Two-fluid equilibria with flow
International Nuclear Information System (INIS)
Steinhauer, L.
1999-01-01
The formalism is developed for flowing two-fluid equilibria. The equilibrium system is governed by a pair of second order partial differential equations for the magnetic stream function and the ion stream function plus a Bernoulli-like equation for the density. There are six arbitrary surface function. There are separate characteristic surfaces for each species, which are the guiding-center surfaces. This system is a generalization of the familiar Grad-Shafranov system for a single-fluid equilibrium without flow, which has only one equation and two arbitrary surface functions. In the case of minimum energy equilibria, the six surface functions take on particular forms. (author)
On Equilibria of the Two-fluid Model in Magnetohydrodynamics
International Nuclear Information System (INIS)
Frantzeskakis, Dimitri J.; Stratis, Ioannis G.; Yannacopoulos, Athanasios N.
2004-01-01
We show how the equilibria of the two-fluid model in magnetohydrodynamics can be described by the double curl equation and through the study of this equation we study some properties of these equilibria
MHD stability of vertically asymmetric tokamak equilibria
International Nuclear Information System (INIS)
Dalhed, H.E.; Grimm, R.C.; Johnson, J.L.
1981-03-01
The ideal MHD stability properties of a special class of vertically asymmetric tokamak equilibria are examined. The calculations confirm that no major new physical effects are introduced and the modifications can be understood by conventional arguments. The results indicate that significant departures from up-down symmetry can be tolerated before the reduction in β becomes important for reactor operation
Computation of tokamak equilibria with steady flow
International Nuclear Information System (INIS)
Kerner, W.; Tokuda, Shinji
1987-08-01
The equations for ideal MHD equilibria with stationary flow are reexamined and addressed as numerically applied to tokamak configurations with a free plasma boundary. Both the isothermal (purely toroidal flow) and the poloidal flow cases are treated. Experiment-relevant states with steady flow (so far only in the toroidal direction) are computed by the modified SELENE40 code. (author)
Two-fluid and parallel compressibility effects in tokamak plasmas
International Nuclear Information System (INIS)
Sugiyama, L.E.; Park, W.
1998-01-01
The MHD, or single fluid, model for a plasma has long been known to provide a surprisingly good description of much of the observed nonlinear dynamics of confined plasmas, considering its simple nature compared to the complexity of the real system. On the other hand, some of the supposed agreement arises from the lack of the detailed measurements that are needed to distinguish MHD from more sophisticated models that incorporate slower time scale processes. At present, a number of factors combine to make models beyond MHD of practical interest. Computational considerations still favor fluid rather than particle models for description of the full plasma, and suggest an approach that starts from a set of fluid-like equations that extends MHD to slower time scales and more accurate parallel dynamics. This paper summarizes a set of two-fluid equations for toroidal (tokamak) geometry that has been developed and tested as the MH3D-T code [1] and some results from the model. The electrons and ions are described as separate fluids. The code and its original MHD version, MH3D [2], are the first numerical, initial value models in toroidal geometry that include the full 3D (fluid) compressibility and electromagnetic effects. Previous nonlinear MHD codes for toroidal geometry have, in practice, neglected the plasma density evolution, on the grounds that MHD plasmas are only weakly compressible and that the background density variation is weaker than the temperature variation. Analytically, the common use of toroidal plasma models based on aspect ratio expansion, such as reduced MHD, has reinforced this impression, since this ordering reduces plasma compressibility effects. For two-fluid plasmas, the density evolution cannot be neglected in principle, since it provides the basic driving energy for the diamagnetic drifts of the electrons and ions perpendicular to the magnetic field. It also strongly influences the parallel dynamics, in combination with the parallel thermal
Ballooning stable high beta tokamak equilibria
International Nuclear Information System (INIS)
Tuda, Takashi; Azumi, Masafumi; Kurita, Gen-ichi; Takizuka, Tomonori; Takeda, Tatsuoki
1981-04-01
The second stable regime of ballooning modes is numerically studied by using the two-dimensional tokamak transport code with the ballooning stability code. Using the simple FCT heating scheme, we find that the plasma can locally enter this second stable regime. And we obtained equilibria with fairly high beta (β -- 23%) stable against ballooning modes in a whole plasma region, by taking into account of finite thermal diffusion due to unstable ballooning modes. These results show that a tokamak fusion reactor can operate in a high beta state, which is economically favourable. (author)
Two-Fluid and Resistive Nonlinear Simulations of Tokamak Equilibrium, Stability, and Reconnection
International Nuclear Information System (INIS)
Jardin, S.; Sovinec, C.; Breslau, J.; Ferraro, N.; Hudson, S.; King, J.; Kruger, S.; Ramos, J.; Schnack, D.
2008-01-01
The NIMROD and M3D/M3D-C1 codes now each have both a resistive MHD and a two-fluid (2F) capability including gyroviscosity and Hall terms. We describe: (1) a nonlinear 3D verification test in the resistive MHD regime in which the two codes are in detailed agreement, (2) new studies that illuminate the effect of two-fluid physics on spontaneous rotation in tokamaks, (3) studies of nonlinear reconnection in regimes of relevance to fusion plasmas with peak nonlinear reconnection rates that are essentially independent of the resistivity, and (4) linear two-fluid tearing mode calculations including electron mass that agree with analytic studies over a wide range of parameter regimes
Application of a two fluid theoretical plasma transport model on current tokamak reactor designs
International Nuclear Information System (INIS)
Ibrahim, E.; Fowler, T.K.
1987-06-01
In this work, the new theoretical transport models to TIBER II design calculations are described and the results are compared with recent experimental data in large tokamaks (TFTR, JET). Tang's method is extended to a two-fluid model treating ions and electrons separately. This allows for different ion and electron temperatures, as in recent low-density experiments in TFTR, and in the TIBER II design itself. The discussion is divided into two parts: (1) Development of the theoretical transport model and (2) calibration against experiments and application to TIBER II
A two-fluid interpretation of low frequency modes in Tokamaks
International Nuclear Information System (INIS)
Thyagaraja, A.; Haas, F.A.
1983-01-01
The linear stability of low frequency modes (ω/ωsub(ci) << 1) of a dissipationless two-fluid cylindrical analogue of Tokamak is investigated. The eigenvalue problem comprises a coupled first-order and second-order differential equation. Given certain plausible assumptions, the case of an internal resonant point is solved analytically. The resulting modes and frequencies are qualitatively similar to those observed. The analogue of the MHD uniform current model is solved exactly and the usual MHD marginal stability boundary is shown to be modified. More general considerations show, that even in the absence of dissipation, the magnetic field is not ''frozen'' to the ions or the electrons. Furthermore, in general the MHD equations can only be recovered by a limiting process which is inappropriate to Tokamaks. For very low frequencies (ω << ω*), however, single and two-fluid theories predict the same magnetic field structure but different electric fields. The present analysis which covers frequencies from zero to ωsub(Alfven), including drift and acoustic frequencies predicts that both discrete and continuum modes can be unstable which is in contrast to ideal MHD. (author)
Numerical study of two-fluid flowing equilibria of helicity-driven spherical torus plasmas
International Nuclear Information System (INIS)
Kanki, T.; Nagata, M.; Uyama, T.
2004-01-01
Two-fluid flowing equilibrium configurations of a helicity-driven spherical torus (HD-ST) are numerically determined by using the combination of the finite difference and the boundary element methods. It is found from the numerical results that electron fluids near the central conductor are tied to an external toroidal field and ion fluids are not. The magnetic configurations change from the high-q HD-ST (q>1) with paramagnetic toroidal field and low-β (volume average β value, ∼ 2%) through the helicity-driven spheromak and RFP (reverse field pinch) to the ultra low-q HD-ST (0 ∼ 18%) as the external toroidal field at the inner edge regions decreases and reverses the sign. The two-fluid effects are more significant in this equilibrium transition when the ion diamagnetic drift is dominant in the flowing two-fluid. (authors)
Ballooning mode second stability region for sequences of tokamak equilibria
International Nuclear Information System (INIS)
Sugiyama, L.; Mark, J.W.K.
A numerical study of several sequences of tokamak equilibria derived from two flux conserving sequences confirms the tendency of high n ideal MHD ballooning modes to stabilize for values of the plasma beta greater than a second critical beta, for sufficiently favorable equilibria. The major stabilizing effect of increasing the inverse rotational transform profile q(Psi) for equilibria with the same flux surface geometry is shown. The unstable region shifts toward larger shear d ln q/d ln γ and the width of the region measured in terms of the poloidal beta or a pressure gradient parameter, for fixed shear, decreases. The smaller aspect ratio sequences are more sensitive to changes in q and have less stringent limits on the attainable value of the plasma beta in the high beta stable region. Finally, the disconnected mode approximation is shown to provide a reasonable description of the second high beta stability boundary
International Nuclear Information System (INIS)
Von Nessi, G T; Hole, M J
2014-01-01
We present recent results and technical breakthroughs for the Bayesian inference of tokamak equilibria using force-balance as a prior constraint. Issues surrounding model parameter representation and posterior analysis are discussed and addressed. These points motivate the recent advancements embodied in the Bayesian Equilibrium Analysis and Simulation Tool (BEAST) software being presently utilized to study equilibria on the Mega-Ampere Spherical Tokamak (MAST) experiment in the UK (von Nessi et al 2012 J. Phys. A 46 185501). State-of-the-art results of using BEAST to study MAST equilibria are reviewed, with recent code advancements being systematically presented though out the manuscript. (paper)
Magnetohydrodynamic equilibria and local stability of axisymmetric tokamak plasmas
International Nuclear Information System (INIS)
Peng, Y.K.M.; Dory, R.A.; Nelson, D.B.; Sayer, R.O.
1976-07-01
Axisymmetric magnetohydrodynamic equilibria are evaluated in terms of the Mercier Stability Criterion. The parameters of interest include poloidal beta (β/sub p/), current and pressure profile widths, D-shaped and doublet plasmas with elongation (sigma) and triangularity (delta), and the aspect ratio (A). For marginal local stability, the critical values of β, plasma current, and the safety factor q with fixed toroidal field at the geometric center of the plasma are obtained. It is shown that for a wide range of profiles in a D-shaped plasma with A = 3, the highest critical β occurs at β/sub p/ = 2.4, sigma = 1.65, and delta = 0.5. If the toroidal field at the coil surface is fixed, the highest critical pressure occurs near A approximately 3 to 4, given reasonable distance between the coils and the plasma edge. Calculations for a Doublet II-A plasma with sigma = 3 show that with similar pressure profile the highest critical β occurs at β/sub p/ = 1 and is 84 percent of the highest critical β for the D-shaped plasmas. Critical values of ohmic heating power density are also found to be comparable for the two plasma shapes. A D-shaped plasma with the above parameters is suggested for use in future high-β tokamak devices
Marx, Alain; Lütjens, Hinrich
2017-03-01
A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.
Ferraro, N. M.; Jardin, S. C.; Lao, L. L.; Shephard, M. S.; Zhang, F.
2016-05-01
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Energy Technology Data Exchange (ETDEWEB)
Ferraro, N. M., E-mail: nferraro@pppl.gov; Lao, L. L. [General Atomics, La Jolla, California 92186 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Shephard, M. S.; Zhang, F. [Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
2016-05-15
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
On tokamak equilibria with a zero current or negative current central region
International Nuclear Information System (INIS)
Chu, M.S.; Parks, P.B.
2002-01-01
Several tokamak experiments have reported the development of a central region with vanishing currents (the current hole). The straightforward application of results from the work of Greene, Johnson and Weimer [Phys. Fluids 14, 671 (1971)] on a tokamak equilibrium to these plasmas leads to the apparent singularities in several physical quantities including the Shafranov shift and casts doubts on the existence of this type of equilibria. In this paper, the above quoted equilibrium theory is re-examined and extended to include equilibria with a current hole. It is shown that singularities can be circumvented and that equilibria with a central current hole do satisfy the magnetohydrodynamic equilibrium condition with regular behavior for all the physical quantities and do not lead to infinitely large Shafranov shifts. Isolated equilibria with negative current in the central region could exist. But equilibria with negative currents in general do not have neighboring equilibria and thus cannot have experimental realization, i.e., no negative currents can be driven in the central region
Magnetic field structure of experimental high beta tokamak equilibria
International Nuclear Information System (INIS)
Deniz, A.V.
1986-01-01
The magnetic field structure of several low and high β tokamaks in the Columbia High Beta Tokamak (HBT) was determined by high-impedance internal magnetic probes. From the measurement of the magnetic field, the poloidal flux, toroidal flux, toroidal current, and safety factor are calculated. In addition, the plasma position and cross-sectional shape are determined. The extent of the perturbation of the plasma by the probe was investigated and was found to be acceptably small. The tokamaks have major radii of approx.0.24 m, minor radii of approx.0.05 m, toroidal plasma current densities of approx.10 6 A/m 2 , and line-integrated electron densities of approx.10 20 m -2 . The major difference between the low and high β tokamaks is that the high β tokamak was observed to have an outward shift in major radius of both the magnetic center and peak of the toroidal current density. The magnetic center moves inward in major radius after 20 to 30 μsec, presumably because the plasma maintains major radial equilibrium as its pressure decreases from radiation due to impurity atoms. Both the equilibrium and the production of these tokamaks from a toroidal field stabilized z-pinch are modeled computationally. One tokamak evolves from a state with low β features, through a possibly unstable state, to a state with high β features
Non-existence of Normal Tokamak Equilibria with Negative Central Current
International Nuclear Information System (INIS)
Hammett, G.W.; Jardin, S.C.; Stratton, B.C.
2003-01-01
Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current-drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated
Analytic, high β, flux conserving equilibria for cylindrical tokamaks
International Nuclear Information System (INIS)
Sigmar, D.J.; Vahala, G.
1978-09-01
Using Grad's theory of generalized differential equations, the temporal evolution from low to high β due to ''adiabatic'' and nonadiabatic (i.e., neutral beam injection) heating of a cylindrical tokamak plasma with circular cross section and peaked current profiles is calculated analytically. The influence of shaping the initial safety factor profile and the beam deposition profile and the effect of minor radius compression on the equilibrium is analyzed
Analytic, high β, flux conserving equilibria for cylindrical tokamaks
International Nuclear Information System (INIS)
Sigmar, D.J.; Vahala, G.
1978-01-01
Using Grad's theory of generalized differential equations, the temporal evolution from low to high β due to ''adiabatic'' and nonadiabatic (i.e., neutral beam injection) heating of a cylindrical tokamak plasma with circular cross section and peaked current profiles is calculated analytically. The influence of shaping the initial safety factor profile and the beam deposition profile and the effect of minor radius compression on the equilibrium is analyzed
A comprehensive theory of the equilibria in a tokamak and a reversed field pinch
International Nuclear Information System (INIS)
Chiyoda, Katsuji
1996-01-01
The equilibrium configuration of a tokamak is analysed by the equilibrium equations derived for analysing a reversed field pinch (RFP). The expressions of the magnetic field and the toroidal shift in the internal plasma region and the external vacuum region are obtained. The expressions in the vacuum region become the Shafranov's expressions, when the plasma-center coordinates is used. Discontinuities of the equilibrium quantities are considered. It is concluded that the equilibrium equations are applicable also to the tokamak plasma and that the difference of the equilibria between the tokamak and the RFP stems from the choices of the pressure and the toroidal current function. A feature of our theory is that any ordering to the safety factor is not imposed. (author)
Edge stability and pedestal profile sensitivity of snowflake diverted equilibria in the TCV Tokamak
International Nuclear Information System (INIS)
Medvedev, S.Yu.; Ivanov, A.A.; Martynov, A.A.; Poshekhonov, Yu.Yu.; Behn, R.; Martin, Y.R.; Moret, J.M.; Piras, F.; Pitzschke, A.; Pochelon, A.; Sauter, O.; Villard, L.
2010-01-01
A second order null divertor (snowflake) has been successfully created and controlled in the TCV tokamak[1] (F. Piras et al., Plasma Phys. Control. Fusion, 2009). The results of ideal MHD edge stability computations show an enhancement of the edge stability properties of the snowflake equilibria compared to standard x-point configurations[2] (S. Yu. Medvedev et al., 36th EPS Conference on Plasma Physics, 2009). However, a sensitivity study of the stability limits to variations of the pedestal profiles is essential for making conclusions about possibilities of ELM control in snowflake plasmas. Variations of the edge stability and beta limits for several types of snowflake equilibria, different values of triangularity and various pedestal profiles are investigated (copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Stability of high-beta tokamak equilibria and transport in Belt-Pinch IIa
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Becker, G; Gruber, O; Krause, H; Mast, F; Wilhelm, R [Association Euratom-Max-Planck-Institut fuer Plasmaphysik, Garching (Germany, F.R.)
1978-01-01
In Belt-Pinch IIa, highly elongated equilibria with poloidal beta values up to the aspect ratio have been achieved. In these tokamak-like configurations, no fast-growing MHD instabilities such as external kink and ballooning modes have been observed. Rigid displacement instabilities have been stabilized by an appropriate poloidal magnetic field configuration and by a conducting shell. By comparing simulation experiments using the Garching high-beta transport code with measurements, it has been found that in the collision-dominated plasma no anomalously enhanced transport occurs. Transport theory in the Pfirsch-Schlueter regime, which includes elongation and high-beta effects, has been confirmed by the experiment. In particular, it has been shown that the perpendicular electrical conductivity is also classical. Detailed investigations of oxygen and carbon impurity losses demonstrated that the impurity subprograms commonly used for tokamaks underestimate the radiation losses in the range Tsub(e)=10 to 30 eV.
EFFECT OF PROFILES AND SHAPE ON IDEAL STABILITY OF ADVANCED TOKAMAK EQUILIBRIA
Energy Technology Data Exchange (ETDEWEB)
MAKOWSKI,MA; CASPER,TA; FERRON,JR; TAYLOR,TS; TURNBULL,AD
2003-08-01
OAK-B135 The pressure profile and plasma shape, parameterized by elongation ({kappa}), triangularity ({delta}), and squareness ({zeta}), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P{sub 0}/
{approx} 2.0-4.5, weak negative central shear, high q{sub min} (> 2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs.
Effect of Profiles and Space on Ideal Stability of Advanced Tokamak Equilibria
Energy Technology Data Exchange (ETDEWEB)
Makowski, M A; Casper, T A; Ferron, J R; Taylor, T S; Turnbull, A D
2003-07-07
The pressure profile and plasma shape, parameterized by elongation ({kappa}), triangularity ({delta}), and squareness ({zeta}), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P{sub 0}/{l_angle}P{r_brace} {approx} 2.0-4.5, weak negative central shear, high q{sub min} (>2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs.
EFFECT OF PROFILES AND SHAPE ON IDEAL STABILITY OF ADVANCED TOKAMAK EQUILIBRIA
International Nuclear Information System (INIS)
MAKOWSKI, M.A.; CASPER, T.A.; FERRON, J.R.; TAYLOR, T.S.; TURNBULL, A.D.
2003-01-01
OAK-B135 The pressure profile and plasma shape, parameterized by elongation (κ), triangularity ((delta)), and squareness (ζ), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P 0 / ∼ 2.0-4.5, weak negative central shear, high q min (> 2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs
Effect of Profiles and Space on Ideal Stability of Advanced Tokamak Equilibria
International Nuclear Information System (INIS)
Makowski, M A; Casper, T A; Ferron, J R; Taylor, T S; Turnbull, A D
2003-01-01
The pressure profile and plasma shape, parameterized by elongation (κ), triangularity ((delta)), and squareness (ζ), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P 0 /(l a ngle)P} ∼ 2.0-4.5, weak negative central shear, high q min (>2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs
Stable equilibria for bootstrap-current-driven low aspect ratio tokamaks
International Nuclear Information System (INIS)
Miller, R.L.; Lin-Liu, Y.R.; Turnbull, A.D.; Chan, V.S.; Pearlstein, L.D.; Sauter, O.; Villard, L.
1997-01-01
Low aspect ratio tokamaks (LATs) can potentially provide a high ratio of plasma pressure to magnetic pressure β and high plasma current I at a modest size. This opens up the possibility of a high-power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma current, which requires operating at high β p . A high value of the Troyon factor β N and strong shaping is required to allow simultaneous operation at a high-β and high bootstrap fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect ratio 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both β N and β are defined in terms of the vacuum toroidal field. Equilibria with β N ≥8 and β∼35%endash 55% exist that are stable to n=∞ ballooning modes. The highest β case is shown to be stable to n=0,1,2,3 kink modes with a conducting wall. copyright 1997 American Institute of Physics
Theory and computation of general force balance in non-axisymmetric tokamak equilibria
Park, Jong-Kyu; Logan, Nikolas; Wang, Zhirui; Kim, Kimin; Boozer, Allen; Liu, Yueqiang; Menard, Jonathan
2014-10-01
Non-axisymmetric equilibria in tokamaks can be effectively described by linearized force balance. In addition to the conventional isotropic pressure force, there are three important components that can strongly contribute to the force balance; rotational, anisotropic tensor pressure, and externally given forces, i.e. ∇ --> p + ρv-> . ∇ --> v-> + ∇ --> . Π + f-> = j-> × B-> , especially in, but not limited to, high β and rotating plasmas. Within the assumption of nested flux surfaces, Maxwell equations and energy minimization lead to the modified-generalized Newcomb equation for radial displacements with simple algebraic relations for perpendicular and parallel displacements, including an inhomogeneous term if any of the forces are not explicitly dependent on displacements. The general perturbed equilibrium code (GPEC) solves this force balance consistent with energy and torque given by external perturbations. Local and global behaviors of solutions will be discussed when ∇ --> . Π is solved by the semi-analytic code PENT and will be compared with MARS-K. Any first-principle transport code calculating ∇ --> . Π or f-> , e.g. POCA, can also be incorporated without demanding iterations. This work was supported by DOE Contract DE-AC02-09CH11466.
International Nuclear Information System (INIS)
Hasegawa, Yukihiro; Nakamura, Yukiharu; Shirai, Hiroshi; Hamamatsu, Kiyotaka; Harada, Yoshio; Kikuchi, Mitsuru; Nakata, Yoshihiro
1999-01-01
In order to provide a set of magnetohydrodynamic (MHD) equilibrium database which is indispensable for both the studies on improvement of energy confinement and stabilization of MHD activities in tokamaks, a high speed data-processing system synchronizing with J T-60 discharge sequence was newly developed by utilizing the latest model of hugh speed workstation and by optimizing the parallel processing technique to perform fast calculation of MHD equilibria. This high speed system was found to have a sufficient ability to complete the whole equilibrium calculations during each inter-shot period. Cooperating with the mass data storage subsystem preserving the latest equilibrium database automatically, the animated discharge monitoring subsystem provides valuable information for the J T-60 operator to determine control parameters of the succeeding discharge. This report describes the system performance realized in the J T-60 experiment. (author)
International Nuclear Information System (INIS)
Okano, K.; Ogawa, Y.; Naitou, H.
1988-07-01
A new MHD-equilibrium/current-drive analysis code was developed to analyse the high beta tokamak equilibria consistent with the beam driven current profiles. In this new code, the critical beta equilibrium, which is stable against the ballooning mode, the kink mode and the Mercier mode, is determined first using MHD equilibrium and stability analysis codes (EQLAUS/ERATO). Then, the current drive parameters and the plasma parameters, required to sustain this critical beta equilibrium, are determined by iterative calculations. The beam driven current profiles are evaluated by the Fokker-Planck calculations on individual flux surfaces, where the toroidal effects on the beam ion and plasma electron trajectories are considered. The pressure calculation takes into account the beam ion and fast alpha components. A peculiarity of our new method is that the obtained solution is not only consistent with the MHD equilibrium but also consistent with the critical beta limit conditions, in the current profile and the pressure profile. Using this new method, β ∼ 21 % bean and β ∼ 6 % D-type critical beta equilibria were scanned for various parameters; the major radius, magnetic field, temperature, injection energy, etc. It was found that the achievable Q value for the bean type was always about 30 % larger than for the D-type cases, where Q = fusion power/beam power. With strong beanness, Q ∼ 6 for DEMO type tokamaks (∼500 MWth) and Q ∼ 20 for power reactor size (4.5 GWth) are achievable. On the other hand, the Q value would not exceed sixteen for the D-type machines. (author)
Directory of Open Access Journals (Sweden)
Ap Kuiroukidis
2018-01-01
Full Text Available We consider a generalized Grad–Shafranov equation (GGSE in a triangularity-deformed axisymmetric toroidal coordinate system and solve it numerically for the generic case of ITER-like and JET-like equilibria with non-parallel flow. It turns out that increase of the triangularity improves confinement by leading to larger values of the toroidal beta and the safety factor. This result is supported by the application of a criterion for linear stability valid for equilibria with flow parallel to the magnetic field. Also, the parallel flow has a weaker stabilizing effect.
Helical equilibria and criteria for the kink instability of cylindrical tokamak
International Nuclear Information System (INIS)
Inoue, Sanae; Itoh, Kimitaka; Yoshikawa, Shoichi.
1974-10-01
Helical equilibria and criteria for the kink instability have been obtained numerically for various current distribution, including camel hump distribution. It is found that the unstable region expressed by q(a) is the largest in the case of uniform current. (auth.)
Stability of highly shifted equilibria in a large aspect ratio low-field tokamak
International Nuclear Information System (INIS)
Gourdain, P.-A.; Leboeuf, J.-N.; Neches, R. Y.
2007-01-01
In the long run, the economics of fusion will dictate that reactors confine large plasma pressure rather efficiently. A possible route manifests itself as equilibria with large shift of the plasma magnetic axis. This shift compresses the flux surfaces on the outer part of the plasma, hereby increasing the allowable plasma pressure a machine can confine for a given toroidal magnetic field, which is the main cost of the device. As a first step toward a reactor, we propose investigating the stability of such configurations in a low magnetic field high aspect ratio machine. By focusing our arguments solely on the shape of the toroidal plasma current density profile we discuss the stability of highly shifted equilibria and their robustness to current profile variations that could occur in actual experiments. The evolution of the plasma parameters, as the beta poloidal is increased, is also examined to give a better understanding of the difference in performance between the various regimes
Three-dimensional tokamak equilibria and stellarators with two-dimensional magnetic symmetry
International Nuclear Information System (INIS)
Garabedian, P.R.
1997-01-01
Three-dimensional computer codes have been developed to simulate equilibrium, stability and transport in tokamaks and stellarators. Bifurcated solutions of the tokamak problem suggest that three-dimensional effects may be more important than has generally been thought. Extensive calculations have led to the discovery of a stellarator configuration with just two field periods and with aspect ratio 3.2 that has a magnetic field spectrum B mn with toroidal symmetry. Numerical studies of equilibrium, stability and transport for this new device, called the Modular Helias-like Heliac 2 (MHH2), will be presented. (author)
Three-dimensional tokamak equilibria in the presence of resonant field errors
International Nuclear Information System (INIS)
Reiman, A.; Monticello, D.
1992-01-01
Numerical solutions are described for three-dimensional MHD equilibria in the presence of resonant magnetic field perturbations. The effects of a realistic spectrum of resonant field errors are calculated for a range of current profiles. It is found that field errors of the magnitude existing in present day devices, and contemplated for future devices, can produce a set of magnetic islands occupying a significant fraction of the plasma cross-section
Neoclassical transport analysis for a class of high-β tokamak equilibria
International Nuclear Information System (INIS)
Rieser, H.; Werthmann, H.; Kuhn, S.
1995-01-01
Balescu's neoclassical transport theory is extended to the case of non-circular flux-surface geometries. Modified classical and neoclassical transport equations, governing particle and heat fluxes in the short- and long-mean-free-path regimes, are derived. These equations are shown to coincide to leading order with the corresponding equations given by Hirshman and Sigmar. They are then applied to an ideal MHD equilibrium, suitable as a simplified but analytically tractable model of a high-β tokamak. Numerical results for the radial profiles of the global (i.e. flux-surface integrated) particle and heat fluxes in the classical, Pfirsch-Schlueter and banana regimes are presented for geometry and plasma parameters realized in some tokamaks, like the divertor and injection tokamak experiment (DITE). This spatial representation provides direct insight into the overall collisional transport behaviour of a given equilibrium, whereas the anomalous transport problem is not addressed here. Our results demonstrate that for a given pressure profile the global neoclassical fluxes may depend very sensitively on the temperature profiles and that, in particular, the global classical and neoclassical ion heat fluxes exhibit a characteristic non-monotonic behaviour. (author)
Modeling of LH current drive in self-consistent elongated tokamak MHD equilibria
International Nuclear Information System (INIS)
Blackfield, D.T.; Devoto, R.S.; Fenstermacher, M.E.; Bonoli, P.T.; Porkolab, M.; Yugo, J.
1989-01-01
Calculations of non-inductive current drive typically have been used with model MHD equilibria which are independently generated from an assumed toroidal current profile or from a fit to an experiment. Such a method can lead to serious errors since the driven current can dramatically alter the equilibrium and changes in the equilibrium B-fields can dramatically alter the current drive. The latter effect is quite pronounced in LH current drive where the ray trajectories are sensitive to the local values of the magnetic shear and the density gradient. In order to overcome these problems, we have modified a LH simulation code to accommodate elongated plasmas with numerically generated equilibria. The new LH module has been added to the ACCOME code which solves for current drive by neutral beams, electric fields, and bootstrap effects in a self-consistent 2-D equilibrium. We briefly describe the model in the next section and then present results of a study of LH current drive in ITER. 2 refs., 6 figs., 2 tabs
International Nuclear Information System (INIS)
Welander, A.S.; Deranian, R.D.; Humphreys, D.A.; Leuer, J.A.; Walker, M.L.
2005-01-01
Tokamak control design relies on an accurate linear model of the plasma response, which can often dominate the local field variations in regions under active feedback control. For example, when fluxes at selected points on the plasma boundary are regulated in DIII-D, the plasma response to a change in a coil current gives rise to a flux change which can be larger than and opposite to the flux change caused by the coil alone.In the past, rigid plasma models have been used for linear stability and shape control design. In a rigid model, the plasma current profile is considered fixed and moves rigidly in response to control coils to maintain radial and vertical force balance. In a nonrigid model, however, changes in the plasma shape and current profile are taken into account. Such models are expected to be important for future advanced tokamak control design. The present work describes development of a nonrigid plasma response model for high-accuracy multivariable control design and provides comparisons of model predictions against DIII-D experimental data. The linear perturbed plasma response model is calculated rapidly from an existing equilibrium solution
International Nuclear Information System (INIS)
Wesson, John.
1996-01-01
This book is the first compiled collection about tokamak. At first chapter tokamak is represented from fusion point of view and also the necessary conditions for producing power. The following chapters are represent plasma physics, the specifications of tokamak, plasma heating procedures and problems related to it, equilibrium, confinement, magnetohydrodynamic stability, instabilities, plasma material interaction, plasma measurement and experiments regarding to tokamak; an addendum is also given at the end of the book
International Nuclear Information System (INIS)
Fitzgerald, M.; Hole, M.J.; Appel, L.C.
2013-01-01
A new force balance model for the EFIT magnetohydrodynamic equilibrium technique for tokamaks is presented which includes the full toroidal flow and anisotropy changes to the Grad–Shafranov equation. The free functions are poloidal flux functions and all non-linear contributions to the toroidal current density are treated iteratively. The parallel heat flow approximation chosen for the model is that parallel temperature is a flux function and that both parallel and perpendicular pressures may be described using parallel and perpendicular temperatures. This choice for the fluid thermodynamics has been shown elsewhere to be the same as a guiding-centre kinetic solution of the same problem under the same assumptions. The model reduces identically to the static and isotropic Grad–Shafranov equation in the appropriate limit as different flux functions are set to zero. An analytical solution based on a modified Soloviev solution for non-zero toroidal flow and anisotropy is also presented. The force balance model has been demonstrated in the code EFIT TENSOR, a branch of the existing code EFIT++. Benchmark results for EFIT TENSOR are presented and the more complicated force balance model is found to converge to force balance similarly to the usual EFIT model and with comparable speed. (paper)
International Nuclear Information System (INIS)
Peng, Y.K.M.
1978-04-01
A tokamak configuration is proposed that permits the rapid replacement of a plasma discharge in a ''burn'' chamber by another one in a time scale much shorter than the elementary thermal time constant of the chamber first wall. With respect to the chamber, the effective duty cycle factor can thus be made arbitrarily close to unity minimizing the cyclic thermal stress in the first wall. At least one plasma discharge always exists in the new tokamak configuration, hence, a continuous tokamak. By incorporating adiabatic toroidal compression, configurations of continuous tokamak compressors are introduced. To operate continuous tokamaks, it is necessary to introduce the concept of mixed poloidal field coils, which spatially groups all the poloidal field coils into three sets, all contributing simultaneously to inducing the plasma current and maintaining the proper plasma shape and position. Preliminary numerical calculations of axisymmetric MHD equilibria in continuous tokamaks indicate the feasibility of their continued plasma operation. Advanced concepts of continuous tokamaks to reduce the topological complexity and to allow the burn plasma aspect ratio to decrease for increased beta are then suggested
Neoclassical MHD equilibria with ohmic current
International Nuclear Information System (INIS)
Tokuda, Shinji; Takeda, Tatsuoki; Okamoto, Masao.
1989-01-01
MHD equilibria of tokamak plasmas with neoclassical current effects (neoclassical conductivity and bootstrap current) were calculated self-consistently. Neoclassical effects on JFT-2M tokamak plasmas, sustained by ohmic currents, were studied. Bootstrap currents flow little for L-mode type equilibria because of low attainable values of poloidal beta, β J . H-mode type equilibria give bootstrap currents of 30% ohmic currents for β J attained by JFT-2M and 100% for β J ≥ 1.5, both of which are sufficient to change the current profiles and the resultant MHD equilibria. Neoclassical conductivity which has roughly half value of the classical Spitzer conductivity brings peaked ohmic current profiles to yield low safety factor at the magnetic axis. Neoclassical conductivity reduces the value of effective Z(Z eff ) which is necessary to give the observed one-turn voltage but it needs impurities accumulating at the center when such peaked current profiles are not observed. (author)
Determination of 3D Equilibria from Flux Surface Knowledge Only
International Nuclear Information System (INIS)
Mynick, H.E.; Pomphrey, N.
2001-01-01
We show that the method of Christiansen and Taylor, from which complete tokamak equilibria can be determined given only knowledge of the shape of the flux surfaces, can be extended to 3-dimensional equilibria, such as those of stellarators. As for the tokamak case, the given geometric knowledge has a high degree of redundancy, so that the full equilibrium can be obtained using only a small portion of that information
On the stability of dissipative MHD equilibria
International Nuclear Information System (INIS)
Teichmann, J.
1979-04-01
The global stability of stationary equilibria of dissipative MHD is studied uisng the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian system with the full dissipative operators are given. The case of the two-fluid isentropic flow is discussed. (orig.)
International Nuclear Information System (INIS)
Hicks, H.R.; Dory, R.A.; Holmes, J.A.
1983-01-01
We illustrate in some detail a 2D inverse-equilibrium solver that was constructed to analyze tokamak configurations and stellarators (the latter in the context of the average method). To ensure that the method is suitable not only to determine equilibria, but also to provide appropriately represented data for existing stability codes, it is important to be able to control the Jacobian, tilde J is identical to delta(R,Z)/delta(rho, theta). The form chosen is tilde J = J 0 (rho)R/sup l/rho where rho is a flux surface label, and l is an integer. The initial implementation is for a fixed conducting-wall boundary, but the technique can be extended to a free-boundary model
Multiple equilibria of divertor plasmas
International Nuclear Information System (INIS)
Vu, H.X.; Prinja, A.K.
1993-01-01
A one-dimensional, two-fluid transport model with a temperature-dependent neutral recycling coefficient is shown to give rise to multiple equilibria of divertor plasmas (bifurcation). Numerical techniques for obtaining these multiple equilibria and for examining their stability are presented. Although these numerical techniques have been well known to the scientific community, this is the first time they have been applied to divertor plasma modeling to show the existence of multiple equilibria as well as the stability of these solutions. Numerical and approximate analytical solutions of the present one-dimensional transport model both indicate that there exists three steady-state solutions corresponding to (1) a high-temperature, low-density equilibrium, (2) a low-temperature, high-density equilibrium, and (3) an intermediate-temperature equilibrium. While both the low-temperature and the high-temperature equilibria are stable, with respect to small perturbations in the plasma conditions, the intermediate-temperature equilibrium is physically unstable, i.e., any small perturbation about this equilibrium will cause a transition toward either the high-temperature or low-temperature equilibrium
Spherical tokamak without external toroidal fields
International Nuclear Information System (INIS)
Kaw, P.K.; Avinash, K.; Srinivasan, R.
2001-01-01
A spherical tokamak design without external toroidal field coils is proposed. The tokamak is surrounded by a spheromak shell carrying requisite force free currents to produce the toroidal field in the core. Such equilibria are constructed and it is indicated that these equilibria are likely to have robust ideal and resistive stability. The advantage of this scheme in terms of a reduced ohmic dissipation is pointed out. (author)
Attractive evolutionary equilibria
Joosten, Reinoud A.M.G.; Roorda, Berend
2011-01-01
We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain evolutionary
Free-boundary perturbed MHD equilibria
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Nührenberg, C
2012-01-01
The concept of perturbed ideal MHD equilibria [Boozer A H and Nuhrenberg C 2006 Phys. Plasmas 13 102501] is employed to study the influence of external error-fields and of small plasma-pressure changes on toroidal plasma equilibria. In tokamak and stellarator free-boundary calculations, benchmarks were successful of the perturbed-equilibrium version of the CAS3D stability code [Nührenberg C et al. 2009 Phys. Rev. Lett. 102 235001] with the ideal MHD equilibrium code NEMEC [Hirshman S P et al. 1986 Comput. Phys. Commun. 43 143].
Two-fluid hydrodynamic model for semiconductors
DEFF Research Database (Denmark)
Maack, Johan Rosenkrantz; Mortensen, N. Asger; Wubs, Martijn
2018-01-01
The hydrodynamic Drude model (HDM) has been successful in describing the optical properties of metallic nanostructures, but for semiconductors where several different kinds of charge carriers are present an extended theory is required. We present a two-fluid hydrodynamic model for semiconductors...
Numerical computation of FCT equilibria by inverse equilibrium method
International Nuclear Information System (INIS)
Tokuda, Shinji; Tsunematsu, Toshihide; Takeda, Tatsuoki
1986-11-01
FCT (Flux Conserving Tokamak) equilibria were obtained numerically by the inverse equilibrium method. The high-beta tokamak ordering was used to get the explicit boundary conditions for FCT equilibria. The partial differential equation was reduced to the simultaneous quasi-linear ordinary differential equations by using the moment method. The regularity conditions for solutions at the singular point of the equations can be expressed correctly by this reduction and the problem to be solved becomes a tractable boundary value problem on the quasi-linear ordinary differential equations. This boundary value problem was solved by the method of quasi-linearization, one of the shooting methods. Test calculations show that this method provides high-beta tokamak equilibria with sufficiently high accuracy for MHD stability analysis. (author)
Free-Boundary 3D Equilibria and Resistive Wall Instabilities with Extended-MHD
Ferraro, N. M.
2015-11-01
The interaction of the plasma with external currents, either imposed or induced, is a critical element of a wide range of important tokamak phenomena, including resistive wall mode (RWM) stability and feedback control, island penetration and locking, and disruptions. A model of these currents may be included within the domain of extended-MHD codes in a way that preserves the self-consistency, scalability, and implicitness of their numerical methods. Such a model of the resistive wall and non-axisymmetric coils is demonstrated using the M3D-C1 code for a variety of applications, including RWMs, perturbed non-axisymmetric equilibria, and a vertical displacement event (VDE) disruption. The calculated free-boundary equilibria, which include Spitzer resistivity, rotation, and two-fluid effects, are compared to external magnetic and internal thermal measurements for several DIII-D discharges. In calculations of the perturbed equilibria in ELM suppressed discharges, the tearing response at the top of the pedestal is found to correlate with the onset of ELM suppression. Nonlinear VDE calculations, initialized using a vertically unstable DIII-D equilibrium, resolve in both space and time the currents induced in the wall and on the plasma surface, and also the currents flowing between the plasma and the wall. The relative magnitude of these contributions and the total impulse to the wall depend on the resistive wall time, although the maximum axisymmetric force on the wall over the course of the VDE is found to be essentially independent of the wall conductivity. This research was supported by US DOE contracts DE-FG02-95ER54309, DE-FC02-04ER54698 and DE-AC52-07NA27344.
Two-fluid mixing in a microchannel
International Nuclear Information System (INIS)
Liu Yingzheng; Kim, Byoung Jae; Sung, Hyung Jin
2004-01-01
A numerical study of the mixing of two fluids (pure water and a solution of glycerol in water) in a microchannel was carried out. By varying the glycerol content of the glycerol/water solution, the variation in mixing behavior with changes in the difference in the properties of the two fluids (e.g., viscosity, density and diffusivity) was investigated. The mixing phenomena were tested for three micromixers: a squarewave mixer, a three-dimensional serpentine mixer and a staggered herringbone mixer. The governing equations of continuity, momentum and solute mass fraction were solved numerically. To evaluate mixing performance, a criterion index of mixing uniformity was proposed. In the systems considered, the Reynolds number based on averaged properties was Re=1 and 10. For low Reynolds number (Re=1), the mixing performance varied inversely with mass fraction of glycerol due to the dominance of molecular diffusion. The mixing performance deteriorated due to a significant reduction in the residence time of the fluid inside the mixers
Attractive evolutionary equilibria
Roorda, Berend; Joosten, Reinoud
2011-01-01
We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain evolutionary dynamics. For instance, each attractive evolutionarily stable strategy is an attractive evolutionarily stable equilibrium for certain barycentric ray-projection dynamics, and vice versa.
Two-fluid turbulence including electron inertia
Energy Technology Data Exchange (ETDEWEB)
Andrés, Nahuel, E-mail: nandres@iafe.uba.ar; Gómez, Daniel [Instituto de Astronomía y Física del Espacio, CC. 67, suc. 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, 1428 Buenos Aires (Argentina); Gonzalez, Carlos; Martin, Luis; Dmitruk, Pablo [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, 1428 Buenos Aires (Argentina)
2014-12-15
We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure, and electron inertia. According to this description, each plasma species introduces a new spatial scale: the ion inertial length λ{sub i} and the electron inertial length λ{sub e}, which are not present in the traditional MHD description. In the present paper, we seek for possible changes in the energy power spectrum in fully developed turbulent regimes, using numerical simulations of the two-fluid equations in two-and-a-half dimensions. We have been able to reproduce different scaling laws in different spectral ranges, as it has been observed in the solar wind for the magnetic energy spectrum. At the smallest wavenumbers where plain MHD is valid, we obtain an inertial range following a Kolmogorov k{sup −5∕3} law. For intermediate wavenumbers such that λ{sub i}{sup −1}≪k≪λ{sub e}{sup −1}, the spectrum is modified to a k{sup −7∕3} power-law, as has also been obtained for Hall-MHD neglecting electron inertia terms. When electron inertia is retained, a new spectral region given by k>λ{sub e}{sup −1} arises. The power spectrum for magnetic energy in this region is given by a k{sup −11∕3} power law. Finally, when the terms of electron inertia are retained, we study the self-consistent electric field. Our results are discussed and compared with those obtained in the solar wind observations and previous simulations.
Axisymmetric control in tokamaks
International Nuclear Information System (INIS)
Humphreys, D.A.
1991-02-01
Vertically elongated tokamak plasmas are intrinsically susceptible to vertical axisymmetric instabilities as a result of the quadrupole field which must be applied to produce the elongation. The present work analyzes the axisymmetric control necessary to stabilize elongated equilibria, with special application to the Alcator C-MOD tokamak. A rigid current-conserving filamentary plasma model is applied to Alcator C-MOD stability analysis, and limitations of the model are addressed. A more physically accurate nonrigid plasma model is developed using a perturbed equilibrium approach to estimate linearized plasma response to conductor current variations. This model includes novel flux conservation and vacuum vessel stabilization effects. It is found that the nonrigid model predicts significantly higher growth rates than predicted by the rigid model applied to the same equilibria. The nonrigid model is then applied to active control system design. Multivariable pole placement techniques are used to determine performance optimized control laws. Formalisms are developed for implementing and improving nominal feedback laws using the C-MOD digital-analog hybrid control system architecture. A proportional-derivative output observer which does not require solution of the nonlinear Ricatti equation is developed to help accomplish this implementation. The nonrigid flux conserving perturbed equilibrium plasma model indicates that equilibria with separatrix elongation of at least κ sep = 1.85 can be stabilized robustly with the present control architecture and conductor/sensor configuration
Active Polar Two-Fluid Macroscopic Dynamics
Pleiner, Harald; Svensek, Daniel; Brand, Helmut R.
2014-03-01
We study the dynamics of systems with a polar dynamic preferred direction. Examples include the pattern-forming growth of bacteria (in a solvent, shoals of fish (moving in water currents), flocks of birds and migrating insects (flying in windy air). Because the preferred direction only exists dynamically, but not statically, the macroscopic variable of choice is the macroscopic velocity associated with the motion of the active units. We derive the macroscopic equations for such a system and discuss novel static, reversible and irreversible cross-couplings connected to this second velocity. We find a normal mode structure quite different compared to the static descriptions, as well as linear couplings between (active) flow and e.g. densities and concentrations due to the genuine two-fluid transport derivatives. On the other hand, we get, quite similar to the static case, a direct linear relation between the stress tensor and the structure tensor. This prominent ``active'' term is responsible for many active effects, meaning that our approach can describe those effects as well. In addition, we also deal with explicitly chiral systems, which are important for many active systems. In particular, we find an active flow-induced heat current specific for the dynamic chiral polar order.
Thermonuclear ignition in the next generation tokamaks
International Nuclear Information System (INIS)
Johner, J.
1989-04-01
The extrapolation of experimental rules describing energy confinement and magnetohydrodynamic - stability limits, in known tokamaks, allow to show that stable thermonuclear ignition equilibria should exist in this configuration, if the product aB t x of the dimensions by a magnetic-field power is large enough. Quantitative application of this result to several next-generation tokamak projects show that those kinds of equilibria could exist in such devices, which would also have enough additional heating power to promote an effective accessible ignition
Maximum entropy tokamak configurations
International Nuclear Information System (INIS)
Minardi, E.
1989-01-01
The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. (author)
Some stable hydromagnetic equilibria
Energy Technology Data Exchange (ETDEWEB)
Johnson, J L; Oberman, C R; Kulsrud, R M; Frieman, E A [Project Matterhorn, Princeton University, Princeton, NJ (United States)
1958-07-01
We have been able to find and investigate the properties of equilibria which are hydromagnetically stable. These equilibria can be obtained, for example, by wrapping conductors helically around the stellarator tube. Systems with I = 3 or 4 are indicated to be optimum for stability purposes. In some cases an admixture of I = 2 fields can be advantageous for achieving equilibrium. (author)
Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Johnson, J.L.; Dalhed, H.E.; Greene, J.M.
1978-07-01
Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given
Energy Technology Data Exchange (ETDEWEB)
White, R B [Princeton Univ., NJ (USA). Plasma Physics Lab.
1989-01-01
The book covers the consequences of ideal and resistive magnetohydrodynamics, these theories being responsible for most of what is well understood regarding the physics of tokamak discharges. The focus is on the description of equilibria, the linear and nonlinear theory of large scale modes, and single particle guiding center motion, including simple neoclassical effects. modern methods of general magnetic coordinates are used, and the student is introduced to the onset of chaos in Hamiltonian systems in the discussion of destruction of magnetic surfaces. Much of the book is devoted to the description of the limitations placed on tokamak operating parameters given by ideal and resistive modes, and current ideas about how to extend and optimize these parameters. (author). refs.; figs.
Equilibrium Reconstruction in EAST Tokamak
International Nuclear Information System (INIS)
Qian Jinping; Wan Baonian; Shen Biao; Sun Youwen; Liu Dongmei; Xiao Bingjia; Ren Qilong; Gong Xianzu; Li Jiangang; Lao, L. L.; Sabbagh, S. A.
2009-01-01
Reconstruction of experimental axisymmetric equilibria is an important part of tokamak data analysis. Fourier expansion is applied to reconstruct the vessel current distribution in EFIT code. Benchmarking and testing calculations are performed to evaluate and validate this algorithm. Two cases for circular and non-circular plasma discharges are presented. Fourier expansion used to fit the eddy current is a robust method and the real time EFIT can be introduced to the plasma control system in the coming campaign. (magnetically confined plasma)
Ideal MHD beta-limits of poloidally asymmetric equilibria
Energy Technology Data Exchange (ETDEWEB)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in ..beta../sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is ..beta../sub critical/ approx. = 6.5%.
Ideal MHD beta-limits of poloidally asymmetric equilibria
International Nuclear Information System (INIS)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in β/sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is β/sub critical/ approx. = 6.5%
Learning efficient correlated equilibria
Borowski, Holly P.; Marden, Jason R.; Shamma, Jeff S.
2014-01-01
The majority of distributed learning literature focuses on convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific correlated equilibria. In this paper, we provide one such algorithm which guarantees that the agents' collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Learning efficient correlated equilibria
Borowski, Holly P.
2014-12-15
The majority of distributed learning literature focuses on convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific correlated equilibria. In this paper, we provide one such algorithm which guarantees that the agents\\' collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Numerical studies of edge localized instabilities in tokamaks
International Nuclear Information System (INIS)
Wilson, H.R.; Snyder, P.B.; Huysmans, G.T.A.; Miller, R.L.
2002-01-01
A new computational tool, edge localized instabilities in tokamaks equilibria (ELITE), has been developed to help our understanding of short wavelength instabilities close to the edge of tokamak plasmas. Such instabilities may be responsible for the edge localized modes observed in high confinement H-mode regimes, which are a serious concern for next step tokamaks because of the high transient power loads which they can impose on divertor target plates. ELITE uses physical insight gained from analytic studies of peeling and ballooning modes to provide an efficient way of calculating the edge ideal magnetohydrodynamic stability properties of tokamaks. This paper describes the theoretical formalism which forms the basis for the code
Magnetohydrodynamic motion of a two-fluid plasma
Burby, J. W.
2017-08-01
The two-fluid Maxwell system couples frictionless electrons and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, as well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from the two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-order closure may be obtained in the closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-order bracket gives explicit expressions for a number of the full closure's conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.
Stability of high β large aspect ratio tokamaks
International Nuclear Information System (INIS)
Cowley, S.C.
1991-10-01
High β(β much-gt ε/q 2 ) large aspect ratio (ε much-gt 1) tokamak equilibria are shown to be always stable to ideal M.H.D. modes that are localized about a flux surface. Both the ballooning and interchange modes are shown to be stable. This work uses the analytic high β large aspect ratio tokamak equilibria developed by Cowley et.al., which are valid for arbitrary pressure and safety factor profiles. The stability results make no assumption about these profiles or the shape of the boundary. 14 refs., 4 figs
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
Laszlo Tisza and the two-fluid model of superfluidity
Balibar, Sébastien
2017-11-01
The "two-fluid model" of superfluidity was first introduced by Laszlo Tisza in 1938. On that year, Tisza published the principles of his model as a brief note in Nature and two articles in French in the Comptes rendus de l'Académie des sciences, followed in 1940 by two other articles in French in the Journal de physique et le Radium. In 1941, the two-fluid model was reformulated by Lev Landau on a more rigorous basis. Successive experiments confirmed the revolutionary idea introduced by Tisza: superfluid helium is indeed a surprising mixture of two fluids with independent velocity fields. His prediction of the existence of heat waves, a consequence of his model, was also confirmed. Then, it took several decades for the superfluidity of liquid helium to be fully understood.
Institutions, Equilibria and Efficiency
DEFF Research Database (Denmark)
Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria in such set...... in OLG, learning in OLG and in games, optimal pricing of derivative securities, the impact of heterogeneity...
Generalized Roe's numerical scheme for a two-fluid model
International Nuclear Information System (INIS)
Toumi, I.; Raymond, P.
1993-01-01
This paper is devoted to a mathematical and numerical study of a six equation two-fluid model. We will prove that the model is strictly hyperbolic due to the inclusion of the virtual mass force term in the phasic momentum equations. The two-fluid model is naturally written under a nonconservative form. To solve the nonlinear Riemann problem for this nonconservative hyperbolic system, a generalized Roe's approximate Riemann solver, is used, based on a linearization of the nonconservative terms. A Godunov type numerical scheme is built, using this approximate Riemann solver. 10 refs., 5 figs,
Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation
International Nuclear Information System (INIS)
Pletzer, A.; Zakharov, L.E.
1999-01-01
The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory
Fusion burn equilibria sensitive to the ratio between energy and helium transport
Jakobs, M.A.; Lopes Cardozo, N.J.; Jaspers, R.J.E.
2014-01-01
An analysis of the burn equilibria of fusion reactors of the tokamak family is presented. The global (zero-dimensional) analysis is self-consistent in that it takes into account the dependence of the energy confinement on the variables of the burning plasma, such as temperature and density.
Magnetoacoustic heating and FCT-equilibria in the belt pinch
International Nuclear Information System (INIS)
Erckmann, V.
1983-02-01
In the HECTOR belt pinch of high β plasma is produced by magnetic compression in a Tokamak geometry. After compresseion the initial β value can be varied between 0.2 and 0.8. During 5 μs the plasma is further heated by a fast magnetoacoustic wave with a frequency near the first harmonic of the ion cyclotronfrequency. For the first time the β-value of a pinch plasma could be increased further from 0.34 after compression to 0.46 at the end of the rf-heating cycle. By proper selection of the final β-value the region for resonance absorption of the heating wave can be shifted. Strong heating (200 MW) has been observed in the cases, where the resonance region has been located in the center of the plasma. In deuterium discharges an increase in ion temperature is observed during the heating process, whereas the electrons are energetically decoupled, showing no temperature increase. Strong plasma losses are found in the 200 MW range after the rf-heating process. The dominant mechanisms are charge exchange collisions with neutral gas atoms. During rf-heating and the subsequent cooling phase the magnetic flux is frozen due to the high conductivity of the plasma. The observed equilibria could be identified as flux conserving Tokamak (FCT) equilibria. Based on a two-dimensional code the time-evolution of the equilibria has been calculated. The q-profiles are time-independent, with increasing β the magnetic axis of the plasma is shifted towards the outer boundary of the torus, and finally the linear relation between β and βsub(pol), which is characteristic for low-β-equilibria, is no longer valid. Thus for the first time the existence of FCT-equilibria at high β has been demonstrated experimentally together with a qualitative agreement with FCT-theory. (orig./AH) [de
Two-fluid hydrodynamic modes in a trapped superfluid gas
International Nuclear Information System (INIS)
Taylor, E.; Griffin, A.
2005-01-01
In the collisional region at finite temperatures, the collective modes of superfluids are described by the Landau two-fluid hydrodynamic equations. This region can now be probed over the entire BCS-Bose-Einstein-condensate crossover in trapped Fermi superfluids with a Feshbach resonance, including the unitarity region. Building on the approach initiated by Zaremba, Nikuni, and Griffin in 1999 for trapped atomic Bose gases, we present a variational formulation of two-fluid hydrodynamic collective modes based on the work of Zilsel in 1950 developed for superfluid helium. Assuming a simple variational Ansatz for the superfluid and normal fluid velocities, the frequencies of the hydrodynamic modes are given by solutions of coupled algebraic equations, with constants only involving spatial integrals over various equilibrium thermodynamic derivatives. This variational approach is both simpler and more physical than a direct attempt to solve the Landau two-fluid differential equations. Our two-fluid results are shown to reduce to those of Pitaevskii and Stringari for a pure superfluid at T=0
Analytic description of tokamak equilibrium sustained by high fraction bootstrap current
International Nuclear Information System (INIS)
Shi Bingren
2002-01-01
Recently, to save the current drive power and to obtain more favorable confinement merit for tokamak reactor, large faction bootstrap current sustained equilibrium has attracted great interests both theoretically and experimentally. An powerful expanding technique and the tokamak ordering are used to expand the Grad-Shafranov equation to obtain a series of ordinary differential equations which allow for different sets of input parameters. The fully bootstrap current sustained tokamak equilibria are then solved analytically
Axisymmetric instability in a noncircular tokamak
International Nuclear Information System (INIS)
Lipschultz, B.
1979-10-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes - the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria
International Nuclear Information System (INIS)
Rome, J.A.; Peng, Y.K.M.
1978-09-01
Guiding center orbits in noncircular axisymmetric tokamak plasmas are studied in the constants of motion (COM) space of (v, zeta, psi/sub m/). Here, v is the particle speed, zeta is the pitch angle with respect to the parallel equilibrium current, J/sub parallels/, and psi/sub m/ is the maximum value of the poloidal flux function (increasing from the magnetic axis) along the guiding center orbit. Two D-shaped equilibria in a flux-conserving tokamak having β's of 1.3% and 7.7% are used as examples. In this space, each confined orbit corresponds to one and only one point and different types of orbits (e.g., circulating, trapped, stagnation and pinch orbits) are represented by separate regions or surfaces in the space. It is also shown that the existence of an absolute minimum B in the higher β (7.7%) equilibrium results in a dramatically different orbit topology from that of the lower β case. The differences indicate the confinement of additional high energy (v → c, within the guiding center approximation) trapped, co- and countercirculating particles whose orbit psi/sub m/ falls within the absolute B well
Validation of Numerical Two-Fluid and Kinetic Plasma Models
Energy Technology Data Exchange (ETDEWEB)
Daniel Barnes
2011-03-25
This was a four year grant commencing October 1, 2003 and finishing September 30, 2007. The funding was primarily used to support the work of the Principal Investigator, who collaborated with Profs. Scott Parker and John Cary at U. Colorado, and with two students, N. Xiang and J. Cheng also of U. Colorado. The technical accomplishments of this grant can be found in the publications listed in the final Section here. The main accomplishments of the grant work were: (1) Development and implementation of time-implicit two-fluid simulation methods in collaboration with the NIMROD team; and (2) Development and testing of a new time-implicit delta-f, energy-conserving method The basic two-fluid method, with many improvements is used in present NIMROD calculations. The energy-conserving delta-f method is under continuing development under contract between Coronado Consulting, a New Mexico sole proprietorship and the Oak Ridge National Laboratory.
Analytic, two fluid, field reversed configuration equilibrium with sheared rotation
International Nuclear Information System (INIS)
Sobehart, J.R.
1989-01-01
A two fluid model is used to derive an analytical equilibrium for elongated field reversed configurations containing shear in both the electron and ion velocity profiles. Like some semiempirical models used previously, the analytical expressions obtained provide a satisfactory fit to the experimental results for all radii with a few key parameters. The present results reduce to the rigid rotor model and the infinite conductivity case for a specific choice of the parameters
Nonlinear evolution of magnetic islands in a two fluid torus
International Nuclear Information System (INIS)
Sugiyama, L.E.; Park, W.
1996-01-01
A numerical model MH3D-T for the two fluid description of macroscopic evolution in a full three dimensional torus has been developed. Based on the perturbative drift ordering, generalized to arbitrary perturbation size, the model follows the full temperature evolution, including the thermal equilibration along the magnetic field. It contains the diamagnetic drifts, ion gyroviscous stress tensor, and the Hall term in Ohm's law. Electron inertia is neglected. The numerical model solves the same equations in a torus and in several simplified configurations. It has been benchmarked against the diamagnetic ω* i stabilization of the resistive m = 1, n = 1 reconnecting mode in a cylinder. The nonlinear evolution of resistive magnetic islands with m,n ≠ 1,1 in a cylinder is found to agree with previous analytic and reduced-torus results, which show that the diamagnetic rotation vanishes early in the island evolution and the saturated island size is determined by the same external driving factor Δ' as in MHD. The two fluid evolution in a full torus, however, differs from that in a cylinder and from the resistive MHD evolution. The poloidal rotation velocity undergoes a degree of poloidal momentum damping in the torus, even without neoclassical effects. The two fluid magnetic island grows faster, nonlinearly, than the resistive MHD island, and also couples different toroidal harmonics more effectively. Plasma compressibility and processes operating along the magnetic field play a much more important role than in MHD or in simple geometry. The two fluid model contains all the important neoclassical fluid effects except for the b circ ∇ circ Π parallelj viscous force terms. The addition of these terms is in progress
Survey of linear MHD stability in tokamak configurations
International Nuclear Information System (INIS)
Wakatani, M.
1977-01-01
The results found by MHD stability studies for both low-beta and high-beta tokamaks are reviewed. The stability against kink-ballooning modes in equilibria surrounded by vacuum or a layer of force free currents is considered. Internal kink modes and the relation to interchange modes, which should be considered after external kink modes are suppressed, are surveyed
International Nuclear Information System (INIS)
Robinson, D.C.
1987-01-01
With the advent of the new large tokamaks JET, JT-60 and TFTR important advances in magnetic confinement have been made. These include the exploitation of radio frequency and neutral beam heating on a much larger scale than previously, the demonstration of regimes of improved confinement and the demonstration of current drive at the Megamp level. A number of small and medium sized tokamaks have also come into operation recently such as WT-3 in Japan with an emphasis on radio frequency current drive and HL-1 a medium sized tokamak in China. Each of these new tokamaks is addressing specific problems which remain for the future development of the system. Of these particular problems: β, density and q limits remain important issues for the future development of the tokamak. β limits are being addressed on the DIII-D device in the USA. The anomalous confinement that the tokamak displays is being explored in detail on the TEXT device in the USA. Two other problems are impurity control and current drive. There is significant emphasis on divertor configurations at the present time with their enhanced confinement in the so called H mode. Due to improved discharge cleaning techniques and the ability to repetitively refuel using pellets, purer plasmas can be obtained even without divertors. Current drive remains a crucial issue for quasi of near steady state operation of the tokamak in the future and many current drive schemes are being investigated. (author) [pt
International Nuclear Information System (INIS)
Scheffel, J.
1982-04-01
Ideal MHD-equilibria for the toroidal EXTRAP configuration have been computed with an equilibrium code. The free-boundary prob- lem is solved by using the condition that the current density is proportional to r on a flux surface. It is found that the toroidal Z-pinch, initially induced in the central zero-field region of a transverse octupole field, drifts radially outwards producing an inverse -D shaped cross-section. The plasma current of this high- beta equilibrium may be increased if the plasma is pushed back by altering the external confining magnetic field as demonstrated. (Author)
Resurrecting Equilibria Through Cycles
DEFF Research Database (Denmark)
Barnett, Richard C.; Bhattacharya, Joydeep; Bunzel, Helle
equilibria because they asymptotically violate some economic restriction of the model. The literature has always ruled out such paths. This paper studies a pure-exchange monetary overlapping generations economy in which real balances cycle forever between momentary equilibrium points. The novelty is to show...... that segments of the offer curve that have been previously ignored, can in fact be used to produce asymptotically valid cyclical paths. Indeed, a cycle can bestow dynamic validity on momentary equilibrium points that had erstwhile been classified as dynamically invalid....
Linear waves in two-fluid relativistic gasdynamics
International Nuclear Information System (INIS)
Gavrikov, M.B.; Solov'ev, L.S.
1988-01-01
This paper is devoted to the development of a theory of waves propagating in a two-component gaseous medium. In all cases considered the authors use only the method of two-fluid relativistic electromagnetic gasdynamics in the framework of the special relativity theory. They pay special attention to the problem of the interaction in a mixture of both neutral and charged gases when they move relative to one another. This interaction is for charged gases responsible for the appearance of ohmic resistance to an electrical current
A numerical method for a transient two-fluid model
International Nuclear Information System (INIS)
Le Coq, G.; Libmann, M.
1978-01-01
The transient boiling two-phase flow is studied. In nuclear reactors, the driving conditions for the transient boiling are a pump power decay or/and an increase in heating power. The physical model adopted for the two-phase flow is the two fluid model with the assumption that the vapor remains at saturation. The numerical method for solving the thermohydraulics problems is a shooting method, this method is highly implicit. A particular problem exists at the boiling and condensation front. A computer code using this numerical method allow the calculation of a transient boiling initiated by a steady state for a PWR or for a LMFBR
Effect of impurity radiation on tokamak equilibrium
International Nuclear Information System (INIS)
Rebut, P.H.; Green, B.J.
1977-01-01
The energy loss from a tokamak plasma due to the radiation from impurities is of great importance in the overall energy balance. Taking the temperature dependence of this loss for two impurities characteristic of those present in existing tokamak plasmas, the condition for radial power balance is derived. For the impurities considered (oxygen and iron) it is found that the radiation losses are concentrated in a thin outer layer of the plasma and the equilibrium condition places an upper limit on the plasma paraticle number density in this region. This limiting density scales with mean current density in the same manner as is experimentally observed for the peak number density of tokamak plasmas. The stability of such equilibria is also discussed. (author)
Ripple induced trapped particle loss in tokamaks
International Nuclear Information System (INIS)
White, R.B.
1996-05-01
The threshold for stochastic transport of high energy trapped particles in a tokamak due to toroidal field ripple is calculated by explicit construction of primary resonances, and a numerical examination of the route to chaos. Critical field ripple amplitude is determined for loss. The expression is given in magnetic coordinates and makes no assumptions regarding shape or up-down symmetry. An algorithm is developed including the effects of prompt axisymmetric orbit loss, ripple trapping, convective banana flow, and stochastic ripple loss, which gives accurate ripple loss predictions for representative Tokamak Fusion Test Reactor and International Thermonuclear Experimental Reactor equilibria. The algorithm is extended to include the effects of collisions and drag, allowing rapid estimation of alpha particle loss in tokamaks
Institutions, Equilibria and Efficiency
DEFF Research Database (Denmark)
Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria in such set......Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria...... in such settings is proven under very general preference assumptions. The model is extended to include geographical location choice, a commodity space incorporating manufacturing imprecision and preferences for club-membership, schools and firms. Inefficiencies arising from household externalities or group...... membership are evaluated. Core equivalence is shown for bargaining economies. The theory of risk aversion is extended and the relation between risk taking and wealth is experimentally investigated. Other topics include: determinacy in OLG with cash-in-advance constraints, income distribution and democracy...
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
Energy Technology Data Exchange (ETDEWEB)
Loizu, J. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany); Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Hudson, S. R.; Bhattacharjee, A.; Lazerson, S. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Helander, P. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany)
2015-09-15
We consider the linear and nonlinear ideal plasma response to a boundary perturbation in a screw pinch. We demonstrate that three-dimensional, ideal-MHD equilibria with continuously nested flux-surfaces and with discontinuous rotational-transform across the resonant rational-surfaces are well defined and can be computed both perturbatively and using fully nonlinear equilibrium calculations. This rescues the possibility of constructing MHD equilibria with current sheets and continuous, smooth pressure profiles. The results predict that, even if the plasma acts as a perfectly conducting fluid, a resonant magnetic perturbation can penetrate all the way into the center of a tokamak without being shielded at the resonant surface.
ALFVEN WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
Energy Technology Data Exchange (ETDEWEB)
Soler, R.; Ballester, J. L.; Terradas, J. [Departament de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Carbonell, M., E-mail: roberto.soler@uib.es, E-mail: joseluis.ballester@uib.es, E-mail: jaume.terradas@uib.es, E-mail: marc.carbonell@uib.es [Departament de Matematiques i Informatica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain)
2013-04-20
Alfven waves are a particular class of magnetohydrodynamic waves relevant in many astrophysical and laboratory plasmas. In partially ionized plasmas the dynamics of Alfven waves is affected by the interaction between ionized and neutral species. Here we study Alfven waves in a partially ionized plasma from the theoretical point of view using the two-fluid description. We consider that the plasma is composed of an ion-electron fluid and a neutral fluid, which interact by means of particle collisions. To keep our investigation as general as possible, we take the neutral-ion collision frequency and the ionization degree as free parameters. First, we perform a normal mode analysis. We find the modification due to neutral-ion collisions of the wave frequencies and study the temporal and spatial attenuation of the waves. In addition, we discuss the presence of cutoff values of the wavelength that constrain the existence of oscillatory standing waves in weakly ionized plasmas. Later, we go beyond the normal mode approach and solve the initial-value problem in order to study the time-dependent evolution of the wave perturbations in the two fluids. An application to Alfven waves in the low solar atmospheric plasma is performed and the implication of partial ionization for the energy flux is discussed.
Neutronic analysis of two-fluid thorium molten salt reactor
International Nuclear Information System (INIS)
Frybort, Jan; Vocka, Radim
2009-01-01
The aim of this paper is to evaluate features of the two-fluid MSBR through a parametric study and compare its properties to one-fluid MSBR concepts. The starting point of the analysis is the original ORNL 1000 MWe reactor design, although simplified to some extent. We studied the influence of dimensions of distinct reactor parts - fuel and fertile channels radius, plenum height, design etc. - on fundamental reactor properties: breeding ratio and doubling time, reactor inventory, graphite lifetime, and temperature feedback coefficients. The calculations were carried out using MCNP5 code. Based on obtained results we proposed an improved reactor design. Our results show clear advantages of the concept with two separate fluoride salts if compared to the one fluid concept in breading, doubling time, and temperature feedback coefficients. Limitations of the two-fluid concept - particularly the graphite lifetime - are also pointed out. The reactor design can be a subject of further optimizations, namely from the viewpoint of reactor safety. (author)
Vortex dynamics in the two-fluid model
International Nuclear Information System (INIS)
Thouless, D. J.; Geller, M. R.; Vinen, W. F.; Fortin, J.-Y.; Rhee, S. W.
2001-01-01
We have used two-fluid dynamics to study the discrepancy between the work of Thouless, Ao, and Niu (TAN) and that of Iordanskii. In TAN no transverse force on a vortex due to normal fluid flow was found, whereas the earlier work found a transverse force proportional to normal fluid velocity u n and normal fluid density ρ n . We have linearized the time-independent two-fluid equations about the exact solution for a vortex, and find three solutions that are important in the region far from the vortex. Uniform superfluid flow gives rise to the usual superfluid Magnus force. Uniform normal fluid flow gives rise to no forces in the linear region, but does not satisfy reasonable boundary conditions at short distances. A logarithmically increasing normal fluid flow gives a viscous force. As in classical hydrodynamics, and as in the early work of Hall and Vinen, this logarithmic increase must be cut off by nonlinear effects at large distances; this gives a viscous force proportional to u n /lnu n , and a transverse contribution that goes like u n /(lnu n ) 2 , even in the absence of an explicit Iordanskii force. In the limit u n ->0 the TAN result is obtained, but at nonzero u n there are important corrections that were not found in TAN. We argue that the Magnus force in a superfluid at nonzero temperature is an example of a topological relation for which finite-size corrections may be large
Large interface simulation in an averaged two-fluid code
International Nuclear Information System (INIS)
Henriques, A.
2006-01-01
Different ranges of size of interfaces and eddies are involved in multiphase flow phenomena. Classical formalisms focus on a specific range of size. This study presents a Large Interface Simulation (LIS) two-fluid compressible formalism taking into account different sizes of interfaces. As in the single-phase Large Eddy Simulation, a filtering process is used to point out Large Interface (LI) simulation and Small interface (SI) modelization. The LI surface tension force is modelled adapting the well-known CSF method. The modelling of SI transfer terms is done calling for classical closure laws of the averaged approach. To simulate accurately LI transfer terms, we develop a LI recognition algorithm based on a dimensionless criterion. The LIS model is applied in a classical averaged two-fluid code. The LI transfer terms modelling and the LI recognition are validated on analytical and experimental tests. A square base basin excited by a horizontal periodic movement is studied with the LIS model. The capability of the model is also shown on the case of the break-up of a bubble in a turbulent liquid flow. The break-up of a large bubble at a grid impact performed regime transition between two different scales of interface from LI to SI and from PI to LI. (author) [fr
Physics parameter space of tokamak ignition devices
International Nuclear Information System (INIS)
Selcow, E.C.; Peng, Y.K.M.; Uckan, N.A.; Houlberg, W.A.
1985-01-01
This paper describes the results of a study to explore the physics parameter space of tokamak ignition experiments. A new physics systems code has been developed to perform the study. This code performs a global plasma analysis using steady-state, two-fluid, energy-transport models. In this paper, we discuss the models used in the code and their application to the analysis of compact ignition experiments. 8 refs., 8 figs., 1 tab
Adsorption analysis equilibria and kinetics
Do, Duong D
1998-01-01
This book covers topics of equilibria and kinetics of adsorption in porous media. Fundamental equilibria and kinetics are dealt with for homogeneous as well as heterogeneous particles. Five chapters of the book deal with equilibria and eight chapters deal with kinetics. Single component as well as multicomponent systems are discussed. In kinetics analysis, we deal with the various mass transport processes and their interactions inside a porous particle. Conventional approaches as well as the new approach using Maxwell-Stefan equations are presented. Various methods to measure diffusivity, such
Quantum equilibria for macroscopic systems
International Nuclear Information System (INIS)
Grib, A; Khrennikov, A; Parfionov, G; Starkov, K
2006-01-01
Nash equilibria are found for some quantum games with particles with spin-1/2 for which two spin projections on different directions in space are measured. Examples of macroscopic games with the same equilibria are given. Mixed strategies for participants of these games are calculated using probability amplitudes according to the rules of quantum mechanics in spite of the macroscopic nature of the game and absence of Planck's constant. A possible role of quantum logical lattices for the existence of macroscopic quantum equilibria is discussed. Some examples for spin-1 cases are also considered
Quantum equilibria for macroscopic systems
Energy Technology Data Exchange (ETDEWEB)
Grib, A [Department of Theoretical Physics and Astronomy, Russian State Pedagogical University, St. Petersburg (Russian Federation); Khrennikov, A [Centre for Mathematical Modelling in Physics and Cognitive Sciences Vaexjoe University (Sweden); Parfionov, G [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation); Starkov, K [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation)
2006-06-30
Nash equilibria are found for some quantum games with particles with spin-1/2 for which two spin projections on different directions in space are measured. Examples of macroscopic games with the same equilibria are given. Mixed strategies for participants of these games are calculated using probability amplitudes according to the rules of quantum mechanics in spite of the macroscopic nature of the game and absence of Planck's constant. A possible role of quantum logical lattices for the existence of macroscopic quantum equilibria is discussed. Some examples for spin-1 cases are also considered.
Jump conditions in transonic equilibria
International Nuclear Information System (INIS)
Guazzotto, L.; Betti, R.; Jardin, S. C.
2013-01-01
In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto et al.[Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that “standard” (low-β, large aspect ratio) transonic equilibria satisfy the correct jump condition with very good approximation even if the jump condition is not explicitly imposed. On the other hand, it is also found that high-β, low aspect ratio equilibria require the correct jump condition to be explicitly imposed. Various numerical approaches are described to modify FLOW to include the jump condition. It is proved that the new methods converge to the correct solution even in extreme cases of very large β, while they agree with the results obtained with the old implementation of FLOW in lower-β equilibria.
Pierce instability and bifurcating equilibria
International Nuclear Information System (INIS)
Godfrey, B.B.
1981-01-01
The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities
Tokamak power systems studies at ANL
International Nuclear Information System (INIS)
Baker, C.C.; Ehst, D.A.; Brooks, J.N.; Evans, K. Jr.
1986-01-01
A number of advances in plasma physics and engineering promise to greatly improve the reactor prospects of tokamaks. The following features, in particular, are examined: (a) large aspect ratio (A ≅ 6), which may ease maintenance; (b) high beta (β ≥ 0.20) without indentation, which brings the maximum toroidal field down to about 7 T; (c) low toroidal current (I ≅ 5MA), which reduces the cost of the current drive and equilibrium field system; and (d) steady state operation with current density control via fast and slow wave current drive. The key to high beta operation with low toroidal current lies in utilizing second stability regime equilibria with the required current distributions produced by an appropriate selection of wave driver frequencies and power spectra. The ray tracing and current drive calculation is self-consistent with the actual magnetic fields produced in the plasma. In addition to matching desirable high-beta equilibria, this method is capable of producing a large variety of new equilibria, many of which look attractive. The impurity control activities in TPSS have emphasized the self-pumping concept as applied to using the entire first wall or ''slot'' limiters. The blanket design effort has emphasized liquid metal and Flibe concepts. The reference concept is a liquid lithium/vanadium, self-cooled configuration. Overall, there exists a number of major design improvements which will substantially improve the attractiveness of tokamak reactors
Czech Academy of Sciences Publication Activity Database
Řípa, Milan; Křenek, Petr
2011-01-01
Roč. 17, č. 1 (2011), s. 32-34 ISSN 1210-4612 Institutional research plan: CEZ:AV0Z20430508 Keywords : fusion * tokamak * Compass * Golem * Institute of Plasma Physics AVCR v.v * NBI * diagnostics Subject RIV: BL - Plasma and Gas Discharge Physics
Energetically resolved multiple-fluid equilibria of tokamak plasmas
International Nuclear Information System (INIS)
Hole, M J; Dennis, G
2009-01-01
In many magnetically confined fusion experiments, a significant fraction of the stored energy of the plasma resides in energetic, or non-thermal, particle populations. Despite this, most equilibrium treatments are based on MHD: a single fluid treatment which assumes a Maxwell-Boltzmann distribution function. Detailed magnetic reconstruction based on this treatment ignore the energetic complexity of the plasma and can result in model-data inconsistencies, such as thermal pressure profiles which are inconsistent with the total stored kinetic energy of the plasma. Alternatively, ad hoc corrections to the pressure profile, such as summing the energetic and thermal pressures, have poor theoretical justification. Motivated by this omission, we generalize ideal MHD one step further: we consider multiple quasi-neutral fluids, each in thermal equilibrium and each thermally insulated from each other-no population mixing occurs. Kinetically, such a model may be able to describe the ion or electron distribution function in regions of velocity phase space with a large number of particles, at the expense of more weakly populated phase space, which may have uncharacteristically high temperature and hence pressure. As magnetic equilibrium effects increase with the increase in pressure, our work constitutes an upper limit to the effect of energetic particles. When implemented into an existing solver, FLOW (Guazzotto et al 2004 Phys. Plasmas 11, 604-14), it becomes possible to qualitatively explore the impact of resolving the energetic populations on plasma equilibrium configurations in realistic geometry. Deploying the modified code, FLOW-M, on a high performance spherical torus configuration, we find that the effect of variations of the pressure, poloidal flow and toroidal flow of the energetic populations is qualitatively similar to variations in the background plasma. We also study the robustness of the equilibrium to uncertainties in the current profile and the energetic toroidal rotation or energetic pressure profile. For constant toroidal current and stored energy, the change in the poloidal flux with changes in the current profile is similar irrespective of whether the toroidal rotation or pressure was changed, indicating insensitivity to whether uncertainties lie in the pressure or toroidal rotation profiles. We conclude that to a first approximation, lumping the energetic and thermal fluids together, as is done for many equilibrium solvers, qualitatively produces correct results.
Neoclassical toroidal viscosity in perturbed equilibria with general tokamak geometry
Energy Technology Data Exchange (ETDEWEB)
Logan, Nikolas C.; Park, Jong-Kyu; Kim, Kimin; Wang, Zhirui [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Berkery, John W. [Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States)
2013-12-15
This paper presents a calculation of neoclassical toroidal viscous torque independent of large-aspect-ratio expansions across kinetic regimes. The Perturbed Equilibrium Nonambipolar Transport (PENT) code was developed for this purpose, and is compared to previous combined regime models as well as regime specific limits and a drift kinetic δf guiding center code. It is shown that retaining general expressions, without circular large-aspect-ratio or other orbit approximations, can be important at experimentally relevant aspect ratio and shaping. The superbanana plateau, a kinetic resonance effect recently recognized for its relevance to ITER, is recovered by the PENT calculations and shown to require highly accurate treatment of geometric effects.
Collisionless current sheet equilibria
Neukirch, T.; Wilson, F.; Allanson, O.
2018-01-01
Current sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.
Two-fluid Numerical Simulations of Solar Spicules
Energy Technology Data Exchange (ETDEWEB)
Kuźma, Błażej; Murawski, Kris; Kayshap, Pradeep; Wójcik, Darek [Group of Astrophysics, University of Maria Curie-Skłodowska, ul. Radziszewskiego 10, 20-031 Lublin (Poland); Srivastava, Abhishek Kumar; Dwivedi, Bhola N., E-mail: blazejkuzma1@gmail.com [Department of Physics, Indian Institute of Technology (BHU), Varanasi-221005 (India)
2017-11-10
We aim to study the formation and evolution of solar spicules by means of numerical simulations of the solar atmosphere. With the use of newly developed JOANNA code, we numerically solve two-fluid (for ions + electrons and neutrals) equations in 2D Cartesian geometry. We follow the evolution of a spicule triggered by the time-dependent signal in ion and neutral components of gas pressure launched in the upper chromosphere. We use the potential magnetic field, which evolves self-consistently, but mainly plays a passive role in the dynamics. Our numerical results reveal that the signal is steepened into a shock that propagates upward into the corona. The chromospheric cold and dense plasma lags behind this shock and rises into the corona with a mean speed of 20–25 km s{sup −1}. The formed spicule exhibits the upflow/downfall of plasma during its total lifetime of around 3–4 minutes, and it follows the typical characteristics of a classical spicule, which is modeled by magnetohydrodynamics. The simulated spicule consists of a dense and cold core that is dominated by neutrals. The general dynamics of ion and neutral spicules are very similar to each other. Minor differences in those dynamics result in different widths of both spicules with increasing rarefaction of the ion spicule in time.
Two-fluid model stability, simulation and chaos
Bertodano, Martín López de; Clausse, Alejandro; Ransom, Victor H
2017-01-01
This book addresses the linear and nonlinear two-phase stability of the one-dimensional Two-Fluid Model (TFM) material waves and the numerical methods used to solve it. The TFM fluid dynamic stability is a problem that remains open since its inception more than forty years ago. The difficulty is formidable because it involves the combined challenges of two-phase topological structure and turbulence, both nonlinear phenomena. The one dimensional approach permits the separation of the former from the latter. The authors first analyze the kinematic and Kelvin-Helmholtz instabilities with the simplified one-dimensional Fixed-Flux Model (FFM). They then analyze the density wave instability with the well-known Drift-Flux Model. They demonstrate that the Fixed-Flux and Drift-Flux assumptions are two complementary TFM simplifications that address two-phase local and global linear instabilities separately. Furthermore, they demonstrate with a well-posed FFM and a DFM two cases of nonlinear two-phase behavior that are ...
MAGNETOACOUSTIC WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
Energy Technology Data Exchange (ETDEWEB)
Soler, Roberto; Ballester, Jose Luis [Departament de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Carbonell, Marc, E-mail: roberto.soler@uib.es, E-mail: joseluis.ballester@uib.es, E-mail: marc.carbonell@uib.es [Departament de Matemàtiques i Informàtica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain)
2013-11-01
Compressible disturbances propagate in a plasma in the form of magnetoacoustic waves driven by both gas pressure and magnetic forces. In partially ionized plasmas the dynamics of ionized and neutral species are coupled due to ion-neutral collisions. As a consequence, magnetoacoustic waves propagating through a partially ionized medium are affected by ion-neutral coupling. The degree to which the behavior of the classic waves is modified depends on the physical properties of the various species and on the relative value of the wave frequency compared to the ion-neutral collision frequency. Here, we perform a comprehensive theoretical investigation of magnetoacoustic wave propagation in a partially ionized plasma using the two-fluid formalism. We consider an extensive range of values for the collision frequency, ionization ratio, and plasma β, so that the results are applicable to a wide variety of astrophysical plasmas. We determine the modification of the wave frequencies and study the frictional damping due to ion-neutral collisions. Approximate analytic expressions for the frequencies are given in the limit case of strongly coupled ions and neutrals, while numerically obtained dispersion diagrams are provided for arbitrary collision frequencies. In addition, we discuss the presence of cutoffs in the dispersion diagrams that constrain wave propagation for certain combinations of parameters. A specific application to propagation of compressible waves in the solar chromosphere is given.
Two-fluid model for locomotion under self-confinement
Reigh, Shang Yik; Lauga, Eric
2017-09-01
The bacterium Helicobacter pylori causes ulcers in the stomach of humans by invading mucus layers protecting epithelial cells. It does so by chemically changing the rheological properties of the mucus from a high-viscosity gel to a low-viscosity solution in which it may self-propel. We develop a two-fluid model for this process of swimming under self-generated confinement. We solve exactly for the flow and the locomotion speed of a spherical swimmer located in a spherically symmetric system of two Newtonian fluids whose boundary moves with the swimmer. We also treat separately the special case of an immobile outer fluid. In all cases, we characterize the flow fields, their spatial decay, and the impact of both the viscosity ratio and the degree of confinement on the locomotion speed of the model swimmer. The spatial decay of the flow retains the same power-law decay as for locomotion in a single fluid but with a decreased magnitude. Independent of the assumption chosen to characterize the impact of confinement on the actuation applied by the swimmer, its locomotion speed always decreases with an increase in the degree of confinement. Our modeling results suggest that a low-viscosity region of at least six times the effective swimmer size is required to lead to swimming with speeds similar to locomotion in an infinite fluid, corresponding to a region of size above ≈25 μ m for Helicobacter pylori.
MAGNETOACOUSTIC WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
International Nuclear Information System (INIS)
Soler, Roberto; Ballester, Jose Luis; Carbonell, Marc
2013-01-01
Compressible disturbances propagate in a plasma in the form of magnetoacoustic waves driven by both gas pressure and magnetic forces. In partially ionized plasmas the dynamics of ionized and neutral species are coupled due to ion-neutral collisions. As a consequence, magnetoacoustic waves propagating through a partially ionized medium are affected by ion-neutral coupling. The degree to which the behavior of the classic waves is modified depends on the physical properties of the various species and on the relative value of the wave frequency compared to the ion-neutral collision frequency. Here, we perform a comprehensive theoretical investigation of magnetoacoustic wave propagation in a partially ionized plasma using the two-fluid formalism. We consider an extensive range of values for the collision frequency, ionization ratio, and plasma β, so that the results are applicable to a wide variety of astrophysical plasmas. We determine the modification of the wave frequencies and study the frictional damping due to ion-neutral collisions. Approximate analytic expressions for the frequencies are given in the limit case of strongly coupled ions and neutrals, while numerically obtained dispersion diagrams are provided for arbitrary collision frequencies. In addition, we discuss the presence of cutoffs in the dispersion diagrams that constrain wave propagation for certain combinations of parameters. A specific application to propagation of compressible waves in the solar chromosphere is given
The CHEASE code for toroidal MHD equilibria
Energy Technology Data Exchange (ETDEWEB)
Luetjens, H. [Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique; Bondeson, A. [Chalmers Univ. of Technology, Goeteborg (Sweden). Inst. for Electromagnetic Field Theory and Plasma Physics; Sauter, O. [ITER-San Diego, La Jolla, CA (United States)
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function {Psi}. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs.
The CHEASE code for toroidal MHD equilibria
International Nuclear Information System (INIS)
Luetjens, H.
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function Ψ. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs
Axisymmetric Plasma Equilibria in General Relativity
Elsässer, Klaus
Axisymmetric plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species; they remain arbitrary if no gain and loss processes are considered, in close analogy to the free flux functions in ideal magnetohydrodynamics. Several simplifying assumptions allow the reduction of the basic equations to one single scalar equation for the stream function χ of positrons or ions, respectively, playing the rôle of the Grad/Shafranov equation in magnetohydrodynamics; in particular, Maxwell's equations can be solved analytically for a quasineutral plasma when both the charge density and the toroidal electric current density are negligible (in contrast to the Tokamak situation). The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio me/mi. The χ-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
Magnetic mapping of the TBR-1 tokamak
International Nuclear Information System (INIS)
Matta, Jose Antonio Sevidanes da.
1994-01-01
Axisymmetric hydromagnetic equilibria for an ideal conducting current fluid are described by means of an asymptotic expansion in powers of the inverse aspect ratio (ε α/R 0 ) that satisfies the Grad-Shafranov equation (equilibrium condition). The main profiles for these equilibria were computer. The effect of non-axisymmetric perturbations on the magnetic surfaces if the tokamak TBR-1 is investigated. The used method is able to show how magnetic field from external helical currents split the rational magnetic surface giving rise to the chain of magnetic islands. The Poincare map of the field line perturbed by resonant helical windings has been obtained numerically for the typical TBR-1 parameters. For increasing parameters of perturbation secondary resonances were observed, that transform the bound-state-like contours of a given island into similar structures of secondary magnetic islands. These results were used to determine the spectrum of the perturbation created by resonant helical windings. (author). 87 refs., 30 figs
High-beta tokamak research. Annual progress report, 1 August 1982-1 August 1983
International Nuclear Information System (INIS)
Navratil, G.A.
1983-08-01
The main research objectives during the past year fell into four areas: (1) detailed observations over a range of high-beta tokamak equilibria; (2) fabrication of an improved and more flexible high-beta tokamak based on our understanding of the present Torus II; (3) extension of the pulse length to 100 usec with power crowbar operation of the equilibrium field coil sets; and (4) comparison of our equilibrium and stability observations with computational models of MHD equilibrium and stability
Two-fluid model LES of a bubble column
International Nuclear Information System (INIS)
Brahma N Reddy Vanga; Martin A Lopez de Bertodano; Eckhard Krepper; Alexandr Zaruba; Horst-Michael Prasser
2005-01-01
The hydrodynamics of a rectangular bubble column operating in the dispersed bubbly regime has been numerically investigated using a two-fluid model Large Eddy Simulation (LES). Experimental data were obtained to validate the model. LES computational fluid dynamic calculations of the transient flow for the bubble column were performed to account for the turbulence in the liquid phase. The computational mesh is of the same scale as the bubble size. The sub grid-scale Reynolds stresses were calculated with the Smagorinsky model. Furthermore, the effect of the bubbles on the turbulence in the continuous phase was modeled using Sato's eddy viscosity model for bubble-induced turbulence. Mean quantities were computed by averaging over a time period that was longer than the dynamic time scales of the turbulence, in particular the void fraction and the average velocity of the bubbles. A systematic analysis of the effect of the interfacial momentum transfer terms on these quantities has been conducted. The bubble column was locally aerated using a sparger located in the center of the bottom plate. The experimental studies involve wire-mesh tomography measurements for void fraction and bubble size distributions and digital image processing of high speed camera images for estimation of bubble velocities, size distributions and flow patterns. Experiments were performed for various aspect ratios (height of water column to width ratio) and superficial gas velocities. It was found that the non-drag bubble forces play a very prominent role in the predicting the correct flow pattern and void fraction distributions. In the calculations, the lift force and the wall force were considered. A 'wall peak' in the time averaged void fraction distribution has been experimentally observed and this cannot be predicted without including these non-drag forces in the numerical calculations. In this paper, experimental data are compared with the results of the numerical simulations. (authors)
Learning to Play Efficient Coarse Correlated Equilibria
Borowski, Holly P.; Marden, Jason R.; Shamma, Jeff S.
2018-01-01
The majority of the distributed learning literature focuses on convergence to Nash equilibria. Coarse correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However
International Nuclear Information System (INIS)
1991-05-01
The technical reports in this document were presented at the IAEA Technical Committee Meeting ''Research on Small Tokamaks'', September 1990, in three sessions, viz., (1) Plasma Modes, Control, and Internal Phenomena, (2) Edge Phenomena, and (3) Advanced Configurations and New Facilities. In Section (1) experiments at controlling low mode number modes, feedback control using external coils, lower-hybrid current drive for the stabilization of sawtooth activity and continuous (1,1) mode, and unmodulated and fast modulated ECRH mode stabilization experiments were reported, as well as the relation to disruptions and transport of low m,n modes and magnetic island growth; static magnetic perturbations by helical windings causing mode locking and sawtooth suppression; island widths and frequency of the m=2 tearing mode; ultra-fast cooling due to pellet injection; and, finally, some papers on advanced diagnostics, i.e., lithium-beam activated charge-exchange spectroscopy, and detection through laser scattering of discrete Alfven waves. In Section (2), experimental edge physics results from a number of machines were presented (positive biasing on HYBTOK II enhancing the radial electric field and improving confinement; lower hybrid current drive on CASTOR improving global particle confinement, good current drive efficiency in HT-6B showing stabilization of sawteeth and Mirnov oscillations), as well as diagnostic developments (multi-chord time resolved soft and ultra-soft X-ray plasma radiation detection on MT-1; measurements on electron capture cross sections in multi-charged ion-atom collisions; development of a diagnostic neutral beam on Phaedrus-T). Theoretical papers discussed the influence of sheared flow and/or active feedback on edge microstability, large edge electric fields, and two-fluid modelling of non-ambipolar scrape-off layers. Section (3) contained (i) a proposal to construct a spherical tokamak ''Proto-Eta'', (ii) an analysis of ultra-low-q and runaway
Kinetic energy principle and neoclassical toroidal torque in tokamaks
International Nuclear Information System (INIS)
Park, Jong-Kyu
2011-01-01
It is shown that when tokamaks are perturbed, the kinetic energy principle is closely related to the neoclassical toroidal torque by the action invariance of particles. Especially when tokamaks are perturbed from scalar pressure equilibria, the imaginary part of the potential energy in the kinetic energy principle is equivalent to the toroidal torque by the neoclassical toroidal viscosity. A unified description therefore should be made for both physics. It is also shown in this case that the potential energy operator can be self-adjoint and thus the stability calculation can be simplified by minimizing the potential energy.
Fusion-product transport in axisymmetric tokamaks: losses and thermalization
International Nuclear Information System (INIS)
Hively, L.M.
1980-01-01
High-energy fusion-product losses from an axisymmetric tokamak plasma are studied. Prompt-escape loss fluxes (i.e. prior to slowing down) are calculated including the non-separable dependence of flux as a function of poloidal angle and local angle-of-incidence at the first wall. Fusion-product (fp) thermalization and heating are calculated assuming classical slowing down. The present analytical model describes fast ion orbits and their distribution function in realistic, high-β, non-circular tokamak equilibria. First-orbit losses, trapping effects, and slowing-down drifts are also treated
Axisymmetric stability of vertically asymmetric tokamaks at large beta poloidal
International Nuclear Information System (INIS)
Yamazaki, K.; Fishman, H.; Okabayashi, M.; Todd, A.M.M.
1981-09-01
The stability of high-β vertically asymmetric tokamak equilibria to rigid displacements is investigated analytically. It is found that vertical stability at large beta poloidal is mainly determined by a coupling between the shape of the plasma surface and the Shafranov shift of the magnetic axis. To the lowest order, symmetric components of the plasma surface shape are found to be the critical destabilizing elements. Asymmetric components have little effect. The inclusion of higher order terms in the high β tokamak expansion leads to further destabilization. Qualitative agreement between these analytic results and numerical stability calculations using the PEST code is demonstrated
Linear and nonlinear kinetic-stability studies in tokamaks
International Nuclear Information System (INIS)
Tang, W.M.; Chance, M.S.; Chen, L.; Krommes, J.A.; Lee, W.W.; Rewoldt, G.
1982-09-01
This paper presents results of theoretical investigations on important linear kinetic properties of low frequency instabilities in toroidal systems and on nonlinear processes which could significantly influence their impact on anomalous transport. Analytical and numerical methods and also particle simulations have been employed to carry out these studies. In particular, the following subjects are considered: (1) linear stability analysis of kinetic instabilities for realistic tokamak equilibria and the application of such calculations to the PDX and PLT tokamak experiments including the influence of a hot beam-ion component; (2) determination of nonlinearly saturated, statistically steady states of three interacting drift modes; and (3) gyrokinetic particle simulation of drift instabilities
Time evolution of tokamak states with flow
International Nuclear Information System (INIS)
Kerner, W.; Weitzner, H.
1985-12-01
The general dissipative Braginskii single-fluid model is applied to simulate tokamak transport. An expansion with respect to epsilon = (ω/sub i/tau/sub i/) -1 , the factor by which perpendicular and parallel transport coefficients differ, yields a numerically tractable scheme. The resulting 1-1/2 D procedure requires computation of 2D toroidal equilibria with flow together with the solution of a system of ordinary 1D flux-averaged equations for the time evolution of the profiles. 13 refs
Partial Cooperative Equilibria: Existence and Characterization
Directory of Open Access Journals (Sweden)
Amandine Ghintran
2010-09-01
Full Text Available We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.
Models for impurity effects in tokamaks
International Nuclear Information System (INIS)
Hogan, J.T.
1980-03-01
Models for impurity effects in tokamaks are described with an emphasis on the relationship between attainment of high β and impurity problems. We briefly describe the status of attempts to employ neutral beam heating to achieve high β in tokamaks and propose a qualitative model for the mechanism by which heavy metal impurities may be produced in the startup phase of the discharge. We then describe paradoxes in impurity diffusion theory and discuss possible resolutions in terms of the effects of large-scale islands and sawtooth oscillations. Finally, we examine the prospects for the Zakharov-Shafranov catastrophe (long time scale disintegration of FCT equilibria) in the context of present and near-term experimental capability
Stability of multihelical tearing modes in shaped tokamaks
International Nuclear Information System (INIS)
Kerner, W.; Tasso, H.
1982-03-01
The stability of multihelical tearing modes in tokamaks with shaped cross-sections is determined numerically. The method allows inclusion of a large number of singular surfaces resolved with high accuracy. Poloidal and radial couplings are discussed and the convergence is well understood. High poloidal m number modes are found to be unstable for typical equilibria. Completely stable current distributions have been constructed for D-shaped plasmas. (orig.)
Stackelberg equilibria and horizontal differentiation
Lambertini, Luca
1993-01-01
This paper proposes a taxonomy of the Stackelberg equilibria emerging from a standard game of horizontal differentiation à la Hotelling in which the strategy set of the sellers in the location stage is the real axis. Repeated leadership appears the most advantageous position. Furthermore, this endogenously yields vertical differentiation between products at equilibrium.
Economic comparison of MHD equilibrium options for advanced steady state tokamak power plants
International Nuclear Information System (INIS)
Ehst, D.A.; Kessel, C.E.; Jardin, S.C.; Krakowski, R.A.; Bathke, C.G.; Mau, T.K.; Najmabadi, F.
1998-01-01
Progress in theory and in tokamak experiments leads to questions of the optimal development path for commercial tokamak power plants. The economic prospects of future designs are compared for several tokamak operating modes: (high poloidal beta) first stability, second stability and reverse shear. Using a simplified economic model and selecting uniform engineering performance parameters, this comparison emphasizes the different physics characteristics - stability and non- inductive current drive - of the various equilibria. The reverse shear mode of operation is shown to offer the lowest cost of electricity for future power plants. (author)
Two-Fluid Mathematical Models for Blood Flow in Stenosed Arteries: A Comparative Study
Directory of Open Access Journals (Sweden)
Sankar DS
2009-01-01
Full Text Available The pulsatile flow of blood through stenosed arteries is analyzed by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is assumed as a (i Herschel-Bulkley fluid and (ii Casson fluid. Perturbation method is used to solve the resulting system of non-linear partial differential equations. Expressions for various flow quantities are obtained for the two-fluid Casson model. Expressions of the flow quantities obtained by Sankar and Lee (2006 for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is found that the plug flow velocity and velocity distribution of the two-fluid Casson model are considerably higher than those of the two-fluid Herschel-Bulkley model. It is also observed that the pressure drop, plug core radius, wall shear stress and the resistance to flow are significantly very low for the two-fluid Casson model than those of the two-fluid Herschel-Bulkley model. Hence, the two-fluid Casson model would be more useful than the two-fluid Herschel-Bulkley model to analyze the blood flow through stenosed arteries.
International Nuclear Information System (INIS)
Cumyn, P.B.
A consortium of five organizations under the leadership of IREQ, the Institute de Recherche d'Hydro-Quebec has completed a conceptual design study for a tokamak device, and in January 1981 its construction was authorized with funding being provided principally by Hydro-Quebec and the National Research Council, as well as by the Ministre d'Education du Quebec and Natural Sciences and Engineering Research Council of Canada (NSERC). The device will form the focus of Canada's magnetic-fusion program and will be located in IREQ's laboratories in Varennes. Presently the machine layout is being finalized from the physics point of view and work has started on equipment design and specification. The Tokamak de Varennes will be an experimental device, the purpose of which is to study plasma and other fusion related phenomena. In particular it will study: 1. Plasma impurities and plasma/liner interaction; 2. Long pulse or quasi-continuous operation using plasma rampdown and eventually plasma current reversal in order to maintain the plasma; and 3. Advanced diagnostics
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
International Nuclear Information System (INIS)
Ottaviani, M.; Tebaldi, C.
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
A fast, user-friendly code for calculating magnetohydrodynamic equilibria
International Nuclear Information System (INIS)
Haney, S.W.; Freidberg, J.P.; Solomon, C.J.
1995-01-01
Using variational techniques, we have developed a fast, user-friendly code for computing approximate, but highly accurate fixed boundary magnetohydrodynamic equilibria for tokamak plasmas. The variational procedure simplifies the problem---a two-dimensional nonlinear partial differential equation---to a set of nonlinear algebraic equations. The reduced problem can be readily solved on workstations or personal computers. This allows us to exploit sophisticated graphical user interfaces that make supplying calculation data and viewing results easy. This ease-of-use, along with the semianalytic nature of our calculation, allows researchers to routinely incorporate equilibrium information into their work. It also provides a tool for educators teaching fusion theory. We describe the variational formulation, the speed and accuracy of the computer implementation, and the design and operation of a user-friendly graphical interface
International Nuclear Information System (INIS)
Haines, M.G.
1984-01-01
The physical conditions required for breakeven in thermonuclear fusion are derived, and the early conceptual ideas of magnetic confinement and subsequent development are followed, leading to present-day large scale tokamak experiments. Confinement and diffusion are developed in terms of particle orbits, whilst magnetohydrodynamic stability is discussed from energy considerations. From these ideas are derived the scaling laws that determine the physical size and parameters of this fusion configuration. It becomes clear that additional heating is required. However there are currently several major gaps in our understanding of experiments; the causes of anomalous electron energy loss and the major current disruption, the absence of the 'bootstrap' current and what physics determines the maximum plasma pressure consistent with stability. The understanding of these phenomena is a major challenge to plasma physicists. (author)
Nash Equilibria in Fisher Market
Adsul, Bharat; Babu, Ch. Sobhan; Garg, Jugal; Mehta, Ruta; Sohoni, Milind
Much work has been done on the computation of market equilibria. However due to strategic play by buyers, it is not clear whether these are actually observed in the market. Motivated by the observation that a buyer may derive a better payoff by feigning a different utility function and thereby manipulating the Fisher market equilibrium, we formulate the Fisher market game in which buyers strategize by posing different utility functions. We show that existence of a conflict-free allocation is a necessary condition for the Nash equilibria (NE) and also sufficient for the symmetric NE in this game. There are many NE with very different payoffs, and the Fisher equilibrium payoff is captured at a symmetric NE. We provide a complete polyhedral characterization of all the NE for the two-buyer market game. Surprisingly, all the NE of this game turn out to be symmetric and the corresponding payoffs constitute a piecewise linear concave curve. We also study the correlated equilibria of this game and show that third-party mediation does not help to achieve a better payoff than NE payoffs.
Phase equilibria basic principles, applications, experimental techniques
Reisman, Arnold
2013-01-01
Phase Equilibria: Basic Principles, Applications, Experimental Techniques presents an analytical treatment in the study of the theories and principles of phase equilibria. The book is organized to afford a deep and thorough understanding of such subjects as the method of species model systems; condensed phase-vapor phase equilibria and vapor transport reactions; zone refining techniques; and nonstoichiometry. Physicists, physical chemists, engineers, and materials scientists will find the book a good reference material.
Numerical computation of MHD equilibria
International Nuclear Information System (INIS)
Atanasiu, C.V.
1982-10-01
A numerical code for a two-dimensional MHD equilibrium computation has been carried out. The code solves the Grad-Shafranov equation in its integral form, for both formulations: the free-boundary problem and the fixed boundary one. Examples of the application of the code to tokamak design are given. (author)
International Nuclear Information System (INIS)
Furth, H.P.
1984-10-01
The economic prospects of the tokamak are reviewed briefly and found to be favorable - if the size of ignited tokamak plasmas can be kept small and appropriate auxiliary systems can be developed. The main objectives of the Princeton Plasma Physics Laboratory tokamak program are: (1) exploration of the physics of high-temperature toroidal confinement, in TFTR; (2) maximization of the tokamak beta value, in PBX; (3) development of reactor-relevant rf techniques, in PLT
Statistical properties of three-dimensional two-fluid plasma model
Energy Technology Data Exchange (ETDEWEB)
Qaisrani, M. Hasnain [State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, WuHan, Hubei 430074 (China); Xia, ZhenWei [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Zou, Dandan, E-mail: ddzou@hust.edu.cn [State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, WuHan, Hubei 430074 (China); School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023 (China)
2015-09-15
The nonlinear dynamics of incompressible non-dissipative two-fluid plasma model is investigated through classical Gibbs ensemble methods. Liouville's theorem of phase space for each wave number is proved, and the absolute equilibrium spectra for Galerkin truncated two-fluid model are calculated. In two-fluid theory, the equilibrium is built on the conservation of three quadratic invariants: the total energy and the self-helicities for ions and electrons fluid, respectively. The implications of statistic equilibrium spectra with arbitrary ratios of conserved invariants are discussed.
International Nuclear Information System (INIS)
Rawls, J.M.
1979-10-01
An overall review of the tokamak program is given with particular emphasis upon developments over the past five years in the theoretical and experimental elements of the program. A summary of the key operating parameters for the principal tokamaks throughout the world is given. Also discussed are key issues in plasma confinement, plasma heating, and tokamak design
The ICRH tokamak fusion test reactor
International Nuclear Information System (INIS)
Perkins, F.W.
1976-01-01
A Tokamak Fusion Test Reactor where the ion are maintained at Tsub(i) approximately 20keV>Tsub(e) approximately 7keV by ion-cyclotron resonance heating is shown to produce an energy amplification of Q>2 provided the principal ion energy loss channel is via collisional transfer to the electrons. Such a reactor produces 19MW of fusion power to the electrons. Such a reactor produces 19MW of fusion power and requires a 50MHz radio-frequency generator capable of 50MW peak power; it is otherwise compatible with the conceptual design for the Princeton TFTR. The required n tausub(E) values for electrons and ions are respectively ntausub(Ee)>1.5.10 13 cm -3 -sec and ntausub(Ei)>4.10 13 cm -3 -sec. The principal areas where research is needed to establish this concept are: tokamak transport calculations, ICRH physics, trapped-particle instability energy losses, tokamak equilibria with high values of βsub(theta), and, of course, impurities
Stability of relative equilibria of three vortices
DEFF Research Database (Denmark)
Aref, Hassan
2009-01-01
Three point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably mor...
Strong Nash Equilibria and the Potential Maimizer
van Megen, F.J.C.; Facchini, G.; Borm, P.E.M.; Tijs, S.H.
1996-01-01
A class of non cooperative games characterized by a `congestion e ect' is studied, in which there exists a strong Nash equilibrium, and the set of Nash equilibria, the set of strong Nash equilibria and the set of strategy pro les maximizing the potential function coincide.The structure of the class
International Nuclear Information System (INIS)
Reid, R.L.; Barrett, R.J.; Brown, T.G.
1985-03-01
The FEDC Tokamak Systems Code calculates tokamak performance, cost, and configuration as a function of plasma engineering parameters. This version of the code models experimental tokamaks. It does not currently consider tokamak configurations that generate electrical power or incorporate breeding blankets. The code has a modular (or subroutine) structure to allow independent modeling for each major tokamak component or system. A primary benefit of modularization is that a component module may be updated without disturbing the remainder of the systems code as long as the imput to or output from the module remains unchanged
Signaling equilibria in sensorimotor interactions.
Leibfried, Felix; Grau-Moya, Jordi; Braun, Daniel A
2015-08-01
Although complex forms of communication like human language are often assumed to have evolved out of more simple forms of sensorimotor signaling, less attention has been devoted to investigate the latter. Here, we study communicative sensorimotor behavior of humans in a two-person joint motor task where each player controls one dimension of a planar motion. We designed this joint task as a game where one player (the sender) possesses private information about a hidden target the other player (the receiver) wants to know about, and where the sender's actions are costly signals that influence the receiver's control strategy. We developed a game-theoretic model within the framework of signaling games to investigate whether subjects' behavior could be adequately described by the corresponding equilibrium solutions. The model predicts both separating and pooling equilibria, in which signaling does and does not occur respectively. We observed both kinds of equilibria in subjects and found that, in line with model predictions, the propensity of signaling decreased with increasing signaling costs and decreasing uncertainty on the part of the receiver. Our study demonstrates that signaling games, which have previously been applied to economic decision-making and animal communication, provide a framework for human signaling behavior arising during sensorimotor interactions in continuous and dynamic environments. Copyright © 2015 Elsevier B.V. All rights reserved.
Tokamak devices: towards controlled fusion
International Nuclear Information System (INIS)
Trocheris, M.
1975-01-01
The Tokamak family is from Soviet Union. These devices were exclusively studied at the Kurchatov Institute in Moscow for more than ten years. The first occidental Tokamak started in 1970 at Princeton. The TFR (Tokamak Fontenay-aux-Roses) was built to be superior to the Russian T4. Tokamak future is now represented by the JET (Joint European Tokamak) [fr
On steady poloidal and toroidal flows in tokamak plasmas
International Nuclear Information System (INIS)
McClements, K. G.; Hole, M. J.
2010-01-01
The effects of poloidal and toroidal flows on tokamak plasma equilibria are examined in the magnetohydrodynamic limit. ''Transonic'' poloidal flows of the order of the sound speed multiplied by the ratio of poloidal magnetic field to total field B θ /B can cause the (normally elliptic) Grad-Shafranov (GS) equation to become hyperbolic in part of the solution domain. It is pointed out that the range of poloidal flows for which the GS equation is hyperbolic increases with plasma beta and B θ /B, thereby complicating the problem of determining spherical tokamak plasma equilibria with transonic poloidal flows. It is demonstrated that the calculation of the hyperbolicity criterion can be easily modified when the assumption of isentropic flux surfaces is replaced with the more tokamak-relevant one of isothermal flux surfaces. On the basis of the latter assumption, a simple expression is obtained for the variation of density on a flux surface when poloidal and toroidal flows are simultaneously present. Combined with Thomson scattering measurements of density and temperature, this expression could be used to infer information on poloidal and toroidal flows on the high field side of a tokamak plasma, where direct measurements of flows are not generally possible. It is demonstrated that there are four possible solutions of the Bernoulli relation for the plasma density when the flux surfaces are assumed to be isothermal, corresponding to four distinct poloidal flow regimes. Finally, observations and first principles-based theoretical modeling of poloidal flows in tokamak plasmas are briefly reviewed and it is concluded that there is no clear evidence for the occurrence of supersonic poloidal flows.
High #betta# and toroidal effects on the internal kink mode in tokamaks
International Nuclear Information System (INIS)
Schmalz, R.
1982-09-01
The inclusion of high-#betta# and first-order toroidal terms in the reduced set of (resistive) MHD equations affords the possibility of improving the study of tokamak plasma behaviour by three-dimensional numerical simulation. A new code, GALA, based on the reduced equations is developed. It is used to analyse the linear and nonlinear behaviour of the internal kink mode in equilibria which are generated by a simple relaxation procedure. We find that the inclusion of toroidal effects in high-#betta# equilibria provides considerable stabilization. (orig.)
Validation of equilibrium tools on the COMPASS tokamak
Energy Technology Data Exchange (ETDEWEB)
Urban, J., E-mail: urban@ipp.cas.cz [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Appel, L.C. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Artaud, J.F. [CEA, IRFM, F-13108 Saint Paul Lez Durance (France); Faugeras, B. [Laboratoire J.A. Dieudonné, UMR 7351, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02 (France); Havlicek, J. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic); Komm, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Lupelli, I. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Peterka, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic)
2015-10-15
Highlights: • Three equilibrium codes—EFIT++, FREEBIE and VacTH—have been successfully set up and validated on COMPASS. • FREEBIE can predictively calculate the equilibrium and corresponding poloidal field coil currents. • EFIT++ can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. • VacTH is a promising tool for real time plasma shape reconstruction. • Optimized parameters are estimated for EFIT++ and VacTH by a statistical analysis. - Abstract: Various MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developed or considerably updated, are used on the COMPASS tokamak at IPP Prague. MHD equilibrium is a fundamental property of the tokamak plasma, whose knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpreting and planning tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code (Appel et al., 2006), the free-boundary equilibrium code FREEBIE (Artaud and Kim, 2012), and a rapid plasma boundary reconstruction code VacTH (Faugeras et al., 2014). We demonstrate that FREEBIE can calculate the equilibrium and corresponding poloidal field (PF) coils currents consistently with EFIT++ reconstructions from experimental data. Both EFIT++ and VacTH can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. Hence, VacTH is suitable for real-time control. Optimum reconstruction parameters are estimated.
Neoclassical MHD equations for tokamaks
International Nuclear Information System (INIS)
Callen, J.D.; Shaing, K.C.
1986-03-01
The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion
Grid studies for the simulation of resolved structures in an Eulerian two-fluid framework
Energy Technology Data Exchange (ETDEWEB)
Gauss, Friederike, E-mail: f.gauss@hzdr.de; Lucas, Dirk; Krepper, Eckhard
2016-08-15
Highlights: • Elaborated Eulerian two-fluid methods may predict multiphase flow with large differences in interfacial length scales. • A study on the grid requirements of resolved structures in such two-fluid methods is presented. • The two-fluid results are only little dependent on the grid size. • The results justify the resolved treatment of flow structures covering only few grid cells. • A grid-dependent limit between resolved an modeled structures may be established. - Abstract: The influence of the grid size on the rise velocity of a single bubble simulated with an Eulerian two-fluid method is investigated. This study is part of the development of an elaborated Eulerian two-fluid framework, which is able to predict complex flow phenomena as arising in nuclear reactor safety research issues. Such flow phenomena cover a wide range of interfacial length scales. An important aspect of the simulation method is the distinction into small flow structures, which are modeled, and large structures, which are resolved. To investigate the requirements on the numerical grid for the simulation of such resolved structures the velocity of rising gas bubbles is a good example since theoretical values are available. It is well known that the rise velocity of resolved bubbles is clearly underestimated in a one-fluid approach if they span over only few numerical cells. In the present paper it is shown that in the case of the two-fluid model the bubble rise velocity depends only slightly on the grid size. This is explained with the use of models for the gas–liquid interfacial forces. Good approximations of the rise velocity and the bubble shape are obtained with only few grid points per bubble diameter. This result justifies the resolved treatment of flow structures, which cover only few grid cells. Thus, a limit for the distinction into resolved and modeled structures in the two-fluid context may be established.
Learning to Play Efficient Coarse Correlated Equilibria
Borowski, Holly P.
2018-03-10
The majority of the distributed learning literature focuses on convergence to Nash equilibria. Coarse correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific coarse correlated equilibria. In this paper, we provide one such algorithm, which guarantees that the agents’ collective joint strategy will constitute an efficient coarse correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Computing Nash equilibria through computational intelligence methods
Pavlidis, N. G.; Parsopoulos, K. E.; Vrahatis, M. N.
2005-03-01
Nash equilibrium constitutes a central solution concept in game theory. The task of detecting the Nash equilibria of a finite strategic game remains a challenging problem up-to-date. This paper investigates the effectiveness of three computational intelligence techniques, namely, covariance matrix adaptation evolution strategies, particle swarm optimization, as well as, differential evolution, to compute Nash equilibria of finite strategic games, as global minima of a real-valued, nonnegative function. An issue of particular interest is to detect more than one Nash equilibria of a game. The performance of the considered computational intelligence methods on this problem is investigated using multistart and deflection.
Multiple Equilibria in Noisy Rational Expectations Economies
DEFF Research Database (Denmark)
Pálvölgyi, Dömötör; Venter, Gyuri
with a continuous price function. However, we also construct a tractable class of equilibria with discontinuous prices that have very different economic implications, including (i) jumps and crashes, (ii) significant revisions in uninformed belief due to small changes in the market price, (iii) “upward......-sloping” demand curves, (iv) higher prices leading to future returns that are higher in expectation (price drift) and (v) more positively skewed. Discontinuous equilibria can be arbitrarily close to being fully-revealing. Finally, discontinuous equilibria with the same construction also exist in Hellwig (1980)....
Inefficient equilibria in transition economy
Directory of Open Access Journals (Sweden)
Sergei Guriev
1999-01-01
Full Text Available The paper studies a general equilibrium in an economy where all market participants face a bid-ask spread. The spread may be caused by indirect business taxes, middlemen rent-seeking, delays in payments or liquidity constraints or price uncertainty. Wherever it comes from the spread causes inefficiency of the market equilibrium. We discuss some institutions that can decrease the inefficiency. One is second currency (barter exchange in the inter-firm transactions. It is shown that the general equilibrium in an economy with second currency is effective though is still different from Arrow–Debreu equilibrium. Another solution can be introduction of mutual trade credit. In the economy with trade credit there are multiple equilibria that are more efficient than original bid-ask spread but still not as efficient as Arrow–Debreu one, too. The implications for firms' integration and applicability to Russian economy are discussed.
Stability of tearing modes in tokamak plasmas
International Nuclear Information System (INIS)
Hegna, C.C.; Callen, J.D.
1994-02-01
The stability properties of m ≥ 2 tearing instabilities in tokamak plasmas are analyzed. A boundary layer theory is used to find asymptotic solutions to the ideal external kink equation which are used to obtain a simple analytic expression for the tearing instability parameter Δ'. This calculation generalizes previous work on this topic by considering more general toroidal equilibria (however, toroidal coupling effects are ignored). Constructions of Δ' are obtained for plasmas with finite beta and for islands that have nonzero width. A simple heuristic estimate is given for the value of the saturated island width when the instability criterion is violated. A connection is made between the calculation of the asymptotic matching parameter in the finite beta and island width case to the nonlinear analog of the Glasser effect
International Nuclear Information System (INIS)
Song, Yuntao; Wu, Weiyue; Du, Shijun
2014-01-01
Provides a systematic introduction to tokamaks in engineering mechanics. Includes design guides based on full mechanical analysis, which makes it possible to accurately predict load capacity and temperature increases. Presents comprehensive information on important design factors involving materials. Covers the latest advances in and up-to-date references on tokamak devices. Numerous examples reinforce the understanding of concepts and provide procedures for design. Tokamak Engineering Mechanics offers concise and thorough coverage of engineering mechanics theory and application for tokamaks, and the material is reinforced by numerous examples. Chapter topics include general principles, static mechanics, dynamic mechanics, thermal fluid mechanics and multiphysics structural mechanics of tokamak structure analysis. The theoretical principle of the design and the methods of the analysis for various components and load conditions are presented, while the latest engineering technologies are also introduced. The book will provide readers involved in the study of mechanical/fusion engineering with a general understanding of tokamak engineering mechanics.
Self-consistent equilibria in cylindrical reversed-field pinch
International Nuclear Information System (INIS)
Lo Surdo, C.; Paccagnella, R.; Guo, S.
1995-03-01
The object of this work is to study the self-consistent magnetofluidstatic equilibria of a 2-region (plasma + gas) reversed-field pinch (RFP) in cylindrical approximation (namely, with vanishing inverse aspect ratio). Differently from what happens in a tokamak, in a RFP a significant part of the plasma current is driven by a dynamo electric field (DEF), in its turn mainly due to plasma turbulence. So, it is worked out a reasonable mathematical model of the above self-consistent equilibria under the following main points it has been: a) to the lowest order, and according to a standard ansatz, the turbulent DEF say ε t , is expressed as a homogeneous transform of the magnetic field B of degree 1, ε t =(α) (B), with α≡a given 2-nd rank tensor, homogeneous of degree 0 in B and generally depending on the plasma state; b) ε t does not explicitly appear in the plasma energy balance, as it were produced by a Maxwell demon able of extract the corresponding Joule power from the plasma. In particular, it is showed that, if both α and the resistivity tensor η are isotropic and constant, the magnetic field is force-free with abnormality equal to αη 0 /η, in the limit of vanishing β; that is, the well-known J.B. Taylor'result is recovered, in this particular conditions, starting from ideas quite different from the usual ones (minimization of total magnetic energy under constrained total elicity). Finally, the general problem is solved numerically under circular (besides cylindrical) symmetry, for simplicity neglecting the existence of gas region (i.e., assuming the plasma in direct contact with the external wall)
Song, Yuntao; Du, Shijun
2013-01-01
Tokamak Engineering Mechanics offers concise and thorough coverage of engineering mechanics theory and application for tokamaks, and the material is reinforced by numerous examples. Chapter topics include general principles, static mechanics, dynamic mechanics, thermal fluid mechanics and multiphysics structural mechanics of tokamak structure analysis. The theoretical principle of the design and the methods of the analysis for various components and load conditions are presented, while the latest engineering technologies are also introduced. The book will provide readers involved in the study
Advanced Tokamak Stability Theory
Zheng, Linjin
2015-03-01
The intention of this book is to introduce advanced tokamak stability theory. We start with the derivation of the Grad-Shafranov equation and the construction of various toroidal flux coordinates. An analytical tokamak equilibrium theory is presented to demonstrate the Shafranov shift and how the toroidal hoop force can be balanced by the application of a vertical magnetic field in tokamaks. In addition to advanced theories, this book also discusses the intuitive physics pictures for various experimentally observed phenomena.
Development of bubble-induced turbulence model for advanced two-fluid model
International Nuclear Information System (INIS)
Hosoi, Hideaki; Yoshida, Hiroyuki
2011-01-01
A two-fluid model can simulate two-phase flow by computational cost less than detailed two-phase flow simulation method such as interface tracking method. The two-fluid model is therefore useful for thermal hydraulic analysis in the large-scale domain such as rod bundles. However, since the two-fluid model includes a lot of constitutive equations verified by use of experimental results, it has problems that the result of analyses depends on accuracy of the constitutive equations. To solve these problems, an advanced two-fluid model has been developed by Japan Atomic Energy Agency. In this model, interface tracking method is combined with two-fluid model to accurately predict large interface structure behavior. Liquid clusters and bubbles larger than a computational cell are calculated using the interface tracking method, and those smaller than the cell are simulated by the two-fluid model. The constitutive equations to evaluate the effects of small bubbles or droplets on two-phase flow are also required in the advanced two-fluid model, just as with the conventional two-fluid model. However, the dependency of small bubbles and droplets on two-phase flow characteristics is relatively small, and fewer experimental results are required to verify the characteristics of large interface structures. Turbulent dispersion force model is one of the most important constitutive equations for the advanced two-fluid model. The turbulent dispersion force model has been developed by many researchers for the conventional two-fluid model. However, existing models implicitly include the effects of large bubbles and the deformation of bubbles, and are unfortunately not applicable to the advanced two-fluid model. In the previous study, the authors suggested the turbulent dispersion force model based on the analogy of Brownian motion. And the authors improved the turbulent dispersion force model in consideration of bubble-induced turbulence to improve the analysis results for small
Two-fluid effects on pressure-driven modes in a heliotron device
International Nuclear Information System (INIS)
Miura, H.; Ito, A.; Sato, M.; Goto, R.; Hatori, T.
2014-10-01
Two-fluid effects on the ballooning or pressure-driven unstable modes are studied numerically to understand physics in linear and nonlinear evolution of them in a heliotron device. Full 3D simulations for β 0 = 5% unstable magnetic configuration of the large helical device show that the introduction of the two-fluid term brings about broader radial profile and higher growth rate in the linear stage of the evolution, weakened parallel heat conduction, and lead to a saturation profile worse than that in the single-fluid MHD simulation. The numerical results show that suppression of high wave-number modes enhance the growth of low wave-number modes. The two-fluid effects and a plausible mild saturation of ballooning modes is discussed. (author)
Tokamak confinement scaling laws
International Nuclear Information System (INIS)
Connor, J.
1998-01-01
The scaling of energy confinement with engineering parameters, such as plasma current and major radius, is important for establishing the size of an ignited fusion device. Tokamaks exhibit a variety of modes of operation with different confinement properties. At present there is no adequate first principles theory to predict tokamak energy confinement and the empirical scaling method is the preferred approach to designing next step tokamaks. This paper reviews a number of robust theoretical concepts, such as dimensional analysis and stability boundaries, which provide a framework for characterising and understanding tokamak confinement and, therefore, generate more confidence in using empirical laws for extrapolation to future devices. (author)
International Nuclear Information System (INIS)
1986-04-01
This document contains the results of the IAEA Specialists' Meeting on Tokamak Concept Innovations held 13-17 January 1986 in Vienna. Although it is the most advanced fusion reactor concept the tokamak is not without its problems. Most of these problems should be solved within the ongoing R and D studies for the next generation of tokamaks. Emphasis for this meeting was placed on innovations that would lead to substantial improvements in a tokamak reactor, even if they involved a radical departure from present thinking
Route analysis for MHD equilibria
International Nuclear Information System (INIS)
Kikuchi, Fumio; Aizawa, Tatsuhiko
1982-01-01
In Tokamak facilities which are promising in nuclear fusion reactor development, the plasma in the core is often described by MHD approximation. Specifically, since an axisymmetric torus is approximately assumed as the first wall (shell) shape in actual Tokamak facilities, the Grad-Shafranov equation to be satisfied by an axisymmetric equilibrium solution for ideal MHD fluid must be solved, and the characteristics of its solution must be clarified. This paper shows the outline of the numerical calculation which employs both the incremental method taking the particular incremental nodal point values as the control parameters and the interaction method in accordance with Newton method at the same time, the analysis objective being a non-linear eigenvalue problem dealing the boundary of plasma region with surrounding vacuum region as the free boundary. Next, the detailed route analysis of the equilibrium solution is performed, utilizing the above numerical calculation technique, to clarify the effect of shell shape on the behaviour of the equilibrium solution. As the shape of the shell, a rectangular section torus, which have a notch depression at a part of the shell inner boundary, is considered. In the paper, the fundamental MHD equation and its approximate solution by the finite element method, the behaviour of plasma equilibrium solution in a shell having a notch, and the effect of notch shapes on plasma behaviour are described. This analysis verifies the effectiveness of the calculation method. (Wakatsuki, Y.)
Multiple equilibria in a simple elastocapillary system
Taroni, Michele; Vella, Dominic
2012-01-01
properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.
A Parallel Two-fluid Code for Global Magnetic Reconnection Studies
International Nuclear Information System (INIS)
Breslau, J.A.; Jardin, S.C.
2001-01-01
This paper describes a new algorithm for the computation of two-dimensional resistive magnetohydrodynamic (MHD) and two-fluid studies of magnetic reconnection in plasmas. It has been implemented on several parallel platforms and shows good scalability up to 32 CPUs for reasonable problem sizes. A fixed, nonuniform rectangular mesh is used to resolve the different spatial scales in the reconnection problem. The resistive MHD version of the code uses an implicit/explicit hybrid method, while the two-fluid version uses an alternating-direction implicit (ADI) method. The technique has proven useful for comparing several different theories of collisional and collisionless reconnection
Two-fluid modeling of thermal-hydraulic phenomena for best-estimate LWR safety analysis
International Nuclear Information System (INIS)
Yadigaroglu, G.; Andreani, M.
1989-01-01
Two-fluid formulation of the conservation equations has allowed modelling of the two-phase flow and heat transfer phenomena and situations involving strong departures in thermal and velocity equilibrium between the phases. The paper reviews the state of the art in modelling critical flows, and certain phase separation phenomena, as well as post-dryout heat transfer situations. Although the two-fluid models and the codes have the potential for correctly modelling such situations, this potential has not always been fully used in practice. (orig.)
An implicit second order numerical method for two-fluid models
International Nuclear Information System (INIS)
Toumi, I.
1995-01-01
We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)
Magnetohydrodynamic stability of tokamak plasmas with poloidal mode coupling
International Nuclear Information System (INIS)
Shigueoka, H.; Sakanaka, P.H.
1987-01-01
The stability behavior with respect to internal modes is examined for a class of tokamak equilibria with non-circular cross sections. The surfaces of the constant poloidal magnetic flux ψ (R,Z) are obtained numerically by solving the Grad-Shafranov's equation with a specified shape for the outmost plasma surface. The equation of motion for ideal MHD stability is written in a ortogonal coordinate system (ψ, χ, φ). Th e stability analysis is performance numerically in a truncated set of coupled m (poloidal wave number) equations. The calculations involve no approximations, and so all parameters of the equilibrium solution can be arbitrarily varied. (author) [pt
Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows
International Nuclear Information System (INIS)
Tasso, H.; Throumoulopoulos, G.N.
1997-12-01
It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)
Relation of vertical stability and aspect ratio in tokamaks
International Nuclear Information System (INIS)
Stambaugh, R.D.; Lao, L.L.; Lazarus, E.A.
1992-01-01
It is evaluated how the upper limit to plasma elongation κ, caused by vertical stability, varies with the aspect ratio A=R/a of the tokamak. Equilibria were generated with EFITD and the vertical stability was assessed by GATO. For a 'generic' tokamak with a superconducting wall conformal to the plasma shape and a distance 0.5 a away from the plasma edge and a constant current profile (q 0 =1.0, l i ≅1.0, q 95 =3.2) it is found that the maximum stable κ decreased only slowly from 2.65 at A=2.0 to 2.4 at A=6.0. To first order, a reasonable assumption in trade-off studies of new machine designs is no dependence of κ max on A. (author). Letter-to-the-editor. 13 refs, 3 figs, 1 tab
Axisymmetric stability of vertically asymmetric Tokamaks at large beta poloidal
Energy Technology Data Exchange (ETDEWEB)
Yamazaki, K.; Fishman, H.; Okabayashi, M. (Princeton Univ., NJ (USA). Plasma Physics Lab.); Todd, A.M.M. (Grumman Aerospace Corp., Princeton, NJ (USA))
1983-11-01
The rigid-mode stability of high-..beta.. vertically asymmetric Tokamak equilibria with quasi-uniform current profile is investigated analytically using toroidicity-shaping double expansion method. It is found that vertical stability at large beta poloidal is mainly determined by a coupling between the shape of the plasma surface and the Shafranov shift of the magnetic axis. To the lowest order, symmetric components of the plasma surface shape are found to be the critical destabilizing elements. Asymmetric components have little effect. The inclusion of higher order terms in the high-..beta.. Tokamak expansion leads to further destabilization. These analytic insights are qualitatively confirmed by numerical stability calculations using the PEST code with parabolic safety-factor profile.
Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma
Bond, D.; Wheatley, V.; Samtaney, Ravi; Pullin, D. I.
2017-01-01
We computationally investigate the Richtmyer–Meshkov instability of a density interface with a single-mode perturbation in a two-fluid, ion–electron plasma with no initial magnetic field. Self-generated magnetic fields arise subsequently. We study
Mathematical well-posedness of a two-fluid equations for bubbly two-phase flows
International Nuclear Information System (INIS)
Okawa, Tomio; Kataoka, Isao
2000-01-01
It is widely known that two-fluid equations used in most engineering applications do not satisfy the necessary condition for being mathematical well-posed as initial-value problems. In the case of stratified two-phase flows, several researchers have revealed that differential models satisfying the necessary condition are to be derived if the pressure difference between the phases is related to the spatial gradient of the void fraction through the effects of gravity or surface tension. While, in the case of dispersed two-phase flows, no physically reasonable method to derive mathematically well-posed two-fluid model has been proposed. In the present study, particularly focusing on the effect of interfacial pressure terms, we derived the mathematically closed form of the volume-averaged two-fluid model for bubbly two-phase flows. As a result of characteristic analyses, it was shown that the proposed two-fluid equations satisfy the necessary condition of mathematical well-posedness if the void fraction is sufficiently small. (author)
A two-fluid study of oblique tearing modes in a force-free current sheet
Energy Technology Data Exchange (ETDEWEB)
Akçay, Cihan, E-mail: akcay@lanl.gov; Daughton, William [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Lukin, Vyacheslav S. [National Science Foundation, Arlington, Virginia 22230 (United States); Liu, Yi-Hsin [NASA Goddard Space Flight Center, Greenbelt, Maryland 20771 (United States)
2016-01-15
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Since kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicate that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. The resulting theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.
Analysis of time integration methods for the compressible two-fluid model for pipe flow simulations
B. Sanderse (Benjamin); I. Eskerud Smith (Ivar); M.H.W. Hendrix (Maurice)
2017-01-01
textabstractIn this paper we analyse different time integration methods for the two-fluid model and propose the BDF2 method as the preferred choice to simulate transient compressible multiphase flow in pipelines. Compared to the prevailing Backward Euler method, the BDF2 scheme has a significantly
International Nuclear Information System (INIS)
Edelbaum, T.N.; Serben, S.; Var, R.E.
1976-01-01
A computer model of a tokamak experimental power reactor and its control system is being constructed. This simulator will allow the exploration of various open loop and closed loop strategies for reactor control. This paper provides a brief description of the simulator and some of the potential control problems associated with this class of tokamaks
Methods for the design and optimization of shaped tokamaks
International Nuclear Information System (INIS)
Haney, S.W.
1988-05-01
Two major questions associated with the design and optimization of shaped tokamaks are considered. How do physics and engineering constraints affect the design of shaped tokamaks? How can the process of designing shaped tokamaks be improved? The first question is addressed with the aid of a completely analytical procedure for optimizing the design of a resistive-magnet tokamak reactor. It is shown that physics constraints---particularly the MHD beta limits and the Murakami density limit---have an enormous, and sometimes, unexpected effect on the final design. The second question is addressed through the development of a series of computer models for calculating plasma equilibria, estimating poloidal field coil currents, and analyzing axisymmetric MHD stability in the presence of resistive conductors and feedback. The models offer potential advantages over conventional methods since they are characterized by extremely fast computer execution times, simplicity, and robustness. Furthermore, evidence is presented that suggests that very little loss of accuracy is required to achieve these desirable features. 94 refs., 66 figs., 14 tabs
International Nuclear Information System (INIS)
Wesson, John; Campbell, D.J.; Connor, J.W.
1997-01-01
It is interesting to recall the state of tokamak research when the first edition of this book was written. My judgement of the level of real understanding at that time is indicated by the virtual absence of comparisons of experiment with theory in that edition. The need then was for a 'handbook' which collected in a single volume the concepts and models which form the basis of everyday tokamak research. The experimental and theoretical endeavours of the subsequent decade have left almost all of this intact, but have brought a massive development of the subject. Firstly, there are now several areas where the experimental behaviour is described in terms of accepted theory. This is particularly true of currents parallel to the magnetic field, and of the stability limitations on the plasma pressure. Next there has been the research on large tokamaks, hardly started at the writing of the first edition. Now our thinking is largely based on the results from these tokamaks and this work has led to the long awaited achievement of significant amounts of fusion power. Finally, the success of tokamak research has brought us face to face with the problems involved in designing and building a tokamak reactor. The present edition maintains the aim of providing a simple introduction to basic tokamak physics, but also includes an account of the advances outlined above. (Author)
International Nuclear Information System (INIS)
Baker, C.C.
1981-01-01
This paper presents an overview of tokamak reactor studies with particular attention to commercial reactor concepts developed within the last three years. Emphasis is placed on DT fueled reactors for electricity production. A brief history of tokamak reactor studies is presented. The STARFIRE, NUWMAK, and HFCTR studies are highlighted. Recent developments that have increased the commercial attractiveness of tokamak reactor designs are discussed. These developments include smaller plant sizes, higher first wall loadings, improved maintenance concepts, steady-state operation, non-divertor particle control, and improved reactor safety features
International Nuclear Information System (INIS)
Murray, J.G.; Gorker, G.E.
1985-01-01
Tokamak fusion reactors will have large plasma currents of approximately 10 MA with hundreds of megajoules stored in the magnetic fields. When a major plasma instability occurs, the disruption of the plasma current induces voltage in the adjacent conducting structures, giving rise to large transient currents. The induced voltages may be sufficiently high to cause arcing across sector gaps or from one protruding component to another. This report reviews a tokamak arcing scenario and provides guidelines for designing tokamaks to minimize the possibility of arc damage
International Nuclear Information System (INIS)
Bickerton, R.J.
1977-01-01
The survey covers the following topics:- Introduction and history of tokamak research; review of tokamak apparatus, existing and planned; remarks on measurement techniques and their limitations; main results in terms of electron and ion temperatures, plasma density, containment times, etc. Empirical scaling; range of operating densities; impurities, origin, behaviour and control (including divertors); data on fluctuations and instabilities in tokamak plasmas; data on disruptive instabilities; experiments on shaped cross-sections; present experimental evidence on β limits; auxiliary heating; experimental and theoretical problems for the future. (author)
Energy Technology Data Exchange (ETDEWEB)
Murray, J.G.; Gorker, G.E.
1985-01-01
Tokamak fusion reactors will have large plasma currents of approximately 10 MA with hundreds of megajoules stored in the magnetic fields. When a major plasma instability occurs, the disruption of the plasma current induces voltage in the adjacent conducting structures, giving rise to large transient currents. The induced voltages may be sufficiently high to cause arcing across sector gaps or from one protruding component to another. This report reviews a tokamak arcing scenario and provides guidelines for designing tokamaks to minimize the possibility of arc damage.
Two-Fluid Models for Simulating Dispersed Multiphase Flows-A Review
Directory of Open Access Journals (Sweden)
L.X. Zhou
2009-01-01
Full Text Available The development of two-fluid models for simulating dispersed multiphase flows (gas-particle, gas-droplet, bubble-liquid, liquid-particle flows by the present author within the last 20 years is systematically reviewed. The two-fluid models based on Reynolds expansion, time averaging and mass-weighed averaging, and also PDF transport equations are described. Different versions of two-phase turbulence models, including the unified second-order moment (USM and k-ε-kp models, the DSM-PDF model, the SOM-MC model, the nonlinear k-e-kp model, and the USM-Θ model for dense gas-particle flows and their application and experimental validation are discussed.
Validation of Numerical Two-Fluid and Kinetic Plasma Models. Final Report
International Nuclear Information System (INIS)
Barnes, Daniel
2011-01-01
This was a four year grant commencing October 1, 2003 and finishing September 30, 2007. The funding was primarily used to support the work of the Principal Investigator, who collaborated with Profs. Scott Parker and John Cary at U. Colorado, and with two students, N. Xiang and J. Cheng also of U. Colorado. The technical accomplishments of this grant can be found in the publications listed in the final Section here. The main accomplishments of the grant work were: (1) Development and implementation of time-implicit two-fluid simulation methods in collaboration with the NIMROD team; and (2) Development and testing of a new time-implicit delta-f, energy-conserving method The basic two-fluid method, with many improvements is used in present NIMROD calculations. The energy-conserving delta-f method is under continuing development under contract between Coronado Consulting, a New Mexico sole proprietorship and the Oak Ridge National Laboratory.
Collisionless two-fluid theory of toroidal ηi stability
International Nuclear Information System (INIS)
Mondt, J.; Weiland, J.
1989-01-01
A collisionless two-fluid theory based on a fourteen-moment generalization of the 'double-adiabatic' equations is developed to lowest order in the Larmor radius parameter, and applied to derive the toroidal η i stability boundary for all values of the ratio of the density gradient scale length divided by the field curvature length. The present model is an improvement over existing collisional two-fluid models in view of the collisionless nature of the η i instability, while retaining the advantage over kinetic theory of the practability of mode-coupling simulations. The linear stability boundary, linear growth rate and real frequency agree fairly accurately with draft-kinetic theory
Study on application of two-fluid model in narrow annular channel
International Nuclear Information System (INIS)
Chen Jun; Yang Yanhua; Zhao Hua
2007-01-01
The Chexal-Harrison two-phase wall and inter-phase friction models developed by EPRI newly and the simple two-phase wall and inter-phase heat transfer models put forward by the paper are used to set up the two-fluid model which is fitted for boiling heat transfer and flow in narrow annular channel. On the base of the two-fluid model, a thermal hydraulic code-THYME is accomplished. Then the thermal hydraulic characteristic of narrow annular channel is analyzed by RELAP5/MOD3.2 code and THYME code. Compared with experimental data, RELAP5/MOD3.2 underestimates the outlet steam, and the results of THYME is agreed with the experimental data. (authors)
Two-fluid model with droplet size distribution for condensing steam flows
International Nuclear Information System (INIS)
Wróblewski, Włodzimierz; Dykas, Sławomir
2016-01-01
The process of energy conversion in the low pressure part of steam turbines may be improved using new and more accurate numerical models. The paper presents a description of a model intended for the condensing steam flow modelling. The model uses a standard condensation model. A physical and a numerical model of the mono- and polydispersed wet-steam flow are presented. The proposed two-fluid model solves separate flow governing equations for the compressible, inviscid vapour and liquid phase. The method of moments with a prescribed function is used for the reconstruction of the water droplet size distribution. The described model is presented for the liquid phase evolution in the flow through the de Laval nozzle. - Highlights: • Computational Fluid Dynamics. • Steam condensation in transonic flows through the Laval nozzles. • In-house CFD code – two-phase flow, two-fluid monodispersed and polydispersed model.
Two dimensional, two fluid model for sodium boiling in LMFBR fuel assemblies
International Nuclear Information System (INIS)
Granziera, M.R.; Kazimi, M.S.
1980-05-01
A two dimensional numerical model for the simulation of sodium boiling transient was developed using the two fluid set of conservation equations. A semiimplicit numerical differencing scheme capable of handling the problems associated with the ill-posedness implied by the complex characteristic roots of the two fluid problems was used, which took advantage of the dumping effect of the exchange terms. Of particular interest in the development of the model was the identification of the numerical problems caused by the strong disparity between the axial and radial dimensions of fuel assemblies. A solution to this problem was found which uses the particular geometry of fuel assemblies to accelerate the convergence of the iterative technique used in the model. Three sodium boiling experiments were simulated with the model, with good agreement between the experimental results and the model predictions
Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma
Bond, D.
2017-11-03
We computationally investigate the Richtmyer–Meshkov instability of a density interface with a single-mode perturbation in a two-fluid, ion–electron plasma with no initial magnetic field. Self-generated magnetic fields arise subsequently. We study the case where the density jump across the initial interface is due to a thermal discontinuity, and select plasma parameters for which two-fluid plasma effects are expected to be significant in order to elucidate how they alter the instability. The instability is driven via a Riemann problem generated precursor electron shock that impacts the density interface ahead of the ion shock. The resultant charge separation and motion generates electromagnetic fields that cause the electron shock to degenerate and periodically accelerate the electron and ion interfaces, driving Rayleigh–Taylor instability. This generates small-scale structures and substantially increases interfacial growth over the hydrodynamic case.
A development of two-fluid multifield model for low-quality boiling transition simulations
International Nuclear Information System (INIS)
Park, J.W.; Choi, H.B.
1998-09-01
A three-dimensional two-fluid model has been developed using ensemble-averaging techniques. The two-fluid model was closed for two-phase bubbly flows using cell averaging which accounted for the dispersed phase distribution in the region of the averaging volume. The phasic interfacial momentum exchange includes the surface stress developed on the interface which is induced by the relative motion of the phases. Since no direct mean for validating the interfacial pressure model is available, the void wae data has been used. Since the presented model has been rigorously constitute for the bubbly two-phase flow of spherical bubbles, dilute two-phase flow situations, such as the subcooled boiling, can be realistically simulated by the presented local instantaneous form of the average equations. Finally, this model should be able to predict local thermal-hydraulic conditions under which the critical heat flux occurs. (author). 25 refs., 6 figs
Equilibrium, confinement and stability of runaway electrons in tokamaks
International Nuclear Information System (INIS)
Spong, D.A.
1976-03-01
Some of the ramifications of the runaway population in tokamak experiments are investigated. Consideration is given both to the normal operating regime of tokamaks where only a small fraction of high energy runaways are present and to the strong runaway regime where runaways are thought to carry a significant portion of the toroidal current. In particular, the areas to be examined are the modeling of strong runaway discharges, single particle orbit characteristics of runaways, macroscopic beam-plasma equilibria, and stability against kink modes. A simple one-dimensional, time-dependent model has been constructed in relation to strong runaway discharges. Single particle orbits are analyzed in relation to both the strong runaway regime and the weak regime. The effects of vector E x vector B drifts are first considered in strong runaway discharges and are found to lead to a slow inward shrinkage of the beam. Macroscopic beam-plasma equilibria are treated assuming a pressureless relativistic beam with inertia and using an ideal MHD approximation for the plasma. The stability of a toroidal relativistic beam against kink perturbations is examined using several models
Power deposition for ion cyclotron heating in large tokamaks
International Nuclear Information System (INIS)
Hellsten, T.; Villard, L.
1988-01-01
The power deposition profiles during minority ion cyclotron heating are analysed in large tokamaks by using the global, toroidal wave code LION. For tokamaks with large aspect ratio and with circular cross-section, the wave is focused on the magnetic axis and can be absorbed there by cyclotron absorption when the cyclotron resonance passes through the magnetic axis. The power deposition profile is then essentially determined by the Doppler broadening of the ion cyclotron resonance. For equilibria either non-circular or with a small aspect ratio the power deposition profile depends also on the strength of the damping. In this case the power deposition profile can be expressed as a sum of two power deposition profiles. One is related to the power absorbed in a single pass, and its shape is similar to that obtained for large aspect ratio and circular cross-section. The other profile is obtained by calculating the power deposition in the limit of weak damping, in which case the wave electric field is almost constant along the cyclotron resonance layer. A heuristic formula for the power deposition is given. The formula includes a number of calibration curves and functions which has been calculated with the LION code for JET relevant equilibria. The formula enables calculation of the power deposition profile in a simple way when the launched wave spectrum and damping coefficients are known. (author). 7 refs, 11 figs
Effects of q and high beta on tokamak stability
International Nuclear Information System (INIS)
Brickhouse, N.S.; Callen, J.D.; Dexter, R.N.
1984-08-01
In the Columbia University Torus II tokamak plasmas have been studied with volume averaged toroidal beta values as high as 15%. Experimental equilibria have been compared with a 2D free boundary MHD equilibrium code PSEC. The stability of these equilibria has been computed using PEST, the predictions of which are compatible with an observed instability in Torus II which may be characterized as a high toroidal mode number ballooning fluctuation. In the University of Wisconsin Tokapole II tokamak disruptive instability behavior is investigated, with plasma able to be confined on closed magnetic surfaces in the scrape-off region, as the cylindrical edge safety factor is varied from q approx. 3 to q approx. 0.5. It is observed that at q/sub a/ approx. 3 major disruption activity occurs without current terminations, at q/sub a/ less than or equal to 2 well-confined plasmas are obtained without major disruption, and at q/sub a/ approx. 0.5 only partial reconnection accompanies minor disruptions
Steam generator transient studies using a simplified two-fluid computer code
International Nuclear Information System (INIS)
Munshi, P.; Bhatnagar, R.; Ram, K.S.
1985-01-01
A simplified two-fluid computer code has been used to simulate reactor-side (or primary-side) transients in a PWR steam generator. The disturbances are modelled as ramp inputs for pressure, internal energy and mass flow-rate for the primary fluid. The CPU time for a transient duration of 4 s is approx. 10 min on a DEC-1090 computer system. The results are thermodynamically consistent and encouraging for further studies. (author)
Two-fluid static spherical configurations with linear mass function in the Einstein-Cartan theory
International Nuclear Information System (INIS)
Gallakhmetov, A.M.
2002-01-01
In the framework of the Einstein-Cartan theory, two-fluid static spherical configurations with linear mass function are considered. One of these modelling anisotropic matter distributions within star and the other fluid is a perfect fluid representing a source of torsion. It is shown that the solutions of the Einstein equations for anisotropic relativistic spheres in General Relativity may generate the solutions in the Einstein-Cartan theory. Some exact solutions are obtained
Dirac mechanics and Landau two-fluid model in /sup 4/HeII
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Gomez, J [Instituto Universitario Pedagogico de Caracas (Venezuela). Dept. de Matematica y Fisica
1980-07-01
This paper is devoted to the development of the Dirac formalism for singular systems when applied to the Landau two-fluid model in superfluid helium. Notably, the Hamiltonian density is weakly zero (in the sense of Dirac). We obtain the physical and gauge variables and show that all the constraints are of first class and hence that the Dirac bracket coincides with the Poisson bracket. The quantization of this system is left for a future paper.
Cook, G. G.; Khamas, S. K.; Kingsley, S. P.; Woods, R. C.
1992-01-01
The radar cross section and Q factors of electrically small dipole and loop antennas made with a YBCO high Tc superconductor are predicted using a two-fluid-moment method model, in order to determine the effects of finite conductivity on the performances of such antennas. The results compare the useful operating bandwidths of YBCO antennas exhibiting varying degrees of impurity with their copper counterparts at 77 K, showing a linear relationship between bandwidth and impurity level.
Nonlinear full two-fluid study of m=0 sausage instabilities in an axisymmetric Z pinch
International Nuclear Information System (INIS)
Loverich, J.; Shumlak, U.
2006-01-01
A nonlinear full five-moment two-fluid model is used to study axisymmetric instabilities in a Z pinch. When the electron velocity due to the current J is greater than the ion acoustic speed, high wave-number sausage instabilities develop that initiate shock waves in the ion fluid. This condition corresponds to a pinch radius on the order of a few ion Larmor radii
Modified two-fluid model for the two-group interfacial area transport equation
International Nuclear Information System (INIS)
Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.
2003-01-01
This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model
Two-fluid equations for a nuclear system with arbitrary motions
Energy Technology Data Exchange (ETDEWEB)
Kim, Byoung Jae [Chungnam National University, Daejeon (Korea, Republic of); Kim, Kyung Doo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
Ocean nuclear systems include a seabed-type plant, a floating-type plant, and a nuclear-propulsion ship. We asked ourselves, 'What governing equations should be used for ocean nuclear systems?' Since ocean nuclear systems are apt to move arbitrarily, the two-fluid model must be formulated in the non-inertial frame of reference that is undergoing acceleration with respect to an inertial frame. Two-phase flow systems with arbitrary motions are barely reported. Kim et al. (1996) added the centripetal and Euler acceleration forces to the homogeneous equilibrium momentum equation embedded in the RETRAN code. However, they did not look into the mass and energy equations. The purpose of this study is to derive general two-fluid equations in the non-inertial frame of reference, which can be used for safety analysis of ocean nuclear systems. The two-fluid equation forms for scalar properties such as mass, internal energy, and enthalpy equation in the moving frame are the same as those in the absolute frame. On the other hand, the fictitious effect must be included in the momentum equation.
The assessment of two-fluid models using critical flow data
International Nuclear Information System (INIS)
Shome, B.; Lahey, R.T. Jr.
1992-01-01
The behavior of two-phase flow is governed by the thermal-hydraulic transfers occurring across phasic interfaces. If correctly formulated, two-fluid models should yield all conceivable evolutions. Moreover, some experiments may be uniquely qualified for model assessment if they can isolate important closure models. This paper is primarily concerned with the possible assessment of the virtual mass force using air-water critical flow data, in which phase-change effects do not take place. The following conclusions can be drawn from this study: (1) The closure parameters, other than those for cirtual mass, were found to have an insignificant effect on critical flow. In contrast, the void fraction profile and the slip ratio were observed to be sensitive to the virtual mass model. (2) It appears that air-water critical flow experiments may be effectively used for the assessment of the virtual mass force used in two-fluid models. In fact, such experiments are unique in their ability to isolate the spatial gradients in a vm models. It is hoped that this study will help stimulate the conduct of further critical flow experiments for the assessment of two fluid models
Two-fluid dusty shocks: simple benchmarking problems and applications to protoplanetary discs
Lehmann, Andrew; Wardle, Mark
2018-05-01
The key role that dust plays in the interstellar medium has motivated the development of numerical codes designed to study the coupled evolution of dust and gas in systems such as turbulent molecular clouds and protoplanetary discs. Drift between dust and gas has proven to be important as well as numerically challenging. We provide simple benchmarking problems for dusty gas codes by numerically solving the two-fluid dust-gas equations for steady, plane-parallel shock waves. The two distinct shock solutions to these equations allow a numerical code to test different forms of drag between the two fluids, the strength of that drag and the dust to gas ratio. We also provide an astrophysical application of J-type dust-gas shocks to studying the structure of accretion shocks on to protoplanetary discs. We find that two-fluid effects are most important for grains larger than 1 μm, and that the peak dust temperature within an accretion shock provides a signature of the dust-to-gas ratio of the infalling material.
Existence of pareto equilibria for multiobjective games without compactness
Shiraishi, Yuya; Kuroiwa, Daishi
2013-01-01
In this paper, we investigate the existence of Pareto and weak Pareto equilibria for multiobjective games without compactness. By employing an existence theorem of Pareto equilibria due to Yu and Yuan([10]), several existence theorems of Pareto and weak Pareto equilibria for the multiobjective games are established in a similar way to Flores-B´azan.
Free surface modelling with two-fluid model and reduced numerical diffusion of the interface
International Nuclear Information System (INIS)
Strubelj, Luka; Tiselj, Izrok
2008-01-01
Full text of publication follows: The free surface flows are successfully modelled with one of existing free surface models, such as: level set method, volume of fluid method (with/without surface reconstruction), front tracking, two-fluid model (two momentum equations) with modified interphase force and others. The main disadvantage of two-fluid model used for simulations of free surface flows is numerical diffusion of the interface, which can be significantly reduced using the method presented in this paper. Several techniques for reduction of numerical diffusion of the interface have been implemented in the volume of fluid model and are based on modified numerical schemes for advection of volume fraction near the interface. The same approach could be used also for two-fluid method, but according to our experience more successful reduction of numerical diffusion of the interface can be achieved with conservative level set method. Within the conservative level set method, continuity equation for volume fraction is solved and after that the numerical diffusion of the interface is reduced in such a way that the thickness of the interface is kept constant during the simulation. Reduction of the interface diffusion can be also called interface sharpening. In present paper the two-fluid model with interface sharpening is validated on Rayleigh-Taylor instability. Under assumptions of isothermal and incompressible flow of two immiscible fluids, we simulated a system with the fluid of higher density located above the fluid of smaller density in two dimensions. Due to gravity in the system, fluid with higher density moves below the fluid with smaller density. Initial condition is not a flat interface between the fluids, but a sine wave with small amplitude, which develops into a mushroom-like structure. Mushroom-like structure in simulation of Rayleigh-Taylor instability later develops to small droplets as result of numerical dispersion of interface (interface sharpening
Tokamak simulation code manual
International Nuclear Information System (INIS)
Chung, Moon Kyoo; Oh, Byung Hoon; Hong, Bong Keun; Lee, Kwang Won
1995-01-01
The method to use TSC (Tokamak Simulation Code) developed by Princeton plasma physics laboratory is illustrated. In KT-2 tokamak, time dependent simulation of axisymmetric toroidal plasma and vertical stability have to be taken into account in design phase using TSC. In this report physical modelling of TSC are described and examples of application in JAERI and SERI are illustrated, which will be useful when TSC is installed KAERI computer system. (Author) 15 refs., 6 figs., 3 tabs
Lyapunov stability of ideal compressible and incompressible fluid equilibria in three dimensions
International Nuclear Information System (INIS)
Holm, D.D.
1985-08-01
Linearized stability of ideal compressible and incompressible fluid equilibria in three dimensions is analyzed using Lyapunov's direct method. An action principle is given for the Eulerian and Lagrangian fluid descriptions and the family of constants of motion due to symmetry under fluid-particle relabelling is derived in the form of Ertel's theorem for each description. In an augmented Euleriah description, the steady equilibrium flows of these two fluids theories are identified as critical points of the conserved Lyapunov functionals defined by the sum, H + C, of the energy H, and the Ertel constants of motion, C. It turns out that unconditional linear Lyapunov stability of these flows in the norm provided by the second variation of H + C is precluded by vortex-particle stretching, even for otherwise shear-stable flows. Conditional Lyapunov stability of these flows is discussed. 24 refs
Phase equilibria of carbohydrates in polar solvents
DEFF Research Database (Denmark)
Jonsdottir, Svava Osk; Rasmussen, Peter
1999-01-01
A method for calculating interaction energies and interaction parameters with molecular mechanics methods is extended to predict solid-liquid equilibria (SLE) for saccharides in aqueous solution, giving results in excellent agreement with experimental values. Previously, the method has been shown...
Nash equilibria via duality and homological selection
Indian Academy of Sciences (India)
1Quantitative Methods and Information Systems Area, Indian Institute ... The original proof of existence of Nash equilibria [13] uses fairly ...... The fiber over a regular point a of the disk Di consists of three inverse images (labeled. A1,A2,A3 in ...
Equilibrator: Modeling Chemical Equilibria with Excel
Vander Griend, Douglas A.
2011-01-01
Equilibrator is a Microsoft Excel program for learning about chemical equilibria through modeling, similar in function to EQS4WIN, which is no longer supported and does not work well with newer Windows operating systems. Similar to EQS4WIN, Equilibrator allows the user to define a system with temperature, initial moles, and then either total…
Intermediates and Generic Convergence to Equilibria
DEFF Research Database (Denmark)
Marcondes de Freitas, Michael; Wiuf, Carsten; Feliu, Elisenda
2017-01-01
Known graphical conditions for the generic and global convergence to equilibria of the dynamical system arising from a reaction network are shown to be invariant under the so-called successive removal of intermediates, a systematic procedure to simplify the network, making the graphical conditions...
On the stochastic stability of MHD equilibria
International Nuclear Information System (INIS)
Teichmann, J.
1979-07-01
The stochastic stability in the large of stationary equilibria of ideal and dissipative magnetohydrodynamics under the influence of stationary random fluctuations is studied using the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian systems are given. The destabilizing effect of stochastic fluctuations is demonstrated. (orig.)
Joint research using small tokamaks
International Nuclear Information System (INIS)
Gryaznevich, M.P.; Del Bosco, E.; Malaquias, A.; Mank, G.; Oost, G. van
2005-01-01
Small tokamaks have an important role in fusion research. More than 40 small tokamaks are operational. Research on small tokamaks has created a scientific basis for the scaling-up to larger tokamaks. Well-known scientific and engineering schools, which are now determining the main directions of fusion science and technology, have been established through research on small tokamaks. Combined efforts within a network of small and medium size tokamaks will further enhance the contribution of small tokamaks. A new concept of interactive co-ordinated research using small tokamaks in the mainstream fusion science areas, in testing of new diagnostics, materials and technologies as well as in education, training and broadening of the geography of fusion research in the scope of the IAEA Co-ordinated Research Project is presented. (author)
Joint research using small tokamaks
International Nuclear Information System (INIS)
Gryaznevich, M.P.; Bosco, E. Del; Malaquias, A.; Mank, G.; Oost, G. van; He, Yexi; Hegazy, H.; Hirose, A.; Hron, M.; Kuteev, B.; Ludwig, G.O.; Nascimento, I.C.; Silva, C.; Vorobyev, G.M.
2005-01-01
Small tokamaks have an important role in fusion research. More than 40 small tokamaks are operational. Research on small tokamaks has created a scientific basis for the scaling-up to larger tokamaks. Well-known scientific and engineering schools, which are now determining the main directions of fusion science and technology, have been established through research on small tokamaks. Combined efforts within a network of small and medium size tokamaks will further enhance the contribution of small tokamaks. A new concept of interactive coordinated research using small tokamaks in the mainstream fusion science areas, in testing of new diagnostics, materials and technologies as well as in education, training and broadening of the geography of fusion research in the scope of the IAEA Coordinated Research Project, is presented
A consistent thermodynamics of the MHD wave-heated two-fluid solar wind
Directory of Open Access Journals (Sweden)
I. V. Chashei
Full Text Available We start our considerations from two more recent findings in heliospheric physics: One is the fact that the primary solar wind protons do not cool off adiabatically with distance, but appear to be heated. The other one is that secondary protons, embedded in the solar wind as pick-up ions, behave quasi-isothermal at their motion to the outer heliosphere. These two phenomena must be physically closely connected with each other. To demonstrate this we solve a coupled set of enthalpy flow conservation equations for the two-fluid solar wind system consisting of primary and secondary protons. The coupling of these equations comes by the heat sources that are relevant, namely the dissipation of MHD turbulence power to the respective protons at the relevant dissipation scales. Hereby we consider both the dissipation of convected turbulences and the dissipation of turbulences locally driven by the injection of new pick-up ions into an unstable mode of the ion distribution function. Conversion of free kinetic energy of freshly injected secondary ions into turbulence power is finally followed by partial reabsorption of this energy both by primary and secondary ions. We show solutions of simultaneous integrations of the coupled set of differential thermodynamic two-fluid equations and can draw interesting conclusions from the solutions obtained. We can show that the secondary proton temperature with increasing radial distance asymptotically attains a constant value with a magnitude essentially determined by the actual solar wind velocity. Furthermore, we study the primary proton temperature within this two-fluid context and find a polytropic behaviour with radially and latitudinally variable polytropic indices determined by the local heat sources due to dissipated turbulent wave energy. Considering latitudinally variable solar wind conditions, as published by McComas et al. (2000, we also predict latitudinal variations of primary proton temperatures at
A consistent thermodynamics of the MHD wave-heated two-fluid solar wind
Directory of Open Access Journals (Sweden)
I. V. Chashei
2003-07-01
Full Text Available We start our considerations from two more recent findings in heliospheric physics: One is the fact that the primary solar wind protons do not cool off adiabatically with distance, but appear to be heated. The other one is that secondary protons, embedded in the solar wind as pick-up ions, behave quasi-isothermal at their motion to the outer heliosphere. These two phenomena must be physically closely connected with each other. To demonstrate this we solve a coupled set of enthalpy flow conservation equations for the two-fluid solar wind system consisting of primary and secondary protons. The coupling of these equations comes by the heat sources that are relevant, namely the dissipation of MHD turbulence power to the respective protons at the relevant dissipation scales. Hereby we consider both the dissipation of convected turbulences and the dissipation of turbulences locally driven by the injection of new pick-up ions into an unstable mode of the ion distribution function. Conversion of free kinetic energy of freshly injected secondary ions into turbulence power is finally followed by partial reabsorption of this energy both by primary and secondary ions. We show solutions of simultaneous integrations of the coupled set of differential thermodynamic two-fluid equations and can draw interesting conclusions from the solutions obtained. We can show that the secondary proton temperature with increasing radial distance asymptotically attains a constant value with a magnitude essentially determined by the actual solar wind velocity. Furthermore, we study the primary proton temperature within this two-fluid context and find a polytropic behaviour with radially and latitudinally variable polytropic indices determined by the local heat sources due to dissipated turbulent wave energy. Considering latitudinally variable solar wind conditions, as published by McComas et al. (2000, we also predict latitudinal variations of primary proton temperatures at
Numerical simulation of countercurrent flow based on two-fluid model
Energy Technology Data Exchange (ETDEWEB)
Chen, H.D. [Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082 (China); School of Electric Power, South China University of Technology, Guangzhou 510640 (China); Zhang, X.Y., E-mail: zxiaoying@mail.sysu.edu.cn [Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082 (China)
2017-03-15
Highlights: • Using one-dimensional two-fluid model to help understanding counter-current flow two-phase flows. • Using surface tension model to make the one-dimensional two-fluid flow model well-posed. • Solving the governing equations with a modified SIMPLE algorithm. • Validating code with experimental data and applying it to vertical air/steam countercurrent flow condition - Abstract: In order to improve the understanding of counter-current two-phase flows, a transient analysis code is developed based on one-dimensional two-fluid model. A six equation model has been established and a two phase pressure model with surface tension term, wall drag force and interface shear terms have been used. Taking account of transport phenomenon, heat and mass transfer models of interface were incorporated. The staggered grids have been used in discretization of equations. For validation of the model and code, a countercurrent air-water problem in one experimental horizontal stratified flow has been considered firstly. Comparison of the computed results and the experimental one shows satisfactory agreement. As the full problem for investigation, one vertical pipe with countercurrent flow of steam-water and air-water at same boundary condition has been taken for study. The transient distribution of liquid fraction, liquid velocity and gas velocity for selected positions of steam-water and air-water problem were presented and discussed. The results show that these two simulations have similar transient behavior except that the distribution of gas velocity for steam-water problem have larger oscillation than the one for air-water. The effect of mesh size on wavy characteristics of interface surface was also investigated. The mesh size has significant influence on the simulated results. With the increased refinement, the oscillation gets stronger.
Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas
Zhu, Jian-Zhou
2018-03-01
The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known "frozen-in" to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, "Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation," Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, "Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces," J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the "vertical velocity" (or the passive scalar) and the "vertical vorticity," may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.
A PISO-like algorithm to simulate superfluid helium flow with the two-fluid model
Soulaine, Cyprien; Allain, Hervé; Baudouy, Bertrand; Van Weelderen, Rob
2015-01-01
This paper presents a segregated algorithm to solve numerically the superfluid helium (He II) equations using the two-fluid model. In order to validate the resulting code and illustrate its potential, different simulations have been performed. First, the flow through a capillary filled with He II with a heated area on one side is simulated and results are compared to analytical solutions in both Landau and Gorter–Mellink flow regimes. Then, transient heat transfer of a forced flow of He II is investigated. Finally, some two-dimensional simulations in a porous medium model are carried out.
Relaxation and Numerical Approximation of a Two-Fluid Two-Pressure Diphasic Model
International Nuclear Information System (INIS)
Ambroso, A.; Chalons, Ch.; Galie, Th.; Chalons, Ch.; Coquel, F.; Coquel, F.
2009-01-01
This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural phase space, and exactly captures the coupling waves between the two phases. Numerical evidences are given to corroborate the validity of our approach. (authors)
Two-fluid model of the superconductivity in the BCS's theory
International Nuclear Information System (INIS)
Rangelov, J.
1977-01-01
The coefficients of Bogolubov-Valatin's transformation are chosen in accordance with the two-fluid model of superconductivity. The energy spectrum of superconducting quasi-particles is obtained as a solution of the linearized equation of motion of interacting particles. The energy distribution of the superconducting and normal quasi-particles is discussed from a new view-point. The correlation between the quasi-particles forming the Cooper's pair is discussed in accordance with the proposed ideas. The tunnelling of the normal quasi-particles in systems M-I-S and S 1 -I-S 2 is investigated qualitatively
Study of blood flow in several benchmark micro-channels using a two-fluid approach
Wu, Wei-Tao; Yang, Fang; Antaki, James F.; Aubry, Nadine; Massoudi, Mehrdad
2015-01-01
It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated ...
Advanced commercial tokamak study
International Nuclear Information System (INIS)
Thomson, S.L.; Dabiri, A.E.; Keeton, D.C.; Brown, T.G.; Bussell, G.T.
1985-12-01
Advanced commercial tokamak studies were performed by the Fusion Engineering Design Center (FEDC) as a participant in the Tokamak Power Systems Studies (TPSS) project coordinated by the Office of Fusion Energy. The FEDC studies addressed the issues of tokamak reactor cost, size, and complexity. A scoping study model was developed to determine the effect of beta on tokamak economics, and it was found that a competitive cost of electricity could be achieved at a beta of 10 to 15%. The implications of operating at a beta of up to 25% were also addressed. It was found that the economics of fusion, like those of fission, improve as unit size increases. However, small units were found to be competitive as elements of a multiplex plant, provided that unit cost and maintenance time reductions are realized for the small units. The modular tokamak configuration combined several new approaches to develop a less complex and lower cost reactor. The modular design combines the toroidal field coil with the reactor structure, locates the primary vacuum boundary at the reactor cell wall, and uses a vertical assembly and maintenance approach. 12 refs., 19 figs
Energy Technology Data Exchange (ETDEWEB)
Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, University of Tokyo, 113-0033 (Japan)
2016-11-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron–positron or an electron–proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten–Lax–Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.
Second order numerical method of two-fluid model of air-water flow
International Nuclear Information System (INIS)
Tiselj, I.; Petelin, S.
1995-01-01
Model considered in this paper is six-equation two-fluid model used in computer code RELAP5. Air-water equations were taken in a code named PDE to avoid additional problems caused by condensation or vaporization. Terms with space derivatives were added in virtual mass term in momentum equations to ensure the hyperbolicity of the equations. Numerical method in PDE code is based on approximate Riemann solvers. Equations are solved on non-staggered grid with explicit time advancement and with upwind discretization of the convective terms in characteristic form of the equations. Flux limiters are used to find suitable combinations of the first (upwind) and the second order (Lax-Wendroff) discretization s which ensure second order accuracy on smooth solutions and damp oscillations around the discontinuities. Because of the small time steps required and because of its non-dissipative nature the scheme is suitable for the prediction of the fast transients: pressure waves, shock and rarefaction waves, water hammer or critical flow. Some preliminary results are presented for a shock tube problem and for Water Faucet problem - problems usually used as benchmarks for two-fluid computer codes. (author)
Fluid Dynamics And Mass Transfer In Two-Fluid Taylor-Couette Flow
International Nuclear Information System (INIS)
Baier, G.; Graham, M.D.
1998-01-01
The Taylor-Couette instability of a single liquid phase can be used to enhance mass transfer processes such as filtration and membrane separations. We consider here the possibility of using this instability to enhance interphase transport in a two-fluid systems, with a view toward improved liquid-liquid extractions for biotechnology applications. We investigate the centrifugal instability of a pair of radially stratified immiscible liquids in the annular gap between concentric, corotating cylinders: two-fluid Taylor-Couette flow. Experiments show that a two-layer flow with a well-defined interface and Taylor vortices in each phase can be obtained. The experimental results are in good agreement with predictions of inviscid arguments based on a two-phase extension of Rayleigh's criterion, as well as with detailed linear stability calculations. For a given geometry, the most stable configuration occurs for fluids of roughly (exactly in the inviscid limit) equal dynamic viscosities. A number of preliminary mass transfer experiments have also been performed, in the presence of axial counterflow. The onset of Taylor vortices coincides with a clear decrease in the extent of axial dispersion and an increase in the rate of interphase transport, thus suggesting that this flow geometry may provide an effective means for countercurrent chromatographic separations
Analysis of subcooled boiling with the two-fluid particle interaction method
International Nuclear Information System (INIS)
Shirakawa, Noriyuki; Horie, Hideki; Yamamoto, Yuichi; Tsunoyama, Shigeaki
2003-01-01
A particle interaction method called MPS (the Moving Particle Semi-implicit method), which formulates the differential operators in Navier-Stokes' equation as interactions between particles characterized by a kernel function, has been developed in recent years. We have extended this method to a two-fluid system with a potential-type surface tension in order to analyze the two-phase flow without experimental correlation. This extended method (Two-Fluid MPS: TF-MPS) was successfully applied to a subcooled boiling experiment. The most important element in any effective subcooled boiling model is to be able to accurately calculate where significant void fraction appears, that is, the location of the void departure point. The location of the initial void ejection into the subcooled liquid core can be determined fairly well experimentally and conventionally is given in terms of a critical subcooling. We investigated the relation between Stanton and Peclet numbers at the void departure point in the calculated results with TF-MPS method, varying the inlet water velocity to change Peclet number. (author)
ALFVÉN WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
International Nuclear Information System (INIS)
Soler, R.; Ballester, J. L.; Terradas, J.; Carbonell, M.
2013-01-01
Alfvén waves are a particular class of magnetohydrodynamic waves relevant in many astrophysical and laboratory plasmas. In partially ionized plasmas the dynamics of Alfvén waves is affected by the interaction between ionized and neutral species. Here we study Alfvén waves in a partially ionized plasma from the theoretical point of view using the two-fluid description. We consider that the plasma is composed of an ion-electron fluid and a neutral fluid, which interact by means of particle collisions. To keep our investigation as general as possible, we take the neutral-ion collision frequency and the ionization degree as free parameters. First, we perform a normal mode analysis. We find the modification due to neutral-ion collisions of the wave frequencies and study the temporal and spatial attenuation of the waves. In addition, we discuss the presence of cutoff values of the wavelength that constrain the existence of oscillatory standing waves in weakly ionized plasmas. Later, we go beyond the normal mode approach and solve the initial-value problem in order to study the time-dependent evolution of the wave perturbations in the two fluids. An application to Alfvén waves in the low solar atmospheric plasma is performed and the implication of partial ionization for the energy flux is discussed.
Advanced statistics for tokamak transport colinearity and tokamak to tokamak variation
International Nuclear Information System (INIS)
Riedel, K.S.
1989-03-01
This is a compendium of three separate articles on the statistical analysis of tokamak transport. The first article is an expository introduction to advanced statistics and scaling laws. The second analyzes two important problems of tokamak data---colinearity and tokamak to tokamak variation in detail. The third article generalizes the Swamy random coefficient model to the case of degenerate matrices. Three papers have been processed separately
A three field two fluid CFD model for the bubbly-cap bubble regime
International Nuclear Information System (INIS)
Martin Lopez de Bertodano; Xiaodong Sun; Mamoru Ishii; Asim Ulke
2005-01-01
Full text of publication follows: The lateral phase distribution of a two phase duct flow in the cap bubble regime is analyzed with a three dimensional three field two-fluid CFD model based on the turbulent k-ε model for bubbly flows developed by Lopez de Bertodano et. al. [2]. The turbulent diffusion of the bubbles is the dominant phase distribution mechanism. A new analytic result is presented to support the development of the model for the bubble induced turbulent diffusion force. New experimental data obtained with a state-of-the-art four sensor miniature conductivity probe are used to validate the two-fluid model. The focus of this work is modeling the transport of the dispersed phase. Previous work (e.g., Lopez de Bertodano et. al.) was focused on the interfacial forces of drag, lift and virtual mass. However, the dispersion of the bubbles by the turbulent eddies of the continuous phase must be considered too. The rigorous formulation of a model for the turbulent dispersion of the bubbles results in a turbulent diffusion force which is obtained from a probability distribution function average (i.e., Boltzmann averaging) of the dispersed phase momentum equation. This force was recently applied to a turbulent bubbly jet with small bubbles (i.e., 1 mm diameter) without adjusting any coefficient. However, the application of this force to industrial conditions (i.e., larger bubbles) requires specific two-phase flow experimental data to calibrate the model due to the uncertainties of the flow around large bubbles. In particular the void distribution and the interfacial area concentration are measured in a mixture of big and small bubbles. The state-of-the-art miniaturized four-sensor conductivity probe developed by Kim et al. [3] is used to obtain the interfacial area concentration in complex two-phase flow situations. This probe can discriminate between small and large bubbles so it offers an opportunity to perform further developments of the multidimensional two-fluid
International Nuclear Information System (INIS)
Anon.
1988-01-01
The Microwave Tokamak Experiment, now under construction at the Laboratory, will use microwave heating from a free-electron laser. The intense microwave pulses will be injected into the tokamak to realize several goals, including a demonstration of the effects of localized heat deposition within magnetically confined plasma, a better understanding of energy confinement in tokamaks, and use of the new free-electron laser technology for plasma heating. The experiment, soon to be operational, provides an opportunity to study dense plasmas heated by powers unprecedented in the electron-cyclotron frequency range required by the especially high magnetic fields used with the MTX and needed for reactors. 1 references, 5 figures, 3 tables
International Nuclear Information System (INIS)
Wootton, A.J.
1993-04-01
This progress report covers the period from November 1, 1990 to April 30, 1993. During that period, TEXT was operated as a circular tokamak with a material limiter. It was devoted to the study of basic plasma physics, in particular to study of fluctuations, turbulence, and transport. The purpose is to operate and maintain TEXT Upgrade as a complete facility for applied tokamak physics, specifically to conduct a research program under the following main headings: (1) to elucidate the mechanisms of working gas, impurity, and thermal transport in tokamaks, in particular to understand the role of turbulence; (2) to study physics of the edge plasma, in particular the turbulence; (3) to study the physics or resonant magnetic fields (ergodic magnetic divertors, intra island pumping); and (4) to study the physics of electron cyclotron heating (ECRH). Results of studies in each of these areas are reported
Magnetic ''islandography'' in tokamaks
International Nuclear Information System (INIS)
Callen, J.D.; Waddell, B.V.; Hicks, H.R.
1978-09-01
Tearing modes are shown to be responsible for most of the experimentally observed macroscopic behavior of tokamak discharges. The effects of these collective magnetic perturbations on magnetic topology and plasma transport in tokamaks are shown to provide plausible explanations for: internal disruptions (m/n = 1); Mirnov oscillations (m/n = 2,3...); and major disruptions (coupling of 2/1-3/2 modes). The nonlinear evolution of the tearing modes is followed with fully three-dimensional computer codes. The effects on plasma confinement of the magnetic islands or stochastic field lines induced by the macroscopic tearing modes are discussed and compared with experiment. Finally, microscopic magnetic perturbations are shown to provide a natural model for the microscopic anomalous transport processes in tokamaks
Accelerator technology in tokamaks
International Nuclear Information System (INIS)
Kustom, R.L.
1977-01-01
This article presents the similarities in the technology required for high energy accelerators and tokamak fusion devices. The tokamak devices and R and D programs described in the text represent only a fraction of the total fusion program. The technological barriers to producing successful, economical tokamak fusion power plants are as many as the plasma physics problems to be overcome. With the present emphasis on energy problems in this country and elsewhere, it is very likely that fusion technology related R and D programs will vigorously continue; and since high energy accelerator technology has so much in common with fusion technology, more scientists from the accelerator community are likely to be attracted to fusion problems
3D simulation studies of tokamak plasmas using MHD and extended-MHD models
International Nuclear Information System (INIS)
Park, W.; Chang, Z.; Fredrickson, E.; Fu, G.Y.; Pomphrey, N.; Sugiyama, L.E.
1997-01-01
The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-β disruption studies in reversed shear plasmas using the MHD level MH3D code, ω *i stabilization and nonlinear island rotation studies using the two-fluid level MH3D-T code, studies of nonlinear saturation of TAE modes using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D ++ code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree well with experimental data
International Nuclear Information System (INIS)
Steiner, D.; Embrechts, M.
1990-07-01
This is a status report on technical progress relative to the tasks identified for the fifth year of Grant No. FG02-85-ER52118. The ARIES tokamak reactor study is a multi-institutional effort to develop several visions of the tokamak as an attractive fusion reactor with enhanced economic, safety, and environmental features. The ARIES study is being coordinated by UCLA and involves a number of institutions, including RPI. The RPI group has been pursuing the following areas of research in the context of the ARIES-I design effort: MHD equilibrium and stability analyses; plasma-edge modeling and blanket materials issues. Progress in these areas is summarized herein
Internal disruption in tokamaks
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Savrukhin, P.V.
1990-01-01
A review of results of experimental and theoretical investigations of internal disruption in tokamaks is given. Specific features of various types of saw-tooth oscillations are described and their classification is performed. Theoretical models of the process of development of internal disruption instability are discussed. Effect of internal disruption on parameters of plasma, confined in tokamak, is considered. Scalings of period and amplitude of saw-tooth oscillations, as well as version radius are presented. Different methods for stabilizing instability of internal disruption are described
International Nuclear Information System (INIS)
Unterberg, Bernhard; Samm, Ulrich
2004-01-01
An overview is given of recent results obtained in tokamak devices. We introduce basic confinement scenarios as L-mode, H-mode and plasmas with an internal transport barrier and discuss methods for profile control. Important findings in DT-experiments at JET as α-particle heating are described. Methods for power exhaust like plasma regimes with a radiating mantle and radiative divertor scenarios are discussed. The overall impact of plasma edge conditions on the general plasma performance in tokamaks is illustrated by describing the impact of wall conditions on confinement and the edge operational diagram of H-mode plasmas
Internal disruptions in tokamaks
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Savrukhin, P.V.
1990-01-01
Experimental and theoretical studies of the phenomenon of internal disruptions in tokamaks are reviewed. A classification scheme is introduced and the features of different types of sawtooth oscillations are described. A theoretical model for the development of the internal disruption instability is discussed. The effect of internal disruptions on the parameters of plasma confined in tokamaks is discussed. Scaling laws for the period and amplitude of sawtooth oscillations, as well as for the inversion radius, are presented. Different methods of stabilizing the internal disruption instability are described
Stability analysis for the Big Dee upgrade of the Doublet III tokamak
International Nuclear Information System (INIS)
Helton, F.J.; Luxon, J.L.
1987-01-01
Ideal magnetohydrodynamic stability analysis has been carried out for configurations expected in the Big Dee tokamak, an upgrade of the Doublet III tokamak into a non-circular cross-section device which began operation early in 1986. The results of this analysis support theoretical predictions as follows: Since the maximum value of beta stable to ballooning and Mercier modes, which we denote β c , increases with inverse aspect ratio, elongation and triangularity, the Big Dee is particularly suited to obtain high values of β c and there exist high β c Big Dee equilibria for large variations in all relevant plasma parameters. The beta limits for the Big Dee are consistent with established theory as summarized in present scaling laws. High beta Big Dee equilibria are continuously accessible when approached through changes in all relevant input parameters and are structurally stable with respect to variations of input plasma parameters. Big Dee beta limits have a smooth dependence on plasma parameters such as β p and elongation. These calculations indicate that in the actual running of the device the Big Dee high beta equilibria should be smoothly accessible. Theory predicts that the limiting plasma parameters, such as beta, total plasma current and plasma pressure, which can be obtained within the operating limits of the Big Dee are reactor relevant. Thus the Big Dee should be able to use its favourable ideal MHD scaling and controlled plasma shaping to attain reactor relevant parameters in a moderate sized device. (author)
High-pressure fluid-phase equilibria: Experimental methods and systems investigated (2000-2004)
DEFF Research Database (Denmark)
Dohrn, Ralf; Peper, Stephanie; Fonseca, José
2010-01-01
As a part of a series of reviews, a compilation of systems for which high-pressure phase-equilibrium data were published between 2000 and 2004 is given. Vapor-liquid equilibria, liquid-liquid equilibria, vapor-liquid-liquid equilibria,solid-liquid equilibria, solid-vapor equilibria, solid-vapor-l...
Gyrokinetic magnetohydrodynamics and the associated equilibria
Lee, W. W.; Hudson, S. R.; Ma, C. H.
2017-12-01
The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee ["Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective," Phys. Plasmas 23, 070705 (2016)], and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, ϕ, and the vector potential, A , and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when ϕ→0 and A becomes constant in time, which, in turn, gives ∇.(J∥+J⊥)=0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. These gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.
Multiple equilibria in a simple elastocapillary system
Taroni, Michele
2012-09-28
We consider the elastocapillary interaction of a liquid drop placed between two elastic beams, which are both clamped at one end to a rigid substrate. This is a simple model system relevant to the problem of surface-tension-induced collapse of flexible micro-channels that has been observed in the manufacture of microelectromechanical systems (MEMS). We determine the conditions under which the beams remain separated, touch at a point, or stick along a portion of their length. Surprisingly, we show that in many circumstances multiple equilibrium states are possible. We develop a lubrication-type model for the flow of liquid out of equilibrium and thereby investigate the stability of the multiple equilibria. We demonstrate that for given material properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.
Gyro-fluid and two-fluid theory and simulations of edge-localized-modes
Energy Technology Data Exchange (ETDEWEB)
Xu, X. Q.; Dimits, A.; Joseph, I.; Umansky, M. V. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Xi, P. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); School of Physics, Peking University, Beijing (China); Xia, T. Y.; Gui, B. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China); Kim, S. S.; Park, G. Y.; Rhee, T.; Jhang, H. [WCI Center for Fusion Theory, National Fusion Research Institute, Daejon 305-333 (Korea, Republic of); Diamond, P. H. [WCI Center for Fusion Theory, National Fusion Research Institute, Daejon 305-333 (Korea, Republic of); Center for Astrophysics and Space Sciences and Department of Physics, University of California, San Diego, La Jolla, California 92093-0424 (United States); Dudson, B. [University of York, Heslington, York YO10 5DD (United Kingdom); Snyder, P. B. [General Atomics, San Diego, California 92186 (United States)
2013-05-15
This paper reports on the theoretical and simulation results of a gyro-Landau-fluid extension of the BOUT++ code, which contributes to increasing the physics understanding of edge-localized-modes (ELMs). Large ELMs with low-to-intermediate-n peeling-ballooning (P-B) modes are significantly suppressed due to finite Larmor radius (FLR) effects when the ion temperature increases. For type-I ELMs, it is found from linear simulations that retaining complete first order FLR corrections as resulting from the incomplete “gyroviscous cancellation” in Braginskii's two-fluid model is necessary to obtain good agreement with gyro-fluid results for high ion temperature cases (T{sub i}≽3 keV) when the ion density has a strong radial variation, which goes beyond the simple local model of ion diamagnetic stabilization of ideal ballooning modes. The maximum growth rate is inversely proportional to T{sub i} because the FLR effect is proportional to T{sub i}. The FLR effect is also proportional to toroidal mode number n, so for high n cases, the P-B mode is stabilized by FLR effects. Nonlinear gyro-fluid simulations show results that are similar to those from the two-fluid model, namely that the P-B modes trigger magnetic reconnection, which drives the collapse of the pedestal pressure. Due to the additional FLR-corrected nonlinear E × B convection of the ion gyro-center density, for a ballooning-dominated equilibrium the gyro-fluid model further limits the radial spreading of ELMs. In six-field two fluid simulations, the parallel thermal diffusivity is found to prevent the ELM encroachment further into core plasmas and therefore leads to steady state L-mode profiles. The simulation results show that most energy is lost via ion channel during an ELM event, followed by particle loss and electron energy loss. Because edge plasmas have significant spatial inhomogeneities and complicated boundary conditions, we have developed a fast non-Fourier method for the computation of
Experimental study of two-fluid effect during magnetic reconnection in the UTST merging experiment
International Nuclear Information System (INIS)
Yamasaki, Kotaro; Takemura, Koichiro; Cao, Qinghong; Watanabe, Takenori G.; Itagaki, Hirotomo; Inomoto, Michiaki; Ono, Yasushi; Kamio, Shuji; Yamada, Takuma
2013-01-01
Radial profile of floating potential inside the current sheet was measured for the purpose of investigating the two-fluid (Hall) effect during magnetic reconnection in the UTST merging experiment. During magnetic reconnection, the floating potential drop was formed spontaneously inside the current sheet, forming a steep electric potential gradient on its both downstream areas. Magnetic probe array measurement indicates that this potential drop appears spontaneously when the reconnection rate rapidly increase due to change in current sheet structure. The IDS probe measurement observed outflow almost equal to poloidal Alfvén speed in radial direction from the X-point, where steep gradient of floating potential is formed. This fact suggests that ion acceleration/heating is caused by the steep potential gradient formed in the downstream by magnetized electrons. (author)
A Study of Two Fluids Mixing in a Helical-Type Micromixer
International Nuclear Information System (INIS)
Hu, Y H; Chang, M; Lin, K H
2006-01-01
The mixing behavior of two fluids in a passive micromixer with Y-type inlet and helical fluid channel, along with herringbone grooves etched on the base of the fluid channel, was studied with computer simulation technique and experiments. The mixing of pure water and acetone solution under different Reynolds numbers and acetone concentrations were investigated. An image inspection method using the variance in contrast of the image gray level as the measurement parameter was adopted to calculate the mixing efficiency distribution. Inspection results show that the mixing efficiency is decreased with the increase of the concentration of the acetone solution, but the mean mixing efficiency around the outlet can reach to a value of 90% even the Reynolds numbers of the fluids were as low as Re = 1, and the best efficiency for the case of Re = 10 is over 98%. The results show that the proposed micromixer is possible applied to the field of biomedical diagnosis
Effect of flow conditions on spray cone angle of a two-fluid atomizer
Energy Technology Data Exchange (ETDEWEB)
Shafaee, Maziar; Banitabaei, Sayed Abdolhossein; Ashjaee, Mehdi; Esfahanian, Vahid [Tehran University, Tehran (Iran, Islamic Republic of)
2011-02-15
A visual study is conducted to determine the effects of operating conditions on the spray cone angle of a two-fluid atomizer. The liquid (water) jets exit from peripheral inclined orifices and are introduced into a high-speed gas (air) stream in the gravitational direction. Using a high-speed imaging system, the spray cone angle is determined for Reynolds numbers ranging from 4x10{sup 4} to 9x10{sup 4} and different Weber numbers up to 140. The droplet sizes (Sauter mean diameter) and their distributions are determined using a Malvern Mastersizer X. The results show that the spray cone angle depends on the operating conditions, especially in lower values of Reynolds and Weber numbers. An empirical correlation is also obtained to predict the spray cone angle in terms of these two parameters.
Relativistic effects on large amplitude nonlinear Langmuir waves in a two-fluid plasma
International Nuclear Information System (INIS)
Nejoh, Yasunori
1994-07-01
Large amplitude relativistic nonlinear Langmuir waves are analyzed by the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two-fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ion mass to electron mass ratio. The constant energy is determined by the specific range of the relativistic effect. In the non-relativistic limit, large amplitude relativistic Langmuir waves do not exist. The present investigation predicts new findings of large amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important. (author)
Advanced Semi-Implicit Method (ASIM) for hyperbolic two-fluid model
International Nuclear Information System (INIS)
Lee, Sung Jae; Chung, Moon Sun
2003-01-01
Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the previous manuscript. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. This Advanced Semi-Implicit Method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity
Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model
Cheviakov, Alexei F.
2018-05-01
A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.
Three-dimensional two-fluid numerical treatment of a reactor vessel in TRAC
International Nuclear Information System (INIS)
Liles, D.R.
1979-01-01
A three-dimensional two-fluid finite difference model has been used in TRAC (Transient Reactor Analysis Code) to represent a pressurized water reactor vessel. Mesh cells may be blocked off completely to represent large flow obstructions such as downcomer walls. The hydrodynamic volumes and flow areas may also be reduced in order to provide a porous matrix simulation of smaller scale strucuture. The finite difference equations are semi-implicit so that stability time scales are associated with material movement and not wave propagation. The block matrix structure is reduced during the implicit pass to a single element seven stripe system which is easily solved iteratively. This procedure has successfully performed numerous simulations of both full sized reactor accidents and smaller scale experments. It has proven to be a useful feature of the TRAC effort
Study of blood flow in several benchmark micro-channels using a two-fluid approach.
Wu, Wei-Tao; Yang, Fang; Antaki, James F; Aubry, Nadine; Massoudi, Mehrdad
2015-10-01
It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model was implemented using OpenFOAM® in which benchmark problems including a sudden expansion and various driven slots and crevices were studied numerically. The numerical results exhibited good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of RBCs.
Simulation of horizontal pipe two-phase slug flows using the two-fluid model
Energy Technology Data Exchange (ETDEWEB)
Ortega Malca, Arturo J. [Pontificia Univ. Catolica do Rio de Janeiro, RJ (Brazil). Dept. de Engenharia Mecanica. Nucleo de Simulacao Termohidraulica de Dutos (SIMDUT); Nieckele, Angela O. [Pontificia Univ. Catolica do Rio de Janeiro, RJ (Brazil). Dept. de Engenharia Mecanica
2005-07-01
Slug flow occurs in many engineering applications, mainly in the transport of hydrocarbon fluids in pipelines. The intermittency of slug flow causes severe unsteady loading on the pipelines carrying the fluids, which gives rise to design problems. Therefore, it is important to be able to predict the onset and development of slug flow as well as slug characteristics. The present work consists in the simulation of two-phase flow in slug pattern through horizontal pipes using the two-fluid model in its transient and one-dimensional form. The advantage of this model is that the flow field is allowed to develop naturally from a given initial conditions as part of the transient calculation; the slug evolves automatically as a product of the computed flow development. Simulations are then carried out for a large number of flow conditions that lead a slug flow. (author)
Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations
Energy Technology Data Exchange (ETDEWEB)
Ohnuki, Akira; Akimoto, Hajime [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kamo, Hideki
1996-11-01
In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A {kappa}-{epsilon} turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)
Modeling and analysis of hydrodynamic instabilities in two-phase flow using two-fluid model
International Nuclear Information System (INIS)
Zhou, J.; Podowski, M.Z.
2001-01-01
Because of the practical importance of two-phase flow instabilities, especially in boiling water nuclear reactor technology, substantial efforts have been made to date to understand the physical phenomena governing such instabilities and to develop computational tools to model the dynamics of marginally-stable/unstable boiling systems. The purpose of this paper is to present an integrated methodology for the analysis of flow-induced instabilities in boiling channels and systems. The major novel aspects of the proposed approach are: (a) it is based on the combined frequency-domain and time-domain methods, the former used to quantify stability margins and to determine the onset of instability conditions, the latter to study the nonlinear system response outside the stability boundaries identified using the nearly-exact results of the frequency-domain analysis; (b) the two-fluid model of two-phase flow has been used for the first time to analytically derive the boiling channel transfer functions for the parallel-channel and channel-to-channel instability modes. In this way, the major characteristics of a boiling system, including the onset-of-instability conditions, can be readily evaluated by using the qualitative frequency-domain approach, whereas the explicit time-domain integration is performed, if necessary, only for the operating conditions that have already been identified as unstable. Both methods use the same physical two-fluid model that, in one case, is linearized and used to derive a rigorous analytical solution in the complex domain, and, in the other case, is solved numerically using an algorithm developed especially for this purpose. The results using both methods have been compared against each other and extensively tested. The testing and validation of the new model included comparisons of the predicted steady-state distributions of major parameters and of the transient channel response against experimental data
Integrable, oblique travelling waves in quasi-charge-neutral two-fluid plasmas
Directory of Open Access Journals (Sweden)
G. M. Webb
2008-02-01
Full Text Available A Hamiltonian description of oblique travelling waves in a two-fluid, charge-neutral, electron-proton plasma reveals that the transverse momentum equations for the electron and proton fluids are exactly integrable in cases where the total transverse momentum flux integrals, P_{y}^{(d} and P_{z}^{(d}, are both zero in the de Hoffman Teller (dHT frame. In this frame, the transverse electric fields are zero, which simplifies the transverse momentum equations for the two fluids. The integrable travelling waves for the case P_{y}^{(d}=P_{z}^{(d}=0, are investigated based on the Hamiltonian trajectories in phase space, and also on the longitudinal structure equation for the common longitudinal fluid velocity component u_{x} of the electron and proton fluids. Numerical examples of a variety of travelling waves in a cold plasma, including oscillitons, are used to illustrate the physics. The transverse, electron and proton velocity components u_{jy} and u_{jz} (j=e, p of the waves exhibit complex, rosette type patterns over several periods for u_{x}. The role of separatrices in the phase space, the rotational integral and the longitudinal structure equation on the different wave forms are discussed.
Revisiting low-fidelity two-fluid models for gas–solids transport
Energy Technology Data Exchange (ETDEWEB)
Adeleke, Najeem, E-mail: najm@psu.edu; Adewumi, Michael, E-mail: m2a@psu.edu; Ityokumbul, Thaddeus
2016-08-15
Two-phase gas–solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas–solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe–Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.
Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations
International Nuclear Information System (INIS)
Ohnuki, Akira; Akimoto, Hajime; Kamo, Hideki.
1996-11-01
In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A κ-ε turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)
Spiral field inhibition of thermal conduction in two-fluid solar wind models
International Nuclear Information System (INIS)
Nerney, S.; Barnes, A.
1978-01-01
The two-fluid solar wind equations, including inhibition of heat conduction by the spiral magnetic field, have been solved for steady radial flow, and the results are compared with those of our previous study of two-fluid models with straight interplanetary field lines. The main effects of the spiral field conduction cutoff are to bottle up electron heat inside 1 AU and to produce adiabatic electron (an proton) temperature profiles at large heliocentric distances. Otherwise, the spiral field models are nearly identical with straight field models with the same temperatures and velocity at 1 AU, except for models associated with very low coronal base densities (n 0 approx.10 6 cm -3 at 1R/sub s/). Low base density spiral models give a nearly isothermal electron temperature profile over 50--100 AU together with high velocities and temperatures at 1 AU. In general, high-velocity models do not agree well with observed high-velocity streams: lower-velocity states can be represented reasonably well at 1 AU, but only for very high proton temperatures (T/sub p/approx.2T/sub e/) at the coronal base. For spherically symmetric base conditions the straight field and spiral field models can be regarded, in lowest order, as approximations to the polar and equatorial three-dimensional flows, respectively. This viewpoint suggests a pole to equator electron temperature gradient in the region 1-10 AU, which would be associated with a meridional velocity of approx.0.5-1.0 km/s, diverging away from the equatorial plane. The formalism developed in this paper shows rather stringent limits to the mass loss rate for conductively driven winds and, in particular, illustrates that putative T Tauri outflows could not be conductively driven
Revisiting low-fidelity two-fluid models for gas–solids transport
International Nuclear Information System (INIS)
Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus
2016-01-01
Two-phase gas–solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas–solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe–Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.
Revisiting low-fidelity two-fluid models for gas-solids transport
Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus
2016-08-01
Two-phase gas-solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas-solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe-Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.
International Nuclear Information System (INIS)
Dory, R.A.; Berger, D.P.; Charlton, L.A.; Hogan, J.T.; Munro, J.K.; Nelson, D.B.; Peng, Y.K.M.; Sigmar, D.J.; Strickler, D.J.
1978-01-01
MHD equilibrium, stability, and transport calculations are made to study the accessibility and behavior of ''high beta'' tokamak plasmas in the range β approximately 5 to 15 percent. For next generation devices, beta values of at least 8 percent appear to be accessible and stable if there is a conducting surface nearby
Sawtooth phenomena in tokamaks
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Savrukhin, P.V.
1989-01-01
A review of experimental and theoretical investigaions of sawtooth phenomena in tokamaks is presented. Different types of sawtooth oscillations, scaling laws and methods of interanl disruption stabilization are described. Theoretical models of the sawtooth instability are discussed. 122 refs.; 4 tabs
International Nuclear Information System (INIS)
Pare, V.K.
1983-01-01
Calculations with several different computer codes based on the resistive MHD equations have shown that (m = 1, n = 1) tearing modes in tokamak plasmas grow by magnetic reconnection. The observable behavior predicted by the codes has been confirmed in detail from the waveforms of signals from x-ray detectors and recently by x-ray tomographic imaging
International Nuclear Information System (INIS)
1993-01-01
This document consists of a collection of papers presented at the IAEA Technical Committee Meeting on Research Using Small Tokamaks. It contains 22 papers on a wide variety of research aspects, including diagnostics, design, transport, equilibrium, stability, and confinement. Some of these papers are devoted to other concepts (stellarators, compact tori). Refs, figs and tabs
International Nuclear Information System (INIS)
1991-01-01
The technical reports contained in this collection of papers on research using small tokamaks fall into four main categories, i.e., (i) experimental work (heating, stability, plasma radial profiles, fluctuations and transport, confinement, ultra-low-q tokamaks, wall physics, a.o.), (ii) diagnostics (beam probes, laser scattering, X-ray tomography, laser interferometry, electron-cyclotron absorption and emission systems), (iii) theory (strong turbulence, effects of heating on stability, plasma beta limits, wave absorption, macrostability, low-q tokamak configurations and bootstrap currents, turbulent heating, stability of vortex flows, nonlinear islands growth, plasma-drift-induced anomalous transport, ergodic divertor design, a.o.), and (iv) new technical facilities (varistors applied to establish constant current and loop voltage in HT-6M), lower-hybrid-current-drive systems for HT-6B and HT-6M, radio-frequency systems for HT-6M ICR heating experimentation, and applications of fiber optics for visible and vacuum ultraviolet radiation detection as applied to tokamaks and reversed-field pinches. A total number of 51 papers are included in the collection. Refs, figs and tabs
International Nuclear Information System (INIS)
Wootton, A.J.; Wiley, J.C.; Edmonds, P.H.; Ross, D.W.
1997-01-01
The possible use of tokamaks for thermonuclear power plants is discussed, in particular tokamaks with low aspect ratio and copper toroidal field coils. Three approaches are presented. First, the existing literature is reviewed and summarized. Second, using simple analytic estimates, the size of the smallest tokamak to produce an ignited plasma is derived. This steady state energy balance analysis is then extended to determine the smallest tokamaks power plant, by including the power required to drive the toroidal field and by considering two extremes of plasma current drive efficiency. Third, the analytic results are augmented by a numerical calculation that permits arbitrary plasma current drive efficiency and different confinement scaling relationships. Throughout, the importance of various restrictions is emphasized, in particular plasma current drive efficiency, plasma confinement, plasma safety factor, plasma elongation, plasma beta, neutron wall loading, blanket availability and recirculation of electric power. The latest published reactor studies show little advantage in using low aspect ratios to obtain a more compact device (and a low cost of electricity) unless either remarkably high efficiency plasma current drive and low safety factor are combined, or unless confinement (the H factor), the permissible elongation and the permissible neutron wall loading increase as the aspect ratio is reduced. These results are reproduced with the analytic model. (author). 22 refs, 3 figs
International Nuclear Information System (INIS)
Wootton, A.J.
1990-04-01
This paper discusses the following work on the text tokamak: data systems; particle confinement; impurity transport; plasma rotation; runaway electrons; electron cyclotron heating; FIR system; transient transport; internal turbulence; edge turbulence; ion temperature; EML experiments; impurity pellet experiments; MHD experiments and analysis; TEXT Upgrade; and Upgrade diagnostics
Uniqueness of Nash equilibria in a quantum Cournot duopoly game
International Nuclear Information System (INIS)
Sekiguchi, Yohei; Sakahara, Kiri; Sato, Takashi
2010-01-01
A quantum Cournot game whose classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties: (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.
State diagrams of tokamaks and state transitions
International Nuclear Information System (INIS)
Minardi, E.
1992-01-01
In a simple one-fluid cylindrical model of transport and of dissipative effects, the family of the magnetic states of the Tokamak which correspond to a vanishing entropy production in the confinement region is characterized by a define relation or ''state equation'' involving the relevant parameters of the discharge. An investigation is made as to how the entropy production changes when the current density profile is rearranged by a perturbation which conserves the poloidal magnetic flux. It is shown that for a sufficiently short time interval, that is to say t 2 E τ s where τ E is the energy confinement time and τ s is the resistive time, neighbouring bifurcating equilibria exist which can be reached with a flux-conserving transition and with increase of the magnetic entropy. The family of these new states can also be characterized by a state equation involving the relevant discharge parameters. When the state equations of the two families are simultaneously satisfied by the same set of parameter values, a flux-conserving, entropy-increasing transition may take place between states of the two families. The modifications of the current density and of the temperature profiles involved in the transition and the conditions that the discharge parameters should satisfy in order that the transition could occur are investigated. (author)
Tokamak power system studies at ANL
International Nuclear Information System (INIS)
Baker, C.C.; Ehst, D.A.; Brooks, J.N.; Evans, K. Jr.
1986-06-01
The following features, in particular, have been examined: (a) large aspect ratio (A ≅ 6), which may ease maintenance; (b) high beta (β ≥ 0.20) without indentation, which brings the maximum toroidal field down to about 6 to 7 T; (c) low toroidal current (I ≅ 4MA), which reduces the cost of the current drive and equilibrium field system; and (d) steady state operation with current density control via fast and slow wave current drive. The key to high beta operation with low toroidal current lies in utilizing second stability regime equilibria with the required current distributions produced by an appropriate selection of wave driver frequencies and power spectra. The ray tracing and current drive calculation is self-consistent with the actual magnetic fields they produce in the plasma. The impurity control activities in TPSS have emphasized the self-pumping concept as applied to using the entire first wall or ''slot'' limiters. The blanket design effort has emphasized liquid metal and Flibe concepts. The reference concept is a liquid lithium/vanadium, self-cooled configuration. Overall, there exists a number of major design improvements which will substantially improve the attractiveness of tokamak reactors
Magnet design approach for pulsed tokamak reactors
International Nuclear Information System (INIS)
Kim, S.H.; Evans, K. Jr.; Ehst, D.A.
1983-12-01
A choice of various operating modes of a tokamak reactor will have considerable impact on the fatigue lives and cost of ohmic heating (OH), equilibrium field (EF), and toroidal field (TF) coils. OH AND EF coil requirements and their costs, as well as the effects of the fringing fields of the EF coils on the TF coils, have been studied under cyclic operation in the range of N = 10 2 to 10 6 cycles, spanning the range from a noninductively driven reactor (STARFIRE) to a conventional ohmically driven reactor. For a reference design of TF coils the design of the central OH solenoid has been studied as a function of its maximum field, B/sup OH/. Increasing requirements for structural support lead to only negligible increases in volt-seconds for B/sup OH/ greater than or equal to 10.0 T. Fatigue failure of the OH coil is not a concern for N less than or equal to 10 5 ; for N approx. 10 6 fatigue limits the strain to small values, resulting in small increases in structural requirements and modest decreases in volt-seconds. Should noninductive current drive be achievable we note that this not only eliminates the OH coil, but it also permits EF coil placement in the inboard region, which facilitates the creation of highly shaped plasma cross sections (large triangularity, or bean-shaped equilibria). We have computed the stored energy, coil configuration and fringing fields for a number of EF coil design options
Energy Technology Data Exchange (ETDEWEB)
Stott, Peter [JET, UK (United Kingdom)
1998-10-01
The first edition of John Wesson's book on tokamaks, published in 1987, established itself as essential reading for researchers in the field of magnetic confinement fusion: it was an excellent introduction for students to tokamak physics and also a valuable reference work for the more experienced. The second edition, published in 1997, has been completely rewritten and substantially enlarged (680 pages compared with 300). The new edition maintains the aim of providing a simple introduction to basic tokamak physics, but also includes discussion of the substantial advances in fusion research during the past decade. The new book, like its predecessor, is well written and commendable for its clarity and accuracy. In fact many of the chapters are written by a series of co-authors bringing the benefits of a wide range of expertise but, by careful editing, Wesson has maintained a uniformity of style and presentation. The chapter headings and coverage for the most part remain the same - but are expanded considerably and brought up to date. The most substantial change is that the single concluding chapter in the first edition on 'Experiments' has been replaced by three chapters: 'Tokamak experiments' which deals with some of the earlier key experiments plus a selection of recent small and medium-sized devices, 'Large experiments' which gives an excellent summary of the main results from the four large tokamaks - TFTR, JET, JT60/JT60U and DIII-D, and 'The future' which gives a very short (possibly too short in my opinion) account of reactors and ITER. This is an excellent book, which I strongly recommend should have a place - on the desk rather than in the bookshelf - of researchers in magnetic confinement fusion. (book review)
International Nuclear Information System (INIS)
Stott, Peter
1998-01-01
The first edition of John Wesson's book on tokamaks, published in 1987, established itself as essential reading for researchers in the field of magnetic confinement fusion: it was an excellent introduction for students to tokamak physics and also a valuable reference work for the more experienced. The second edition, published in 1997, has been completely rewritten and substantially enlarged (680 pages compared with 300). The new edition maintains the aim of providing a simple introduction to basic tokamak physics, but also includes discussion of the substantial advances in fusion research during the past decade. The new book, like its predecessor, is well written and commendable for its clarity and accuracy. In fact many of the chapters are written by a series of co-authors bringing the benefits of a wide range of expertise but, by careful editing, Wesson has maintained a uniformity of style and presentation. The chapter headings and coverage for the most part remain the same - but are expanded considerably and brought up to date. The most substantial change is that the single concluding chapter in the first edition on 'Experiments' has been replaced by three chapters: 'Tokamak experiments' which deals with some of the earlier key experiments plus a selection of recent small and medium-sized devices, 'Large experiments' which gives an excellent summary of the main results from the four large tokamaks - TFTR, JET, JT60/JT60U and DIII-D, and 'The future' which gives a very short (possibly too short in my opinion) account of reactors and ITER. This is an excellent book, which I strongly recommend should have a place - on the desk rather than in the bookshelf - of researchers in magnetic confinement fusion. (book review)
Present status of Tokamak research
International Nuclear Information System (INIS)
Basu, Jayanta
1991-01-01
The scenario of thermonuclear fusion research is presented, and the tokamak which is the most promising candidate as a fusion reactor is introduced. A brief survey is given of the most noteworthy tokamaks in the global context, and fusion programmes relating to Next Step devices are outlined. Supplementary heating of tokamak plasma by different methods is briefly reviewed; the latest achievements in heating to fusion temperatures are also reported. The progress towards the high value of the fusion product necessary for ignition is described. The improvement in plasma confinement brought about especially by the H-mode, is discussed. The latest situation in pushing up Β for increasing the efficiency of a tokamak is elucidated. Mention is made of the different types of wall treatment of the tokamak vessel for impurity control, which has led to a significant improvement in tokamak performance. Different methods of current drive for steady state tokamak operation are reviewed, and the issue of current drive efficiency is addressed. A short resume is given of the various diagnostic methods which are employed on a routine basis in the major tokamak centres. A few diagnostics recently developed or proposed in the context of the advanced tokamaks as well as the Next Step devices are indicated. The important role of the interplay between theory, experiment and simulation is noted, and the areas of investigation requiring concerted effort for further progress in tokamak research are identified. (author). 17 refs
International Nuclear Information System (INIS)
Ane, J.M.; Grandgirard, V.; Albajar, F.; Johner, J.
2001-01-01
A consistent and simple approach to derive plasma scenarios for next step tokamak design is presented. It is based on successive plasma equilibria snapshots from plasma breakdown to end of ramp-down. Temperature and density profiles for each equilibrium are derived from a 2D plasma model. The time interval between two successive equilibria is then computed from the toroidal field magnetic energy balance, the resistive term of which depends on n, T profiles. This approach provides a consistent analysis of plasma performance, flux consumption and PF system, including average voltages waveforms across the PF coils. The plasma model and the Poynting theorem for the toroidal magnetic energy are presented. Application to ITER-FEAT and to M2, a Q=5 machine designed at CEA, are shown. (author)
Shielding of External Magnetic Perturbations By Torque In Rotating Tokamak Plasmas
International Nuclear Information System (INIS)
Park, Jong-Kyu; Boozer, Allen H.; Menard, Jonathan E.; Gerhardt, Stefan P.; Sabbagh, Steve A.
2009-01-01
The imposition of a nonaxisymmetric magnetic perturbation on a rotating tokamak plasma requires energy and toroidal torque. Fundamental electrodynamics implies that the torque is essentially limited and must be consistent with the external response of a plasma equilibrium (rvec f) = (rvec j) x (rvec B). Here magnetic measurements on National Spherical Torus eXperiment (NSTX) device are used to derive the energy and the torque, and these empirical evaluations are compared with theoretical calculations based on perturbed scalar pressure equilibria (rvec f) = (rvec (del))p coupled with the theory of nonambipolar transport. The measurement and the theory are consistent within acceptable uncertainties, but can be largely inconsistent when the torque is comparable to the energy. This is expected since the currents associated with the torque are ignored in scalar pressure equilibria, but these currents tend to shield the perturbation.
Active feedback stabilization of axisymmetric modes in highly elongated tokamak plasmas
International Nuclear Information System (INIS)
Ward, D.J.; Hofmann, F.
1993-07-01
Active feedback stabilization of the vertical instability is studied for highly elongated tokamak plasmas (1≤κ≤3), and evaluated in particular for the TCV configuration. It is shown that the feedback can strongly affect the form of the eigenfunction for these highly elongated equilibria, and this can have detrimental effects on the ability of the feedback system to properly detect and stabilize the plasma. A calculation of the vertical displacement that uses poloidal flux measurements, poloidal magnetic field measurements, and corrections for the vessel eddy currents and active feedback currents was found to be effective even in the cases with the worst deformations of the eigenfunction. We also examine how these deformations affect differently shaped equilibria, and it is seen that the magnitude of the deformation of the eigenfunction is strongly function of the plasma elongation. (author) 15 figs., 13 refs
Modular coils and finite-β operation of a quasi-axially symmetric tokamak
International Nuclear Information System (INIS)
Drevlak, M.
1998-01-01
Quasi-axially symmetric tokamaks (QA tokamaks) are an extension of the conventional tokamak concept. In these devices the magnetic field strength is independent of the generalized toroidal magnetic co-ordinate even though the cross-sectional shape changes. An optimized plasma equilibrium belonging to the class of QA tokamaks has been proposed by Nuehrenberg. It features the small aspect ratio of a tokamak while allowing part of the rotational transform to be generated by the external field. In this article, two particular aspects of the viability of QA tokamaks are explored, namely the feasibility of modular coils and the possibility of maintaining quasi-axial symmetry in the free-boundary equilibria obtained with the coils found. A set of easily feasible modular coils for the configuration is presented. It was designed using the extended version of the NESCOIL code (MERKEL, P., Nucl. Fusion 27 (1987) 867). Using this coil system, free-boundary calculations of the plasma equilibrium were carried out using the NEMEC code (HIRSHMAN, S.P., VAN RIJ, W.I., MERKEL, P., Comput. Phys. Commun. 43 (1986) 143). It is observed that the effects of finite β and net toroidal plasma current can be compensated for with good precision by applying a vertical magnetic field and by separately adjusting the currents of the modular coils. A set of fully three dimensional (3-D) auxiliary coils is proposed to exert control on the rotational transform in the plasma. Deterioration of the quasi-axial symmetry induced by the auxiliary coils can be avoided by adequate adjustment of the currents in the primary coils. Finally, the neoclassical transport properties of the configuration are examined. It is observed that optimization with respect to confinement of the alpha particles can be maintained at operation with finite toroidal current if the aforementioned corrective measures are used. In this case, the neoclassical behaviour is shown to be very similar to that of a conventional tokamak
Axisymmetric instability in a noncircular tokamak: experiment and theory
International Nuclear Information System (INIS)
Lipschultz, B.; Prager, S.C.; Todd, A.M.M.; Delucia, J.
1979-09-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes -- the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria. Experimentally, the square is vertically stable and both dee's unstable to a vertical nonrigid axisymmetric shift. The central magnetic axis displacement grows exponentially with a growth time approximately 10 3 poloidal Alfven times plasma time. Proper initial positioning of the plasma on the midplane allows passive feedback to nonlinearly restore vertical motion to a small stable oscillation. Experimental poloidal flux plots are produced directly from internal magnetic probe measurements
Stability and heating of a poloidal divertor tokamak
International Nuclear Information System (INIS)
Biddle, A.P.; Dexter, R.N.; Holly, D.T.; Lipschultz, B.; Osborne, T.H.; Prager, S.C.; Shepard, D.A.; Sprott, J.C.; Witherspoon, F.D.
1981-01-01
Five experimental studies - two stability and three heating investigations - have been carried out on Tokapole II, a tokamak with a four-node poloidal divertor. After a brief description of the machine, discharges are described with q approximately 0.6 over most of the cross-section without degradation of confinement, observation of axisymmetric instability in dee, inverse-dee and square equilibria, high-power fast-wave ion-cyclotron resonance heating, studies of spatial shear Alfven wave resonances for heating, and reduction of the start-up loop voltage by approximately 60% by microwave pre-ionization at electron-cyclotron resonance. Work on axisymmetric instability and studies of pre-ionization have been described in detail elsewhere and are therefore only briefly mentioned. (author)
Flux surface shape and current profile optimization in tokamaks
International Nuclear Information System (INIS)
Dobrott, D.R.; Miller, R.L.
1977-01-01
Axisymmetric tokamak equilibria of noncircular cross section are analyzed numerically to study the effects of flux surface shape and current profile on ideal and resistive interchange stability. Various current profiles are examined for circles, ellipses, dees, and doublets. A numerical code separately analyzes stability in the neighborhood of the magnetic axis and in the remainder of the plasma using the criteria of Mercier and Glasser, Greene, and Johnson. Results are interpreted in terms of flux surface averaged quantities such as magnetic well, shear, and the spatial variation in the magnetic field energy density over the cross section. The maximum stable β is found to vary significantly with shape and current profile. For current profiles varying linearly with poloidal flux, the highest β's found were for doublets. Finally, an algorithm is presented which optimizes the current profile for circles and dees by making the plasma everywhere marginally stable
Large Aspect Ratio Tokamak Study
International Nuclear Information System (INIS)
Reid, R.L.; Holmes, J.A.; Houlberg, W.A.; Peng, Y.K.M.; Strickler, D.J.; Brown, T.G.; Wiseman, G.W.
1980-06-01
The Large Aspect Ratio Tokamak Study (LARTS) at Oak Ridge National Laboratory (ORNL) investigated the potential for producing a viable longburn tokamak reactor by enhancing the volt-second capability of the ohmic heating transformer through the use of high aspect ratio designs. The plasma physics, engineering, and economic implications of high aspect ratio tokamaks were assessed in the context of extended burn operation. Using a one-dimensional transport code plasma startup and burn parameters were addressed. The pulsed electrical power requirements for the poloidal field system, which have a major impact on reactor economics, were minimized by optimizing the startup and shutdown portions of the tokamak cycle. A representative large aspect ratio tokamak with an aspect ratio of 8 was found to achieve a burn time of 3.5 h at capital cost only approx. 25% greater than that of a moderate aspect ratio design tokamak
Implicit approximate Riemann solver for two fluid two phase flow models
International Nuclear Information System (INIS)
Raymond, P.; Toumi, I.; Kumbaro, A.
1993-01-01
This paper is devoted to the description of new numerical methods developed for the numerical treatment of two phase flow models with two velocity fields which are now widely used in nuclear engineering for design or safety calculations. These methods are finite volumes numerical methods and are based on the use of Approximate Riemann Solver's concepts in order to define convective flux versus mean cell quantities. The first part of the communication will describe the numerical method for a three dimensional drift flux model and the extensions which were performed to make the numerical scheme implicit and to have fast running calculations of steady states. Such a scheme is now implemented in the FLICA-4 computer code devoted to 3-D steady state and transient core computations. We will present results obtained for a steady state flow with rod bow effect evaluation and for a Steam Line Break calculation were the 3-D core thermal computation was coupled with a 3-D kinetic calculation and a thermal-hydraulic transient calculation for the four loops of a Pressurized Water Reactor. The second part of the paper will detail the development of an equivalent numerical method based on an approximate Riemann Solver for a two fluid model with two momentum balance equations for the liquid and the gas phases. The main difficulty for these models is due to the existence of differential modelling terms such as added mass effects or interfacial pressure terms which make hyperbolic the model. These terms does not permit to write the balance equations system in a conservative form, and the classical theory for discontinuity propagation for non-linear systems cannot be applied. Meanwhile, the use of non-conservative products theory allows the study of discontinuity propagation for a non conservative model and this will permit the construction of a numerical scheme for two fluid two phase flow model. These different points will be detailed in that section which will be illustrated by
Dudebout, Nicolas; Shamma, Jeff S.
2014-01-01
This paper proves that exogenous empirical-evidence equilibria (xEEEs) in perfect-monitoring repeated games induce correlated equilibria of the associated one-shot game. An empirical-evidence equilibrium (EEE) is a solution concept for stochastic games. At equilibrium, agents' strategies are optimal with respect to models of their opponents. These models satisfy a consistency condition with respect to the actual behavior of the opponents. As such, EEEs replace the full-rationality requirement of Nash equilibria by a consistency-based bounded-rationality one. In this paper, the framework of empirical evidence is summarized, with an emphasis on perfect-monitoring repeated games. A less constraining notion of consistency is introduced. The fact that an xEEE in a perfect-monitoring repeated game induces a correlated equilibrium on the underlying one-shot game is proven. This result and the new notion of consistency are illustrated on the hawk-dove game. Finally, a method to build specific correlated equilibria from xEEEs is derived.
Dudebout, Nicolas
2014-12-15
This paper proves that exogenous empirical-evidence equilibria (xEEEs) in perfect-monitoring repeated games induce correlated equilibria of the associated one-shot game. An empirical-evidence equilibrium (EEE) is a solution concept for stochastic games. At equilibrium, agents\\' strategies are optimal with respect to models of their opponents. These models satisfy a consistency condition with respect to the actual behavior of the opponents. As such, EEEs replace the full-rationality requirement of Nash equilibria by a consistency-based bounded-rationality one. In this paper, the framework of empirical evidence is summarized, with an emphasis on perfect-monitoring repeated games. A less constraining notion of consistency is introduced. The fact that an xEEE in a perfect-monitoring repeated game induces a correlated equilibrium on the underlying one-shot game is proven. This result and the new notion of consistency are illustrated on the hawk-dove game. Finally, a method to build specific correlated equilibria from xEEEs is derived.
International Nuclear Information System (INIS)
Weldon, D.M.; Murray, J.G.
1983-01-01
Tokamak startup with ohmic heating (OH)-induced voltages requires rather large voltages and power supplies. On present machines, with no radiofrequency (rf)-assist provisions, hundreds of volts have been specified for their designs. With the addition of electron cyclotron resonant heating (ECRH) assist, the design requirements have been lowered. To obtain information on the cost and complexity associated with this ECRH-assisted, OH-pulsed startup voltage for ignition-type machines, a trade-off study was completed. The Fusion Engineering Device (FED) configuration was selected as a model because information was available on the structure. The data obtained are applicable to all tokamaks of this general size and complexity, such as the Engineering Test Reactor
Tokamak fusion reactor exhaust
International Nuclear Information System (INIS)
Harrison, M.F.A.; Harbour, P.J.; Hotston, E.S.
1981-08-01
This report presents a compilation of papers dealing with reactor exhaust which were produced as part of the TIGER Tokamak Installation for Generating Electricity study at Culham. The papers are entitled: (1) Exhaust impurity control and refuelling. (2) Consideration of the physical problems of a self-consistent exhaust and divertor system for a long burn Tokamak. (3) Possible bundle divertors for INTOR and TIGER. (4) Consideration of various magnetic divertor configurations for INTOR and TIGER. (5) A appraisal of divertor experiments. (6) Hybrid divertors on INTOR. (7) Refuelling and the scrape-off layer of INTOR. (8) Simple modelling of the scrape-off layer. (9) Power flow in the scrape-off layer. (10) A model of particle transport within the scrape-off plasma and divertor. (11) Controlled recirculation of exhaust gas from the divertor into the scrape-off plasma. (U.K.)
Axisymmetric tokamak scapeoff transport
International Nuclear Information System (INIS)
Singer, C.E.; Langer, W.D.
1982-08-01
We present the first self-consistent estimate of the magnitude of each term in a fluid treatment of plasma transport for a plasma lying in regions of open field lines in an axisymmetric tokamak. The fluid consists of a pure hydrogen plasma with sources which arise from its interaction with neutral hydrogen atoms. The analysis and results are limited to the high collisionality regime, which is optimal for a gaseous neutralizer divertor, or to a cold plasma mantle in a tokamak reactor. In this regime, both classical and neoclassical transport processes are important, and loss of particles and energy by diamagnetic flow are also significant. The prospect of extending the analysis to the lower collisionality regimes encountered in many existing experiments is discussed
Critical beta for analytical spheromak equilibria
International Nuclear Information System (INIS)
Freire, E.M.; Clemente, R.A.
1985-01-01
The Mercier criterion is applied to two analytical spheromak equilibria, one with a spherical separatrix and the other with a cylindrical one of variable elongation. The maximum beta, defined as the ratio between the plasma pressure and the magnetic pressure averaged over the plasma volume, for which the criterion is satisfied on every magnetic surface, has been obtained. In the spherical model the critical beta is 0.003, while in the cylindrical case it is a function of the elongation of the separatrix with a maximum of 0.083. (author)
High temperature phase equilibria and phase diagrams
Kuo, Chu-Kun; Yan, Dong-Sheng
2013-01-01
High temperature phase equilibria studies play an increasingly important role in materials science and engineering. It is especially significant in the research into the properties of the material and the ways in which they can be improved. This is achieved by observing equilibrium and by examining the phase relationships at high temperature. The study of high temperature phase diagrams of nonmetallic systems began in the early 1900s when silica and mineral systems containing silica were focussed upon. Since then technical ceramics emerged and more emphasis has been placed on high temperature
Solid-phase equilibria on Pluto's surface
Tan, Sugata P.; Kargel, Jeffrey S.
2018-03-01
Pluto's surface is covered by volatile ices that are in equilibrium with the atmosphere. Multicomponent phase equilibria may be calculated using a thermodynamic equation of state and, without additional assumptions, result in methane-rich and nitrogen-rich solid phases. The former is formed at temperature range between the atmospheric pressure-dependent sublimation and condensation points, while the latter is formed at temperatures lower than the sublimation point. The results, calculated for the observed 11 μbar atmospheric pressure and composition, are consistent with recent work derived from observations by New Horizons.
Guiding Center Equations in Toroidal Equilibria
International Nuclear Information System (INIS)
White, Roscoe; Zakharov, Leonid
2002-01-01
Guiding center equations for particle motion in a general toroidal magnetic equilibrium configuration are derived using magnetic coordinates. Previous derivations made use of Boozer coordinates, in which the poloidal and toroidal angle variables are chosen so that the Jacobian is inversely proportional to the square of the magnetic field. It is shown that the equations for guiding center motion in any equilibrium possessing nested flux surfaces have exactly the same simple form as those derived in this special case. This allows the use of more spatially uniform coordinates instead of the Boozer coordinates, greatly increasing the accuracy of calculations in large beta and strongly shaped equilibria
Two-fluid model of the pulsar magnetosphere represented as an axisymmetric force-free dipole
Energy Technology Data Exchange (ETDEWEB)
Petrova, S.A., E-mail: petrova@rian.kharkov.ua [Institute of Radio Astronomy of the NAS of Ukraine, Mystetstv Str., 4, Kharkiv 61002 (Ukraine)
2017-05-01
Based on the exact dipolar solution of the pulsar equation the self-consistent two-fluid model of the pulsar magnetosphere is developed. We concentrate on the low-mass limit of the model, taking into account the radiation damping. As a result, we obtain the particle distributions sustaining the dipolar force-free configuration of the pulsar magnetosphere in case of a slight velocity shear of the electron and positron components. Over most part of the force-free region, the particles follow the poloidal magnetic field lines, with the azimuthal velocities being small. Close to the Y-point, however, the particle motion is chiefly azimuthal and the Lorentz-factor grows unrestrictedly. This may result in the very-high-energy emission from the vicinity of the Y-point and may also imply the magnetocentrifugal formation of a jet. As for the first-order quantities, the longitudinal accelerating electric field is found to change the sign, hinting at coexistence of the polar and outer gaps. Besides that, the components of the plasma conductivity tensor are derived and the low-mass analogue of the pulsar equation is formulated as well.
Modeling of an atomizer for two fluids; Modelacion de un atomizador de dos fluidos
Energy Technology Data Exchange (ETDEWEB)
Tapia Ramirez, Zoili [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)
1998-09-01
The work reported in this article presents the results of the effort to improve the basic understanding of the flow structure that is formed in a two fluid sprayer before and after the interaction between the sprayed fluid and the spraying fluid. The images in the interior of the mixing chamber of the atomizer are shown, which were taken with a high velocity video camera. Also the results of the numerical simulation of the internal flow obtained by means of a package of commercial modeling are shown. [Espanol] El trabajo reportado en este articulo presenta los resultados del esfuerzo por mejorar el entendimiento basico de la estructura del flujo que se forma en un atomizador de dos fluidos antes y despues de la interaccion entre el fluido atomizado y el fluido atomizante. Se muestran imagenes del flujo en el interior de la camara de mezclado del atomizador, las cuales fueron tomadas con una camara de video de alta velocidad. Tambien se incluyen los resultados de la simulacion numerica del flujo interno obtenidas por medio de un paquete de modelacion comercial.
Basic Pilot Code Development for Two-Fluid, Three-Field Model
International Nuclear Information System (INIS)
Jeong, Jae Jun; Bae, S. W.; Lee, Y. J.; Chung, B. D.; Hwang, M.; Ha, K. S.; Kang, D. H.
2006-03-01
A basic pilot code for one-dimensional, transient, two-fluid, three-field model has been developed. Using 9 conceptual problems, the basic pilot code has been verified. The results of the verification are summarized below: - It was confirmed that the basic pilot code can simulate various flow conditions (such as single-phase liquid flow, bubbly flow, slug/churn turbulent flow, annular-mist flow, and single-phase vapor flow) and transitions of the flow conditions. A mist flow was not simulated, but it seems that the basic pilot code can simulate mist flow conditions. - The pilot code was programmed so that the source terms of the governing equations and numerical solution schemes can be easily tested. - The mass and energy conservation was confirmed for single-phase liquid and single-phase vapor flows. - It was confirmed that the inlet pressure and velocity boundary conditions work properly. - It was confirmed that, for single- and two-phase flows, the velocity and temperature of non-existing phase are calculated as intended. - During the simulation of a two-phase flow, the calculation reaches a quasisteady state with small-amplitude oscillations. The oscillations seem to be induced by some numerical causes. The research items for the improvement of the basic pilot code are listed in the last section of this report
Inviscid linear stability analysis of two fluid columns of different densities subject to gravity
Prathama, Aditya; Pantano, Carlos
2017-11-01
We investigate the inviscid linear stability of vertical interface between two fluid columns of different densities under the influence of gravity. In this flow arrangement, the two free streams are continuously accelerating, in contrast to the canonical Kelvin-Helmholtz or Rayleigh-Taylor instabilities whose base flows are stationary (or weakly time dependent). In these classical cases, the temporal evolution of the interface can be expressed as Fourier or Laplace solutions in time. This is not possible in our case; instead, we employ the initial value problem method to solve the equations analytically. The results, expressed in terms of the well-known parabolic cylinder function, indicate that the instability grows as the exponential of a quadratic function of time. The analysis shows that in this accelerating Kelvin-Helmholtz configuration, the interface is unconditionally unstable at all wave modes, despite the presence of surface tension. Department of Energy, National Nuclear Security Administration (Award No. DE-NA0002382) and the California Institute of Technology.
Evaluation of Interfacial Heat Transfer Models for Flashing Flow with Two-Fluid CFD
Directory of Open Access Journals (Sweden)
Yixiang Liao
2018-06-01
Full Text Available The complexity of flashing flows is increased vastly by the interphase heat transfer as well as its coupling with mass and momentum transfers. A reliable heat transfer coefficient is the key in the modelling of such kinds of flows with the two-fluid model. An extensive literature survey on computational modelling of flashing flows has been given in previous work. The present work is aimed at giving a brief review on available theories and correlations for the estimation of interphase heat transfer coefficient, and evaluating them quantitatively based on computational fluid dynamics simulations of bubble growth in superheated liquid. The comparison of predictions for bubble growth rate obtained by using different correlations with the experimental as well as direct numerical simulation data reveals that the performance of the correlations is dependent on the Jakob number and Reynolds number. No generally applicable correlations are available. Both conduction and convection are important in cases of bubble rising and translating in stagnant liquid at high Jakob numbers. The correlations combining the analytical solution for heat diffusion and the theoretical relation for potential flow give the best agreement.
Prediction of subcooled flow boiling characteristics using two-fluid Eulerian CFD model
Energy Technology Data Exchange (ETDEWEB)
Braz Filho, Francisco A.; Ribeiro, Guilherme B., E-mail: gbribeiro@ieav.cta.br; Caldeira, Alexandre D.
2016-11-15
Highlights: • CFD multiphase model is used to predict subcooled flow boiling characteristics. • Better agreement is achieved for higher saturation pressures. • Onset of nucleate boiling and saturated boiling are well predicted. • CFD multiphase model tends to underestimate the void fraction. • Factors were adjusted in order to improve the void fraction results. - Abstract: The present study concerns a detailed analysis of flow boiling phenomena under high pressure systems using a two-fluid Eulerian approach provided by a Computational Fluid Dynamics (CFD) solver. For this purpose, a vertical heated pipe made of stainless steel with an internal diameter of 15.4 mm was considered as the modeled domain. Two different uniform heat fluxes and three saturation pressures were applied to the channel wall, whereas water mass flux of 900 kg/m{sup 2} s was considered for all simulation cases. The model was validated against a set of experimental data and results have indicated a promising use of the CFD technique for estimation of the wall temperature, the liquid bulk temperature and the location of the departure of nucleate boiling. Changes in factors applied in the modeling of the interfacial heat transfer coefficient and bubble departure frequency were suggested, allowing a better prediction of the void fraction along the heated channel. The commercial CFD solver FLUENT 14.5 was used for the model implementation.
Prediction of subcooled flow boiling characteristics using two-fluid Eulerian CFD model
International Nuclear Information System (INIS)
Braz Filho, Francisco A.; Ribeiro, Guilherme B.; Caldeira, Alexandre D.
2016-01-01
Highlights: • CFD multiphase model is used to predict subcooled flow boiling characteristics. • Better agreement is achieved for higher saturation pressures. • Onset of nucleate boiling and saturated boiling are well predicted. • CFD multiphase model tends to underestimate the void fraction. • Factors were adjusted in order to improve the void fraction results. - Abstract: The present study concerns a detailed analysis of flow boiling phenomena under high pressure systems using a two-fluid Eulerian approach provided by a Computational Fluid Dynamics (CFD) solver. For this purpose, a vertical heated pipe made of stainless steel with an internal diameter of 15.4 mm was considered as the modeled domain. Two different uniform heat fluxes and three saturation pressures were applied to the channel wall, whereas water mass flux of 900 kg/m"2 s was considered for all simulation cases. The model was validated against a set of experimental data and results have indicated a promising use of the CFD technique for estimation of the wall temperature, the liquid bulk temperature and the location of the departure of nucleate boiling. Changes in factors applied in the modeling of the interfacial heat transfer coefficient and bubble departure frequency were suggested, allowing a better prediction of the void fraction along the heated channel. The commercial CFD solver FLUENT 14.5 was used for the model implementation.
A two-fluid approximation for calculating the cosmic microwave background anisotropies
Seljak, Uros
1994-01-01
We present a simplified treatment for calculating the cosmic microwave background anisotropy power spectrum in adiabatic models. It consists of solving for the evolution of a two-fluid model until the epoch of recombination and then integrating over the sources to obtain the cosmic microwave background (CMB) anisotropy power spectrum. The approximation is useful both for a physical understanding of CMB anisotropies as well as for a quantitative analysis of cosmological models. Comparison with exact calculations shows that the accuracy is typically 10%-20% over a large range of angles and cosmological models, including those with curvature and cosmological constant. Using this approximation we investigate the dependence of the CMB anisotropy on the cosmological parameters. We identify six dimensionless parameters that uniquely determine the anisotropy power spectrum within our approximation. CMB experiments on different angular scales could in principle provide information on all these parameters. In particular, mapping of the Doppler peaks would allow an independent determination of baryon mass density, matter mass density, and the Hubble constant.
Two-fluid electromagnetic simulations of plasma-jet acceleration with detailed equation-of-state
International Nuclear Information System (INIS)
Thoma, C.; Welch, D. R.; Clark, R. E.; Bruner, N.; MacFarlane, J. J.; Golovkin, I. E.
2011-01-01
We describe a new particle-based two-fluid fully electromagnetic algorithm suitable for modeling high density (n i ∼ 10 17 cm -3 ) and high Mach number laboratory plasma jets. In this parameter regime, traditional particle-in-cell (PIC) techniques are challenging due to electron timescale and lengthscale constraints. In this new approach, an implicit field solve allows the use of large timesteps while an Eulerian particle remap procedure allows simulations to be run with very few particles per cell. Hall physics and charge separation effects are included self-consistently. A detailed equation of state (EOS) model is used to evolve the ion charge state and introduce non-ideal gas behavior. Electron cooling due to radiation emission is included in the model as well. We demonstrate the use of these new algorithms in 1D and 2D Cartesian simulations of railgun (parallel plate) jet accelerators using He and Ar gases. The inclusion of EOS and radiation physics reduces the electron temperature, resulting in higher calculated jet Mach numbers in the simulations. We also introduce a surface physics model for jet accelerators in which a frictional drag along the walls leads to axial spreading of the emerging jet. The simulations demonstrate that high Mach number jets can be produced by railgun accelerators for a variety of applications, including high energy density physics experiments.
Two-fluid electromagnetic simulations of plasma-jet acceleration with detailed equation-of-state
Energy Technology Data Exchange (ETDEWEB)
Thoma, C.; Welch, D. R.; Clark, R. E.; Bruner, N. [Voss Scientific, LLC, Albuquerque, New Mexico 87108 (United States); MacFarlane, J. J.; Golovkin, I. E. [Prism Computational Sciences, Inc., Madison, Wisconsin 53711 (United States)
2011-10-15
We describe a new particle-based two-fluid fully electromagnetic algorithm suitable for modeling high density (n{sub i} {approx} 10{sup 17} cm{sup -3}) and high Mach number laboratory plasma jets. In this parameter regime, traditional particle-in-cell (PIC) techniques are challenging due to electron timescale and lengthscale constraints. In this new approach, an implicit field solve allows the use of large timesteps while an Eulerian particle remap procedure allows simulations to be run with very few particles per cell. Hall physics and charge separation effects are included self-consistently. A detailed equation of state (EOS) model is used to evolve the ion charge state and introduce non-ideal gas behavior. Electron cooling due to radiation emission is included in the model as well. We demonstrate the use of these new algorithms in 1D and 2D Cartesian simulations of railgun (parallel plate) jet accelerators using He and Ar gases. The inclusion of EOS and radiation physics reduces the electron temperature, resulting in higher calculated jet Mach numbers in the simulations. We also introduce a surface physics model for jet accelerators in which a frictional drag along the walls leads to axial spreading of the emerging jet. The simulations demonstrate that high Mach number jets can be produced by railgun accelerators for a variety of applications, including high energy density physics experiments.
Mathematical modeling of impact of two metal plates using two-fluid approach
Utkin, P. S.; Fortova, S. V.
2018-01-01
The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.
The spiral field inhibition of thermal conduction in two-fluid solar wind models
Nerney, S.; Barnes, A.
1978-01-01
The paper reports on two-field models which include the inhibition of thermal conduction by the spiraling interplanetary field to determine whether any of the major conclusions obtained by Nerney and Barnes (1977) needs to be modified. Comparisons with straight field line models reveal that for most base conditions, the primary effect of the inhibition of thermal conduction is the bottling-up of heat in the electrons as well as the quite different temperature profiles at a large heliocentric radius. The spiral field solutions show that coronal hole boundary conditions do not correspond to states of high-speed streams as observed at 1 AU. The two-fluid models suggest that the spiral field inhibition of thermal conduction in the equatorial plane will generate higher gas pressures in comparison with flows along the solar rotation axis (between 1 and 10 AU). In particular, massive outflows of stellar winds, such as outflow from T Tauri stars, cannot be driven by thermal conduction. The conclusions of Nerney and Barnes remain essentially unchanged.
Geometric analysis of the solutions of two-phase flows: two-fluid model
International Nuclear Information System (INIS)
Kestin, J.; Zeng, D.L.
1984-01-01
This report contains a lightly edited draft of a study of the two-fluid model in two-phase flow. The motivation for the study stems from the authors' conviction that the construction of a computer code for any model should be preceded by a geometrical analysis of the pattern of trajectories in the phase space appropriate for the model. Such a study greatly facilitates the understanding of the phenomenon of choking and anticipates the computational difficulties which arise from the existence of singularities. The report contains a derivation of the six conservation equations of the model which includes a consideration of the simplifications imposed on a one-dimensional treatment by the presence of boundary layers at the wall and between the phases. The model is restricted to one-dimensional adiabatic flows of a single substance present in two phases, but thermodynamic equilibrium between the phases is not assumed. The role of closure conditions is defined but no specific closure conditions, or explicit equations of state, are introduced
Formation of intermediate shocks in both two-fluid and hybrid models
International Nuclear Information System (INIS)
Wu, C.C.; Hada, T.
1991-01-01
Intermediate shocks are shocks with shock frame fluid velocities greater than the Alfven speed ahead and less than the Alfven speed behind, or equivalently, across intermediate shocks the sign of the transverse component of the magnetic field changes. These shocks had been considered extraneous, or nonevolutionary, or unstable, and they had been thought not to correspond to physical reality [Germain, 1960; Jeffrey and Taniuti, 1964; Kantrowitz and Petschek, 1966]. However, it has been shown that intermediate shocks can be formed from continuous waves according to dissipative magnetohydrodynamics (MHD) [Wu, 1987, 1988a, b, 1990]. Thus according to the formation argument which requires that physical shocks be formed by the wave steepening process, the intermediate shocks should be considered physical. Here, intermediate shocks are studied in a two-fluid model that includes finite ion inertia dispersion and in a hybrid model in which the full ion dynamics is retained while the electrons are treated as a massless fluid. The authors show that in both models intermediate shocks can be formed through wave steepening, meaning that they are stable and possess shock structures
Extended two-fluid model for simulating magneto-rheological fluid flows
International Nuclear Information System (INIS)
Shivaram, A C
2011-01-01
The current practice of designing magneto-rheological (MR) fluid-based devices is, to a large extent, based on simple phenomenological models like the Bingham model. Though useful for initial force or torque estimation and sizing, these models lack the capability to predict performance degradation due to changes in the particle volume fraction distribution. The present work demonstrates the use of the two-fluid model for predicting the particle volume fraction distribution inside a device in the absence of a field and proposes a novel modeling scheme which can simulate the fluid flow in the presence of a field. This modeling scheme can be used to (a) visualize flow patterns inside a device under various operating conditions, (b) predict the spatial distribution of particles inside a device after multiple operating cycles, (c) assist in estimating the extent of performance degradation due to non-uniform particle distribution and (d) enable testing of various design strategies to mitigate such performance issues using simulations. This is illustrated through numerical examples of a few case studies of typical MR device configurations
Reduction of momentum transfer rates by parallel electric fields: A two-fluid demonstration
International Nuclear Information System (INIS)
Delamere, P.A.; Stenbaek-Nielsen, H.C.; Otto, A.
2002-01-01
Momentum transfer between an ionized gas cloud moving relative to an ambient magnetized plasma is a general problem in space plasma physics. Obvious examples include the Io-Jupiter interaction, comets, and coronal mass ejections. Active plasma experiments have demonstrated that momentum transfer rates associated with Alfven wave propagation are poorly understood. Barium injection experiments from the Combined Release and Radiation Effects Satellite (CRRES) have shown that dense ionized clouds are capable of ExB drifting over large distances perpendicular to the magnetic field. The CRRES 'skidding' distances were much larger than predicted by magnetohydrodynamic theory and it has been proposed that parallel electric fields were a key component in the skidding phenomenon. A two-fluid code was used to demonstrate the role of parallel electric fields in reducing momentum transfer between two distinct plasma populations. In this study, a dense plasma was initialized moving relative to an ambient plasma and perpendicular to B. Parallel electric fields were introduced via a friction term in the electron momentum equation and the collision frequency was scaled in proportion to the field-aligned current density. The simulation results showed that parallel electric fields decreased the decelerating magnetic tension force on the plasma cloud through a magnetic diffusion/reconnection process
Study of blood flow in several benchmark micro-channels using a two-fluid approach
Wu, Wei-Tao; Yang, Fang; Antaki, James F.; Aubry, Nadine; Massoudi, Mehrdad
2015-01-01
It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model was implemented using OpenFOAM® in which benchmark problems including a sudden expansion and various driven slots and crevices were studied numerically. The numerical results exhibited good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of RBCs. PMID:26240438
Basic Pilot Code Development for Two-Fluid, Three-Field Model
Energy Technology Data Exchange (ETDEWEB)
Jeong, Jae Jun; Bae, S. W.; Lee, Y. J.; Chung, B. D.; Hwang, M.; Ha, K. S.; Kang, D. H
2006-03-15
A basic pilot code for one-dimensional, transient, two-fluid, three-field model has been developed. Using 9 conceptual problems, the basic pilot code has been verified. The results of the verification are summarized below: - It was confirmed that the basic pilot code can simulate various flow conditions (such as single-phase liquid flow, bubbly flow, slug/churn turbulent flow, annular-mist flow, and single-phase vapor flow) and transitions of the flow conditions. A mist flow was not simulated, but it seems that the basic pilot code can simulate mist flow conditions. - The pilot code was programmed so that the source terms of the governing equations and numerical solution schemes can be easily tested. - The mass and energy conservation was confirmed for single-phase liquid and single-phase vapor flows. - It was confirmed that the inlet pressure and velocity boundary conditions work properly. - It was confirmed that, for single- and two-phase flows, the velocity and temperature of non-existing phase are calculated as intended. - During the simulation of a two-phase flow, the calculation reaches a quasisteady state with small-amplitude oscillations. The oscillations seem to be induced by some numerical causes. The research items for the improvement of the basic pilot code are listed in the last section of this report.
International Nuclear Information System (INIS)
Tendler, M.
1984-06-01
The energy loss from a tokamak plasma due to neutral hydrogen radiation and recycling is of great importance for the energy balance at the periphery. It is shown that the requirement for thermal equilibrium implies a constraint on the maximum attainable edge density. The relation to other density limits is discussed. The average plasma density is shown to be a strong function of the refuelling deposition profile. (author)
International Nuclear Information System (INIS)
Conn, R.W.
1984-05-01
Recent experiments with a scoop limiter without active internal pumping have been carried out in the PDX tokamak with up to 6MW of auxiliary neutral beam heating. Experiments have also been done with a rotating head pump limiter in the PLT tokamak in conjunction with RF plasma heating. Extensive experiments have been done in the ISX-B tokamak and first experiments have been completed with the ALT-I limiter in TEXTOR. The pump limiter modules in these latter two machines have internal getter pumping. Experiments in ISX-B are with ohmic and auxiliary neutral beam heating. The results in ISX-B and TEXTOR show that active density control and particle removal is achieved with pump limiters. In ISX-B, the boundary layer (or scape-off layer) plasma partially screens the core plasma from gas injection. In both ISX-B and TEXTOR, the pressure internal to the module scales linearly with plasma density but in ISX-B, with neutral beam injection, a nonlinear increase is observed at the highest densities studied. Plasma plugging is the suspected cause. Results from PDX suggest that a region may exist in which core plasma energy confinement improves using a pump limiter during neutral beam injection. Asymmetric radial profiles and an increased edge electron temperature are observed in discharges with improved confinement. The injection of small amounts of neon into ISX-B has more clearly shown an improved electron core energy confinement during neutral beam injection. While carried out with a regular limiter, this Z-mode of operation is ideal for use with pump limiters and should be a way to achieve energy confinement times similar to values for H-mode tokamak plasmas. The implication of all these results for the design of a reactor pump limiter is described
Modular tokamak magnetic system
International Nuclear Information System (INIS)
Yang, T.F.
1988-01-01
This patent describes a tokamak reactor including a vacuum vessel, toroidal confining magnetic field coils disposed concentrically around the minor radius of the vacuum vessel, and poloidal confining magnetic field coils, an ohmic heating coil system comprising at least one magnetic coil disposed concentrically around a toroidal field coil, wherein the magnetic coil is wound around the toroidal field coil such that the ohmic heating coil enclosed the toroidal field coil
International Nuclear Information System (INIS)
Conn, R.W.; California Univ., Los Angeles
1984-01-01
Recent experiments with a scoop limiter without active internal pumping have been carried out in the PDX tokamak with up to 6 MW of auxiliary neutral beam heating. Experiments have also been performed with a rotating head pump limiter in the PLT tokamak in conjunction with RF plasma heating. Extensive experiments have been done in the ISX-B tokamak and first experiments have been completed with the ALT-I limiter in TEXTOR. The pump limiter modules in these latter two machines have internal getter pumping. Experiments in ISX-B are with ohmic and auxiliary neutral beam heating. The results in ISX-B and TEXTOR show that active density control and particle removal is achieved with pump limiters. In ISX-B, the boundary layer (or scrape-off layer) plasma partially screens the core plasma from gas injection. In both ISX-B and TEXTOR, the pressure internal to the module scales linearly with plasma density but in ISX-B, with neutral beam injection, a nonlinear increase is observed at the highest densities studied. Plasma plugging is the suspected cause. Results from PDX suggest that a regime may exist in which core plasma energy confinement improves using a pump limiter during neutral beam injection. Asymmetric radial profiles and an increased edge electron temperature are observed in discharges with improved confinement. The injection of small amounts of neon into ISX-B has more clearly shown an improved electron core energy confinement during neutral beam injection. While carried out with a regular limiter, this 'Z-mode' of operation is ideal for use with pump limiters and should be a way to achieve energy confinement times similar to values for H-mode tokamak plasmas. The implication of all these results for the design of a reactor pump limiter is described. (orig.)
A unifying approach to existence of Nash equilibria
Balder, E.J.
1997-01-01
An approach initiated in [4] is shown to unify results about the existence of (i) Nash equilibria in games with at most countably many players, (ii) Cournot-Nash equilibrium distributions for large, anonymous games, and (iii) Nash equilibria (both mixed and pure) for continuum games. A new, central
TPX tokamak construction management
International Nuclear Information System (INIS)
Knutson, D.; Kungl, D.; Seidel, P.; Halfast, C.
1995-01-01
A construction management contract normally involves the acquisition of a construction management firm to assist in the design, planning, budget conformance, and coordination of the construction effort. In addition the construction management firm acts as an agent in the awarding of lower tier contracts. The TPX Tokamak Construction Management (TCM) approach differs in that the construction management firm is also directly responsible for the assembly and installation of the tokamak including the design and fabrication of all tooling required for assembly. The Systems Integration Support (SIS) contractor is responsible for the architect-engineering design of ancillary systems, such as heating and cooling, buildings, modifications and site improvements, and a variety of electrical requirements, including switchyards and >4kV power distribution. The TCM will be responsible for the procurement of materials and the installation of the ancillary systems, which can either be performed directly by the TCM or subcontracted to a lower tier subcontractor. Assurance that the TPX tokamak is properly assembled and ready for operation when turned over to the operations team is the primary focus of the construction management effort. To accomplish this a disciplined constructability program will be instituted. The constructability effort will involve the effective and timely integration of construction expertise into the planning, component design, and field operations. Although individual component design groups will provide liaison during the machine assembly operations, the construction management team is responsible for assembly
Design constraints for rf-driven steady-state tokamak reactors
International Nuclear Information System (INIS)
Ehst, D.A.
1979-02-01
Plasma current density profiles are computed due to electron Landau damping of lower hybrid waves launched into model tokamak density and temperature profiles. The total current and current profile shape are chosen consistent with magnetohydrodynamic equilibrium for a variety of temperature and density distributions and plasma beta values. Surface current equilibria appear attractive and are accessible to waves with n/sub z/ as low as 1.2. By suitably choosing the spectrum location and width it is possible to drive the 9.8 MA current of a 7.0-m reactor with as little as 2.8% of the fusion power recirculated as rf input from the waveguides
Ideal and resistive MHD stability of internal kink modes in circular and shaped tokamaks
International Nuclear Information System (INIS)
Bondeson, A.; Luetjens, H.; Vlad, G.
1992-01-01
Recent results for the MHD stability of internal kink modes in tokamaks are reviewed. In general, ideal stability is more restrictive than the conventionally cited limit β p p is the poloidal beta at the q = 1 surface). This holds, in particular, for shaped equilibria, where low shear in combination with elliptic shaping can drastically reduce the pressure limit. Also in resistive MHD, interchange effects are frequently destabilizing, and resistive stability at β p ≥0.05 is achieved, for circular section, only with a very restricted class of current profiles, and not at all for JET-shaped cross section. (author) 9 figs., 24 refs
Neoclassical transport coefficients for tokamaks with bean-shaped flux surfaces
International Nuclear Information System (INIS)
Chang, C.S.; Kaye, S.M.
1990-11-01
Simple analytic representations of the neoclassical transport coefficients for indented flux surfaces are presented. It is shown that a transport coefficient for an indented flux surface can be expressed in terms of a linear combination of the previously known transport coefficients for two nonindented flux surfaces. Numerical calculations based on actual equilibria from the PBX-M tokamak indicate that, even for modestly indented flux surfaces, the ion neoclassical thermal transport can be over a factor of two smaller than in a circular plasma with the same midplane radius or with the equivalent areas. 6 refs., 5 figs., 1 tab
Multiple time scale methods in tokamak magnetohydrodynamics
International Nuclear Information System (INIS)
Jardin, S.C.
1984-01-01
Several methods are discussed for integrating the magnetohydrodynamic (MHD) equations in tokamak systems on other than the fastest time scale. The dynamical grid method for simulating ideal MHD instabilities utilizes a natural nonorthogonal time-dependent coordinate transformation based on the magnetic field lines. The coordinate transformation is chosen to be free of the fast time scale motion itself, and to yield a relatively simple scalar equation for the total pressure, P = p + B 2 /2μ 0 , which can be integrated implicitly to average over the fast time scale oscillations. Two methods are described for the resistive time scale. The zero-mass method uses a reduced set of two-fluid transport equations obtained by expanding in the inverse magnetic Reynolds number, and in the small ratio of perpendicular to parallel mobilities and thermal conductivities. The momentum equation becomes a constraint equation that forces the pressure and magnetic fields and currents to remain in force balance equilibrium as they evolve. The large mass method artificially scales up the ion mass and viscosity, thereby reducing the severe time scale disparity between wavelike and diffusionlike phenomena, but not changing the resistive time scale behavior. Other methods addressing the intermediate time scales are discussed
International Nuclear Information System (INIS)
Hennen, B.A.; Westerhof, E.; De Baar, M.R.; Nuij, P.W.J.M.; Steinbuch, M.
2012-01-01
Suppression of tearing modes is essential for the operation of tokamaks. This paper describes the design and simulation of a tearing mode suppression feedback control system for the TEXTOR tokamak. The two main control tasks of this feedback control system are the radial alignment of electron cyclotron resonance heating and current drive (ECRH/ECCD) with a tearing mode and the stabilization of a mode at a specific width. In order to simulate these control tasks, the time evolution of a tearing mode subject to suppression by ECRH/ECCD and destabilization by a magnetic perturbation field is modelled using the generalized Rutherford equation. The model includes an equilibrium model and an ECRH/ECCD launcher model. The dynamics and static equilibria of this model are analysed. The model is linearized and based on the linearized model, linear feedback controllers are designed and simulated, demonstrating both alignment and width control of tearing modes in TEXTOR. (paper)
3D plasma fluid simulations in divertor tokamaks. Final technical report, 1993--1995
International Nuclear Information System (INIS)
Strauss, H.R.
1995-08-01
The main accomplishment of this grant was the development of a finite element time dependent magnetofluid code, FEMHD. The code is nonlinear and three dimensional. In the poloidal plane, the elemental cells of the mesh are triangles, which offer both simplicity and adaptability. In the third, toroidal, direction, there is an option of a standard staggered finite difference mesh, or Fourier transforms. The FEMHD code runs on several platforms, including Crays, UNIX workstations, and a parallel version runs on an IBM SP1. Several problems have been considered with the unstructured mesh FEMHD code. They are (1) MHD simulations in divertor tokamaks; (2) simulations of ELM-like ballooning modes in divertor tokamaks; and (3) reconnection and singular MHD equilibria
Equilibria of perceptrons for simple contingency problems.
Dawson, Michael R W; Dupuis, Brian
2012-08-01
The contingency between cues and outcomes is fundamentally important to theories of causal reasoning and to theories of associative learning. Researchers have computed the equilibria of Rescorla-Wagner models for a variety of contingency problems, and have used these equilibria to identify situations in which the Rescorla-Wagner model is consistent, or inconsistent, with normative models of contingency. Mathematical analyses that directly compare artificial neural networks to contingency theory have not been performed, because of the assumed equivalence between the Rescorla-Wagner learning rule and the delta rule training of artificial neural networks. However, recent results indicate that this equivalence is not as straightforward as typically assumed, suggesting a strong need for mathematical accounts of how networks deal with contingency problems. One such analysis is presented here, where it is proven that the structure of the equilibrium for a simple network trained on a basic contingency problem is quite different from the structure of the equilibrium for a Rescorla-Wagner model faced with the same problem. However, these structural differences lead to functionally equivalent behavior. The implications of this result for the relationships between associative learning, contingency theory, and connectionism are discussed.
Evaluation of two-fluid and drift flux thermohydraulics in APROS code environment
International Nuclear Information System (INIS)
Miettinen, J.; Karppinen, I.; Haenninen, M.; Ylijoki, J.
1999-01-01
The characteristics of the thermohydraulic solutions in APROS are considered for the nuclear power plant modelling. The thermohydraulic model of the APROS plant analyzer includes three levels of solutions, homogeneous 3-equation model, 5-equation drift flux model and 6-equation two-fluid model. In practical modelling of versatile process systems different approaches are selected for different types of the power plant sections. The 3-equation model is used for turbines and auxiliary systems. The 5-equation model and 6-equation model are alternative models for main process sections of the primary and secondary sides. The 5-equation model has been typically selected for the real time applications and the 6-equation model for the safety analysis applications. The validation needs for both approaches are the same. Because the change of the solution mode is an easy task in APROS, the validation tasks are typically performed in parallel for 5-equation and 6-equation models. By calculating in parallel with both models systematic errors in solutions may be pointed out. The testing against both separate effects tests and integral tests is an essential part in the thermohydraulics. In different plant applications different physical features are important. The analysis requirements vary from one application to another. When nodalizations together with increased computer speed are growing up, the earlier validation cases may be insufficient. That is why the content of the code has to be known in detail. Such an expertise in the code development has to be gained that properties of the code against other thermohydraulics codes are known. (author)
On the continuum theory of the two-fluid solar wind for small mass ratio
International Nuclear Information System (INIS)
Johnson, R.S.
1976-01-01
The continuum theory for the two-fluid solar wind is considered. The fluid is assumed to be a fully ionized neutral plasma of electrons and protons which is compressible, viscous and heat conducting with a constant Prandtl number and a viscosity proportional to (temperature) sup(ω), ω > 1. The gas is under the influence of a gravitational field centred on the Sun. It is assumed that the bulk velocity (at any point) is the same for both electrons and protons, but that an energy transfer can occur between the two species due to binary (Coulomb) collisions. The equations are non-dimensionalized and it is shown that the natural parameter to use in the construction of an asymptotic solution is the mass ratio. The limit mass ratio → zero corresponds to the small Prandtl number limit for the one-fluid theory developed by Johnson (Proc. R. Soc. (Lond) A; 347:537 (1976)). By using the method of matched asymptotic expansions, a solution is constructed that starts from the base of the corona and extends out to a diffuse shock layer. The results obtained exactly parallel the one-fluid theory and many details are identified and absorbed into this analysis. It is shown how the temperatures in the corona eventually become the well-known behaviours: rsup(-2/7) (electrons), rsup(-6/7) (protons) when ω = 5/2 and r is the radial coordinate. However, the continuum theory will probably have failed in the shock layer region - the more so since this occurs at about 100 light years distance - and further mathematical details are omitted. The numerical estimates given here compare tolerably well with the observed data and very favourably with other work on the same equations. (author)
Sheffield, J.
1981-08-01
For a specific configuration of magnetic field and plasma to be economically attractive as a commercial source of energy, it must contain a high-pressure plasma in a stable fashion while thermally isolating the plasma from the walls of the containment vessel. The tokamak magnetic configuration is presently the most successful in terms of reaching the considered goals. Tokamaks were developed in the USSR in a program initiated in the mid-1950s. By the early 1970s tokamaks were operating not only in the USSR but also in the U.S., Australia, Europe, and Japan. The advanced state of the tokamak program is indicated by the fact that it is used as a testbed for generic fusion development - for auxiliary heating, diagnostics, materials - as well as for specific tokamak advancement. This has occurred because it is the most economic source of a large, reproducible, hot, dense plasma. The basic tokamak is considered along with tokamak improvements, impurity control, additional heating, particle and power balance in a tokamak, aspects of microscopic transport, and macroscopic stability.
Magnetic confinement experiment -- 1: Tokamaks
International Nuclear Information System (INIS)
Goldston, R.J.
1994-01-01
This report reviews presentations made at the 15th IAEA Conference on Plasma Physics and Controlled Nuclear Fusion on experimental tokamak physics, particularly on advances in core plasma physics, divertor and edge physics, heating and current drive, and tokamak concept optimization
International Nuclear Information System (INIS)
Alladio, F.
1985-01-01
A short summary of the present status of experimental observations, theoretical ideas and understanding of the density limit in tokamaks is presented. It is the result of the discussion that was held on this topic at the 4th European Tokamak Workshop in Copenhagen (December 4th to 6th, 1985). 610 refs
The production of high poloidal tokamak equilibria in Versator II by means of RF current drive
International Nuclear Information System (INIS)
Luckhardt, S.C.; Chen, K.-I.; Kesner, J.; Kirkwood, R.; Lane, B.; Porkolab, M.; Squire, J.
1989-01-01
Experiments on the Versator II device have been carried out in a regime of low plasma current with the aim of reaching high poloidal beta, β p . Lower-Hybrid RF current drive is used to produce an energetic electron population which carries the plasma current and pressure. In this mode of operation, plasmas with εβ p approaching unity appear attainable. Data from equilibrium magnetic analysis, hard x-ray, and density profiles display an outward magnetic axis shift in agreement with equilibrium theory, and further indicate that q(O) is in the range of 4-6. PEST code modeling of these experiments suggests that some of these plasmas may be near or beyond the transition to the second stability region for ballooning modes. (author)
International Nuclear Information System (INIS)
Rogister, A L
2004-01-01
John Wesson's well known book, now re-edited for the third time, provides an excellent introduction to fusion oriented plasma physics in tokamaks. The author's task was a very challenging one, for a confined plasma is a complex system characterised by a variety of dimensionless parameters and its properties change qualitatively when certain threshold values are reached in this multi-parameter space. As a consequence, theoretical description is required at different levels, which are complementary: particle orbits, kinetic and fluid descriptions, but also intuitive and empirical approaches. Theory must be carried out on many fronts: equilibrium, instabilities, heating, transport etc. Since the properties of the confined plasma depend on the boundary conditions, the physics of plasmas along open magnetic field lines and plasma surface interaction processes must also be accounted for. Those subjects (and others) are discussed in depth in chapters 2-9. Chapter 1 mostly deals with ignition requirements and the tokamak concept, while chapter 14 provides a list of useful relations: differential operators, collision times, characteristic lengths and frequencies, expressions for the neoclassical resistivity and heat conduction, the bootstrap current etc. The presentation is sufficiently broad and thorough that specialists within tokamak research can either pick useful and up-to-date information or find an authoritative introduction into other areas of the subject. It is also clear and concise so that it should provide an attractive and accurate initiation for those wishing to enter the field and for outsiders who would like to understand the concepts and be informed about the goals and challenges on the horizon. Validation of theoretical models requires adequately resolved experimental data for the various equilibrium profiles (clearly a challenge in the vicinity of transport barriers) and the fluctuations to which instabilities give rise. Chapter 10 is therefore devoted to
The tokamak as a neutron source
International Nuclear Information System (INIS)
Hendel, H.W.; Jassby, D.L.
1989-11-01
This paper describes the tokamak in its role as a neutron source, with emphasis on experimental results for D-D neutron production. The sections summarize tokamak operation, sources of fusion and non-fusion neutrons, principal neutron detection methods and their calibration, neutron energy spectra and fluxes outside the tokamak plasma chamber, history of neutron production in tokamaks, neutron emission and fusion power gain from JET and TFTR (the largest present-day tokamaks), and D-T neutron production from burnup of D-D tritons. This paper also discusses the prospects for future tokamak neutron production and potential applications of tokamak neutron sources. 100 refs., 16 figs., 4 tabs
DEFF Research Database (Denmark)
Hede, Peter Dybdahl; Bach, Poul; Jensen, Anker Degn
2008-01-01
understood. This paper provides a systematic and up-to-date review of two-fluid nozzle designs and principles together with a presentation of nozzle fundamentals introducing basic nozzle theory and thermodynamics. Correlations for the prediction of mean droplet diameters are reviewed, compared...
International Nuclear Information System (INIS)
Sugiyama, L.E.; Strauss, H.R.; Park, W.; Fu, G.Y.; Breslau, J.A.; Chen, J.
2005-01-01
The basic two-fluid processes, those related to the nonlinearly self-consistent diamagnetic drifts of the electrons and ions, are shown to have fundamentally different effects on the steady state and beta limits of stellarator configurations, compared to MHD predictions. Nonlinear numerical simulation shows that the ideal MHD ballooning modes and the resistive MHD ballooning and interchange modes at relatively high mode numbers, that set the most severe theoretical limits on beta in stellarators with fixed boundary, are easily stabilized by two-fluid effects at realistic parameters, including finite Larmor radius effects related to the ion diamagnetic drift. Magnetic reconnection at low-order rational magnetic surfaces, on the other hand, is enhanced through the parallel component of the two-fluid electron pressure gradient in Ohm's law. The accelerated reconnection rates may impose the true intrinsic limit on beta in stellarators, as a 'soft' or confinement mediated limit in β e , due to steady confinement degradation in the presence of large magnetic islands. Study of the corresponding axisymmetric configurations shows that the helical component of the stellarator configuration provides an important amplifying factor for these effects. The two-fluid results may explain several previously puzzling experimental observations on stellarator behavior. (author)
DEFF Research Database (Denmark)
Olesen, Anders Christian; Berning, Torsten; Kær, Søren Knudsen
2012-01-01
A fully coupled three-dimensional, steady-state, two-fluid, multi-component and non-isothermal DMFC model has been developed in the commercial CFD package CFX 13 (ANSYS inc.). It accounts for the presence of micro porous layers, non-equilibrium phase change, and methanol and water uptake in the i...
B. Koren (Barry); M.R. Lewis; E.H. van Brummelen (Harald); B. van Leer
2001-01-01
textabstractA finite-volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities. The novel ingredient in the method is a two-fluid linearized Godunov scheme, allowing for flux computations in case of different fluids (e.g., water and
Tokamak instrumentation and controls
International Nuclear Information System (INIS)
Becraft, W.R.; Bettis, E.S.; Houlberg, W.A.; Onega, R.J.; Stone, R.S.
1979-02-01
The three areas of study emphasis to date are: (1) Physics implications for controls, (2) Computer simulation, and (3) Shutdown/aborts. This document reports on the FY 78 efforts (the first year of these studies) to address these problems. Transient scenario options for the startup of a tokamak are developed, and the implications for the control system are discussed. This document also presents a hybrid computer simulation (analog and digital) of the Impurity Study Experiment (ISX-B) which is now being used for corroborative controls investigations. The simulation will be expanded to represent a TNS/ETF machine
Demonstration tokamak power plant
International Nuclear Information System (INIS)
Abdou, M.; Baker, C.; Brooks, J.; Ehst, D.; Mattas, R.; Smith, D.L.; DeFreece, D.; Morgan, G.D.; Trachsel, C.
1983-01-01
A conceptual design for a tokamak demonstration power plant (DEMO) was developed. A large part of the study focused on examining the key issues and identifying the R and D needs for: (1) current drive for steady-state operation, (2) impurity control and exhaust, (3) tritium breeding blanket, and (4) reactor configuration and maintenance. Impurity control and exhaust will not be covered in this paper but is discussed in another paper in these proceedings, entitled Key Issues of FED/INTOR Impurity Control System
Analysis of the two-fluid model in fully-developed two-phase flow
International Nuclear Information System (INIS)
Azpitarte, Osvaldo Enrique
2003-01-01
The two fluid model is analysed and applied to solve vertical fully-developed bubbly two-phase flows, both in laminar and turbulent conditions.The laminar model is reduced to two differential equations to solve the gas fraction (ε G ) and the velocity (υ L ).For the turbulent condition, a k - ε model for low Reynolds number is implemented, resulting in a set of differential equations to solve the four variables (ε G , υ L , k and ε) along the whole radial domain (including the laminar sub layer).For laminar condition, the system is initially reduced to a single non-dimensional ordinary equation (O D E) to solve ε G in the central region of the duct, without considering the effect of the wall.The equation is solved using Mathematic a.Analysing the solutions it can be concluded that an exact compensation of the applied pressure gradient with the hydrostatic force ρ e ff g occurs (ρ e ff : effective density of the mixture).This compensation implies that the value of ε G at the center of the duct only depends on the applied pressure gradient (dependency is linear), and that the ε G and υ L profiles are necessarily fl ato The complete problem is dealt numerically through the implementation of a finite element co deo The effect of the walls is included via a model of wall force.When the code is applied to a laminar condition, the conclusions previously obtained solving the O D E are confirmed.It is also possible to analyse the regime in which the pressure gradient is greater than the weight of the pure liquid, in which case a region of strictly zero void fraction develops surrounding the axis of the duct (in upward flow).When the code is applied to a turbulent condition, it is shown that the conclusions obtained for laminar condition can also be applied, but within a range of pressure gradient limited by two transition values (θ 1 and θ 2 ).An analysis of transitions θ 1 and θ 2 allows u s to conclude that their origin is a sudden increase of lateral
Ternary equilibria in bismuth--indium--lead alloys
International Nuclear Information System (INIS)
Liao, K.C.; Johnson, D.L.; Nelson, R.C.
1975-01-01
The liquidus surface is characterized by three binary equilibria. One binary extends from the Pb--Bi peritectic to the Pb--In peritectic. The other two extend from In--Bi eutectics, merge at 50 at. percent Bi and 30 at. percent Pb, and end at the Bi--Pb eutectic. Based on analysis of ternary liquidus contours and vertical sections, it is suggested that solidification for high lead and very high indium alloys occurs from two-phase equilibria. Solidification from all other alloys occurs from three-phase equilibria. Four-phase solidification does not occur in this system
On Pure and (approximate) Strong Equilibria of Facility Location Games
DEFF Research Database (Denmark)
Hansen, Thomas Dueholm; Telelis, Orestis A.
2008-01-01
We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a non-negative weight per agent). Agents using the same facility share fairly its installation cost, but every...... agent pays individually a (weighted) connection cost to the chosen location. We study the Price of Stability (PoS) of pure Nash equilibria and the Price of Anarchy of strong equilibria (SPoA), that generalize pure equilibria by being resilient to coalitional deviations. For unweighted agents on metric...
International Nuclear Information System (INIS)
Doggett, J.; Salpietro, E.; Shatalov, G.
1991-01-01
The results of the Conceptual Design Activities for the International Thermonuclear Experimental Reactor (ITER) are summarized. These activities, carried out between April 1988 and December 1990, produced a consistent set of technical characteristics and preliminary plans for co-ordinated research and development support of ITER; and a conceptual design, a description of design requirements and a preliminary construction schedule and cost estimate. After a description of the design basis, an overview is given of the tokamak device, its auxiliary systems, facility and maintenance. The interrelation and integration of the various subsystems that form the ITER tokamak concept are discussed. The 16 ITER equatorial port allocations, used for nuclear testing, diagnostics, fuelling, maintenance, and heating and current drive, are given, as well as a layout of the reactor building. Finally, brief descriptions are given of the major ITER sub-systems, i.e., (i) magnet systems (toroidal and poloidal field coils and cryogenic systems), (ii) containment structures (vacuum and cryostat vessels, machine gravity supports, attaching locks, passive loops and active coils), (iii) first wall, (iv) divertor plate (design and materials, performance and lifetime, a.o.), (v) blanket/shield system, (vi) maintenance equipment, (vii) current drive and heating, (viii) fuel cycle system, and (ix) diagnostics. 11 refs, figs and tabs
International Nuclear Information System (INIS)
Rudakov, D; Yu, J; Boedo, J; Hollmann, E; Krasheninnikov, S; Moyer, R; Muller, S; Yu, A; Rosenberg, M; Smirnov, R; West, W; Boivin, R; Bray, B; Brooks, N; Hyatt, A; Wong, C; Fenstermacher, M; Groth, M; Lasnier, C; McLean, A; Stangeby, P; Ratynskaia, S; Roquemore, A; Skinner, C; Solomon, W M
2008-01-01
Dust production and accumulation impose safety and operational concerns for ITER. Diagnostics to monitor dust levels in the plasma as well as in-vessel dust inventory are currently being tested in a few tokamaks. Dust accumulation in ITER is likely to occur in hidden areas, e.g. between tiles and under divertor baffles. A novel electrostatic dust detector for monitoring dust in these regions has been developed and tested at PPPL. In DIII-D tokamak dust diagnostics include Mie scattering from Nd:YAG lasers, visible imaging, and spectroscopy. Laser scattering resolves size of particles between 0.16-1.6 (micro)m in diameter; the total dust content in the edge plasmas and trends in the dust production rates within this size range have been established. Individual dust particles are observed by visible imaging using fast-framing cameras, detecting dust particles of a few microns in diameter and larger. Dust velocities and trajectories can be determined in 2D with a single camera or 3D using multiple cameras, but determination of particle size is problematic. In order to calibrate diagnostics and benchmark dust dynamics modeling, pre-characterized carbon dust has been injected into the lower divertor of DIII-D. Injected dust is seen by cameras, and spectroscopic diagnostics observe an increase of carbon atomic, C2 dimer, and thermal continuum emissions from the injected dust. The latter observation can be used in the design of novel dust survey diagnostics
Modelling dust transport in tokamaks
International Nuclear Information System (INIS)
Martin, J.D.; Martin, J.D.; Bacharis, M.; Coppins, M.; Counsell, G.F.; Allen, J.E.; Counsell, G.F.
2008-01-01
The DTOKS code, which models dust transport through tokamak plasmas, is described. The floating potential and charge of a dust grain in a plasma and the fluxes of energy to and from it are calculated. From this model, the temperature of the dust grain can be estimated. A plasma background is supplied by a standard tokamak edge modelling code (B2SOLPS5.0), and dust transport through MAST (the Mega-Amp Spherical Tokamak) and ITER plasmas is presented. We conclude that micron-radius tungsten dust can reach the separatrix in ITER. (authors)
Importance of Plasma Response to Non-axisymmetric Perturbations in Tokamaks
International Nuclear Information System (INIS)
Park, Jong-kyu; Boozer, Allen H.; Menard, Jonathan E.; Garofalo, Andrea M.; Schaffer, Michael J.; Hawryluk, Richard J.; Kaye, Stanley M.; Gerhardt, Stefan P.; Sabbagh, Steve A. and the NSTX Team
2009-01-01
Tokamaks are sensitive to deviations from axisymmetry as small as (delta)B/B 0 ∼ 10 -4 . These non-axisymmetric perturbations greatly modify plasma confinement and performance by either destroying magnetic surfaces with subsequent locking or deforming magnetic surfaces with associated non-ambipolar transport. The Ideal Perturbed Equilibrium Code (IPEC) calculates ideal perturbed equilibria and provides important basis for understanding the sensitivity of tokamak plasmas to perturbations. IPEC calculations indicate that the ideal plasma response, or equivalently the effect by ideally perturbed plasma currents, is essential to explain locking experiments on National Spherical Torus eXperiment (NSTX) and DIII-D. The ideal plasma response is also important for Neoclassical Toroidal Viscosity (NTV) in non-ambipolar transport. The consistency between NTV theory and magnetic braking experiments on NSTX and DIII-D can be improved when the variation in the field strength in IPEC is coupled with generalized NTV theory. These plasma response effects will be compared with the previous vacuum superpositions to illustrate the importance. However, plasma response based on ideal perturbed equilibria is still not sufficiently accurate to predict the details of NTV transport, and can be inconsistent when currents associated with a toroidal torque become comparable to ideal perturbed currents
Re-analysis of exponential rigid-rotor astron equilibria
International Nuclear Information System (INIS)
Lovelace, R.V.; Larrabee, D.A.; Fleischmann, H.H.
1978-01-01
Previous studies of exponential rigid-rotor astron equilibria include particles which are not trapped in the self-field of the configuration. The modification of these studies required to exclude untrapped particles is derived
Tokamak building-design considerations for a large tokamak device
International Nuclear Information System (INIS)
Barrett, R.J.; Thomson, S.L.
1981-01-01
Design and construction of a satisfactory tokamak building to support FED appears feasible. Further, a pressure vessel building does not appear necessary to meet the plant safety requirements. Some of the building functions will require safety class systems to assure reliable and safe operation. A rectangular tokamak building has been selected for FED preconceptual design which will be part of the confinement system relying on ventilation and other design features to reduce the consequences and probability of radioactivity release
Calculation of poloidal rotation in the edge plasma of limiter tokamaks
International Nuclear Information System (INIS)
Gerhauser, H.; Claassen, H.A.
1987-05-01
The existing 2-d two-fluid code for computing the plasma profiles in the scrape-off layer of limiter tokamaks has been further developed to include the effect of poloidal rotation in the basic equations. This rotation is produced by radial electric fields which arise in the limiter shadow due to radial gradients in the Langmuir sheath potential in front of the limiter. As a consequence slight deviations from ambipolar motion must occur. A strong increase of rotation near the separatrix is connected with an electric current circuit closed via the limiter edge. The 2-d profiles of all relevant quantities are calculated and discussed for TEXTOR-typical parameters including also the effect of limiter recycled neutrals. The results agree well with the known experimental evidence on poloidal rotation and should be transferable to all limiter tokamaks. (orig.)
Surface current equilibria from a geometric point of view
International Nuclear Information System (INIS)
Kaiser, R.; Salat, A.
1993-04-01
This paper addresses the inverse problem of the existence of surface current MHD equilibria in toroidal geometry with vanishing magnetic field inside. Inverse means that the plasma-vacuum interface rather than the external wall or conductors are given and the latter remain to be determined. This makes a reformulation of the problem possible in geometric terms: What toroidal surfaces with analytic parameterization allow a simple analytic covering by geodesics? If such a covering by geodesics (field lines) exists, their orthogonal trajectories (current lines) also form a simple covering and are described by a function satisfying a nonlinear partial differential equation of the Hamilton-Jacobi type whose coefficients are combinations of the metric elements of the surface. All known equilibria - equilibria with zero and infinite rotational transform and the symmetric ones in the case of finite rotational transform - turn out to be solutions of separable cases of that equation and allow a unified description if the toroidal surface is parametrized in the moving trihedral associated with a closed curve. Analogously to volume current equilibria, the only continuous symmetries compatible with separability are plane, helical and axial symmetry. In the nonseparable case numerical evidence is presented for cases with chaotic behaviour of geodesics, thus restricting possible equilibria for these surfaces. For weak deviation from axisymmetry KAM-type behaviour is observed, i.e. destruction of geodesic coverings with a low rational rotational transform and preservation of those with irrational rotational transform. A previous attempt to establish three-dimensional surface current equilibria on the basis of the KAM theorem is rejected as incomplete, and a complete proof of the existence of equilibria in the weakly nonaxisymmetric case, based on the twist theorem for mappings, is given. Finally, for a certain class of strong deviations from axisymmetry an analytic criterion is
Computation of Stackelberg Equilibria of Finite Sequential Games
DEFF Research Database (Denmark)
Bosanski, Branislav; Branzei, Simina; Hansen, Kristoffer Arnsfelt
2015-01-01
The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player~1 (the leader) first commits to a strategy that is publicly announced, then Player~2 (the follower) plays a best response to the leader's choice. We study Stackelberg equilibria in finite...... sequential (i.e., extensive-form) games and provide new exact algorithms, approximate algorithms, and hardness results for finding equilibria for several classes of such two-player games....
Field line diversion properties of finite β-helias equilibria
International Nuclear Information System (INIS)
Hayashi, Takaya; Schwenn, Ulrich; Strumberger, Erika.
1992-01-01
The diversion properties of the magnetic field outside the last closed magnetic surface of a Helias stellarator configuration are investigated for finite pressure equilibria. The results indicate that a divertor concept which has been developed from the diversion properties of the corresponding vacuum field can be maintained for finite pressure equilibria. Cross-field particle transport is simulated by a simplified scrape-off layer (SOL) model. (author)
On the uniqueness of fully informative rational expectations equilibria
Peter DeMarzo; Costis Skiadas
1998-01-01
This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as r...
The effect of pressure anisotropy on ballooning modes in tokamak plasmas
Johnston, A.; Hole, M. J.; Qu, Z. S.; Hezaveh, H.
2018-06-01
Edge Localised Modes are thought to be caused by a spectrum of magnetohydrodynamic instabilities, including the ballooning mode. While ballooning modes have been studied extensively both theoretically and experimentally, the focus of the vast majority of this research has been on isotropic plasmas. The prevalence of pressure anisotropy in modern tokamaks thus motivates further study of these modes. This paper presents a numerical analysis of ballooning modes in anisotropic equilibria. The investigation was conducted using the newly-developed codes HELENA+ATF and MISHKA-A, which adds anisotropic physics to equilibria and stability analysis. We have examined the impact of anisotropy on the stability of an n = 30 ballooning mode, confirming results conform to previous calculations in the isotropic limit. Growth rates of ballooning modes in equilibria with different levels of anisotropy were then calculated using the stability code MISHKA-A. The key finding was that the level of anisotropy had a significant impact on ballooning mode growth rates. For {T}\\perp > {T}| | , typical of ICRH heating, the growth rate increases, while for {T}\\perp < {T}| | , typical of neutral beam heating, the growth rate decreases.
Parameter study of high-β tokamak reactors with circular and strongly elongated cross section
International Nuclear Information System (INIS)
Herold, H.
1977-05-01
A simplified reactor model is used to study the influence of critical β-values on economy parameters and dimensions of possible long time pulsed tokamak reactors. Various betas deduced from stability and equilibrium MHD theory are introduced and put into the scaling in context with technological constraints, as maximum B-field, core constraint, maximum wall loading a.o. The plasma physical concepts treated comprise circular and strongly elongated cross section and approximated FCT equilibria. The computational results are presented as plots of possible economy parameter ranges (magnet energy, wall loading, volumina, investment costs per unit power) dependent on β for suitably chosen hierarchies of the constraints. - A burn time reduction by the build ups of α-pressure may be possible for the pressure profile sensitive high-β equilibria (FCT). Burn times in the 1O sec range, resulting from simple estimates, would about cancel the economic advantages of reactors with high-β equilibria compared to a β = 5% standardreactor (UWMAK I). (orig.) [de
MHD activity in the ISX-B tokamak: experimental results and theoretical interpretation
Energy Technology Data Exchange (ETDEWEB)
Carreras, B.A.; Dunlap, J.L.; Bell, J.D.; Charlton, L.A.; Cooper, W.A.; Dory, R.A.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.
1982-01-01
The observed spectrum of MHD fluctuations in the ISX-B tokamak is clearly dominated by the n=1 mode when the q=1 surface is in the plasma. This fact agrees well with theoretical predictions based on 3-D resistive MHD calculations. They show that the (m=1; n=1) mode is then the dominant instability. It drives other n=1 modes through toroidal coupling and n>1 modes through nonlinear couplings. These theoretically predicted mode structures have been compared in detail with the experimentally measured wave forms (using arrays of soft x-ray detectors). The agreement is excellent. More detailed comparisons between theory and experiment have required careful reconstructions of the ISX-B equilibria. The equilibria so constructed have permitted a precise evaluation of the ideal MHD stability properties of ISX-B. The present results indicate that the high ..beta.. ISX-B equilibria are marginally stable to finite eta ideal MHD modes. The resistive MHD calculations also show that at finite ..beta.. there are unstable resistive pressure driven modes.
Natural current profiles in tokamaks
International Nuclear Information System (INIS)
Biskamp, D.
1986-01-01
It is proposed that a certain class of equilibrium, which follow from an elementary variational principle, are the natural current profiles in tokamaks, to which actual discharge profiles tend to relax. (orig.)
Federal Laboratory Consortium — Alcator C-Mod at the Massachusetts Institute of Technology is operated as a DOE national user facility. Alcator C-Mod is a unique, compact tokamak facility that uses...
JUST: Joint Upgraded Spherical Tokamak
International Nuclear Information System (INIS)
Azizov, E.A.; Dvorkin, N.Ya.; Filatov, O.G.
1997-01-01
The main goals, ideas and the programme of JUST, spherical tokamak (ST) for the plasma burn investigation, are presented. The place and prospects of JUST in thermonuclear investigations are discussed. (author)
Preliminary Design of Alborz Tokamak
Mardani, M.; Amrollahi, R.; Saramad, S.
2012-04-01
The Alborz tokamak is a D-shape cross section tokamak that is under construction in Amirkabir University of Technology. The most important part of the tokamak design is the design of TF coils. In this paper a refined design of the TF coil system for the Alborz tokamak is presented. This design is based on cooper cable conductor with 5 cm width and 6 mm thickness. The TF coil system is consist of 16 rectangular shape coils, that makes the magnetic field of 0.7 T at the plasma center. The stored energy in total is 160 kJ, and the power supply used in this system is a capacitor bank with capacity of C = 1.32 mF and V max = 14 kV.
New directions in tokamak reactors
International Nuclear Information System (INIS)
Baker, C.C.
1985-01-01
New directions for tokamak research are briefly mentioned. Some of the areas for new considerations are the following: reactor size, beta ratio, current drivers, blankets, impurity control, and modular designs
International Nuclear Information System (INIS)
Varandas, C.A.F.; Cabral, J.A.C.; Manso, M.E.
1991-01-01
A small tokamak is under construction at the Portuguese Technical Superior Institute. The main objective is to create a home based laboratory in which an independent scientific program might be developed. (L.C.J.A.). 14 refs, 6 figs
Li, Zhaorui; Livescu, Daniel
2017-11-01
The two-fluid plasma equations with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating term have been solved by using the sixth-order non-dissipative compact scheme for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows have been tested against a series of canonical problems, such as Alfven-Whistler dispersion relation, electromagnetic plasma shock, magnetic reconnection, etc. For all test cases, grid convergence tests have been conducted to achieve fully resolved results. The roles of heat flux, viscosity, resistivity, Hall and Biermann battery effects, are investigated for the canonical flows studied.
MINTEQ, Geochemical Equilibria in Ground Water
International Nuclear Information System (INIS)
Krupka, K.M.
1990-01-01
1 - Description of program or function: MINTEQ is a geochemical program to model aqueous solutions and the interactions of aqueous solutions with hypothesized assemblages of solid phases. It was developed for the Environmental Protection Agency to perform the calculations necessary to simulate the contact of waste solutions with heterogeneous sediments or the interaction of ground water with solidified wastes. MINTEQ can calculate ion speciation/solubility, adsorption, oxidation-reduction, gas phase equilibria, and precipitation/dissolution of solid phases. MINTEQ can accept a finite mass for any solid considered for dissolution and will dissolve the specified solid phase only until its initial mass is exhausted. This ability enables MINTEQ to model flow-through systems. In these systems the masses of solid phases that precipitate at earlier pore volumes can be dissolved at later pore volumes according to thermodynamic constraints imposed by the solution composition and solid phases present. The ability to model these systems permits evaluation of the geochemistry of dissolved traced metals, such as low-level waste in shallow land burial sites. MINTEQ was designed to solve geochemical equilibria for systems composed of one kilogram of water, various amounts of material dissolved in solution, and any solid materials that are present. Systems modeled using MINTEQ can exchange energy and material (open systems) or just energy (closed systems) with the surrounding environment. Each system is composed of a number of phases. Every phase is a region with distinct composition and physically definable boundaries. All of the material in the aqueous solution forms one phase. The gas phase is composed of any gaseous material present, and structurally distinct solid forms a separate phase. 2 - Method of solution: MINTEQ applies the fundamental principles of thermodynamics to solve geochemical equilibria from a set of mass balance equations, one for each component. Because the
International Nuclear Information System (INIS)
Papin, M.
2005-06-01
This work dedicated to the study of the hypersonic re-entry of vehicles in the atmosphere crossing clouds of particles implies the study of two-fluid flow and it is shown that some developments can be applied to the two-fluid models used to describe the phase transformation occurring in a target irradiated by laser beams. The calculation of wall fluxes on hypersonic re-entry vehicles requires the modeling of the interactions with clouds. Two-fluid flows posing many physical and mathematical problems, one studies an alternative model due to Abgrall and Saurel: the discrete equation method (DEM). Three axis are chosen. The first proposes a finite volume discretization of the Navier-Stokes equations on hybrid grids adapted to the context. The second extends the DEM within a multi-fluid not-structured N-D framework. A limit study associates an original continuous model to him: it allows to modify usual two-fluid seven equations models to obtain a phasic entropy principle. In spite of good properties, the continuous description of the particles is unsuited to the problem. The last axis is a study of the follow-up of pointwise particles which does not allow realistic calculation of parietal fluxes. An original model, extending the usual hydro-erosion models, however makes it possible to evaluate rebounds, erosion of the body and wall fluxes. The appendices expose approximate and exact Riemann solvers between pure fluids, discretization of the Baer and Nunziato model, and relations describing the atmosphere, water and heat fluxes
Numerical Tokamak Project code comparison
International Nuclear Information System (INIS)
Waltz, R.E.; Cohen, B.I.; Beer, M.A.
1994-01-01
The Numerical Tokamak Project undertook a code comparison using a set of TFTR tokamak parameters. Local radial annulus codes of both gyrokinetic and gyrofluid types were compared for both slab and toroidal case limits assuming ion temperature gradient mode turbulence in a pure plasma with adiabatic electrons. The heat diffusivities were found to be in good internal agreement within ± 50% of the group average over five codes
Spherical tokamak development in Brazil
International Nuclear Information System (INIS)
Ludwig, G.O.; Del Bosco, E.; Ferreira, J.G.; Berni, L.A.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Ueda, M.; Barroso, J.J.; Castro, P.J.; Barbosa, L.F.W.; Patire Junior, H.; The high-power microwave sources group
2003-01-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the steps in the development of the ETE (Experimento Tokamak Esferico) project, its research program, technical characteristics and operating conditions as of December, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Confinement and diffusion in tokamaks
International Nuclear Information System (INIS)
McWilliams, R.
1988-01-01
The effect of electric field fluctuations on confinement and diffusion in tokamak is discussed. Based on the experimentally determined cross-field turbolent diffusion coefficient, D∼3.7*cT e /eB(δn i /n i ) rms which is also derived by a simple theory, the cross-field diffusion time, tp=a 2 /D, is calculated and compared to experimental results from 51 tokamak for standard Ohmic operation
Enhancement of confinement in tokamaks
International Nuclear Information System (INIS)
Furth, H.P.
1986-01-01
The analysis begins by identifying a hypothetical model of tokamak confinement that is designed to take into account the conflict between Tsub(e)(r)-profile shapes arising from microscopic transport and J(r)-profile shapes required for gross stability. On the basis of this model, a number of hypothetical lines of advance are developed. Some TFTR experiments that may point the way to a particularly attractive type of tokamak reactor regime are discussed. (author)
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] (and others)
2003-07-01
The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, G.O.; Del Bosco, E.; Ferreira, J.G.; Berni, L.A.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Ueda, M.; Barroso, J.J.; Castro, P.J. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma; Barbosa, L.F.W. [Universidade do Vale do Paraiba (UNIVAP), Sao Jose dos Campos, SP (Brazil). Faculdade de Engenharia, Arquitetura e Urbanismo; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Div. de Mecanica Espacial e Controle; The high-power microwave sources group
2003-12-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the steps in the development of the ETE (Experimento Tokamak Esferico) project, its research program, technical characteristics and operating conditions as of December, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Spherical tokamak development in Brazil
International Nuclear Information System (INIS)
Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes
2003-01-01
The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
International Nuclear Information System (INIS)
Navratil, G.A.; Mauel, M.E.; Ivers, T.H.; Sankar, M.K.V.; Eisner, E.; Gates, D.; Garofalo, A.; Kombargi, R.; Maurer, D.; Nadle, D.; Xiao, Q.
1993-01-01
During the past 6 months, experiments have been conducted with the HBT-EP tokamak in order to (1) test and evaluate diagnostic systems, (2) establish basic machine operation, (3) document MHD behavior as a function of global discharge parameters, (4) investigate conditions leading to passive stabilization of MHD instabilities, and (5) quantify the external saddle coil current required for DC mode locking. In addition, the development and installation of new hardware systems has occurred. A prototype saddle coil was installed and tested. A five-position (n,m) = (1,2) external helical saddle coil was attached for mode-locking experiments. And, fabrication of the 32-channel UV tomography and the multipass Thomson scattering diagnostics have begun in preparation for installation later this year
Anomalous transport in tokamaks
International Nuclear Information System (INIS)
Wootton, A.J.
1989-01-01
A review is presented of what is known about anomalous transport in tokamaks. It is generally thought that this anomalous transport is the result of fluctuations in various plasma parameters. In the plasma edge detailed measurements of the quantities required to directly determine the fluctuation driven fluxes are available. The total flux of particles is well explained by the measured electrostatic fluctuation driven flux. However, a satisfactory model to explain the origin of the fluctuations has not been identified. The processes responsible for determining the edge energy flux are less clear, but electrostatic convection plays an important part. In the confinement region experimental observations are presently restricted to measurements of density and potential fluctuations and their correlations. The characteristics of the measured fluctuations are discussed and compared with the predictions of various models. Comparisons between measured particle, electron heat and ion heat fluxes, and those fluxes predicted to result from the measured fluctuations, are made. Magnetic fluctuations is discussed
International Nuclear Information System (INIS)
Tenney, F.H.
1976-09-01
A report on one year of study of a tokamak hybrid reactor is presented. The plasma is maintained by both D and T beams. To obtain long burn times a poloidal field divertor is required. Both the single null and the double null style of divertor are considered. The blanket consists of a neutron multiplier region containing natural uranium followed by burner regions of molten salt (flibe) loaded with PuF 3 to enhance the energy multiplication. Economic analysis has been applied only recently to a variety of reactor sizes and plasma conditions. Early indications suggest that the most attractive hybrids will have large plasmas of major radius in excess of 8 meters
International Nuclear Information System (INIS)
Tenney, F.H.
1976-01-01
A report on one year of study of a tokamak hybrid reactor is given. The plasma is maintained by both D and T beams. To obtain long burn times a poloidal field divertor is required. Both the single null and the double null style of divertor are considered. The blanket consists of a neutron multiplier region containing natural uranium followed by burner regions of molten salt (flibe) loaded with PuF 3 to enhance the energy multiplication. Economic analysis has been applied only recently to a variety of reactor sizes and plasma conditions. Early indications suggest that the most attractive hybrids will have large plasmas of major radius in excess of 8 meters
International Nuclear Information System (INIS)
Schmidt, J.
1987-01-01
The author discusses his lab's plan for completing the Compact Ignition Tokamak (CIT) conceptual design during calendar year 1987. Around July 1 they froze the subsystem envelopes on the device to continue with the conceptual design. They did this by formalizing a general requirements document. They have been developing the management plan and submitted a version to the DOE July 10. He describes a group of management activities. They released the vacuum vessel Request For Proposals (RFP) on August 5. An RFP to do a major part of the system engineering on the device is being developed. They intend to assemble the device outside of the test cell, then move it into the the test cell, install it there, and bring to the test cell many of the auxiliary facilities from TFTR, for example, power supplies
Energy Technology Data Exchange (ETDEWEB)
Caldas, Ibere L.; Heller, M.V.A.P.; Brasilio, Z.A. [Sao Paulo Univ., SP, RJ (Brazil). Inst. de Fisica
1997-12-31
Full text. In this work we summarize the results from experiments on electrostatic and magnetic fluctuations in tokamak plasmas. Spectral analyses show that these fluctuations are turbulent, having a broad spectrum of wavectors and a broad spectrum of frequencies at each wavector. The electrostatic turbulence induces unexpected anomalous particle transport that deteriorates the plasma confinement. The relationship of these fluctuations to the current state of plasma theory is still unclear. Furthermore, we describe also attempts to control this plasma turbulence with external magnetic perturbations that create chaotic magnetic configurations. Accordingly, the magnetic field lines may become chaotic and then induce a Lagrangian diffusion. Moreover, to discuss nonlinear coupling and intermittency, we present results obtained by using numerical techniques as bi spectral and wavelet analyses. (author)
International Nuclear Information System (INIS)
Bondeson, A.
1987-01-01
This paper discusses major and minor disruptions in Tokamaks. A number of models and numerical simulations of disruptions based on resistive MHD are reviewed. A discussion is given of how disruptive current profiles are correlated with the experimentally known operational limits in density and current. It is argued that the q a =2 limit is connected with stabilization of the m=2/n=1 tearing mode for a approx.< 2.7 by resistive walls and mode rotation. Experimental and theoretical observations indicate that major disruptions usually occur in at least two phases, first a 'predisruption', or loss of confinement in the region 1 < q < 2, leaving the q approx.= 1 region almost unaffected, followed by a final disruption of the central part, interpreted here as a toroidal n = 1 external kink mode. (author)
Identification of, and transition to, the second region of ideal MHD stability in tokamaks
International Nuclear Information System (INIS)
Sabbagh, S.A.
1990-01-01
The second region of ideal MHD stability in tokamaks is studied by considering the behavior of the second region boundary for self- consistently calculated, marginally stable, second region equilibria and the characteristics of numerically computed transport sequences that achieve second stability. Equilibria with pressure profiles, p(ψ), that are marginally stable to the second region on each flux surface are generated numerically. This constraint eliminates p(ψ) as an independent variable, and reduces the predictor variables to the tokamak parameters and the q profile. The primary response functions considered are the plasma figures of merit, β and var-epsilon β p , and the normalized pressure gradient, α. Variations of the radial wavenumber in the ballooning equation negligibly affect the second region boundary for these equilibria. The second region boundary is sensitive to variations in the q profile at small aspect ratio, A, and will stabilize or destabilize depending on the balance of higher order var-epsilon = A -1 modifications of the normal field line curvature, κ n . These effects are a competition between the stabilizing geometric magnetic well of the toroidal field component of κ n and the destabilizing poloidal field component of κ n . The latter term becomes competitive in high var-epsilon β p plasmas with large Shafranov shifts. Simple analytic models are presented that reproduce the scaling of the marginally stable second region values of α and var-epsilon β p , and stability diagrams illustrating the behavior of the high-n unstable region for various parameters are shown
A modified two-fluid model for the application of two-group interfacial area transport equation
International Nuclear Information System (INIS)
Sun, X.; Ishii, M.; Kelly, J.
2003-01-01
This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Jun; Park, Ik Kyu; Yoon, Han Young [Thermal-Hydraulic Safety Research Division, Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Jae, Byoung [School of Mechanical Engineering, Chungnam National University, Daejeon (Korea, Republic of)
2017-01-15
Two-fluid equations are widely used to obtain averaged behaviors of two-phase flows. This study addresses a problem that may arise when the two-fluid equations are used for multi-dimensional bubbly flows. If steady drag is the only accounted force for the interfacial momentum transfer, the disperse-phase velocity would be the same as the continuous-phase velocity when the flow is fully developed without gravity. However, existing momentum equations may show unphysical results in estimating the relative velocity of the disperse phase against the continuous-phase. First, we examine two types of existing momentum equations. One is the standard two-fluid momentum equation in which the disperse-phase is treated as a continuum. The other is the averaged momentum equation derived from a solid/ fluid particle motion. We show that the existing equations are not proper for multi-dimensional bubbly flows. To resolve the problem mentioned above, we modify the form of the Reynolds stress terms in the averaged momentum equation based on the solid/fluid particle motion. The proposed equation shows physically correct results for both multi-dimensional laminar and turbulent flows.
Predictions of bubbly flows in vertical pipes using two-fluid models in CFDS-FLOW3D code
International Nuclear Information System (INIS)
Banas, A.O.; Carver, M.B.; Unrau, D.
1995-01-01
This paper reports the results of a preliminary study exploring the performance of two sets of two-fluid closure relationships applied to the simulation of turbulent air-water bubbly upflows through vertical pipes. Predictions obtained with the default CFDS-FLOW3D model for dispersed flows were compared with the predictions of a new model (based on the work of Lee), and with the experimental data of Liu. The new model, implemented in the CFDS-FLOW3D code, included additional source terms in the open-quotes standardclose quotes κ-ε transport equations for the liquid phase, as well as modified model coefficients and wall functions. All simulations were carried out in a 2-D axisymmetric format, collapsing the general multifluid framework of CFDS-FLOW3D to the two-fluid (air-water) case. The newly implemented model consistently improved predictions of radial-velocity profiles of both phases, but failed to accurately reproduce the experimental phase-distribution data. This shortcoming was traced to the neglect of anisotropic effects in the modelling of liquid-phase turbulence. In this sense, the present investigation should be considered as the first step toward the ultimate goal of developing a theoretically sound and universal CFD-type two-fluid model for bubbly flows in channels
Predictions of bubbly flows in vertical pipes using two-fluid models in CFDS-FLOW3D code
Energy Technology Data Exchange (ETDEWEB)
Banas, A.O.; Carver, M.B. [Chalk River Laboratories (Canada); Unrau, D. [Univ. of Toronto (Canada)
1995-09-01
This paper reports the results of a preliminary study exploring the performance of two sets of two-fluid closure relationships applied to the simulation of turbulent air-water bubbly upflows through vertical pipes. Predictions obtained with the default CFDS-FLOW3D model for dispersed flows were compared with the predictions of a new model (based on the work of Lee), and with the experimental data of Liu. The new model, implemented in the CFDS-FLOW3D code, included additional source terms in the {open_quotes}standard{close_quotes} {kappa}-{epsilon} transport equations for the liquid phase, as well as modified model coefficients and wall functions. All simulations were carried out in a 2-D axisymmetric format, collapsing the general multifluid framework of CFDS-FLOW3D to the two-fluid (air-water) case. The newly implemented model consistently improved predictions of radial-velocity profiles of both phases, but failed to accurately reproduce the experimental phase-distribution data. This shortcoming was traced to the neglect of anisotropic effects in the modelling of liquid-phase turbulence. In this sense, the present investigation should be considered as the first step toward the ultimate goal of developing a theoretically sound and universal CFD-type two-fluid model for bubbly flows in channels.
Two-fluid 2.5D code for simulations of small scale magnetic fields in the lower solar atmosphere
Piantschitsch, Isabell; Amerstorfer, Ute; Thalmann, Julia Katharina; Hanslmeier, Arnold; Lemmerer, Birgit
2015-08-01
Our aim is to investigate magnetic reconnection as a result of the time evolution of magnetic flux tubes in the solar chromosphere. A new numerical two-fluid code was developed, which will perform a 2.5D simulation of the dynamics from the upper convection zone up to the transition region. The code is based on the Total Variation Diminishing Lax-Friedrichs method and includes the effects of ion-neutral collisions, ionisation/recombination, thermal/resistive diffusivity as well as collisional/resistive heating. What is innovative about our newly developed code is the inclusion of a two-fluid model in combination with the use of analytically constructed vertically open magnetic flux tubes, which are used as initial conditions for our simulation. First magnetohydrodynamic (MHD) tests have already shown good agreement with known results of numerical MHD test problems like e.g. the Orszag-Tang vortex test, the Current Sheet test or the Spherical Blast Wave test. Furthermore, the single-fluid approach will also be applied to the initial conditions, in order to compare the different rates of magnetic reconnection in both codes, the two-fluid code and the single-fluid one.
MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model
International Nuclear Information System (INIS)
Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio
1991-05-01
MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)
The ARIES tokamak reactor study
International Nuclear Information System (INIS)
1989-10-01
The ARIES study is a community effort to develop several visions of tokamaks as fusion power reactors. The aims are to determine the potential economics, safety, and environmental features of a range of possible tokamak reactors, and to identify physics and technology areas with the highest leverage for achieving the best tokamak reactor. Three ARIES visions are planned, each having a different degree of extrapolation from the present data base in physics and technology. The ARIES-I design assumes a minimum extrapolation from current tokamak physics (e.g., 1st stability) and incorporates technological advances that can be available in the next 20 to 30 years. ARIES-II is a DT-burning tokamak which would operate at a higher beta in the 2nd MHD stability regime. It employs both potential advances in the physics and expected advances in technology and engineering. ARIES-II will examine the potential of the tokamak and the D 3 He fuel cycle. This report is a collection of 14 papers on the results of the ARIES study which were presented at the IEEE 13th Symposium on Fusion Engineering (October 2-6, 1989, Knoxville, TN). This collection describes the ARIES research effort, with emphasis on the ARIES-I design, summarizing the major results, the key technical issues, and the central conclusions
Two-dimensional magnetohydrodynamic equilibria with flow and studies of equilibria fluctuations
International Nuclear Information System (INIS)
Agim, Y.Z.
1989-08-01
A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasi-linear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology. In second part of this thesis, magnetic fluctuations due to the thermally excited MHD waves are investigated using fluid and kinetic models to describe stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities which are roughly Lorentzian, exhibit equipartition with no apparent cutoff in wavenumber space and a Bohm-type diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuating-to-equilibrium magnetic field ratio is found to be of the order of 10 -10
Thermodynamic Equilibria and Extrema Analysis of Attainability Regions and Partial Equilibria
Gorban, Alexander N; Kaganovich, Boris M; Keiko, Alexandre V; Shamansky, Vitaly A; Shirkalin, Igor A
2006-01-01
This book discusses mathematical models that are based on the concepts of classical equilibrium thermodynamics. They are intended for the analysis of possible results of diverse natural and production processes. Unlike the traditional models, these allow one to view the achievable set of partial equilibria with regards to constraints on kinetics, energy and mass exchange and to determine states of the studied systems of interest for the researcher. Application of the suggested models in chemical technology, energy and ecology is illustrated in the examples.
Unifying dynamical and structural stability of equilibria
Arnoldi, Jean-François; Haegeman, Bart
2016-09-01
We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.
Axisymmetric plasma equilibria in a Kerr metric
Elsässer, Klaus
2001-10-01
Plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species. The quasi-neutrality assumption (no charge density, no toroidal current) allows to solve Maxwell's equations analytically for any axisymmetric stationary metric, and to reduce the fluid equations to one single scalar equation for the stream function \\chi of the positrons or ions, respectively. The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio m_e/m_i. The \\chi-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
Isotope effects in ion-exchange equilibria in aqueous and mixed solvent systems
International Nuclear Information System (INIS)
Gupta, A.R.
1979-01-01
Isotope effects in ion-exchange equilibria in aqueous and mixed solvents are analyzed in terms of the general features of ion-exchange equilibria and of isotope effects in chemical equilibria. The special role of solvent fractionation effects in ion-exchange equilibria in mixed solvents is pointed out. The various situations arising in isotope fractionation in ion exchange in mixed solvents due to solvent fractionation effects are theoretically discussed. The experimental data on lithium isotope effects in ion-exchange equilibria in mixed solvents are shown to conform to the above situations. The limitations of ion-exchange equilibria in mixed solvents for isotope fractionation are pointed out. 3 tables
Three-dimensional equilibria and transport in RFX-mod: A description using stellarator tools
International Nuclear Information System (INIS)
Gobbin, M.; Bonfiglio, D.; Lorenzini, R.; Marrelli, L.; Martin, P.; Martines, E.; Momo, B.; Predebon, I.; Puiatti, M. E.; Spizzo, G.; Terranova, D.; Boozer, A. H.; Cooper, A. W.; Escande, D. F.; Hirshman, S. P.; Lore, J.; Sanchez, R.; Spong, D. A.; Pomphrey, N.
2011-01-01
RFX-mod self-organized single helical axis (SHAx) states provide a unique opportunity to advance 3D fusion physics and establish a common knowledge basis in a parameter region not covered by stellarators and tokamaks. The VMEC code has been adapted to the reversed-field pinch (RFP) to model SHAx equilibria in fixed boundary mode with experimental measurements as constraint. The averaged particle diffusivity over the helical volume, estimated with the Monte Carlo code ORBIT, has a neoclassical-like dependence on collisionality and does not show the 1/ν trend of un-optimized stellarators. In particular, the helical region boundary, corresponding to an electron transport barrier with zero magnetic shear and improved confinement, has been investigated using numerical codes common to the stellarator community. In fact, the DKES/PENTA codes have been applied to RFP for local neoclassical transport computations, including radial electric field, to estimate thermal diffusion coefficients in the barrier region for typical RFX-mod temperature and density profiles. A comparison with power balance estimates shows that residual chaos due to secondary tearing modes and small-scale turbulence still contribute to drive anomalous transport in the barrier region.
Model for ICRF fast wave current drive in self-consistent MHD equilibria
International Nuclear Information System (INIS)
Bonoli, P.T.; Englade, R.C.; Porkolab, M.; Fenstermacher, M.E.
1993-01-01
Recently, a model for fast wave current drive in the ion cyclotron radio frequency (ICRF) range was incorporated into the current drive and MHD equilibrium code ACCOME. The ACCOME model combines a free boundary solution of the Grad Shafranov equation with the calculation of driven currents due to neutral beam injection, lower hybrid (LH) waves, bootstrap effects, and ICRF fast waves. The equilibrium and current drive packages iterate between each other to obtain an MHD equilibrium which is consistent with the profiles of driven current density. The ICRF current drive package combines a toroidal full-wave code (FISIC) with a parameterization of the current drive efficiency obtained from an adjoint solution of the Fokker Planck equation. The electron absorption calculation in the full-wave code properly accounts for the combined effects of electron Landau damping (ELD) and transit time magnetic pumping (TTMP), assuming a Maxwellian (or bi-Maxwellian) electron distribution function. Furthermore, the current drive efficiency includes the effects of particle trapping, momentum conserving corrections to the background Fokker Planck collision operator, and toroidally induced variations in the parallel wavenumbers of the injected ICRF waves. This model has been used to carry out detailed studies of advanced physics scenarios in the proposed Tokamak Physics Experiment (TPX). Results are shown, for example, which demonstrate the possibility of achieving stable equilibria at high beta and high bootstrap current fraction in TPX. Model results are also shown for the proposed ITER device
Bibliography of fusion product physics in tokamaks
International Nuclear Information System (INIS)
Hively, L.M.; Sigmar, D.J.
1989-09-01
Almost 700 citations have been compiled as the first step in reviewing the recent research on tokamak fusion product effects in tokamaks. The publications are listed alphabetically by the last name of the first author and by subject category
Tokamak engineering test reactor
International Nuclear Information System (INIS)
Conn, R.W.; Jassby, D.L.
1975-07-01
The design criteria for a tokamak engineering test reactor can be met by operating in the two-component mode with reacting ion beams, together with a new blanket-shield design based on internal neutron spectrum shaping. A conceptual reactor design achieving a neutron wall loading of about 1 MW/m 2 is presented. The tokamak has a major radius of 3.05 m, the plasma cross-section is noncircular with a 2:1 elongation, and the plasma radius in the midplane is 55 cm. The total wall area is 149 m 2 . The plasma conditions are T/sub e/ approximately T/sub i/ approximately 5 keV, and ntau approximately 8 x 10 12 cm -3 s. The plasma temperature is maintained by injection of 177 MW of 200-keV neutral deuterium beams; the resulting deuterons undergo fusion reactions with the triton-target ions. The D-shaped toroidal field coils are extended out to large major radius (7.0 m), so that the blanket-shield test modules on the outer portion of the torus can be easily removed. The TF coils are superconducting, using a cryogenically stable TiNb design that permits a field at the coil of 80 kG and an axial field of 38 kG. The blanket-shield design for the inner portion of the torus nearest the machine center line utilizes a neutron spectral shifter so that the first structural wall behind the spectral shifter zone can withstand radiation damage for the reactor lifetime. The energy attenuation in this inner blanket is 8 x 10 -6 . If necessary, a tritium breeding ratio of 0.8 can be achieved using liquid lithium cooling in the []outer blanket only. The overall power consumption of the reactor is about 340 MW(e). A neutron wall loading greater than 1 MW/m 2 can be achieved by increasing the maximum magnetic field or the plasma elongation. (auth)
START: the creation of a spherical tokamak
International Nuclear Information System (INIS)
Sykes, Alan
1992-01-01
The START (Small Tight Aspect Ratio Tokamak) plasma fusion experiment is now operational at AEA Fusion's Culham Laboratory. It is the world's first experiment to explore an extreme limit of the tokamak - the Spherical Tokamak - which theoretical studies predict may have substantial advantages in the search for economic fusion power. The Head of the START project, describes the concept, some of the initial experimental results and the possibility of developing a spherical tokamak power reactor. (author)
Moving Divertor Plates in a Tokamak
International Nuclear Information System (INIS)
Zweben, S.J.; Zhang, H.
2009-01-01
Moving divertor plates could help solve some of the problems of the tokamak divertor through mechanical ingenuity rather than plasma physics. These plates would be passively heated on each pass through the tokamak and cooled and reprocessed outside the tokamak. There are many design options using varying plate shapes, orientations, motions, coatings, and compositions
Fusion potential for spherical and compact tokamaks
International Nuclear Information System (INIS)
Sandzelius, Mikael
2003-02-01
The tokamak is the most successful fusion experiment today. Despite this, the conventional tokamak has a long way to go before being realized into an economically viable power plant. In this master thesis work, two alternative tokamak configurations to the conventional tokamak has been studied, both of which could be realized to a lower cost. The fusion potential of the spherical and the compact tokamak have been examined with a comparison of the conventional tokamak in mind. The difficulties arising in the two configurations have been treated from a physical point of view concerning the fusion plasma and from a technological standpoint evolving around design, materials and engineering. Both advantages and drawbacks of either configuration have been treated relative to the conventional tokamak. The spherical tokamak shows promising plasma characteristics, notably a high β-value but have troubles with high heat loads and marginal tritium breeding. The compact tokamak operates at a high plasma density and a high magnetic field enabling it to be built considerably smaller than any other tokamak. The most notable down-side being high heat loads and neutron transport problems. With the help of theoretical reactor studies, extrapolating from where we stand today, it is conceivable that the spherical tokamak is closer of being realized of the two. But, as this study shows, the compact tokamak power plant concept offers the most appealing prospect
Fusion potential for spherical and compact tokamaks
Energy Technology Data Exchange (ETDEWEB)
Sandzelius, Mikael
2003-02-01
The tokamak is the most successful fusion experiment today. Despite this, the conventional tokamak has a long way to go before being realized into an economically viable power plant. In this master thesis work, two alternative tokamak configurations to the conventional tokamak has been studied, both of which could be realized to a lower cost. The fusion potential of the spherical and the compact tokamak have been examined with a comparison of the conventional tokamak in mind. The difficulties arising in the two configurations have been treated from a physical point of view concerning the fusion plasma and from a technological standpoint evolving around design, materials and engineering. Both advantages and drawbacks of either configuration have been treated relative to the conventional tokamak. The spherical tokamak shows promising plasma characteristics, notably a high {beta}-value but have troubles with high heat loads and marginal tritium breeding. The compact tokamak operates at a high plasma density and a high magnetic field enabling it to be built considerably smaller than any other tokamak. The most notable down-side being high heat loads and neutron transport problems. With the help of theoretical reactor studies, extrapolating from where we stand today, it is conceivable that the spherical tokamak is closer of being realized of the two. But, as this study shows, the compact tokamak power plant concept offers the most appealing prospect.
Moving Divertor Plates in a Tokamak
Energy Technology Data Exchange (ETDEWEB)
S.J. Zweben, H. Zhang
2009-02-12
Moving divertor plates could help solve some of the problems of the tokamak divertor through mechanical ingenuity rather than plasma physics. These plates would be passively heated on each pass through the tokamak and cooled and reprocessed outside the tokamak. There are many design options using varying plate shapes, orientations, motions, coatings, and compositions.
Tokamak Physics Experiment (TPX) design
International Nuclear Information System (INIS)
Schmidt, J.A.
1995-01-01
TPX is a national project involving a large number of US fusion laboratories, universities, and industries. The element of the TPX requirements that is a primary driver for the hardware design is the fact that TPX tokamak hardware is being designed to accommodate steady state operation if the external systems are upgraded from the 1,000 second initial operation. TPX not only incorporates new physics, but also pioneers new technologies to be used in ITER and other future reactors. TPX will be the first tokamak with fully superconducting magnetic field coils using advanced conductors, will have internal nuclear shielding, will use robotics for machine maintenance, and will remove the continuous, concentrated heat flow from the plasma with new dispersal techniques and with special materials that are actively cooled. The Conceptual Design for TPX was completed during Fiscal Year 1993. The Preliminary Design formally began at the beginning of Fiscal Year 1994. Industrial contracts have been awarded for the design, with options for fabrication, of the primary tokamak hardware. A large fraction of the design and R and D effort during FY94 was focused on the tokamak and in turn on the tokamak magnets. The reason for this emphasis is because the magnets require a large design and R and D effort, and are critical to the project schedule. The magnet development is focused on conductor development, quench protection, and manufacturing R and D. The Preliminary Design Review for the Magnets is planned for fall, 1995
Resistive instabilities in tokamaks
International Nuclear Information System (INIS)
Rutherford, P.H.
1985-10-01
Low-m tearing modes constitute the dominant instability problem in present-day tokamaks. In this lecture, the stability criteria for representative current profiles with q(0)-values slightly less than unit are reviewed; ''sawtooth'' reconnection to q(0)-values just at, or slightly exceeding, unity is generally destabilizing to the m = 2, n = 1 and m = 3, n = 2 modes, and severely limits the range of stable profile shapes. Feedback stabilization of m greater than or equal to 2 modes by rf heating or current drive, applied locally at the magnetic islands, appears feasible; feedback by island current drive is much more efficient, in terms of the radio-frequency power required, then feedback by island heating. Feedback stabilization of the m = 1 mode - although yielding particularly beneficial effects for resistive-tearing and high-beta stability by allowing q(0)-values substantially below unity - is more problematical, unless the m = 1 ideal-MHD mode can be made positively stable by strong triangular shaping of the central flux surfaces. Feedback techniques require a detectable, rotating MHD-like signal; the slowing of mode rotation - or the excitation of non-rotating modes - by an imperfectly conducting wall is also discussed
Tokamak experimental power reactor
International Nuclear Information System (INIS)
Stacey, W.M. Jr.; Abdou, M.A.; Brooks, J.N.
1978-01-01
A tokamak experimental power reactor has been designed that is capable of producing net electric power over a wide range of possible operating conditions. A net production of 81 MW of electricity is expected from the design reference conditions that assume a value of 0.07 for beta-toroidal, a maximum toroidal magnetic field of 9 T and a thermal conversion efficiency of 30%. Impurity control is achieved through the use of a low-Z first wall coating. This approach allows a burn time of 60 seconds without the incorporation of a divertor. The system is cooled by a dual pressurized water/steam system that could potentially provide thermal efficiencies as high as 39%. The first surface facing the plasma is a low-Z coated water cooled panel that is attached to a 20 cm thick blanket module. The vacuum boundary is removed a total of 22 cm from the plasma, thereby minimizing the amount of radiation damage in this vital component. Consideration is given in the design to the possible use of the EPR as a materials test reactor. It is estimated that the total system could be built for less than 550 million dollars
Classical tokamak transport theory
International Nuclear Information System (INIS)
Nocentini, Aldo
1982-01-01
A qualitative treatment of the classical transport theory of a magnetically confined, toroidal, axisymmetric, two-species plasma is presented. The 'weakly collisional' ('banana' and 'plateau') and 'collision dominated' ('Pfirsch-Schlueter' and 'highly collisional') regimes, as well as the Ware effect are discussed. The method used to evaluate the diffusion coffieicnts of particles and heat in the weakly collisional regime is based on stochastic argument, that requires an analysis of the characteristic collision frequencies and lengths for particles moving in a tokamak-like magnetic field. The same method is used to evaluate the Ware effect. In the collision dominated regime on the other hand, the particle and heat fluxes across the magnetic field lines are dominated by macroscopic effects so that, although it is possible to present them as diffusion (in fact, the fluxes turn out to be proportional to the density and temperature gradients), a macroscopic treatment is more appropriate. Hence, fluid equations are used to inveatigate the collision dominated regime, to which particular attention is devoted, having been shown relatively recently that it is more complicated than the usual Pfirsch-Schlueter regime. The whole analysis presented here is qualitative, aiming to point out the relevant physical mechanisms involved in the various regimes more than to develop a rigorous mathematical derivation of the diffusion coefficients, for which appropriate references are given. (author)
Tokamak experimental power reactor
International Nuclear Information System (INIS)
Stacey, W.M. Jr.; Abdou, M.A.; Bertoncini, P.J.
1976-01-01
A conceptual design has been developed for a tokamak Experimental Power Reactor to operate at net electrical power conditions with a plant capacity factor of 50 percent for 10 yr. The EPR operates in a pulsed mode at a frequency of approximately 1/min, with approximately 75 percent duty cycle, is capable of producing approximately 72 MWe and requires 42 MWe. The annual tritium consumption is 16 kg. The EPR vacuum chamber is 6.25 m in major radius and 2.4 m in minor radius, is constructed of 2 cm thick stainless steel, and has 2 cm thick detachable, beryllium-coated coolant panels mounted on the interior. A 0.28 m stainless steel blanket and a shield ranging from 0.6 to 1.0 m surround the vacuum vessel. The coolant is H 2 O. Sixteen niobium-titanium superconducting toroidal field coils provide a field of 10 T at the coil and 4.47 T at the plasma. Superconducting ohmic heating and equilibrium field coils provide 135 V-s to drive the plasma current. Plasma heating is accomplished by 12 neutral beam injectors which provide 60 MW. The energy transfer and storage system consists of a central superconducting storage ring, a homopolar energy storage unit, and a variety of inductor-convertors
The role of the spherical tokamak in clarifying tokamak physics
International Nuclear Information System (INIS)
Morris, A.W.; Akers, R.J.; Connor, J.W.; Counsell, G.F.; Gryaznevich, M.P.; Hender, T.C.; Maddison, G.P.; Martin, T.J.; McClements, K.G.; Roach, C.M.; Robinson, D.C.; Sykes, A.; Valovic, M.; Wilson, H.R.; Fonck, R.J.; Gusev, V.; Kaye, S.M.; Majeski, R.; Peng, Y.-K.M.; Medvedev, S.; Sharapov, S.; Walsh, M.J.
1999-01-01
The spherical tokamak (ST) provides a unique environment in which to perform complementary and exacting tests of the tokamak physics required for a burning plasma experiment of any aspect ratio, while also having the potential for long-term fusion applications in its own right. New experiments are coming on-line in the UK (MAST), USA (NSTX, Pegasus), Russia (Globus-M), Brazil (ETE) and elsewhere, and the status of these devices will be reported, along with newly-analysed data from START. Those physics issues where the ST provides an opportunity to remove degeneracy in the databases or clarify one's understanding will be emphasized. (author)
Mathematical Model for Multicomponent Adsorption Equilibria Using Only Pure Component Data
DEFF Research Database (Denmark)
Marcussen, Lis
2000-01-01
A mathematical model for nonideal adsorption equilibria in multicomponent mixtures is developed. It is applied with good results for pure substances and for prediction of strongly nonideal multicomponent equilibria using only pure component data. The model accounts for adsorbent...
Advanced tokamak burning plasma experiment
International Nuclear Information System (INIS)
Porkolab, M.; Bonoli, P.T.; Ramos, J.; Schultz, J.; Nevins, W.N.
2001-01-01
A new reduced size ITER-RC superconducting tokamak concept is proposed with the goals of studying burn physics either in an inductively driven standard tokamak (ST) mode of operation, or in a quasi-steady state advanced tokamak (AT) mode sustained by non-inductive means. This is achieved by reducing the radiation shield thickness protecting the superconducting magnet by 0.34 m relative to ITER and limiting the burn mode of operation to pulse lengths as allowed by the TF coil warming up to the current sharing temperature. High gain (Q≅10) burn physics studies in a reversed shear equilibrium, sustained by RF and NB current drive techniques, may be obtained. (author)
Large aspect ratio tokamak study
International Nuclear Information System (INIS)
Reid, R.L.; Holmes, J.A.; Houlberg, W.A.; Peng, Y.K.M.; Strickler, D.J.; Brown, T.G.; Sardella, C.; Wiseman, G.W.
1979-01-01
The Large Aspect Ratio Tokamak Study (LARTS) investigated the potential for producing a viable long burn tokamak reactor through enhanced volt-second capability of the ohmic heating transformer by employing high aspect ratio designs. The plasma physics, engineering, and economic implications of high aspect ratio tokamaks were accessed in the context of extended burn operation. Plasma startup and burn parameters were addressed using a one-dimensional transport code. The pulsed electrical power requirements for the poloidal field system, which have a major impact on reactor economics, were minimized by optimizing the field in the ohmic heating coil and the wave shape of the ohmic heating discharge. A high aspect ratio reference reactor was chosen and configured
Plasma boundary phenomena in tokamaks
International Nuclear Information System (INIS)
Stangeby, P.C.
1989-06-01
The focus of this review is on processes occurring at the edge, and on the connection between boundary plasma - the scrape-off layer (SOL) and the radiating layer - and central plasma processes. Techniques used for edge diagnosis are reviewed and basic experimental information (n e and T e ) is summarized. Simple models of the SOL are summarized, and the most important effects of the boundary plasma - the influence on the fuel particles, impurities, and energy - on tokamak operation dealt with. Methods of manipulating and controlling edge conditions in tokamaks and the experimental data base for the edge during auxiliary heating of tokamaks are reviewed. Fluctuations and asymmetries at the edge are also covered. (9 tabs., 134 figs., 879 refs.)
Computational studies of tokamak plasmas
International Nuclear Information System (INIS)
Takizuka, Tomonori; Tsunematsu, Toshihide; Tokuda, Shinji
1981-02-01
Computational studies of tokamak plasmas are extensively advanced. Many computational codes have been developed by using several kinds of models, i.e., the finite element formulation of MHD equations, the time dependent multidimensional fluid model, and the particle model with the Monte-Carlo method. These codes are applied to the analyses of the equilibrium of an axisymmetric toroidal plasma (SELENE), the time evolution of the high-beta tokamak plasma (APOLLO), the low-n MHD stability (ERATO-J) and high-n ballooning mode stability (BOREAS) in the INTOR tokamak, the nonlinear MHD stability, such as the positional instability (AEOLUS-P), resistive internal mode (AEOLUS-I) etc., and the divertor functions. (author)
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.; Aarts, D. G. A. L.; Howell, P. D.; Majumdar, A.
2017-01-01
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Hydrostatic Equilibria of Rotating Stars with Realistic Equation of State
Yasutake, Nobutoshi; Fujisawa, Kotaro; Okawa, Hirotada; Yamada, Shoichi
Stars rotate generally, but it is a non-trivial issue to obtain hydrostatic equilibria for rapidly rotating stars theoretically, especially for baroclinic cases, in which the pressure depends not only on the density, but also on the temperature and compositions. It is clear that the stellar structures with realistic equation of state are the baroclinic cases, but there are not so many studies for such equilibria. In this study, we propose two methods to obtain hydrostatic equilibria considering rotation and baroclinicity, namely the weak-solution method and the strong-solution method. The former method is based on the variational principle, which is also applied to the calculation of the inhomogeneous phases, known as the pasta structures, in crust of neutron stars. We found this method might break the balance equation locally, then introduce the strong-solution method. Note that our method is formulated in the mass coordinate, and it is hence appropriated for the stellar evolution calculations.
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.
2017-01-16
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Numerical calculation of axisymmetric non-neutral plasma equilibria
International Nuclear Information System (INIS)
Spencer, R.L.; Rasband, S.N.; Vanfleet, R.R.
1993-01-01
Efficient techniques for computing axisymmetric non-neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite-differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one-half Debye length to achieve the same accuracy
Neoclassical current effects in neutral-beam-heated tokamak discharges
International Nuclear Information System (INIS)
Hogan, J.T.
1981-01-01
There is a long-standing prediction from neoclassical theory that strong contributions to the toroidal current should be driven by friction between trapped and passing particles when βsub(pol) exceeds root (R/a) in a tokamak. A number of neutral-beam heating experiments can now produce such parameters, and it is of interest to calculate the behaviour which should occur in this regime to determine the feasibility of using such a 'bootstrap' current as a steady-state tokamak current source. It is found that the neoclassical current should be large enough to reverse the external loop voltage for typical experimental parameters (ISX-B, in particular) in cases where the total current is fixed and to produce a detectable excess of total current above the pre-programmed (demand) value in cases where the loop voltage is regulated. Other manifestations of such a current should be either: a sharp rise in the central q-value (producing a cessation of internal m=1 and m=2 MHD activity), with an enhancement by two orders of magnitude of ion thermal conductivity (due to the formation of a hollow current density profile and a consequent drop in local values of the poloidal magnetic field in the central plasma region), or an enhanced tendency for disruption (arising from magnetic reconnection in hollow-profile equilibria). Since these gross manifestations are absent in a wide range of experiments on the Impurity Study Experiment (ISX-B), as reported earlier, the conclusion is that the neoclassical current, if present, can have a value no larger than 25% of its theoretically calculated value. Since the neoclassical particle (Ware) pinch is strongly related to the neoclassical current in the theory (Onsager reciprocity), the existence of the particle pinch is thus called into question. (author)
Summary discussion: An integrated advanced tokamak reactor
International Nuclear Information System (INIS)
Sauthoff, N.R.
1994-01-01
The tokamak concept improvement workshop addressed a wide range of issues involved in the development of a more attractive tokamak. The agenda for the workshop progressed from a general discussion of the long-range energy context (with the objective being the identification of a set of criteria and ''figures of merit'' for measuring the attractiveness of a tokamak concept) to particular opportunities for the improvement of the tokamak concept. The discussions concluded with a compilation of research program elements leading to an improved tokamak concept
STARFIRE: a commercial tokamak reactor
International Nuclear Information System (INIS)
1979-12-01
The purpose of this document is to provide an interim status report on the STARFIRE project for the period of May to September 1979. The basic objective of the STARFIRE project is to develop a design concept for a commercial tokamak fusion electric power plant based on the deuterium/tritium/lithium fuel cycle. The key technical objective is to develop the best embodiment of the tokamak as a power reactor consistent with credible engineering solutions to design problems. Another key goal of the project is to give careful attention to the safety and environmental features of a commercial fusion reactor
LHCD experiments on tokamak CASTOR
International Nuclear Information System (INIS)
Zacek, F.; Badalec, J.; Jakubka, J.; Kryska, L.; Preinhaelter, J.; Stoeckel, J.; Valovic, M.; Nanobashvili, S.; Weixelbaum, L.; Wenzel, U.; Spineanu, F.; Vlad, M.
1990-10-01
A short survey is given of the experimental activities at the small Prague tokamak CASTOR. They concern primarily the LH current drive using multijunction waveguide grills as launching antennae. During two last years the, efforts were focused on a study of the electrostatic and magnetic fluctuations under conditions of combined inductive/LHCD regimes and of the relation of the level of these fluctuations to the anomalous particles transport in tokamak CASTOR. Results of the study are discussed in some detail. (author). 24 figs., 51 refs
Wheatley, Vincent; Bond, Daryl; Li, Yuan; Samtaney, Ravi; Pullin, Dale
2017-11-01
The Richtmyer-Meshkov instability (RMI) of a shock accelerated perturbed density interface is important in both inertial confinement fusion and astrophysics, where the materials involved are typically in the plasma state. Initial density interfaces can be due to either temperature or ion-species discontinuities. If the Atwood number of the interfaces and specific heat ratios of the fluids are matched, these two cases behave similarly when modeled using the equations of either hydrodynamics or magnetohydrodynamics. In the two-fluid ion-electron plasma model, however, there is a significant difference between them: In the thermal interface case, there is a discontinuity in electron density that is also subject to the RMI, while for the ion-species interface case there is not. It will be shown via ideal two-fluid plasma simulations that this causes substantial differences in the dynamics of the flow between the two cases. This work was partially supported by the KAUST Office of Sponsored Research under Award URF/1/2162-01.
International Nuclear Information System (INIS)
Mirnov, V.V.
2002-01-01
Large-scale tearing instabilities have long been considered to underlie transport and dynamo processes in the reversed field pinch (RFP). The vast majority of theoretical and computational RFP work has focused on pressureless, single-fluid MHD in cylindrical plasmas driven solely by a toroidal electric field. We report results of five investigations covering two-fluid dynamos, toroidal nonlinear MHD computation, nonlinear computation of Oscillating Field Current Drive (OFCD), the effect of shear flow on tearing instability, and the effect of pressure on resistive instability. The key findings are: (1) two-fluid dynamo arising from the Hall term is much larger than the standard MHD dynamo present in a single-fluid treatment, (2) geometric coupling from toroidicity precludes the occurrence of laminar single helicity states, except for nonreversed plasmas, (3) OFCD, a form of AC helicity injection, can sustain the RFP plasma current, although magnetic fluctuations are enhanced, (4) edge shear flow can destabilize the edge resonant m=0 modes, which occur as spikes in experiment, and (5) pressure driven modes are resistive at low beta, only becoming ideal at extremely high beta. (author)
Miranda, Jose; Brandao, Rodolfo
2017-11-01
We study a family of generalized elastica-like equilibrium shapes that arise at the interface separating two fluids in a curved rotating Hele-Shaw cell. This family of stationary interface solutions consists of shapes that balance the competing capillary and centrifugal forces in such a curved flow environment. We investigate how the emerging interfacial patterns are impacted by changes in the geometric properties of the curved Hele-Shaw cell. A vortex-sheet formalism is used to calculate the two-fluid interface curvature, and a gallery of possible shapes is provided to highlight a number of peculiar morphological features. A linear perturbation theory is employed to show that the most prominent aspects of these complex stationary patterns can be fairly well reproduced by the interplay of just two interfacial modes. The connection of these dominant modes to the geometry of the curved cell, as well as to the fluid dynamic properties of the flow, is discussed. We thank CNPq (Brazilian Research Council) for financial support under Grant No. 304821/2015-2.
Energy Technology Data Exchange (ETDEWEB)
Cachard, F. de [Laboratory for Thermal Hydraulics, Villigen (Switzerland)
1995-09-01
Inverted-Annular Film-Boiling (IAFB) is one of the post-burnout heat transfer modes taking place during the reflooding phase of the loss-of-coolant accident, when the liquid at the quench front is subcooled. Under IAFB conditions, a continuous, liquid core is separated from the wall by a superheated vapour film. the heat transfer rate in IAFB is influenced by the flooding rate, liquid subcooling, pressure, and the wall geometry and temperature. These influences can be accounted by a two-fluid model with physically sound closure laws for mass, momentum and heat transfers between the wall, the vapour film, the vapour-liquid interface, and the liquid core. Such closure laws have been developed and adjusted using IAFB-relevant experimental results, including heat flux, wall temperature and void fraction data. The model is extensively assessed against data from three independent sources. A total of 46 experiments have been analyzed. The overall predictions are good. The IAFB-specific closure laws proposed have also intrinsic value, and may be used in other two-fluid models. They should allow to improve the description of post-dryout, low quality heat transfer by the safety codes.
Nash Equilibria in Symmetric Graph Games with Partial Observation
DEFF Research Database (Denmark)
Bouyer, Patricia; Markey, Nicolas; Vester, Steen
2017-01-01
We investigate a model for representing large multiplayer games, which satisfy strong symmetry properties. This model is made of multiple copies of an arena; each player plays in his own arena, and can partially observe what the other players do. Therefore, this game has partial information...... and symmetry constraints, which make the computation of Nash equilibria difficult. We show several undecidability results, and for bounded-memory strategies, we precisely characterize the complexity of computing pure Nash equilibria for qualitative objectives in this game model....
Nash Equilibria in Symmetric Games with Partial Observation
DEFF Research Database (Denmark)
Bouyer, Patricia; Markey, Nicolas; Vester, Steen
2014-01-01
We investigate a model for representing large multiplayer games, which satisfy strong symmetry properties. This model is made of multiple copies of an arena; each player plays in his own arena, and can partially observe what the other players do. Therefore, this game has partial information...... and symmetry constraints, which make the computation of Nash equilibria difficult. We show several undecidability results, and for bounded-memory strategies, we precisely characterize the complexity of computing pure Nash equilibria (for qualitative objectives) in this game model....
Recent progress in the relative equilibria of point vortices — In memoriam Hassan Aref
DEFF Research Database (Denmark)
Beelen, Peter; Brøns, Morten; Krishnamurthy, Vikas S.
2013-01-01
Hassan Aref, who sadly passed away in 2011, was one of the world's leading researchers in the dynamics and equilibria of point vortices. We review two problems on the subject of point vortex relative equilibria in which he was engaged at the time of his death: bilinear relative equilibria...
International Nuclear Information System (INIS)
Kelly, J.L.; Rose, R.P.
1981-01-01
At a time when the potential benefits of various energy options are being seriously evaluated in many countries through-out the world, it is both timely and important to evaluate the practical application of fusion reactors for their economical production of nuclear fissile fuels from fertile fuels. The fusion hybrid reactor represents a concept that could assure the availability of adequate fuel supplies for a proven nuclear technology and have the potential of being an electrical energy source as opposed to an energy consumer as are the present fuel enrichment processes. Westinghouse Fusion Power Systems Department, under Contract No. EG-77-C-02-4544 with the Department of Energy, Office of Fusion Energy, has developed a preliminary conceptual design for an early twenty-first century fusion hybrid reactor called the commercial Tokamak Hybrid Reactor (CTHR). This design was developed as a first generation commercial plant producing fissile fuel to support a significant number of client Light Water Reactor (LWR) Plants. To the depth this study has been performed, no insurmountable technical problems have been identified. The study has provided a basis for reasonable cost estimates of the hybrid plants as well as the hybrid/LWR system busbar electricity costs. This energy system can be optimized to have a net cost of busbar electricity that is equivalent to the conventional LWR plant, yet is not dependent on uranium ore prices or standard enrichment costs, since the fusion hybrid can be fueled by numerous fertile fuel resources. A nearer-term concept is also defined using a beam driven fusion driver in lieu of the longer term ignited operating mode. (orig.)
Tokamak Plasmas : Mirnov coil data analysis for tokamak ADITYA
Indian Academy of Sciences (India)
The spatial and temporal structures of magnetic signal in the tokamak ADITYA is analysed using recently developed singular value decomposition (SVD) technique. The analysis technique is ﬁrst tested with simulated data and then applied to the ADITYA Mirnov coil data to determine the structure of current peturbation as ...
DEFF Research Database (Denmark)
Krøll, Annette Elisabeth; Marcussen, Lis
1997-01-01
An equilibrium equation for pure component adsorption is compared to experiments and to the vacancy solution theory. The investigated equilibrium equation is a special case of a model for prediction of multicomponent adsorption equilibria.The vacancy solution theory for multicomponent systems...... requires binary experimental data for determining the interaction parameters of the Wilson equation; thus a large number of experiments are needed. The multicomponent equilibria model which is investigated for single component systems in this work is based on pure component data only. This means...... that the requirement for experimental data is reduced significantly.The two adsorption models are compared, using experimental pure gas adsorption data found in literature. The results obtained by the models are in close agreement for pure component equilibria and they give a good description of the experimental data...
Energy Technology Data Exchange (ETDEWEB)
Guillemaud, V
2007-03-15
This thesis is devoted to the modelling and numerical simulation of liquid-vapor flows. In order to describe these phase transition flows, a two-fluid two-pressure approach is considered. This description of the liquid-vapor mixing is associated to the seven-equation model introduced by Baer and Nunziato. This work investigates the properties of this model in order to simulate the phase transition flows occurring in nuclear engineering. First, a theoretical thermodynamic framework is constructed to describe the liquid-vapor mixing. Provided with this framework, various modelling choices are suggested for the interaction terms between the phases. These closure laws comply with an entropy inequality. The mathematical properties of this model are thereafter examined. The convective part is associated to a nonconservative hyperbolic system. First, we focus on the definition of its weak solutions. Several flow regimes for the two-phase mixing derive from this analysis. Such regimes for the two-phase flows are analogous to the torrential and fluvial regimes for the shallow-water equations. Furthermore, we establish the linear and nonlinear stabilities of the liquid-vapor equilibrium. Finally, the implementation of a turbulence model and the introduction of a reconstruction process for the interfacial area are investigated in order to refine the description of the interfacial transfers. Using a fractional step approach, a Finite Volume method is at last constructed to simulate this model. First, various nonconservative adaptations of standard Riemann solvers are developed to approach the convective part. Unlike the classic nonconservative framework, these schemes converge towards the same solution. Furthermore, a new relaxation scheme is proposed to approach the interfacial transfers. Provided with these schemes, the whole numerical method preserves the liquid-vapor equilibria. Using this numerical method, a careful comparison between the one- and two-pressure two-fluid
Energy losses on tokamak startup
International Nuclear Information System (INIS)
Murray, J.G.; Rothe, K.E.; Bronner, G.
1983-01-01
During the startup of a tokamak reactor using poloidal field (PF) coils to induce plasma currents, the conducting structures carry induced currents. The associated energy losses in the circuits must be provided by the startup coils and the PF system. This paper provides quantitative and comparitive values for the energies required as a function of the thickness or resistivity of the torus shells
Prospects for Tokamak Fusion Reactors
International Nuclear Information System (INIS)
Sheffield, J.; Galambos, J.
1995-01-01
This paper first reviews briefly the status and plans for research in magnetic fusion energy and discusses the prospects for the tokamak magnetic configuration to be the basis for a fusion power plant. Good progress has been made in achieving fusion reactor-level, deuterium-tritium (D-T) plasmas with the production of significant fusion power in the Joint European Torus (up to 2 MW) and the Tokamak Fusion Test Reactor (up to 10 MW) tokamaks. Advances on the technologies of heating, fueling, diagnostics, and materials supported these achievements. The successes have led to the initiation of the design phases of two tokamaks, the International Thermonuclear Experimental Reactor (ITER) and the US Toroidal Physics Experiment (TPX). ITER will demonstrate the controlled ignition and extended bum of D-T plasmas with steady state as an ultimate goal. ITER will further demonstrate technologies essential to a power plant in an integrated system and perform integrated testing of the high heat flux and nuclear components required to use fusion energy for practical purposes. TPX will complement ITER by testing advanced modes of steady-state plasma operation that, coupled with the developments in ITER, will lead to an optimized demonstration power plant
Integral torque balance in tokamaks
International Nuclear Information System (INIS)
Pustovitov, V.D.
2011-01-01
The study is aimed at clarifying the balance between the sinks and sources in the problem of intrinsic plasma rotation in tokamaks reviewed recently by deGrassie (2009 Plasma Phys. Control. Fusion 51 124047). The integral torque on the toroidal plasma is calculated analytically using the most general magnetohydrodynamic (MHD) plasma model taking account of plasma anisotropy and viscosity. The contributions due to several mechanisms are separated and compared. It is shown that some of them, though, possibly, important in establishing the rotation velocity profile in the plasma, may give small input into the integral torque, but an important contribution can come from the magnetic field breaking the axial symmetry of the configuration. In tokamaks, this can be the error field, the toroidal field ripple or the magnetic perturbation created by the correction coils in the dedicated experiments. The estimates for the error-field-induced electromagnetic torque show that the amplitude of this torque is comparable to the typical values of torques introduced into the plasma by neutral beam injection. The obtained relations allow us to quantify the effect that can be produced by the existing correction coils in tokamaks on the plasma rotation, which can be used in experiments to study the origin and physics of intrinsic rotation in tokamaks. Several problems are proposed for theoretical studies and experimental tests.
ECRH Studies on Tokamak Plasmas.
1980-10-10
r.I*cru.Dtrtibution uUnliited 300 Unicorn Pork Drive Woburn, Massachusetts 04801 ECRH STUDIES ON TOKAMAK PLASMAS JAYCOR Project No. 6183 Final Report...up techniques now in use or being suggested, include growing the plasma from a small minor radius or applying a negative voltage spike immediately
Tokamak and RFP ignition requirements
International Nuclear Information System (INIS)
Werley, K.A.
1991-01-01
A plasma model is applied to calculate numerically transport- confinement (nτ E ) requirements and steady-state operation tokamak. The CIT tokamak and RFP ignition conditions are examined. Physics differences between RFP and tokamaks, and their consequences for a DT ignition machine, are discussed. The ignition RFP, compared to a tokamak, has many physics advantages, including ohmic heating to ignition (no need for auxiliary heating systems), higher beta, low ignition current, less sensitivity of ignition requirements to impurity effects, no hard disruptions (associated with beta or density limits), and successful operation with high radiation fractions (f RAD ∼ 0.95). These physics advantages, coupled with important engineering advantages associated with lower external magnetic fields, larger aspect ratios, and smaller plasma cross sections translate into significant cost reductions for both ignition and power reactor. The primary drawback of the RFP is the uncertainty that the present confinement scaling will extrapolate to reactor regimes. The 4-MA ZTH was expected to extend the nτ E transport scaling data three order of magnitude above ZT-40M results, and if the present scaling held, to achieve a DT-equivalent scientific energy breakeven, Q=1. A basecase RFP ignition point is identified with a plasma current of 8.1 MA and no auxiliary heating. 16 refs., 4 figs., 1 tab
Tokamak impurity-control techniques
International Nuclear Information System (INIS)
Schmidt, J.A.
1980-01-01
A brief review is given of the impurity-control functions in tokamaks, their relative merits and disadvantages and some prominent edge-interaction-control techniques, and there is a discussion of a new proposal, the particle scraper, and its potential advantages. (author)
An enhanced tokamak startup model
Goswami, Rajiv; Artaud, Jean-François
2017-01-01
The startup of tokamaks has been examined in the past in varying degree of detail. This phase typically involves the burnthrough of impurities and the subsequent rampup of plasma current. A zero-dimensional (0D) model is most widely used where the time evolution of volume averaged quantities determines the detailed balance between the input and loss of particle and power. But, being a 0D setup, these studies do not take into consideration the co-evolution of plasma size and shape, and instead assume an unchanging minor and major radius. However, it is known that the plasma position and its minor radius can change appreciably as the plasma evolves in time to fill in the entire available volume. In this paper, an enhanced model for the tokamak startup is introduced, which for the first time takes into account the evolution of plasma geometry during this brief but highly dynamic period by including realistic one-dimensional (1D) effects within the broad 0D framework. In addition the effect of runaway electrons (REs) has also been incorporated. The paper demonstrates that the inclusion of plasma cross section evolution in conjunction with REs plays an important role in the formation and development of tokamak startup. The model is benchmarked against experimental results from ADITYA tokamak.
Multimegawatt neutral beams for tokamaks
International Nuclear Information System (INIS)
Kunkel, W.B.
1979-03-01
Most of the large magnetic confinement experiments today and in the near future use high-power neutral-beam injectors to heat the plasma. This review briefly describes this remarkable technique and summarizes recent results as well as near term expectations. Progress has been so encouraging that it seems probable that tokamaks will achieve scientific breakeven before 1990
Joint research using small tokamaks
Czech Academy of Sciences Publication Activity Database
Gryaznevich, M.P.; Del Bosco, E.; Malaquias, A.; Mank, G.; Van Oost, G.; He, Yexi; Hegazy, H.; Hirose, A.; Hron, Martin; Kuteev, B.; Ludwig, G.O.; Nascimento, I.C.; Silva, C.; Vorobyev, G.M.
2005-01-01
Roč. 45, č. 10 (2005), S245-S254 ISSN 0029-5515. [Fusion Energy Conference contributions. Vilamoura, 1.11.2004-6.11.2004] Institutional research plan: CEZ:AV0Z20430508 Keywords : small tokamaks * thermonuclear fusion Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.418, year: 2005
Stochastic Equilibria under Imprecise Deviations in Terminal-Reward Concurrent Games
Directory of Open Access Journals (Sweden)
Patricia Bouyer
2016-09-01
Full Text Available We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward objectives, and their existence is undecidable with qualitative reachability objectives (and only three players. However, these results rely on the fact that the players can enforce infinite plays while trying to improve their payoffs. In this paper, we introduce a relaxed notion of equilibria, where deviations are imprecise. We prove that contrary to Nash equilibria, such (stationary equilibria always exist, and we develop a PSPACE algorithm to compute one.
Stability of equilibria for a two-phase osmosis model
Lippoth, F.; Prokert, G.
2012-01-01
For a two-phase moving boundary problem modelling the motion of a semipermeable membrane by osmotic pressure and surface tension, we prove that the manifold of equilibria is locally exponentially attractive. Our method relies on maximal regularity results for parabolic systems with relaxation type
A Numerical Algorithm to find All Scalar Feedback Nash Equilibria
Engwerda, J.C.
2013-01-01
Abstract: In this note we generalize a numerical algorithm presented in [9] to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is based on
Computing Proper Equilibria of Zero-Sum Games
DEFF Research Database (Denmark)
Miltersen, Peter Bro; Sørensen, Troels Bjerre
2007-01-01
We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a linear (in the number of pure strategies of the two players) number of linear programs of roughly the same dimensions as the standard linear programs describing the Nash equilibria of the game....
Shallow-water vortex equilibria and their stability
Energy Technology Data Exchange (ETDEWEB)
Plotka, H; Dritschel, D G, E-mail: hanna@mcs.st-andrews.ac.uk, E-mail: dgd@mcs.st-andrews.ac.uk [School of Mathematics and Statistics, University of St Andrews, North Haugh, St. Andrews KY16 9SS (United Kingdom)
2011-12-22
We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L{sub D} called the 'Rossby deformation length' relating the strength of stratification to that of the background rotation rate. Specifically, L{sub D} = c/f where c={radical}gH is a characteristic gravity-wave speed, g is gravity (or 'reduced' gravity in a two-layer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallow-water model to generate what we call 'quasi-equilibria'. These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
Asset pricing puzzles explained by incomplete Brownian equilibria
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
Predicting phase equilibria in one-component systems
Korchuganova, M. R.; Esina, Z. N.
2015-07-01
It is shown that Simon equation coefficients for n-alkanes and n-alcohols can be modeled using critical and triple point parameters. Predictions of the phase liquid-vapor, solid-vapor, and liquid-solid equilibria in one-component systems are based on the Clausius-Clapeyron relation, Van der Waals and Simon equations, and the principle of thermodynamic similarity.
Field line diversion properties of finite β Helias equilibria
International Nuclear Information System (INIS)
Hayashi, T.; Schwenn, U.; Strumberger, E.
1992-03-01
The diversion properties of the magnetic field outside the last closed magnetic surface of a Helias stellarator configuration are investigated for finite β-equilibria. The results support a divertor concept which has been developed from the diversion properties of the corresponding vacuum field. Cross-field transport is simulated by a simplified scrape-off layer (SOL) model. (author)
From Singularity Theory to Finiteness of Walrasian Equilibria
DEFF Research Database (Denmark)
Castro, Sofia B.S.D.; Dakhlia, Sami F.; Gothen, Peter
The paper establishes that for an open and dense subset of smooth exchange economies, the number of Walrasian equilibria is finite. In particular, our results extend to non-regular economies; it even holds when restricted to the subset of critical ones. The proof rests on concepts from singularity...... theory....
Close pairs of relative equilibria for identical point vortices
DEFF Research Database (Denmark)
Dirksen, Tobias; Aref, Hassan
2011-01-01
Numerical solution of the classical problem of relative equilibria for identical point vortices on the unbounded plane reveals configurations that are very close to the analytically known, centered, symmetrically arranged, nested equilateral triangles. New numerical solutions of this kind are fou...
Cryptographically Blinded Games: Leveraging Players' Limitations for Equilibria and Profit
DEFF Research Database (Denmark)
Hubacek, Pavel; Park, Sunoo
2014-01-01
In this work we apply methods from cryptography to enable mutually distrusting players to implement broad classes of mediated equilibria of strategic games without trusted mediation. Our implementation uses a pre-play 'cheap talk' phase, consisting of non- binding communication between players...
International Nuclear Information System (INIS)
Connor, J.W.; Helander, P.; Thyagaraja, A.; Andersson, F.; Fueloep, T.; Eriksson, L.-G.; Romanelli, M.
2001-01-01
This paper summarises a number of distinct, but related, pieces of work on key confinement issues for tokamaks, in particular the formation of internal and edge transport barriers, both within turbulent and neoclassical models, and radial diffusion of avalanching runaway electrons. First-principle simulations of tokamak turbulence and transport using the two-fluid, electromagnetic, global code CUTIE are described. The code has demonstrated the spontaneous formation of internal transport barriers near mode rational surfaces, in qualitative agreement with observations on JET and RTP. The theory of neoclassical transport in an impure, toroidal plasma has been extended to allow for steeper pressure and temperature gradients than are usually considered, and is then found to become nonlinear under conditions typical of the tokamak edge. For instance, the particle flux is found to be a nonmonotonic function of the gradients, thus allowing for a bifurcation in the ion particle flux. Finally, it is shown that radial diffusion caused by magnetic fluctuations can effectively suppress avalanches of runaway electrons if the fluctuation amplitude exceeds δB/B∼10 -3 . (author)
Directory of Open Access Journals (Sweden)
Haixu Liu
2016-01-01
Full Text Available A pure two-fluid model was used for investigating transverse liquid jet to a supersonic crossflow. The well-posedness problem of the droplet phase governing equations was solved by applying an equation of state in the kinetic theory. A k-ε-kp turbulence model was used to simulate the turbulent compressible multiphase flow. Separation of boundary layer in front of the liquid jet was predicted with a separation shock induced. A bow shock was found to interact with the separation shock in the simulation result, and the adjustment of shock structure caused by the interaction described the whipping phenomena. The predicted penetration height showed good agreement with the empirical correlations. In addition, the turbulent kinetic energies of both the gas and droplet phases were presented for comparison, and effects of the jet-to-air momentum flux ratio and droplet diameter on the penetration height were also examined in this work.
Energy Technology Data Exchange (ETDEWEB)
Ninokata, H. [Tokyo Institute of Technology (Japan); Deguchi, A. [ENO Mathematical Analysis, Tokyo (Japan); Kawahara, A. [Kumamoto Univ., Kumamoto (Japan)
1995-09-01
A new void drift model for the subchannel analysis method is presented for the thermohydraulics calculation of two-phase flows in rod bundles where the flow model uses a two-fluid formulation for the conservation of mass, momentum and energy. A void drift model is constructed based on the experimental data obtained in a geometrically simple inter-connected two circular channel test sections using air-water as working fluids. The void drift force is assumed to be an origin of void drift velocity components of the two-phase cross-flow in a gap area between two adjacent rods and to overcome the momentum exchanges at the phase interface and wall-fluid interface. This void drift force is implemented in the cross flow momentum equations. Computational results have been successfully compared to experimental data available including 3x3 rod bundle data.
International Nuclear Information System (INIS)
Neves Conti, T. das.
1983-01-01
A numerical method is developed to simulate adiabatic, transient, two-dimensional two-phase flow. The two-fluid model is used to obtain the mass and momentum conservation equations. These are solved by an iterative algorithm emphoying a time-marching scheme. Based on the corrective procedure of Hirt and Harlow a poisson equation is derived for the pressure field. This equation is finite-differenced and solved by a suitable matrix inversion technique. In the absence of experiment results several numerical tests were made in order to chec accuracy, convergence and stability of the proposed method. Several tests were also performed to check whether the behavior of void fraction and phasic velocities conforms with previous observations. (Author) [pt
Quantum mechanical description of the two fluid model of liquid /sup 4/He solving the Bloch equation
International Nuclear Information System (INIS)
Fung, P.C.W.; Lam, C.C.
1986-01-01
The authors apply the U-matrix theory recently developed (Lam and Fung, Phys. Rev. A, vol.27, p.1760, 1983) to study certain physical properties of liquid /sup 4/He across a range of temperatures including the lambda -point. They propose a model for the chemical potential mu which is constant above T/sub lambda / but is a function of T below T/sub lambda /. They have discovered that the super-particles 'emerge' mathematically due to the uncommutability of the Hamiltonians at different temperatures, leading to a quantum mechanical description of the two-fluid model. Using the two-particle potential function deduced from scattering data, they have calculated numerically the approximate values of the number density for a range of temperatures starting from T/sub lambda /, taking the hard-core diameter Delta , 'effective chemical potential' mu ' as parameters
DEFF Research Database (Denmark)
Olesen, Anders Christian; Berning, Torsten; Kær, Søren Knudsen
2012-01-01
A fully coupled three-dimensional, steady-state, two-fluid, multi-component and non-isothermal DMFC model has been developed in the commercial CFD package CFX 13 (ANSYS inc.). It accounts for the presence of micro porous layers, non-equilibrium phase change, and methanol and water uptake...... in the ionomer phase of the catalytic layer, and detailed membrane transport of methanol and water. In order to verify the models ability to predict methanol crossover, simulation results are compared with experimental measurements under different current densities along with air and methanol stoichiometries....... Methanol crossover is indirectly measured based on the combined anode and cathode exhaust CO2 mole fraction and by accounting for the CO2 production at the anode as a function of current density. This approach is simple and assumes that all crossed over methanol is oxidized. Moreover, it takes CO2...
International Nuclear Information System (INIS)
Kataoka, Isao; Tomiyama, Akio
2004-01-01
The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill
Advanced statistics for tokamak transport colinearity and tokamak to tokamak variation
International Nuclear Information System (INIS)
Riedel, K.S.
1989-01-01
This paper is an expository introduction to advanced statistics and scaling laws and their application to tokamak devices. Topics of discussion are as follows: implicit assumptions in the standard analysis; advanced regression techniques; specialized tools in statistics and their applications in fusion physics; and improved datasets for transport studies
On Nash-Equilibria of Approximation-Stable Games
Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh
One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.
Resistive toroidal stability of internal kink modes in circular and shaped tokamaks
International Nuclear Information System (INIS)
Bondeson, A.; Luetjens, H.; Vlad, G.
1991-12-01
The linear resistive magnetohydrodynamical (MHD) stability of the n=1 internal kink mode in tokamaks is studied by toroidal computations. The stabilizing influence of small aspect ratio is confirmed, but it is found that shaping of the cross section influences the internal kink mode significantly. For finite pressure and small resistivity, curvature effects at the q=1 surface make the stability sensitively dependent on shape, and ellipticity (including JET shape) is destabilizing. Only a very restricted set of finite pressure equilibria is completely stable for q 0 <1. A typical result is that the resistive kink mode is slowed down by toroidal effects to a weak tearing/resistive interchange mode. It is suggested that weak resistive instabilities are stabilized during the ramp phase of the sawteeth by effects not included in the linear resistive MHD model. Possible mechanisms for triggering a sawtooth crash are discussed. (author) 18 figs., 34 refs
Stability analysis of internal ideal modes in low-shear tokamaks
International Nuclear Information System (INIS)
Wahlberg, C.; Graves, J. P.
2007-01-01
The stability of internal, ideal modes in tokamaks with low magnetic shear in the plasma core is analyzed. For equilibria with large aspect ratio, a parabolic pressure profile and a flat q profile in the core, an exact solution of the ideal magnetohydrodynamic (MHD) stability equations is found. The solution includes the eigenfunctions and the complete spectra of two distinctly different MHD phenomena: A family of fast-growing, Mercier-unstable global eigenmodes localized in a low-shear region with q 1 in the core. In the latter case the solution in addition includes one unstable eigenmode, if beta is larger than a critical value depending on the width of the low-shear region and on the q-profile in the edge region
Radial effects in heating and thermal stability of a sub-ignited tokamak
International Nuclear Information System (INIS)
Fuchs, V.; Shoucri, M.M.; Thibaudeau, G.; Harten, L.; Bers, A.
1982-02-01
The existence of thermally stable sub-ignited equilibria of a tokamak reactor, sustained in operation by a feedback-controlled supplementary heating source, is demonstrated. The establishment of stability depends on a number of radially non-uniform, nonlinear processes whose effect is analyzed. One-dimensional (radial) stability analyses of model transport equations, together with numerical results from a 1-D transport code, are used in studying the heating of DT-plasmas in the thermonuclear regime. Plasma core supplementary heating is found to be a thermally more stable process than bulk heating. In the presence of impurity line radiation, however, core-heated temperature profiles may collapse, contracting inward from the limiter, the result of an instability caused by the increasing nature of the radiative cooling rate, with decreasing temperature. Conditions are established for the realization of a sub-ignited high-Q, toroidal reactor plasma with appreciable output power
Measurement of high-beta tokamak pressure profiles with multipoint Thomson scattering
International Nuclear Information System (INIS)
Levinton, F.M.
1983-01-01
A multipoint Thomson-scattering system has been developed to obtain pressure profiles along the major radius of Torus II, a high-beta tokamak. The profiles obtained during the 20 to 25 μs lifetime of the discharge indicates that the plasma has a peak temperature of 80 eV and density of 1.0 x 10 15 cm - 3 . The profiles remain fairly constant during this time until the equilibrium is lost, after which the temperature and density decays to 10 eV and 10 14 cm - 3 very quickly (approx. 1 μs). Experimental results show Torus II has a high-beta ( approx. 10%) equilibrium, with a strong shift of the peak of the pressure profile towards the outside. Numerical results from a 2-D free boundary MHD equilibrium code have obtained equilibria which closely approximate the experimentally measured profiles
Aspect Ratio Scaling of Ideal No-wall Stability Limits in High Bootstrap Fraction Tokamak Plasmas
International Nuclear Information System (INIS)
Menard, J.E.; Bell, M.G.; Bell, R.E.; Gates, D.A.; Kaye, S.M.; LeBlanc, B.P.; Maingi, R.; Sabbagh, S.A.; Soukhanovskii, V.; Stutman, D.
2003-01-01
Recent experiments in the low aspect ratio National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40 (2000) 557] have achieved normalized beta values twice the conventional tokamak limit at low internal inductance and with significant bootstrap current. These experimental results have motivated a computational re-examination of the plasma aspect ratio dependence of ideal no-wall magnetohydrodynamic stability limits. These calculations find that the profile-optimized no-wall stability limit in high bootstrap fraction regimes is well described by a nearly aspect ratio invariant normalized beta parameter utilizing the total magnetic field energy density inside the plasma. However, the scaling of normalized beta with internal inductance is found to be strongly aspect ratio dependent at sufficiently low aspect ratio. These calculations and detailed stability analyses of experimental equilibria indicate that the nonrotating plasma no-wall stability limit has been exceeded by as much as 30% in NSTX in a high bootstrap fraction regime
Microwave Tokamak Experiment: Overview and status
International Nuclear Information System (INIS)
1990-05-01
The Microwave Tokamak Experiment, now under construction at the Laboratory, will use microwave heating from a free-electron laser. The intense microwave pulses will be injected into the tokamak to realize several goals, including a demonstration of the effects of localized heat deposition within magnetically confined plasma, a better understanding of energy confinement in tokamaks, and use of the new free-electron laser technology for plasma heating. 3 figs., 3 tabs
Combined confinement system applied to tokamaks
International Nuclear Information System (INIS)
Ohkawa, Tihiro
1986-01-01
From particle orbit point of view, a tokamak is a combined confinement configuration where a closed toroidal volume is surrounded by an open confinement system like a magnetic mirror. By eliminating a cold halo plasma, the energy loss from the plasma becomes convective. The H-mode in diverted tokamaks is an example. Because of the favorable scaling of the energy confinement time with temperature, the performance of the tokamak may be significantly improved by taking advantage of this effect. (author)
Presheath profiles in simulated tokamak edge plasmas
International Nuclear Information System (INIS)
LaBombard, B.; Conn, R.W.; Hirooka, Y.; Lehmer, R.; Leung, W.K.; Nygren, R.E.; Ra, Y.; Tynan, G.
1988-04-01
The PISCES plasma surface interaction facility at UCLA generates plasmas with characteristics similar to those found in the edge plasmas of tokamaks. Steady state magnetized plasmas produced by this device are used to study plasma-wall interaction phenomena which are relevant to tokamak devices. We report here progress on some detailed investigations of the presheath region that extends from a wall surface into these /open quotes/simulated tokamak/close quotes/ edge plasma discharges along magnetic field lines
High poloidal beta equilibria in TFTR limited by a natural inboard poloidal field null
International Nuclear Information System (INIS)
Sabbagh, S.A.; Gross, R.A.; Mauel, M.E.; Navratil, G.A.; Bell, M.G.; Bell, R.; Bitter, M.; Bretz, N.L.; Budny, R.V.; Bush, C.E.; Chance, M.S.; Efthimion, P.C.; Fredrickson, E.D.; Hatcher, R.; Hawryluk, R.J.; Hirshman, S.P.; Janos, A.C.; Jardin, S.C.; Jassby, D.L.; Manickam, J.; McCune, D.C.; McGuire, K.M.; Medley, S.S.; Mueller, D.; Nagayama, Y.; Owens, D.K.; Okabayashi, M.; Park, H.K.; Ramsey, A.T.; Stratton, B.C.; Synakowski, E.J.; Taylor, G.; Wieland, R.M.; Zarnstorff, M.C.; Kesner, J.; Marmar, E.S.; Terry, J.L.
1991-07-01
Recent operation of the Tokamak Fusion Test Reactor TFTR, has produced plasma equilibria with values of Λ triple-bond β p eq + l i /2 as large as 7, εβ p dia triple-bond 2μ 0 ε /much-lt B p much-gt 2 as large as 1.6, and Troyon normalized diamagnetic beta, β N dia triple-bond 10 8 t perpendicular>aB 0 /I p as large as 4.7. When εβ p dia approx-gt 1.25, a separatrix entered the vacuum chamber, producing a naturally diverted discharge which was sustained for many energy confinement times, τ E . The largest values of εβ p and plasma stored energy were obtained when the plasma current was ramped down prior to neutral beam injection. The measured peak ion and electron temperatures were as large as 24 keV and 8.5 keV, respectively. Plasma stored energy in excess of 2.5 MJ and τ E greater than 130 msec were obtained. Confinement times of greater than 3 times that expected from L-mode predictions have been achieved. The fusion power gain. Q DD , reached a values of 1.3 x 10 -3 in a discharge with I p = 1 MA and εβ p dia = 0.85. A large, sustained negative loop voltage during the steady state portion of the discharge indicates that a substantial non-inductive component of I p exists in these plasmas. Transport code analysis indicates that the bootstrap current constitutes up to 65% of I p . Magnetohydrodynamic (MHD) ballooning stability analysis shows that while these plasmas are near, or at the β p limit, the pressure gradient in the plasma core is in the first region of stability to high-n modes. 24 refs., 10 figs
International Nuclear Information System (INIS)
Throumoulopoulos, G.N.; Tasso, H.
2003-01-01
The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η (parallel) and η (perpendicular) parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η (parallel) (ψ) or η (perpendicular) (ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η (parallel) and η (perpendicular) profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η (perpendicular) >η (parallel) . For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI 2 /dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η (perpendicular) -η (parallel) for the reversed-field pinch scaling, B p ≅B t , is nearly two times larger than that for the tokamak scaling, B p ≅0.1B t (B p and B t are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of - but not inconsistent with - Pfirsch-Schlueter diffusion, indicate that
Throumoulopoulos, G. N.; Tasso, H.
2003-06-01
The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η∥ and η⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η∥(ψ) or η⊥(ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η∥ and η⊥ profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η⊥>η∥. For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI2/dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η⊥-η∥ for the reversed-field pinch scaling, Bp≈Bt, is nearly two times larger than that for the tokamak scaling, Bp≈0.1Bt (Bp and Bt are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of—but not inconsistent with—Pfirsch-Schlüter diffusion, indicate that parallel flows might result in a reduction of the diffusion observed in magnetically confined plasmas.
Improvement of the tokamak concept
Energy Technology Data Exchange (ETDEWEB)
Laurent, L
1994-12-31
Improvement of the tokamak concept is highly desirable to reduce the size and capital cost of a device able to ignite to increase the plasma pressure, i.e. the power density to reduce the cost of electricity, and to increase the fraction of bootstrap current to render the tokamak compatible with continuous operation. The most important results obtained in this field are summarized, and the options are shown which are still open and explored by the various experiments. Various effects of the plasma shaping are discussed, plasma configurations with both high {beta}{sub N} and H{sub G} are explored, and the issues of stable steady state and of the plasma edge are briefly discussed. (R.P.). 65 refs., 2 tabs.
Advanced commercial Tokamak optimization studies
International Nuclear Information System (INIS)
Whitley, R.H.; Berwald, D.H.; Gordon, J.D.
1985-01-01
Our recent studies have concentrated on developing optimal high beta (bean-shaped plasma) commercial tokamak configurations using TRW's Tokamak Reactor Systems Code (TRSC) with special emphasis on lower net electric power reactors that are more easily deployable. A wide range of issues were investigated in the search for the most economic configuration: fusion power, reactor size, wall load, magnet type, inboard blanket and shield thickness, plasma aspect ratio, and operational β value. The costs and configurations of both steady-state and pulsed reactors were also investigated. Optimal small and large reactor concepts were developed and compared by studying the cost of electricity from single units and from multiplexed units. Multiplexed units appear to have advantages because they share some plant equipment and have lower initial capital investment as compared to larger single units
Flux driven turbulence in tokamaks
International Nuclear Information System (INIS)
Garbet, X.; Ghendrih, P.; Ottaviani, M.; Sarazin, Y.; Beyer, P.; Benkadda, S.; Waltz, R.E.
1999-01-01
This work deals with tokamak plasma turbulence in the case where fluxes are fixed and profiles are allowed to fluctuate. These systems are intermittent. In particular, radially propagating fronts, are usually observed over a broad range of time and spatial scales. The existence of these fronts provide a way to understand the fast transport events sometimes observed in tokamaks. It is also shown that the confinement scaling law can still be of the gyroBohm type in spite of these large scale transport events. Some departure from the gyroBohm prediction is observed at low flux, i.e. when the gradients are close to the instability threshold. Finally, it is found that the diffusivity is not the same for a turbulence calculated at fixed flux than at fixed temperature gradient, with the same time averaged profile. (author)
Options for an ignited tokamak
International Nuclear Information System (INIS)
Sheffield, J.
1984-02-01
It is expected that the next phase of the fusion program will involve a tokamak with the goals of providing an ignited plasma for pulses of hundreds of seconds. A simple model is described in this memorandum which establishes the physics conditions for such a self-sustaining plasma, for given ion and electron thermal diffusivities, in terms of R/a, b/a, I, B/q, epsilon β/sub p/, anti T/sub i/, and anti T/sub e//anti T/sub i/. The model is used to produce plots showing the wide range of tokamaks that may ignite or have a given ignition margin. The constraints that limit this range are discussed
Plasma diagnostics on large tokamaks
International Nuclear Information System (INIS)
Orlinskij, D.V.; Magyar, G.
1988-01-01
The main tasks of the large tokamaks which are under construction (T-15 and Tore Supra) and of those which have already been built (TFTR, JET, JT-60 and DIII-D) together with their design features which are relevant to plasma diagnostics are briefly discussed. The structural features and principal characteristics of the diagnostic systems being developed or already being used on these devices are also examined. The different diagnostic methods are described according to the physical quantities to be measured: electric and magnetic diagnostics, measurements of electron density, electron temperature, the ion components of the plasma, radiation loss measurements, spectroscopy of impurities, edge diagnostics and study of plasma stability. The main parameters of the various diagnostic systems used on the six large tokamaks are summarized in tables. (author). 351 refs, 44 figs, 22 tabs
Starfire: a commercial tokamak reactor
International Nuclear Information System (INIS)
Baker, C.C.; Abdou, M.A.; DeFreece, D.A.; Trachsel, C.A.; Graumann, D.; Kokoszenski, J.
1979-01-01
The basic objective of the STARFIRE Project is to develop a design concept for a commercial tokamak fusion electric power plant based on the deuterium/tritium/lithium fuel cycle. The key technical objective is to develop the best embodiment of the tokamak as a power reactor consistent with credible engineering solutions to design problems. Another key goal of the project is to give careful attention to the safety and environmental features of a commercial fusion reactor. The STARFIRE Project was initiated in May 1979, with the goal of completing the design study by October 1980. The purpose of this paper is to present an overview of the major parameters and design features that have been tentatively selected for STARFIRE
Comprehensive numerical modelling of tokamaks
International Nuclear Information System (INIS)
Cohen, R.H.; Cohen, B.I.; Dubois, P.F.
1991-01-01
We outline a plan for the development of a comprehensive numerical model of tokamaks. The model would consist of a suite of independent, communicating packages describing the various aspects of tokamak performance (core and edge transport coefficients and profiles, heating, fueling, magnetic configuration, etc.) as well as extensive diagnostics. These codes, which may run on different computers, would be flexibly linked by a user-friendly shell which would allow run-time specification of packages and generation of pre- and post-processing functions, including workstation-based visualization of output. One package in particular, the calculation of core transport coefficients via gyrokinetic particle simulation, will become practical on the scale required for comprehensive modelling only with the advent of teraFLOP computers. Incremental effort at LLNL would be focused on gyrokinetic simulation and development of the shell
Magnetic island formation in tokamaks
International Nuclear Information System (INIS)
Yoshikawa, S.
1989-04-01
The size of a magnetic island created by a perturbing helical field in a tokamak is estimated. A helical equilibrium of a current- carrying plasma is found in a helical coordinate and the helically flowing current in the cylinder that borders the plasma is calculated. From that solution, it is concluded that the helical perturbation of /approximately/10/sup /minus/4/ of the total plasma current is sufficient to cause an island width of approximately 5% of the plasma radius. 6 refs
Relaxed states of tokamak plasmas
International Nuclear Information System (INIS)
Kucinski, M.Y.; Okano, V.
1993-01-01
The relaxed states of tokamak plasmas are studied. It is assumed that the plasma relaxes to a quasi-steady state which is characterized by a minimum entropy production rate, compatible with a number of prescribed conditions and pressure balance. A poloidal current arises naturally due to the anisotropic resistivity. The minimum entropy production theory is applied, assuming the pressure equilibrium as fundamental constraint on the final state. (L.C.J.A.)
Runaway electrons during tokamak startup
International Nuclear Information System (INIS)
Sharma, A.S.; Jayakumar, R.
1988-01-01
Runaway electrons significantly affect the plasma and impurity evolution during tokamak startup. During its rise, a runaway pulse stores magnetic flux inductively; this is then released during the decay phase of the runaway pulse. This process affects plasma formation, current initiation and current buildup. Because of their relativistic velocities the runaway electrons have higher ionization and excitation rates than the plasma electrons. This leads to a significant modification of the impurity behaviour and consequently the plasma evolution. (author). 20 refs, 8 figs
Minimum scaling laws in tokamaks
International Nuclear Information System (INIS)
Zhang, Y.Z.; Mahajan, S.M.
1986-10-01
Scaling laws governing anomalous electron transport in tokamaks with ohmic and/or auxiliary heating are derived using renormalized Vlasov-Ampere equations for low frequency electromagnetic microturbulence. It is also shown that for pure auxiliary heating (or when auxiliary heating power far exceeds the ohmic power), the energy confinement time scales as tau/sub E/ ∼ P/sub inj//sup -1/3/, where P/sub inj/ is the injected power
Gyrosheath near the tokamak edge
International Nuclear Information System (INIS)
Hazeltine, R.D.; Xiao, H.; Valanju, P.M.
1993-03-01
A new model for the structure of the radial electric field profile in the edge during the H-mode is proposed. Charge separation caused by the difference between electron and ion gyromotion, or more importantly in a tokamak, the banana motion (halo effect) can self-consistently produce an electric dipole moment that causes the sheared radial electric field. The calculated results based on the model are consistent with D-III D and TEXTOR experimental results
Tokamak plasma boundary layer model
International Nuclear Information System (INIS)
Volkov, T.F.; Kirillov, V.D.
1983-01-01
A model has been developed for the limiter layer and for the boundary region of the plasma column in a tokamak to facilitate analytic calculations of the thickness of the limiter layers, the profiles and boundary values of the temperature and the density under various conditions, and the difference between the electron and ion temperatures. This model can also be used to analyze the recycling of neutrals, the energy and particle losses to the wall and the limiter, and other characteristics
Shear Alfven waves in tokamaks
International Nuclear Information System (INIS)
Kieras, C.E.
1982-12-01
Shear Alfven waves in an axisymmetric tokamak are examined within the framework of the linearized ideal MHD equations. Properties of the shear Alfven continuous spectrum are studied both analytically and numerically. Implications of these results in regards to low frequency rf heating of toroidally confined plasmas are discussed. The structure of the spatial singularities associated with these waves is determined. A reduced set of ideal MHD equations is derived to describe these waves in a very low beta plasma
Adjoint sensitivity analysis of the RELAPS/MOD3.2 two-fluid thermal-hydraulic code system
International Nuclear Information System (INIS)
Ionescu-Bujor, M.
2000-10-01
This work presents the implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for the non-equilibrium, non-homogeneous two-fluid model, including boron concentration and non-condensable gases, of the RELAP5/MOD3.2 code. The end-product of this implementation is the Adjoint Sensitivity Model (ASM-REL/TF), which is derived for both the differential and discretized equations underlying the two-fluid model with non-condensable(s). The consistency requirements between these two representations are also highlighted. The validation of the ASM-REL/TF has been carried out by using sample problems involving: (i) liquid-phase only, (ii) gas-phase only, and (iii) two-phase mixture (of water and steam). Thus the 'Two-Loops with Pumps' sample problem supplied with RELAP5/MOD3.2 has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when only the liquid-phase is present. Furthermore, the 'Edwards Pipe' sample problem, also supplied with RELAP5/MOD3.2, has been used to verify the accuracy and stability of the numerical solution of the ASM-REL/TF when both (i.e., liquid and gas) phases are present. In addition, the accuracy and stability of the numerical solution of the ASM-REL/TF have been verified when only the gas-phase is present by using modified 'Two-Loops with Pumps' and the 'Edwards Pipe' sample problems in which the liquid and two-phase fluids, respectively, were replaced by pure steam. The results obtained for these sample problems depict typical sensitivities of junction velocities and volume-averaged pressures to perturbations in initial conditions, and indicate that the numerical solution of the ASM-REL/TF is as robust, stable, and accurate as the original RELAP5/MOD3.2 calculations. In addition, the solution of the ASM-REL/TF has been used to calculate sample sensitivities of volume-averaged pressures to variations in the pump head. (orig.) [de
Yoon, Young Dae
2017-10-01
A generalized, intuitive two-fluid picture of 2D non-driven collisionless magnetic reconnection is described using results from a full-3D numerical simulation. The relevant two-fluid equations simplify to the condition that the flux associated with canonical circulation Q =me ∇ ×ue +qe B is perfectly frozen into the electron fluid. Q is the curl of P =meue +qe A , which is the electron canonical momenrum. Since ∇ . Q = 0 , the Q flux tubes are incompressible and so have a fixed volume. Because they are perfectly frozen into the electron fluid, the Q flux tubes cannot reconnect. Following the behavior of these Q flux tubes provides an intuitive insight into 2D collisionless reconnection of B . In the reconnection geometry, a small perturbation to the central electron current sheet effectively brings a localized segment of a Q flux tube towards the X-point. This flux tube segment is convected downwards with the central electron current, effectively stretching the flux tube, decreasing its cross-section to maintain a fixed volume and so increasing the magnitude of Q . Also, because Q is the sum of the electron vorticity and the magnetic field, the two terms may change in such a way that one term becomes smaller while the other becomes larger while preserving constant Q flux. This allows magnetic reconnection, which is a conversion of magnetic field into particle velocity, to occur without any dissipation mechanism. The entire process has positive feedback with no restoring mechanism and therefore is an instability. The Q motion provides an interpretation for other phenomena as well, such as spiked central electron current filaments. The simulated reconnection rate was found to agree with a previous analytical calculation having the same geometry. Energy analysis shows that the magnetic energy is converted and propagated mainly in the form of the Poynting flux, while helicity analysis shows that the canonical helicity ∫ P . QdV as a whole must be considered when
Discharge cleaning for a tokamak
International Nuclear Information System (INIS)
Ishii, Shigeyuki
1983-01-01
Various methods of discharge cleaning for tokamaks are described. The material of the first walls of tokamaks is usually stainless steel, inconel, titanium and so on. Hydrogen is exclusively used as the discharge gas. Glow discharge cleaning (GDC), Taylor discharge cleaning (TDC), and electron cyclotron resonance discharge cleaning (ECR-DC) are discussed in this paper. The cleaning by GDC is made by moving a movable anode to the center of a tokamak vassel. Taylor found the good cleaning effect of induced discharge by high pressure and low power discharge. This is called TDC. When the frequency of high frequency discharge in a magnetic field is equal to that of the electron cyclotron resonance, the break down potential is lowered if the pressure is sufficiently low. The ECR-CD is made by using this effect. In TDC and ECR-DC, the electron temperature, which has a close relation to the production rate of H 0 , can be controlled by the pressure. In GDC, the operating pressure was improved by the radio frequency glow (RG) method. However, there is still the danger of arcing. In case of GDC and ECR-DC, the position of plasma can be controlled, but not in case of TDC. The TDC is accepted by most of takamak devices in the world. (Kato, T.)
Magnetic confinement experiment. I: Tokamaks
International Nuclear Information System (INIS)
Goldston, R.J.
1995-08-01
Reports were presented at this conference of important advances in all the key areas of experimental tokamak physics: Core Plasma Physics, Divertor and Edge Physics, Heating and Current Drive, and Tokamak Concept Optimization. In the area of Core Plasma Physics, the biggest news was certainly the production of 9.2 MW of fusion power in the Tokamak Fusion Test Reactor, and the observation of unexpectedly favorable performance in DT plasmas. There were also very important advances in the performance of ELM-free H- (and VH-) mode plasmas and in quasi-steady-state ELM'y operation in JT-60U, JET, and DIII-D. In all three devices ELM-free H-modes achieved nTτ's ∼ 2.5x greater than ELM'ing H-modes, but had not been sustained in quasi-steady-state. Important progress has been made on the understanding of the physical mechanism of the H-mode in DIII-D, and on the operating range in density for the H-mode in Compass and other devices
Edge Plasma Response to Non-Axisymmetric Fields in Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Ferraro, N. M.; Lao, L. L.; Buttery, R. J.; Evans, T. E.; Snyder, P. B.; Wade, M.R., E-mail: ferraro@fusion.gat.com [General Atomics, San Diego (United States); Moyer, R. A.; Orlov, D. M. [University of California San Diego, La Jolla (United States); Lanctot, M. J. [Lawrence Livermore National Laboratory, Livermore (United States)
2012-09-15
Full text: The application of non-axisymmetric fields is found to have significant effects on the transport and stability of H-mode tokamak plasmas. These effects include dramatic changes in rotation and particle transport, and may lead to the partial or complete suppression of edge-localized modes (ELMs) under some circumstances. The physical mechanism underlying these effects is presently not well understood, in large part because the response of the plasma to non- axisymmetric fields is significant and complex. Here, recent advances in modeling the plasma response to non-axisymmetric fields are discussed. Calculations using a resistive two-fluid model in diverted toroidal geometry confirm the special role of the perpendicular electron velocity in suppressing the formation of islands in the plasma. The possibility that islands form near the top of the pedestal, where the zero-crossing of the perpendicular electron velocity may coincide with a mode-rational surface, is explored, and the implications for ELM suppression are discussed. Modeling results are compared with empirical data. It is shown that numerical modeling is successful in reproducing some experimentally observed effects of applied non-axisymmetric fields on the edge temperature and density profiles. The numerical model self-consistently includes the plasma, separatrix, and scrape-off layer. Rotation and diamagnetic effects are also included self-consistently. Solutions are calculated using the M3D-C1 extended-MHD code. (and others)
Optimization and control of plasma shape and current profile in non-circular cross-section tokamaks
International Nuclear Information System (INIS)
Moore, R.W.; Bernard, L.C.; Chan, V.S.
1981-01-01
Tokamaks with elongated, non-circular cross-sections are under consideration as fusion reactors because they have the potential for stable operation at high β. Ideal MHD theory, however, predicts that careful current profile control will be required to achieve the potential high-β advantages of non-circular cross-sections. In this paper, high-β equilibria which are stable to all ideal MHD modes are found by optimizing the plasma shape and current profile for doublets, up-down asymmetric dees, and symmetric dees. The ideal MHD stability of these equilibria for low toroidal mode number n is analysed with a global MHD stability code, GATO. The stability to high-n modes is analysed with a localized ballooning code, BLOON. The attainment of high β is facilitated by an automated optimization search on shape and current parameters. The equilibria are calculated with a free-boundary equilibrium code using coils appropriate for the Doublet III experimental device. The optimal equilibria are characterized by broad current profiles with values of βsub(poloidal) approximately equal to 1. Experimental realization of the shapes and current profiles giving the highest β limits is explored with a 1 1/2-D transport code, which simulates the time evolution of the 2-D MHD equilibrium while calculating consistent current profiles from a 1-D transport model. Transport simulations indicate that nearly optimal shapes may be obtained provided that the currents in the field-shaping coils are appropriately programmed and the plasma current profile is sufficiently broad. Obtaining broad current profiles is possible by current ramping, neutral-beam heating, and electron-cyclotron heating. With combinations of these techniques it is possible to approach the optimum β predicted by the MHD theory. (author)
Sloshing-ion equilibria in the TARA endplugs
International Nuclear Information System (INIS)
Hokin, S.; Kesner, J.
1983-11-01
We have employed a modified version of the LLNL Bounce-average Fokker-Planck code to model neutral beam-produced sloshing-ion equilibria in the TARA endplugs. The questions we have addressed concern the effect of deuterium beam operation as opposed to hydrogen operation, and the advantage of using full-energy beams rather than the usual three-component beams. We find that, for the expected base case TARA operating parameters, a 40% savings in required beam power is attained by using deuterium beams rather than hydrogen beams, and that the use of full-energy beams results in an additional 26% power savings for these parameters. For higher plasma temperatures the use of full-energy beams becomes significantly advantagous. We have also investigated the equilibria of two possible alternate mirror configurations for the TARA endplugs, believed to be more stable to trapped particle modes, and report those results here
Phase diagrams and heterogeneous equilibria a practical introduction
Predel, Bruno; Pool, Monte
2004-01-01
This graduate-level textbook provides an introduction to the practical application of phase diagrams. It is intended for students and researchers in chemistry, metallurgy, mineralogy, and materials science as well as in engineering and physics. Heterogeneous equilibria are described by a minimum of theory illustrated by practical examples and realistic case discussions from the different fields of application. The treatment of the physical and energetic background of phase equilibria leads to the discussion of the thermodynamics of mixtures and the correlation between energetics and composition. Thus, tools for the prediction of energetic, structural, and physical quantities are provided. The authors treat the nucleation of phase transitions, the production and stability of technologically important metastable phases, and metallic glasses. Furthermore, the text also concisely presents the thermodynamics and composition of polymer systems.
Extended Group Contribution Model for Polyfunctional Phase Equilibria
DEFF Research Database (Denmark)
Abildskov, Jens
of physical separation processes. In a thermodynamic sense, design requires detailed knowledge of activity coefficients in the phases at equilibrium. The prediction of these quantities from a minimum of experimental data is the broad scope of this thesis. Adequate equations exist for predicting vapor......Material and energy balances and equilibrium data form the basis of most design calculations. While material and energy balances may be stated without much difficulty, the design engineer is left with a choice between a wide variety of models for describing phase equilibria in the design......-liquid equilibria from data on binary mixtures, composed of structurally simple molecules with a single functional group. More complex is the situation with mixtures composed of structurally more complicated molecules or molecules with more than one functional group. The UNIFAC method is extended to handle...
International Nuclear Information System (INIS)
Yao, W.; Coste, P.; Bestion, D.; Boucker, M.
2003-01-01
In this paper, a local 3D two-fluid model for a turbulent stratified flow with/without condensation, which can be used to predict two-phase pressurized thermal shock, is presented. A modified turbulent K- model is proposed with turbulence production induced by interfacial friction. A model of interfacial friction based on a interfacial sublayer concept and three interfacial heat transfer models, namely, a model based on the small eddies controlled surface renewal concept (HDM, Hughes and Duffey, 1991), a model based on the asymptotic behavior of the Eddy Viscosity (EVM), and a model based on the Interfacial Sublayer concept (ISM) are implemented into a preliminary version of the NEPTUNE code based on the 3D module of the CATHARE code. As a first step to apply the above models to predict the two-phase thermal shock, the models are evaluated by comparison of calculated profiles with several experiments: a turbulent air-water stratified flow without interfacial heat transfer; a turbulent steam-water stratified flow with condensation; turbulence induced by the impact of a water jet in a water pool. The prediction results agree well with the experimental data. In addition, the comparison of three interfacial heat transfer models shows that EVM and ISM gave better prediction results while HDM highly overestimated the interfacial heat transfers compared to the experimental data of a steam water stratified flow