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Microinstability-based model for anomalous thermal confinement in tokamaks

Description: This paper deals with the formulation of microinstability-based thermal transport coefficients (chi/sub j/) for the purpose of modelling anomalous energy confinement properties in tokamak plasmas. Attention is primarily focused on ohmically heated discharges and the associated anomalous electron thermal transport. An appropriate expression for chi/sub e/ is developed which is consistent with reasonable global constraints on the current and electron temperature profiles as well as with the key properties of the kinetic instabilities most likely to be present. Comparisons of confinement scaling trends predicted by this model with the empirical ohmic data base indicate quite favorable agreement. The subject of anomalous ion thermal transport and its implications for high density ohmic discharges and for auxiliary-heated plasmas is also addressed.
Date: March 1, 1986
Creator: Tang, W.M.
Partner: UNT Libraries Government Documents Department

Kinetic studies of anomalous transport

Description: Progress in achieving a physics-based understanding of anomalous transport in toroidal systems has come in large part from investigations based on the proposition that low frequency electrostatic microinstabilities are dominant in the bulk ( confinement'') region of these plasmas. Although the presence here of drift-type modes dependent on trapped particle and ion temperature gradient driven effects appears to be consistent with a number of important observed confinement trends, conventional estimates for these instabilities cannot account for the strong current (I{sub p}) and /or q-scaling frequently found in empirically deduced global energy confinement times for auxiliary-heated discharges. The present paper deals with both linear and nonlinear physics features, ignored in simpler estimates, which could introduce an appreciable local dependence on current. It is also pointed out that while the thermal flux characteristics of drift modes have justifiably been the focus of experimental studies assessing their relevance, other transport properties associated with these microinstabilities should additionally be examined. Accordingly, the present paper provides estimates and discusses the significance of anomalous energy exchange between ions and electrons when fluctuations are present. 19 refs., 3 figs.
Date: November 1, 1990
Creator: Tang, W.M.
Partner: UNT Libraries Government Documents Department

Toroidal microinstability studies of high temperature tokamaks

Description: Results from comprehensive kinetic microinstability calculations are presented showing the effects of toroidicity on the ion temperature gradient mode and its relationship to the trapped-electron mode in high-temperature tokamak plasmas. The corresponding particle and energy fluxes have also been computed. It is found that, although drift-type microinstabilities persist over a wide range of values of the ion temperature gradient parameter /eta//sub i/ /equivalent to/ (dlnT/sub i//dr)/(dlnn/sub i//dr), the characteristic features of the dominant mode are those of the /eta//sub i/-type instability when /eta//sub i/ > /eta//sub ic/ /approximately/1.2 to 1.4 and of the trapped-electron mode when /eta//sub i/ < /eta//sub ic/. 16 refs., 7 figs.
Date: July 1, 1989
Creator: Rewoldt, G. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Influence of anomalous thermal losses of ignition conditions

Description: In the process of achieving ignition conditions, it is likely that microinstabilities, which lead to anomalous thermal transport of the fusing nuclei, will be present. When such phenomena are taken into account, an appropriate formulation of ignition criteria becomes necessary. In particular, a new type of plasma density limit is identified.
Date: May 1, 1986
Creator: Coppi, B. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Electron energy transport and magnetic curvature driven modes

Description: A transport coefficient for anomalous electron thermal conduction is constructed on the basis of the so-called Principle of Profile Consistency. It is assumed that the relevant modes in plasma where a substantial fraction of the electron population is magnetically trapped produce magnetic reconnection at a microscopic level and are driven by the combined effects of the plasma pressure gradient and the magnetic field curvature. Consequently, the scaling for the electron energy confinement time exhibits a strongly favorable dependence on the radius of magnetic curvature.
Date: October 1, 1984
Creator: Coppi, B. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Influence of hot beam ions on MHD ballooning modes in tokamaks

Description: It has recently been proposed that the presence of high energy ions from neutral beam injection can have a strong stabilizing effect on kinetically-modified ideal MHD ballooning modes in tokamaks. In order to assess realistically the importance of such effects, a comprehensive kinetic stability analysis, which takes into account the integral equation nature of the basic problem, has been applied to this investigation. In the collisionless limit, the effect of adding small fractions of hot beam ions is indeed found to be strongly stabilizing. On the other hand, for somewhat larger fractions of hot ions, a new beam-driven mode is found to occur with a growth rate comparable in magnitude to the growth rate of the MHD ballooning mode in the absence of hot ions. This implies that there should be an optimal density of hot particles which minimizes the strength of the relevant instabilities. Employing non-Maxwellian equilibrium distribution functions to model the beam species makes a quantitative, but not qualitative, difference in the results. Adding collisions to the calculation tends to reduce considerably the stabilizing effect of the hot ions.
Date: July 1, 1984
Creator: Rewoldt, G. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Kinetic and resistive effects on interchange instabilities for a cylindrical model spheromak

Description: The stabilizing influence of diamagnetic drift effects on ideal and resistive interchange modes is investigated. A resistive-ballooning-mode equation is derived using a kinetic theory approach and is applied to a cylindrical model spheromak equilibrium. It is found that these kinetic effects can significantly improve the ..beta.. limits for collisionless interchange stability. For the resistive modes, the diamagnetic drift terms lead to growth rates which scale linearly with resistivity and are considerably reduced in magnitude. However, the resistive interchange growth rates estimated for near-term spheromak parameters remain significant.
Date: April 1, 1983
Creator: Hammett, G.W. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Two-dimensional analysis of trapped-ion eigenmodes

Description: A fully two-dimensional eigenmode analysis of the trapped-ion instability in axisymmetric toroidal geometry is presented. The calculations also takes into account the basic dynamics associated with other low frequency modes such as the trapped-electron instability and the ion-temperature-gradient instability. The poloidal structure of the mode is taken into account by Fourier expanding the perturbed electrostatic potential, PHI, in theta.
Date: November 1, 1979
Creator: Marchand, R.; Tang, W.M. & Rewoldt, G.
Partner: UNT Libraries Government Documents Department

Doppler model for adiabatic toroidal compressor driftwave frequency profiles

Description: Microwave and CO/sub 2/ laser scattering experiments on ATC (Adiabatic Toroidal Compressor) Tokamak have shown that there exists a spectrum of fluctuations with parallel bar f parallel bar = parallel bar ..omega../2..pi.. parallel bar less than or equal to 1 MHz at wavelengths lambda approximately 0.28 cm and with parallel bar f parallel bar less than or equal to 400 kHz for lambda approximately 1 cm. However, a typical maximum frequency calculated for given experimental density and temperature profiles is f less than or equal to 150 kHz for the longer wavelengths and differs with the experimental results by roughly a factor of 2 or 3. At shorter wavelengths the calculated maximum f is less than or equal to 100 kHz, which differs quite substantially with the experimental result. This discrepancy is interpreted as evidence of vector E x vector B Doppler shift from a radial electric field.
Date: October 1, 1977
Creator: Koch, R.A. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Microinstabilities in weak density gradient tokamak systems

Description: A prominent characteristic of auxiliary-heated tokamak discharges which exhibit improved (''H-mode type'') confinement properties is that their density profiles tend to be much flatter over most of the plasma radius. Depsite this favorable trend, it is emphasized here that, even in the limit of zero density gradient, low-frequency microinstabilities can persist due to the nonzero temperature gradient.
Date: April 1, 1986
Creator: Tang, W.M.; Rewoldt, G. & Chen, L.
Partner: UNT Libraries Government Documents Department

Gyrokinetic particle simulation of ion temperature gradient drift instabilities

Description: Ion temperature gradient drift instabilities have been investigated using gyrokinetic particle simulation techniques for the purpose of identifying the mechanisms responsible for their nonlinear saturation as well as the associated anomalous transport. For simplicity, the simulation has been carried out in a shear-free slab geometry, where the background pressure gradient is held fixed in time to represent quasistatic profiles typical of tokamak discharges. It is found that the nonlinearly generated zero-frequency responses for the ion parallel momentum and pressure are the dominant mechanisms giving rise to saturation. This is supported by the excellent agreement between the simulation results and those obtained from mode coupling calculations.
Date: April 1, 1987
Creator: Lee, W.W. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Properties of ion temperature gradient drift instabilities in H-mode plasmas

Description: Experimental results from tokamaks such as DIII-D and JET have indicated that the electron density profile in H-mode (''high- confinement'') discharges can be nearly flat over most of the plasma, and, in some cases, even inverted (outwardly peaked). These conditions have very interesting implications for pictures of anomalous thermal transport based on the presence of ion temperature gradient drift instabilities. The present paper includes a new derivation of the ion temperature gradient threshold for weak density gradient /eta//sub i/ modes when ion transit resonances are taken into account; and the first derivation of threshold conditions for the onset of /eta//sub i/-modes when /eta//sub i/ is negative along with the properties of these negative /eta//sub i/ instabilities when the thresholds are exceeded. Possible consequences for confinement in H-mode plasmas are discussed. 32 refs., 8 figs.
Date: November 1, 1988
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Destabilization of the trapped electron mode by magnetic curvature drift resonances

Description: Electron curvature drift resonances, ignored in earlier work on the trapped-electron modes, are found to exert a strong destabilizing influence in the lower collision frequency range of these instabilities. Effects arising from ion temperature gradients, shear, and finite ion gyroradius are included with these vector nebla-drifts in the analysis, and the resultant eigenvalue equation is solved by numerical procedures rather than the commonly used perturbation techniques. For typical tokamak parameters the maximum growth rates are found to be increased over earlier estimates by roughly a factor of 4, and requirements on magnetic shear strength for stabilization are likewise more severe and very difficult to satisfy. For inverted density profiles, this new destabilizing effect is rendered ineffective, with the result that the modes can be stabilized for achievable values of shear provided the temperature gradients are not too severe. Estimates of the particle and thermal energy transport are given for both normal and inverted profiles. (auth)
Date: December 1, 1975
Creator: Adam, J.C.; Tang, W.M. & Rutherford, P.H.
Partner: UNT Libraries Government Documents Department

Influence of radial electric field on Alfven-type instabilities

Description: The influence of the large scale radial electric field, E{sub r}{sup (0)} on the frequency of shear-Alfven-type instability is analyzed. A frozen-in-flux constraint and the moderate-{beta} ion gyrokinetic equation are used in the derivation. The analysis indicates that the frequency predicted by a theory with E{sub r}{sup (0)} effect should be Doppler-shifted by k {center_dot} V{sub E} for comparison to the experimentally observed frequency. A specific example of the practical relevance of the result is given regarding possible identification of the edge-localized-mode-associated magnetic activity recently observed in PBX-M tokamak experiment.
Date: March 1, 1994
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

IAEA Theory Summary 1998 IAEA Meeting, Yokohama, Japan - Oct. 17--24, 1998

Description: This is a summary of the advances in magnetic fusion energy theory research presented at the 17th International Atomic Energy Agency Fusion Energy Conference from 17--24 October, 1998 in Yokohama, Japan. Theory and simulation results from this conference provided encouraging evidence of significant progress in understanding the physics of thermonuclear plasmas. Indeed, the grand challenge for this field is to acquire the basic understanding that can readily enable the innovations which would make fusion energy practical. In this sense, as depicted in Fig. 1, research in fusion energy is increasingly able to be categorized as fitting well the ''Pasteur's Quadrant'' paradigm, where the research strongly couples basic science (''Bohr's Quadrant'') to technological impact (''Edison's Quadrant''). As supported by some of the work presented at this conference, this trend will be further enhanced by advanced simulations. Eventually, realistic three-dimensional modeling capabilities, when properly combined with rapid and complete data interpretation of results from both experiments and simulations, can contribute to a greatly enhanced cycle of understanding and innovation. Plasma science theory and simulation have provided reliable foundations for this improved modeling capability, and the exciting advances in high-performance computational resources have further accelerated progress.
Date: August 7, 2000
Creator: Tang, W.M.
Partner: UNT Libraries Government Documents Department

Nonlinear theory of collisionless trapped ion modes

Description: A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level {delta}n/n{sub 0} is lower than the conventional mixing length estimate, {Delta}r/L{sub n} (ii) the ion temperature fluctuation level {delta}T{sub i}/T{sub i} significantly exceeds the density fluctuation level {delta}n/n{sub 0}; and (iii) the parallel ion velocity fluctuation level {delta}v{sub i}{sub {parallel}}/v{sub Ti} is expected to be negligible.
Date: March 1, 1996
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

Description: The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.
Date: March 1, 1994
Creator: Artun, M. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Introduction to Gyrokinetic Theory with Applications in Magnetic Confinement Research in Plasma Physics

Description: The present lecture provides an introduction to the subject of gyrokinetic theory with applications in the area of magnetic confinement research in plasma physics--the research arena from which this formalism was originally developed. It was presented as a component of the ''Short Course in Kinetic Theory within the Thematic Program in Partial Differential Equations'' held at the Fields Institute for Research in Mathematical Science (24 March 2004). This lecture also discusses the connection between the gyrokinetic formalism and powerful modern numerical simulations. Indeed, simulation, which provides a natural bridge between theory and experiment, is an essential modern tool for understanding complex plasma behavior. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modeling. This was enabled by two key factors: (i) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (ii) access to powerful new computational resources.
Date: January 3, 2005
Creator: Tang, W.M.
Partner: UNT Libraries Government Documents Department

Influence of diamagnetic drifts on critical beta in tokamaks

Description: In specific cases the critical beta (..beta../sub c/) for stability against internal magnetohydrodynamic (MHD) ballooning modes can be improved significantly by taking into account the stabilizing influence of the ion diamagnetic drifts. This kinetic modification to the ideal MHD analysis together with radial corrections to the local theory are included in a calculation of ..beta../sub c/ as a function of toroidal mode number (n) for a particular tokamak equilibrium sequence of interest.
Date: May 1, 1982
Creator: Tang, W.M.; Dewar, R.L. & Manickam, J.
Partner: UNT Libraries Government Documents Department

Experimental investigation of the nonlinear evolution of an impurity-driven drift wave

Description: An impurity-driven drift wave is observed to be destabilized by the reversed density gradient of a singly-ionized heavy-impurity-ion population in a Q-machine plasma. The evolution of the instability is investigated as it progresses from the initial linear exponential growth phase, into a nonlinear saturated state, whereupon strong radially outward anomalous diffusion is observed. The relationship between the anomalous diffusion coefficient and the wave amplitude is in agreement with estimates obtained from the nonlinear drift-wave turbulence theory of Dupree.
Date: April 1, 1982
Creator: Allen, G.R.; Yamada, M.; Rewoldt, G. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Anomalous thermal confinement in ohmically heated tokamaks

Description: A model is proposed to explain the behavior of the gross energy confinement time in ohmically heated tokamak plasmas. The analysis takes into account the effect of the anomalous thermal conductivity due to small scale turbulence and of the macroscopic MHD behavior, which provides some constraints on the temperature profile. Results indicate that the thermal conductivity associated with the dissipative trapped-electron mode and with the ion temperature gradient (eta/sub i/) mode can account, respectively, for the Neo-Alcator scaling and the saturation of the energy confinement time with density. Comparisons with experimental results show reasonable agreement. 32 refs., 12 figs.
Date: February 1, 1986
Creator: Romanelli, F.; Tang, W.M. & White, R.B.
Partner: UNT Libraries Government Documents Department

Nonlinear evolution of drift instabilities in the presence of collisions

Description: Nonlinear evolution of drift instabilities in the presence of electron-ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation techniques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms responsible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift wave problems in more complicated geometries. The results indicate that the electron E x B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with ephi/T/sub e/ approx. = (..omega../sub l//..cap omega../sub i/)/(k/sub perpendicular/rho/sub s/)/sup 2/. The associated quasilinear diffusion, which increases with collisionality, takes the form of D/sub ql/ approx. = ..gamma../sub l//k/sub perpendicular//sup 2/, where ..omega../sub l/ and ..gamma../sub l/ are the linear frequency and growth rate, respectively. In the steady state, the diffusion process becomes stochastic in nature. The relevant mechanisms here are related to the velocity-space nonlinearities and background fluctuations. The magnitude of the diffusion at this stage can be comparable to that of quasilinear diffusion in the presence of collisions, and it remains finite even in the collisionless limit.
Date: July 1, 1986
Creator: Federici, J.F.; Lee, W.W. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Two-dimensional calculation of finite-beta modifications of drift and trapped-electron modes

Description: A previous electrostatic calculation for the two-dimensional spatial structure of drift and trapped-electron modes is extended to include finite-..beta.. effects. Specifically, the parallel perturbed vector potential and the parallel Ampere's law are added to the calculation. Illustrative results are presented.
Date: May 1, 1980
Creator: Rewoldt, G.; Tang, W.M. & Frieman, E.A.
Partner: UNT Libraries Government Documents Department