agreement between theory and the measurements. The results of such simulations will be presented.
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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). DOI:10.1088/0741-3335/54/11/115006 · 2.39 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.
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    ABSTRACT: Nonlinear gyrokinetic simulations of impurity transport are compared to experimental impurity transport for the first time. The GYRO code (Candy and Waltz 2003 J. Comput. Phys.186 545) was used to perform global, nonlinear gyrokinetic simulations of impurity transport for a standard Alcator C-Mod, L-mode discharge. The laser blow-off technique was combined with soft x-ray measurements of a single charge state of calcium to provide time-evolving profiles of this non-intrinsic, non-recycling impurity over a radial range of 0.0 ⩽ r/a ⩽ 0.6. Experimental transport coefficient profiles and their uncertainties were extracted from the measurements using the impurity transport code STRAHL and rigorous Monte Carlo error analysis. To best assess the agreement of gyrokinetic simulations with the experimental profiles, the sensitivity of the GYRO predicted impurity transport to a wide range of turbulence-relevant plasma parameters was investigated. A direct comparison of nonlinear gyrokinetic simulation and experiment is presented with an in depth discussion of error sources and a new data analysis methodology.
    Nuclear Fusion 06/2012; 52(6). DOI:10.1088/0029-5515/52/6/063002 · 3.24 Impact Factor
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    ABSTRACT: Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.
    Physics of Plasmas 05/2012; 19(5). DOI:10.1063/1.3694113 · 2.25 Impact Factor
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    ABSTRACT: Ohmic energy confinement saturation is found to be closely related to core toroidal rotation reversals in Alcator C-Mod tokamak plasmas. Rotation reversals occur at a critical density, depending on the plasma current and toroidal magnetic field, which coincides with the density separating the linear Ohmic confinement regime from the saturated Ohmic confinement regime. The rotation is directed co-current at low density and abruptly changes direction to counter-current when the energy confinement saturates as the density is increased. Since there is a bifurcation in the direction of the rotation at this critical density, toroidal rotation reversal is a very sensitive indicator in the determination of the regime change. The reversal and confinement saturation results can be unified, since these processes occur in a particular range of the collisionality.
    Physics of Plasmas 05/2012; 19(5). DOI:10.1063/1.3695213 · 2.25 Impact Factor
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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 05/2012; 19(5). DOI:10.1063/1.3694668 · 2.25 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.

Publication Stats

1k Citations
185.24 Total Impact Points

Institutions

  • 1995–2014
    • Massachusetts Institute of Technology
      • Plasma Science and Fusion Center (PSFC)
      Cambridge, Massachusetts, United States
  • 2006
    • Cornell University
      • Department of Physics
      Итак, New York, United States
  • 1994–2006
    • Princeton University
      • Princeton Plasma Physics Laboratory
      Princeton, NJ, United States
  • 2004
    • University of Maryland, College Park
      Maryland, United States
  • 1997
    • Columbia University
      • Department of Applied Physics and Applied Mathematics
      New York, New York, United States