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W. A. Houlberg

Bio: W. A. Houlberg is an academic researcher from Oak Ridge National Laboratory. The author has contributed to research in topics: Tokamak & Collisionality. The author has an hindex of 4, co-authored 4 publications receiving 799 citations.

Papers
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TL;DR: In this article, a multi-species fluid model is described for the steady state parallel and radial force balance equations in axisymmetric tokamak plasmas, and the bootstrap current, electrical resistivity and particle and heat fluxes are evaluated in terms of the rotation velocities and friction and viscosity coefficients.
Abstract: A multi-species fluid model is described for the steady state parallel and radial force balance equations in axisymmetric tokamak plasmas. The bootstrap current, electrical resistivity, and particle and heat fluxes are evaluated in terms of the rotation velocities and friction and viscosity coefficients. A recent formulation of the neoclassical plasma viscosity for arbitrary shape and aspect ratio (including the unity aspect ratio limit), arbitrary collisionality, and orbit squeezing from strong radial electric fields is used to illustrate features of the model. The bootstrap current for the very low aspect ratio National Spherical Torus Experiment [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] is compared with other models; the largest differences occur near the plasma edge from treatment of the collisional contributions. The effects of orbit squeezing on bootstrap current, thermal and particle transport, and poloidal rotation are illustrated for an enhanced reverse shear plasma in the Tokamak Fusion Test Reactor [D. Meade and the TFTR Group, Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, p. 9]. Multiple charge states of impurities are incorporated using the reduced ion charge state formalism for computational efficiency. Because the force balance equations allow for inclusion of external momentum and heat sources and sinks they can be used for general plasma rotation studies while retaining the multi-species neoclassical effects.

568 citations

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TL;DR: In this article, the poloidal momentum balance equation in tokamaks was shown to have bifurcated solutions; the up-down poloidal flow velocity Up can suddenly become more positive when the ion collisionality decreases.
Abstract: The poloidal momentum balance equation in tokamaks is shown to have bifurcated solutions; the poloidal flow velocity Up can suddenly become more positive when the ion collisionality decreases. The corresponding radial electric field Er becomes more negative, suppresses turbulent fluctuations, and improves plasma confinement. A heuristic argument is employed to illustrate the effects of Er on turbulent fluctuations. A more negative value of Er and/or a more positive value of dEr /dr can suppress the fluctuation amplitudes, if dP/dr<0 (with r the local minor raidus and P the plasma pressure). The theory is employed to explain the L–H transition observed in tokamaks.

240 citations

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TL;DR: In this article, it was shown that toroidal magnetic fleld ripple induced particle ∞ux can drive poloidal E£B speed to bifurcate over the local maximum of the nonlinear poloidal (or parallel) viscosity.
Abstract: It is shown that toroidal magnetic fleld ripple induced particle ∞ux can drive poloidal E£B speed to bifurcate over the local maximum of the nonlinear poloidal (or parallel) viscosity. Here,E is the electric fleld andB is the magnetic fleld. This mechansim, together with the turbulence suppression due to the radial gradient of the E£B and diamagnetic angular velocity, is employed to explain enhanced reversed shear mode observed in the core region of tokamaks.

22 citations


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TL;DR: The ExB shear stabilization model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition as mentioned in this paper.
Abstract: One of the scientific success stories of fusion research over the past decade is the development of the ExB shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high)-mode to VH (very high)-mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with ExB velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of ExB shear on the growth, radial extent and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number ways to change the radial electric field Er. An important theme in this area is the synergistic effect of ExB velocity shear and magnetic shear. Although the ExB velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of ExB velocity shear and facilitate turbulence stabilization.

1,251 citations

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TL;DR: The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions.
Abstract: The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

798 citations

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TL;DR: In this article, a code solving the Fokker-planck equation with the full collision operator and including the variation along the magnetic field line, coupled with the adjoint function formalism, has been used to calculate these coefficients in arbitrary equilibrium and collisionality regimes.
Abstract: Expressions for the neoclassical resistivity and the bootstrap current coefficients in terms of aspect ratio and collisionality are widely used in simulating toroidal axisymmetric equilibria and transport evolution. The formulas used are in most cases based on works done 15–20 years ago, where the results have been obtained for large aspect ratio, small or very large collisionality, or with a reduced collision operator. The best expressions to date and to our knowledge are due to Hirshman [S. P. Hirshman, Phys. Fluids 31, 3150 (1988)] for arbitrary aspect ratio in the banana regime and Hinton–Hazeltine [F. L. Hinton and R. D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976)] for large aspect ratio and arbitrary collisionality regime. A code solving the Fokker–Planck equation with the full collision operator and including the variation along the magnetic field line, coupled with the adjoint function formalism, has been used to calculate these coefficients in arbitrary equilibrium and collisionality regimes. The coefficients have been obtained for a wide variety of plasma and equilibrium parameters and a comprehensive set of formulas, which have been fitted to the code results within 5%, is proposed for evaluating the neoclassical conductivity and the bootstrap current coefficients. This extends previous works and also highlights inaccuracies in the previous formulas in this wide plasma parameter space.

763 citations

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TL;DR: In this paper, the suppression of turbulence by the E×B flow shear and parallel Flow Shear in an arbitrary shape finite aspect ratio tokamak plasma using the two point nonlinear analysis was investigated.
Abstract: The suppression of turbulence by the E×B flow shear and parallel flow shear is studied in an arbitrary shape finite aspect ratio tokamak plasma using the two point nonlinear analysis previously utilized in a high aspect ratio tokamak plasma [Phys. Plasmas 1, 2940 (1994)]. The result shows that only the E×B flow shear is responsible for the suppression of flute‐like fluctuations. This suppression occurs regardless of the plasma rotation direction and is, therefore, relevant for the very high (VH) mode plasma core as well as for the high (H) mode plasma edge. Experimentally observed in–out asymmetry of fluctuation reduction behavior can be addressed in the context of flux expansion and magnetic field pitch variation on a given flux surface. The adverse effect of neutral particles on confinement improvement is also discussed in the context of the charge exchange induced parallel momentum damping.

552 citations

Journal ArticleDOI
TL;DR: In this paper, the authors reviewed the physics of diveror in tokamaks from an experimental point of view, although where possible simple analytic modelling is included, and provided a framework for comparison of the experimental results with simply derived expectations.
Abstract: The physics of divertors in tokamaks is reviewed, primarily from an experimental point of view, although where possible simple analytic modelling is included. The paper covers the four main subject areas at issue in divertor research: (1) the wide dispersal of plasma power exhausted from the main plasma, (2) the production of sufficiently high gas pressures in the vicinity of pump ducts to enable the removal of fuel and helium (`ash') gas from the system, (3) the elimination or reduction of impurity production and (4) the screening of impurities produced, or intentionally added, at the plasma boundary from the plasma core. A simple analytic model, the `two-point' model, is introduced early in the paper and provides a framework for comparison of the experimental results, drawn from many machines, with simply derived expectations. Conclusions regarding the direction of future research priorities are made.

362 citations