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Journal ArticleDOI

Comparisons and physics basis of tokamak transport models and turbulence simulations

TL;DR: In this paper, the authors compared the performance of gyrokinetic and gyrofluid simulations of ion-temperature gradient (ITG)instability and turbulence in tokamak plasmas as well as some tokak plasma thermal transportmodels.
Abstract: The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient(ITG)instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transportmodels, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the models show good agreements in their predictions and assumptions for the linear growth rates and frequencies. There are some differences associated with different equilibria. However, there are significant differences in the transport levels between the models. The causes of some of the differences are examined in some detail, with particular attention to numerical convergence in the turbulence simulations (with respect to simulation mesh size, system size and, for particle-based simulations, the particle number). The implications for predictions of fusion plasma performance are also discussed.
Citations
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Journal ArticleDOI
TL;DR: A comprehensive review of zonal flow phenomena in plasmas is presented in this article, where the focus is on zonal flows generated by drift waves and the back-interaction of ZF on the drift waves, and various feedback loops by which the system regulates and organizes itself.
Abstract: A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.

1,739 citations

Journal ArticleDOI
TL;DR: The nonlinear gyrokinetic equations play a fundamental role in our understanding of the long-time behavior of strongly magnetized plasmas as mentioned in this paper, and they have been used to describe the turbulent evolution of low-frequency electromagnetic fluctuations in a nonuniform magnetization with arbitrary magnetic geometry.
Abstract: Nonlinear gyrokinetic equations play a fundamental role in our understanding of the long-time behavior of strongly magnetized plasmas. The foundations of modern nonlinear gyrokinetic the- ory are based on three important pillars: (1) a gyrokinetic Vlasov equation written in terms of a gyrocenter Hamiltonian with quadratic low-frequency ponderomotive-like terms; (2) a set of gyrokinetic Maxwell (Poisson-Ampere) equations written in terms of the gyrocenter Vlasov dis- tribution that contain low-frequency polarization (Poisson) and magnetization (Ampere) terms derived from the quadratic nonlinearities in the gyrocenter Hamiltonian; and (3) an exact energy conservationlaw for the gyrokineticVlasov-Maxwell equations that includes all the relevant linear and nonlinear coupling terms. The foundations of nonlinear gyrokinetic theory are reviewed with an emphasis on the rigorous applications of Lagrangian and Hamiltonian Lie-transform perturba- tion methods used in the variationalderivationof nonlineargyrokineticVlasov-Maxwell equations. The physical motivations and applications of the nonlinear gyrokinetic equations, which describe the turbulent evolution of low-frequency electromagnetic fluctuations in a nonuniform magnetized plasmas with arbitrary magnetic geometry, are also discussed.

1,010 citations

Journal ArticleDOI
TL;DR: In this article, collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations via two massively parallel, fully gyrokinetic Vlasov codes.
Abstract: Collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations To this aim, two massively parallel, fully gyrokinetic Vlasov codes are used, both including electromagnetic effects Somewhat surprisingly, and unlike in the analogous case of ion-temperature-gradient-driven (ITG) turbulence, we find that the turbulent electron heat flux is significantly underpredicted by simple mixing length estimates in a certain parameter regime (ŝ∼1, low α) This observation is directly linked to the presence of radially highly elongated vortices (“streamers”) which lead to very effective cross-field transport The simulations therefore indicate that ETG turbulence is likely to be relevant to magnetic confinement fusion experiments

946 citations

Journal ArticleDOI
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

Journal Article
TL;DR: The advantages of nuclear fusion as an energy source and research progress in this area are summarized in this article, where the current state of the art is described, including the Compact Ignition Tokamak (CIT), International Thermonuclear Experimental Reactor (ITER), and a US design called TIBER II.
Abstract: The advantages of nuclear fusion as an energy source and research progress in this area are summarized. The current state of the art is described. Laser fusion, inertial confinement fusion, and magnetic fusion (the tokamak) are explained, the latter in some detail. Remaining problems and planned future reactors are considered. They are the Compact Ignition Tokamak (CIT), the International Thermonuclear Experimental Reactor (ITER), and a US design called TIBER II. The design of the latter is shown. >

596 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
18 Sep 1998-Science
TL;DR: Three-dimensional gyrokinetic simulations of microturbulence in magnetically confined toroidal plasmas with massively parallel computers showed that, with linear flow damping, an asymptotic residual flow develops in agreement with analytic calculations.
Abstract: Three-dimensional gyrokinetic simulations of microturbulence in magnetically confined toroidal plasmas with massively parallel computers showed that, with linear flow damping, an asymptotic residual flow develops in agreement with analytic calculations. Nonlinear global simulations of instabilities driven by temperature gradients in the ion component of the plasma support the view that turbulence-driven fluctuating zonal flows can substantially reduce turbulent transport. Finally, the outstanding differences in the flow dynamics observed in global and local simulations are found to be due to profile variations.

921 citations

Journal ArticleDOI
TL;DR: A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed in this paper.
Abstract: A nonlinear gyrokinetic formalism for low‐frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed The nonlinear equations thus derived are valid in the strong‐turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magnetic field geometries The specific case of axisymmetric tokamaks is then considered and a model nonlinear equation is derived for electrostatic drift waves Also, applying the formalism to the shear Alfven wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear‐Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects In particular, wave energy is found to cascade in wavenumber instead of frequency

763 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that linear collisionless processes do not damp poloidal flows driven by ion-temperature-gradient (ITG) turbulence, since these flows play an important role in saturating the level of the turbulence.
Abstract: We show that linear collisionless processes do not damp poloidal flows driven by ion-temperature-gradient (ITG) turbulence. Since these flows play an important role in saturating the level of the turbulence, this level, as well as the transport caused by ITG modes, may be overestimated by gyrofluid simulations, which employ linear collisionless rotation damping.

607 citations

Journal Article
TL;DR: The advantages of nuclear fusion as an energy source and research progress in this area are summarized in this article, where the current state of the art is described, including the Compact Ignition Tokamak (CIT), International Thermonuclear Experimental Reactor (ITER), and a US design called TIBER II.
Abstract: The advantages of nuclear fusion as an energy source and research progress in this area are summarized. The current state of the art is described. Laser fusion, inertial confinement fusion, and magnetic fusion (the tokamak) are explained, the latter in some detail. Remaining problems and planned future reactors are considered. They are the Compact Ignition Tokamak (CIT), the International Thermonuclear Experimental Reactor (ITER), and a US design called TIBER II. The design of the latter is shown. >

596 citations