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W.M. Solomon

Bio: W.M. Solomon is an academic researcher from Princeton Plasma Physics Laboratory. The author has contributed to research in topics: Tokamak & Rotation. The author has an hindex of 16, co-authored 34 publications receiving 827 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the rotation measurements were found to be consistent with the radial electric field determined independently from multiple impurity species as well as from motional Stark effect spectroscopic measurements.
Abstract: Despite the importance of rotation in fusion plasmas, our present understanding of momentum transport is inadequate. The lack of understanding is in part related to the difficulty of performing accurate rotation measurements, especially for poloidal rotation. Recently, measurements of poloidal rotation for impurity ions (Z>1) have been obtained in the core of DIII-D [J. L. Luxon, Nucl. Fusion 42, 6114 (2002)] plasmas using charge exchange recombination spectroscopy. The inferred poloidal rotation is based on careful consideration of the effective energy-dependent cross section and of the gyromotion of the ions. The rotation measurements are found to be consistent with the radial electric field determined independently from multiple impurity species as well as from motional Stark effect spectroscopic measurements. The poloidal rotation measurements have been compared with predictions based on the neoclassical theory of poloidal rotation from the code NCLASS [W. A. Houlberg et al., Phys. Plasmas 4, 3230 (1997)]. The comparison shows that the neoclassically predicted poloidal rotation is in general significantly smaller than the actual measurements.

112 citations

Journal ArticleDOI
TL;DR: In the absence of any auxiliary torque input, the DIII-D plasma consists of nonzero toroidal angular momentum, in other words, it rotates as mentioned in this paper, which is referred to as intrinsic rotation.
Abstract: In the absence of any auxiliary torque input, the DIII-D plasma consists of nonzero toroidal angular momentum, in other words, it rotates. This effect is commonly observed in tokamaks, being referred to as intrinsic rotation. Measurements of intrinsic rotation profiles have been made in DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] H-mode discharges, with both Ohmic heating (OH) and electron cyclotron heating (ECH) in which there is no auxiliary torque. Recently, the H-mode data set has been extended with the newly configured DIII-D simultaneous co- and counter-directed neutral beam injection (NBI) capability resulting in control of the local torque deposition, where co and counter refer to the direction relative to the toroidal plasma current. Understanding intrinsic rotation is important for projection toward burning plasma performance where any NBI torque will be relatively small. The toroidal velocity is recognizably important regarding issues of stability and confinement. In DIII-D ECH H-modes the r...

112 citations

Journal ArticleDOI
TL;DR: Luxon et al. as mentioned in this paper measured the main ion rotation in deuterium plasmas, particularly in regions of the plasma with steep pressure gradients where very large differences can be expected between bulk ion and impurity rotation.
Abstract: Bulk ion toroidal rotation plays a critical role in controlling microturbulence and MHD stability as well as yielding important insight into angular momentum transport and the investigation of intrinsic rotation. So far, our understanding of bulk plasma flow in hydrogenic plasmas has been inferred from impurity ion velocity measurements and neoclassical theoretical calculations. However, the validity of these inferences has not been tested rigorously through direct measurement of the main-ion rotation in deuterium plasmas, particularly in regions of the plasma with steep pressure gradients where very large differences can be expected between bulk ion and impurity rotation. New advances in the analysis of wavelength-resolved Dα emission on the DIII-D tokamak [J. L. Luxon et al., Fusion Sci. Technol. 48, 807 (2002)] have enabled accurate measurements of the main-ion (deuteron) temperature and toroidal rotation. The Dα emission spectrum is accurately fit using a model that incorporates thermal deuterium char...

62 citations

Journal ArticleDOI
TL;DR: In this article, the impurity transport in the DIII-D tokamak was investigated in stationary high confinement (H-mode) regimes without edge localized modes (ELMs).
Abstract: Impurity transport in the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] is investigated in stationary high confinement (H-mode) regimes without edge localized modes (ELMs). In plasmas maintained by resonant magnetic perturbation (RMP), ELM-suppression, and QH-mode, the confinement time of fluorine (Z = 9) is equivalent to that in ELMing discharges with 40 Hz ELMs. For selected discharges with impurity injection, the impurity particle confinement time compared to the energy confinement time is in the range of τp/τe≈2−3. In QH-mode operation, the impurity confinement time is shown to be smaller for intense, coherent magnetic, and density fluctuations of the edge harmonic oscillation than weaker fluctuations. Transport coefficients are derived from the time evolution of the impurity density profile and compared to neoclassical and turbulent transport models NEO and TGLF. Neoclassical transport of fluorine is found to be small compared to the experimental values. In the ELMing and RMP ELM-suppress...

54 citations

Journal ArticleDOI
TL;DR: In this paper, the stability limits in plasmas with core transport barriers have been observed at moderate values of βN (<3) because of the pressure peaking which normally develops from improved core confinement.
Abstract: High values of normalized β (βN∼4) and safety factor (qmin∼2) have been sustained simultaneously for ∼2s in DIII-D [J.L. Luxon, Nucl. Fusion 42, 64 (2002)], suggesting a possible path to high fusion performance, steady-state tokamak scenarios with a large fraction of bootstrap current. The combination of internal transport barrier and negative central magnetic shear at high β results in high confinement (H89P>2.5) and large bootstrap current fraction (fBS>60%) with good alignment. Previously, stability limits in plasmas with core transport barriers have been observed at moderate values of βN (<3) because of the pressure peaking which normally develops from improved core confinement. In recent DIII-D experiments, the internal transport barrier is clearly observed in the electron density and in the ion temperature and rotation profiles at ρ∼0.5 but not in the electron temperature profile, which is very broad. The misalignment of Ti and Te gradients may help to avoid a large local pressure gradient. Furtherm...

54 citations


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TL;DR: Alfven wave instability in toroidally confined plasmas is studied in this paper, where the authors identify three types of Alfven wave instabilities: frequency crossings of counterpropagating waves, extremum of the continuous spectrum, and reversed shear Alfven eigenmode.
Abstract: Superthermal energetic particles (EP) often drive shear Alfven waves unstable in magnetically confined plasmas. These instabilities constitute a fascinating nonlinear system where fluid and kinetic nonlinearities can appear on an equal footing. In addition to basic science, Alfven instabilities are of practical importance, as the expulsion of energetic particles can damage the walls of a confinement device. Because of rapid dispersion, shear Alfven waves that are part of the continuous spectrum are rarely destabilized. However, because the index of refraction is periodic in toroidally confined plasmas, gaps appear in the continuous spectrum. At spatial locations where the radial group velocity vanishes, weakly damped discrete modes appear in these gaps. These eigenmodes are of two types. One type is associated with frequency crossings of counterpropagating waves; the toroidal Alfven eigenmode is a prominent example. The second type is associated with an extremum of the continuous spectrum; the reversed shear Alfven eigenmode is an example of this type. In addition to these normal modes of the background plasma, when the energetic particle pressure is very large, energetic particle modes that adopt the frequency of the energetic particle population occur. Alfven instabilities of all three types occur in every toroidal magnetic confinement device with an intense energetic particle population. The energetic particles are most conveniently described by their constants of motion. Resonances occur between the orbital frequencies of the energetic particles and the wave phase velocity. If the wave resonance with the energetic particle population occurs where the gradient with respect to a constant of motion is inverted, the particles transfer energy to the wave, promoting instability. In a tokamak, the spatial gradient drive associated with inversion of the toroidal canonical angular momentum Pζ is most important. Once a mode is driven unstable, a wide variety of nonlinear dynamics is observed, ranging from steady modes that gradually saturate, to bursting behavior reminiscent of relaxation oscillations, to rapid frequency chirping. An analogy to the classic one-dimensional problem of electrostatic plasma waves explains much of this phenomenology. EP transport can be convective, as when the wave scatters the particle across a topological boundary into a loss cone, or diffusive, which occurs when islands overlap in the orbital phase space. Despite a solid qualitative understanding of possible transport mechanisms, quantitative calculations using measured mode amplitudes currently underestimate the observed fast-ion transport. Experimentally, detailed identification of nonlinear mechanisms is in its infancy. Beyond validation of theoretical models, the future of the field lies in the development of control tools. These may exploit EP instabilities for beneficial purposes, such as favorably modifying the current profile, or use modest amounts of power to govern the nonlinear dynamics in order to avoid catastrophic bursts.

431 citations

Journal ArticleDOI
TL;DR: The robust, robust, compact (ARC) as discussed by the authors is the product of a conceptual design study aimed at reducing the size, cost and complexity of a combined fusion nuclear science facility (FNSF) and demonstration fusion Pilot power plant.

340 citations

Journal ArticleDOI
TL;DR: In this article, the intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases.
Abstract: Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with M-A alpha beta(N), although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with beta(N) = 2.6, an intrinsic rotation Alfven Mach number of M-A similar or equal to 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input.

305 citations

Journal ArticleDOI
TL;DR: In this article, a heuristic model for the plasma scrape-off width in low-gas-puff tokamak H-mode plasmas is introduced, which is a modification for open field lines of Pfirsch- Schl¨ uter flows to include order-unity sinks to the divertors.
Abstract: A heuristic model for the plasma scrape-off width in low-gas-puff tokamak H-mode plasmas is introduced. Grad B and curv B drifts into the scrape-off layer (SOL) are balanced against near-sonic parallel flows out of the SOL, to the divertor plates. The overall particle flow pattern posited is a modification for open field lines of Pfirsch‐ Schl¨ uter flows to include order-unity sinks to the divertors. These assumptions result in an estimated SOL width of ∼2aρp/R. They also result in a first-principles calculation of the particle confinement time of H-mode plasmas, qualitatively consistent with experimental observations. It is next assumed that anomalous perpendicular electron thermal diffusivity is the dominant source of heat flux across the separatrix, investing the SOL width, derived above, with heat from the main plasma. The separatrix temperature is calculated based on a two-point model balancing power input to the SOL with Spitzer‐H¨ arm parallel thermal conduction losses to the divertor. This results in a heuristic closed-form prediction for the power scrape-off width that is in reasonable quantitative agreement both in absolute magnitude and in scaling with recent experimental data. Further work should include full numerical calculations, including all magnetic and electric drifts, as well as more thorough comparison with experimental data. (Some figures may appear in colour only in the online journal)

304 citations

Journal Article
TL;DR: In this paper, a new theory-based transport model with comprehensive physics (trapping, general toroidal geometry, fully electromagnetic, electron-ion collisions, impurity ions) has been developed.
Abstract: A new theory-based transport model with comprehensive physics (trapping, general toroidal geometry, fully electromagnetic, electron-ion collisions, impurity ions) has been developed. The core of the model is the new trapped-gyro-Landau-fluid (TGLF) equations, which provide a fast and accurate approximation to the linear eigenmodes for gyrokinetic drift-wave instabilities (trapped ion and electron modes, ion and electron temperature gradient modes, and kinetic ballooning modes). The new TGLF transport model is more accurate, and has an extended range of validity, compared to its predecessor GLF23. The TGLF model unifies trapped and passing particles in a single set of gyro-Landau-fluid equations. A model for the averaging of the Landau resonance by the trapped particles makes the equations work seamlessly over the whole drift-wave wave-number range from trapped ion modes to electron temperature gradient modes. A fast eigenmode solution method enables unrestricted magnetic geometry. The transport model uses...

246 citations