WorldWideScience

Sample records for normal tokamak equilibria

  1. 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

  2. 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

  3. 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)

  4. 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)

  5. 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

  6. Recent developments in Bayesian inference of tokamak plasma equilibria and high-dimensional stochastic quadratures

    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)

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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)

  13. 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.)

  14. Stability of high-beta tokamak equilibria and transport in Belt-Pinch IIa

    Energy Technology Data Exchange (ETDEWEB)

    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.

  15. 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.

  16. 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.

  17. 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

  18. 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

  19. 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

  20. Theory and computation of general force balance in non-axisymmetric tokamak equilibria

    Science.gov (United States)

    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.

  1. Multi-region approach to free-boundary three-dimensional tokamak equilibria and resistive wall instabilities

    Science.gov (United States)

    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.

  2. Multi-region approach to free-boundary three-dimensional tokamak equilibria and resistive wall instabilities

    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.

  3. Development and performance of high speed processing system of magnetohydrodynamic equilibria for discharge analyses on the J T-60 tokamak

    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)

  4. Study of critical beta non-circular tokamak equilibria sustained in steady state by beam driven currents

    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)

  5. Tokamak equilibria with non-parallel flow in a triangularity-deformed axisymmetric toroidal coordinate system

    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.

  6. 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.)

  7. Optimization study of normal conductor tokamak for commercial neutron source

    Science.gov (United States)

    Fujita, T.; Sakai, R.; Okamoto, A.

    2017-05-01

    The optimum conceptual design of tokamak with normal conductor coils was studied for minimizing the cost for producing a given neutron flux by using a system code, PEC. It is assumed that the fusion neutrons are used for burning transuranics from the fission reactor spent fuel in the blanket and a fraction of the generated electric power is circulated to opearate the tokamak with moderate plasma fusion gain. The plasma performance was assumed to be moderate ones; {β\\text{N}}~∼ ~3{--}4 in the aspect ratio A~=~2{--}3 and {{H}98y2}~=~1 . The circulating power is an important factor affecting the cost. Though decreasing the aspect ratio is useful to raise the plasma beta and decrease the toroidal field, the maximum field in the coil starts to rise in the very low aspect ratio range and then the circulating power increases with decrease in the plasma aspect ratio A below A~∼ ~2 , while the construction cost increases with A . As a result, the cost per neutron has its minimum around A~∼ ~2.2 , namely, between ST and the conventional tokamak. The average circulating power fraction is expected to be ~51%.

  8. 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

  9. 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)

  10. 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

  11. 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)

  12. 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

  13. Nonrigid, Linear Plasma Response Model Based on Perturbed Equilibria for Axisymmetric Tokamak Control Design

    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

  14. Tokamak

    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

  15. Thermal loads on tokamak plasma-facing components during normal operation and disruptions

    International Nuclear Information System (INIS)

    McGrath, R.T.

    1990-01-01

    Power loadings experienced by tokamak plasma-facing components during normal operation and during off-normal events are discussed. A model for power and particle flow in the tokamak boundary layer is presented and model predictions are compared to infrared measurements of component heating. The inclusion of the full three-dimensional geometry of the components and of the magnetic flux surface is very important in the modeling. Experimental measurements show that misalignment of component armour tile surfaces by only a millimeter can lead to significant localized heating. An application to the design of plasma-facing components for future machines is presented. Finally, thermal loads expected during tokamak disruptions are discussed. The primary problems are surface melting and vaporization due to localized intense heating during the disruption thermal quench and volumetric heating of the component armour and structure due to localised impact of runaway electrons. (author)

  16. EFIT tokamak equilibria with toroidal flow and anisotropic pressure using the two-temperature guiding-centre plasma

    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)

  17. Physics of collisionless scrape-off-layer plasma during normal and off-normal Tokamak operating conditions

    International Nuclear Information System (INIS)

    Hassanein, A.; Konkashbaev, I.

    1999-01-01

    The structure of a collisionless scrape-off-layer (SOL) plasma in tokamak reactors is being studied to define the electron distribution function and the corresponding sheath potential between the divertor plate and the edge plasma. The collisionless model is shown to be valid during the thermal phase of a plasma disruption, as well as during the newly desired low-recycling normal phase of operation with low-density, high-temperature, edge plasma conditions. An analytical solution is developed by solving the Fokker-Planck equation for electron distribution and balance in the SOL. The solution is in good agreement with numerical studies using Monte-Carlo methods. The analytical solutions provide an insight to the role of different physical and geometrical processes in a collisionless SOL during disruptions and during the enhanced phase of normal operation over a wide range of parameters

  18. Continuous tokamaks

    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

  19. 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)

  20. 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

  1. Inverse plasma equilibria

    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

  2. Potential off-normal events and associated radiological source terms for the compact ignition tokamak: Fusion Safety Program

    International Nuclear Information System (INIS)

    Holland, D.F.; Lyon, R.E.

    1987-10-01

    The Compact Ignition Tokamak (CIT), the latest step in the United States program to develop the commercial application of fusion power, is designed as the first fusion device to achieve ignition conditions. It is to be constructed near Princeton, New Jersey on the site of the existing Tokamak Fusion Test Reactor (TFTR). To address the environmental impact and public safety concerns, a preliminary analysis was performed of potential off-normal radiological releases. Operational occurrences, natural phenomena, accidents with external origins, and accidents external to the PPPL site were considered as potential sources for off-normal events. Based on an initial screening, events were selected for preliminary analysis. Included in these events were tritium releases from the tritium delivery and recovery system, tritium releases from the torus, releases of activated nitrogen from the test cell or cryostat, seismic events, and shipping accidents. In each case, the design considerations related to the event were reviewed and the release scenarios discussed. Because of the complexity of some of the proposed safety systems, in some cases event trees were used to describe the accident scenarios. For each scenario, the probability was estimated as well as the release magnitude, isotope, chemical form, and release mode. 10 refs., 17 figs., 5 tabs

  3. 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)

  4. Attractive evolutionary equilibria

    NARCIS (Netherlands)

    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

  5. Modelling of transient electromagnetics in Tokamaks during off-normal conditions

    Science.gov (United States)

    Schneider, J. H.; Crutzen, Y. R.; Papadopoulos, S.; Richard, N.

    1993-03-01

    During plasma disruption events in Tokamaks, a considerable amount of magnetic and thermal energy is associated to the transfer of plasma current into eddy and Halo currents. In this paper, a predictive numerical modelling is described concerning plasma-wall interactions during disruptive instabilities. Preliminary results are presented, giving an estimation of heat transfer interaction with electromagnetic phenomena. Eddy currents and heat deposition increase significantly with decreasing disruption time. An estimation of the order of magnitude of Halo currents and associated forces on plasma-facing conducting components is also presented. Durant une disruption de plasma dans les Tokamaks, une quantité considérable d'énergie magnétique et thermique est associée au transfert de courant de plasma sous forme de courants de Foucault et de “Halo”. Cette contribution décrit un modèle numérique capable de prédire les interactions plasma-première paroi durant ces instabilités disruptives. La présentation de résultats préliminaires comprend une estimation de l'interaction entre le phénomène électromagnétique et le transfert de chaleur. Les courants de Foucault et les pertes Joule augmentent fortement quand la durée de disruption devient plus brève. Une évaluation de l'ordre de grandeur des courants de “Halo” et des forces résultantes, appliqués aux composants métalliques placés face au plasma, est également illustrée.

  6. Free-boundary perturbed MHD equilibria

    International Nuclear Information System (INIS)

    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].

  7. Implementing a finite-state off-normal and fault response system for disruption avoidance in tokamaks

    Science.gov (United States)

    Eidietis, N. W.; Choi, W.; Hahn, S. H.; Humphreys, D. A.; Sammuli, B. S.; Walker, M. L.

    2018-05-01

    A finite-state off-normal and fault response (ONFR) system is presented that provides the supervisory logic for comprehensive disruption avoidance and machine protection in tokamaks. Robust event handling is critical for ITER and future large tokamaks, where plasma parameters will necessarily approach stability limits and many systems will operate near their engineering limits. Events can be classified as off-normal plasmas events, e.g. neoclassical tearing modes or vertical displacements events, or faults, e.g. coil power supply failures. The ONFR system presented provides four critical features of a robust event handling system: sequential responses to cascading events, event recovery, simultaneous handling of multiple events and actuator prioritization. The finite-state logic is implemented in Matlab®/Stateflow® to allow rapid development and testing in an easily understood graphical format before automated export to the real-time plasma control system code. Experimental demonstrations of the ONFR algorithm on the DIII-D and KSTAR tokamaks are presented. In the most complex demonstration, the ONFR algorithm asynchronously applies ‘catch and subdue’ electron cyclotron current drive (ECCD) injection scheme to suppress a virulent 2/1 neoclassical tearing mode, subsequently shuts down ECCD for machine protection when the plasma becomes over-dense, and enables rotating 3D field entrainment of the ensuing locked mode to allow a safe rampdown, all in the same discharge without user intervention. When multiple ONFR states are active simultaneously and requesting the same actuator (e.g. neutral beam injection or gyrotrons), actuator prioritization is accomplished by sorting the pre-assigned priority values of each active ONFR state and giving complete control of the actuator to the state with highest priority. This early experience makes evident that additional research is required to develop an improved actuator sharing protocol, as well as a methodology to

  8. 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)

  9. 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.

  10. Attractive evolutionary equilibria

    OpenAIRE

    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.

  11. 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

  12. 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

  13. 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

  14. 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)

  15. 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)

  16. 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

  17. Theory of tokamak plasmas

    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.

  18. 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)

  19. 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%.

  20. 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%

  1. Learning efficient correlated equilibria

    KAUST Repository

    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.

  2. Learning efficient correlated equilibria

    KAUST Repository

    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.

  3. 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

  4. 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

  5. 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...

  6. 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

  7. Fusion burn equilibria sensitive to the ratio between energy and helium transport

    NARCIS (Netherlands)

    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.

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. Topology of tokamak orbits

    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

  14. 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

  15. Tokamak experiments

    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

  16. Toroidal Extrap Equilibria

    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)

  17. 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....

  18. 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)

  19. 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

  20. 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...

  1. 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.

  2. Adsorption analysis equilibria and kinetics

    CERN Document Server

    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

  3. 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

  4. 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.

  5. Data-driven robust control of the plasma rotational transform profile and normalized beta dynamics for advanced tokamak scenarios in DIII-D

    Energy Technology Data Exchange (ETDEWEB)

    Shi, W.; Wehner, W.P.; Barton, J.E.; Boyer, M.D. [Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015 (United States); Schuster, E., E-mail: schuster@lehigh.edu [Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015 (United States); Moreau, D. [CEA, IRFM, F-13018 St Paul lez Durance (France); Walker, M.L.; Ferron, J.R.; Luce, T.C.; Humphreys, D.A.; Penaflor, B.G.; Johnson, R.D. [General Atomics, San Diego, CA 92121 (United States)

    2017-04-15

    A control-oriented, two-timescale, linear, dynamic, response model of the rotational transform ι profile and the normalized beta β{sub N} is proposed based on experimental data from the DIII-D tokamak. Dedicated system-identification experiments without feedback control have been carried out to generate data for the development of this model. The data-driven dynamic model, which is both device-specific and scenario-specific, represents the response of the ι profile and β{sub N} to the electric field due to induction as well as to the heating and current drive (H&CD) systems during the flat-top phase of an H-mode discharge in DIII-D. The control goal is to use both induction and the H&CD systems to locally regulate the plasma ι profile and β{sub N} around particular target values close to the reference state used for system identification. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed-sensitivity robust control design problem is formulated based on the dynamic model to synthesize a stabilizing feedback controller without input constraints that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is then augmented with an anti-windup compensator, which keeps the given controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop system unmodified when no saturation is present. The proposed controller represents one of the first feedback profile controllers integrating magnetic and kinetic variables ever implemented and experimentally tested in DIII-D. The preliminary experimental results presented in this work, although limited in number and constrained by actuator problems and design limitations, as it will be reported, show good progress towards routine current profile control in DIII-D and leave valuable lessons

  6. 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.

  7. 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

  8. 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

  9. Tokamak COMPASS

    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

  10. 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.

  11. 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.

  12. Collisionless current sheet equilibria

    Science.gov (United States)

    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.

  13. 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.

  14. 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

  15. Axisymmetric Plasma Equilibria in General Relativity

    Science.gov (United States)

    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.

  16. 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

  17. 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

  18. Learning to Play Efficient Coarse Correlated Equilibria

    KAUST Repository

    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

  19. 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.

  20. 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

  1. 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

  2. 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

  3. 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

  4. 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.

  5. 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

  6. 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

  7. 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.)

  8. Stackelberg equilibria and horizontal differentiation

    OpenAIRE

    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.

  9. 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

  10. 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)

  11. Varennes Tokamak

    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

  12. 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)

  13. 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

  14. Tokamak physics

    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)

  15. Nash Equilibria in Fisher Market

    Science.gov (United States)

    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.

  16. Phase equilibria basic principles, applications, experimental techniques

    CERN Document Server

    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.

  17. 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)

  18. PPPL tokamak program

    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

  19. Status of tokamak research

    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

  20. 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

  1. 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...

  2. Strong Nash Equilibria and the Potential Maimizer

    NARCIS (Netherlands)

    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

  3. Tokamak Systems Code

    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

  4. 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

  5. Signaling equilibria in sensorimotor interactions.

    Science.gov (United States)

    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.

  6. 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

  7. 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.)

  8. 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.

  9. 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

  10. Economic considerations of commercial tokamak options

    International Nuclear Information System (INIS)

    Dabiri, A.E.

    1986-05-01

    Systems studies have been performed to assess commercial tokamak options. Superconducting, as well as normal, magnet coils in either first or second stability regimes have been considered. A spherical torus (ST), as well as an elongated tokamak (ET), is included in the study. The cost of electricity (COE) is selected as the figure of merit, and beta and first-wall neutron wall loads are selected to represent the physics and technology characteristics of various options. The results indicate that an economical optimum for tokamaks is predicted to require a beta of around 10%, as predicted to be achieved in the second stability regime, and a wall load of about 5 MW/m 2 , which is assumed to be optimum technologically. This tokamak is expected to be competitive with fission plants if efficient, noninductive current drive is developed. However, if this regime cannot be attained, all other tokamaks operating in the first stability regime, including spherical torus and elongated tokamak and assuming a limiting wall load of 5 MW/m 2 , will compete with one another with a COE of about 50 mill/kWh. This 40% higher than the COE for the optimum reactor in the second stability regime with fast-wave current drive. The above conclusions pertain to a 1200-MW(e) net electric power plant. A comparison was also made between ST, ET, and superconducting magnets in the second stability regime with fast-wave current drive at 600 MW(e)

  11. Learning to Play Efficient Coarse Correlated Equilibria

    KAUST Repository

    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.

  12. Computing Nash equilibria through computational intelligence methods

    Science.gov (United States)

    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.

  13. 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)....

  14. 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.

  15. 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

  16. Tokamak engineering mechanics

    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.

  17. 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)

  18. Tokamak engineering mechanics

    CERN Document Server

    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

  19. Advanced Tokamak Stability Theory

    Science.gov (United States)

    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.

  20. 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)

  1. Tokamak concept innovations

    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

  2. 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.)

  3. Multiple equilibria in a simple elastocapillary system

    KAUST Repository

    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.

  4. 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

  5. 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.)

  6. 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

  7. 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.

  8. Tokamak control simulator

    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

  9. Anomalous periodic disruptions in tokamak plasma

    International Nuclear Information System (INIS)

    Montvai, A.; Tegze, M.; Valyi, I.

    1982-09-01

    Anomalously strong, periodic instabilities were observed in the MT-1 tokamak. Characteristics of these instabilities were partly similar to those of internal disruptions, but there were features making them different from the normal relaxational oscillations. Basic characteristics of the phenomenon were studied with the aid of generally used diagnostics. (author)

  10. 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

  11. Tokamaks. 2. ed.

    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)

  12. Tokamak reactor studies

    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

  13. Tokamak ARC damage

    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

  14. Survey of Tokamak experiments

    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)

  15. Tokamak ARC damage

    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.

  16. 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

  17. 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

  18. 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

  19. 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)

  20. Existence of pareto equilibria for multiobjective games without compactness

    OpenAIRE

    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.

  1. 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

  2. Ideal MHD stability of high poloidal beta equilibria in TFTR

    International Nuclear Information System (INIS)

    Sabbagh, S.A.; Mauel, M.E.; Navratil, G.A.; Bell, M.G.; Budny, R.V.; Chance, M.S.; Fredrickson, E.D.; Jardin, S.C.; Manickam, J.; McCune, D.C.; McGuire, K.M.; Wieland, R.M.; Zarnstorff, M.C.; Phillips, M.W.; Hughes, M.H.; Kesner, J.

    1991-01-01

    Recent experiments in TFTR have expanded the operating space of the device to include plasmas with values of var-epsilon β p dia ≡ 2μ 0 var-epsilon perpendicular >/ p >> 2 as large as 1.6, and Troyon normalized diamagnetic beta β N dia ≡ β t perpendicular aB t /10 -8 I p as large as 4.7. At values of var-epsilon β p dia ≥ 1.3, a separatrix was observed to enter the vacuum vessel, producing a naturally diverted discharge. Plasmas with large values of var-epsilon β p dia were created with both the plasma current, I p , held constant and with I p decreased, or ramped down, before the start of neutral beam injection. A convenient characterization of the change in I p using experimental parameters can be defined by the ratio of I p before the ramp down, to I p during the neutral beam heating phase, F I p . The ideal MHD stability of these equilibria is investigated to determine their location in stability space, and to study the role of plasma current and pressure profile modification in the creation of these high var-epsilon β p and β N plasmas. The evolution of these plasmas is modelled from experimental data using the TRANSP code. Two-dimensional equilibria are computed from the TRANSP results and used as input to both high and low-n stability codes including PEST. The high var-epsilon β p equilibria, which generally have an oblate cross-sectional shape, are in the first stability region to high-n ballooning modes. At constant I p , these equilibria generally have maximum pressure gradients near the magnetic axis and are stable to n=1 modes without a stabilizing conducting wall. The effect of the current profile shape on the stability of low-n kink/ballooning modes and the requirements for these plasmas to access the second stability region are examined. 6 refs

  3. 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...

  4. 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 ...

  5. Equilibrator: Modeling Chemical Equilibria with Excel

    Science.gov (United States)

    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…

  6. 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.)

  7. 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...

  8. 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.)

  9. 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)

  10. 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

  11. Enhancement of confinement in tokamaks

    International Nuclear Information System (INIS)

    Furth, H.P.

    1986-05-01

    A plausible interpretation of the experimental evidence is that energy confinement in tokamaks is governed by two separate considerations: (1) the need for resistive MHD kink-stability, which limits the permissible range of current profiles - and therefore normally also the range of temperature profiles; and (2) the presence of strongly anomalous microscopic energy transport near the plasma edge, which calibrates the amplitude of the global temperature profile, thus determining the energy confinement time tau/sub E/. Correspondingly, there are two main paths towards the enhancement of tokamak confinement: (1) Configurational optimization, to increase the MHD-stable energy content of the plasma core, can evidently be pursued by varying the cross-sectional shape of the plasma and/or finding stable radial profiles with central q-values substantially below unity - but crossing from ''first'' to ''second'' stability within the peak-pressure region would have the greatest ultimate potential. (2) Suppression of edge turbulence, so as to improve the heat insulation in the outer plasma shell, can be pursued by various local stabilizing techniques, such as use of a poloidal divertor. The present confinement model and initial TFTR pellet-injection results suggest that the introduction of a super-high-density region within the plasma core should be particularly valuable for enhancing ntau/subE/. In D-T operation, a centrally peaked plasma pressure profile could possibly lend itself to alpha-particle-driven entry into the second-stability regime

  12. 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

  13. INTEGRATED PLASMA CONTROL FOR ADVANCED TOKAMAKS

    International Nuclear Information System (INIS)

    HUMPHREYS, D.A.; FERRON, J.R.; JOHNSON, R.D; LEUER, J.A.; PENAFLOR, B.G.; WALKER, M.L.; WELANDER, A.S.; KHAYRUTDINOV, R.R; DOKOUKA, V.; EDGELL, D.H.; FRANSSON, C.M.

    2004-03-01

    OAK-B135 Advanced tokamaks (AT) are distinguished from conventional tokamaks by their high degree of shaping, achievement of profiles optimized for high confinement and stability characteristics, and active stabilization of MHD instabilities to attain high values of normalized beta and confinement. These high performance fusion devices thus require accurate regulation of the plasma boundary, internal profiles, pumping, fueling, and heating, as well as simultaneous and well-coordinated MHD control action to stabilize such instabilities as tearing modes and resistive wall modes. Satisfying the simultaneous demands on control accuracy, reliability, and performance for all of these subsystems requires a high degree of integration in both design and operation of the plasma control system in an advanced tokamak. The present work describes the approach, benefits, and progress made in integrated plasma control with application examples drawn from the DIII-D tokamak. The approach includes construction of plasma and system response models, validation of models against operating experiments, design of integrated controllers which operate in concert with one another as well as with supervisory modules, simulation of control action against off-line and actual machine control platforms, and iteration of the design-test loop to optimize performance

  14. 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

  15. Discrete Alfven waves in the TORTUS tokamak

    International Nuclear Information System (INIS)

    Amagishi, Y.; Ballico, M.J.; Cross, R.C.; Donnely, I.J.

    1989-01-01

    Discrete Alfven Waves (DAWs) have been observed as antenna resistance peaks and as enhanced edge fields in the TORTUS tokamak during Alfven wave heating experiments. A kinetic theory code has been used to calculate the antenna loading and the structure of the DAW fields for a range of plasma current and density profiles. There is fair agreement between the measured and predicted amplitude of the DAW fields in the plasma edge when both are normalized to the same antenna power

  16. Fusion technology applications of the spherical tokamak

    International Nuclear Information System (INIS)

    Robinson, D.C.; Akers, R.; Allfrey, S.J.

    1999-01-01

    Fusion technology applications of the spherical tokamak are presented, exploiting its high β capability, normal conducting TF coils, compact core, high natural elongation, disruption resilience and low capital cost. We concentrate here on two particular applications: a volume neutron source (VNS) for component testing and a power plant, addressing engineering and physics issues for steady state operation. The prospect of nearer term burning plasma ST devices are discussed in the conclusions. (author)

  17. Fusion technology applications of the spherical tokamak

    International Nuclear Information System (INIS)

    Robinson, D.C.; Akers, R.; Allfrey, S.J.

    2001-01-01

    Fusion technology applications of the spherical tokamak are presented, exploiting its high β capability, normal conducting TF coils, compact core, high natural elongation, disruption resilience and low capital cost. We concentrate here on two particular applications: a volume neutron source (VNS) for component testing and a power plant, addressing engineering and physics issues for steady state operation. The prospect of nearer term burning plasma ST devices are discussed in the conclusions. (author)

  18. Microwave Tokamak Experiment

    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

  19. Texas Experimental Tokamak

    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

  20. 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

  1. 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

  2. High-pressure fluid phase equilibria phenomenology and computation

    CERN Document Server

    Deiters, Ulrich K

    2012-01-01

    The book begins with an overview of the phase diagrams of fluid mixtures (fluid = liquid, gas, or supercritical state), which can show an astonishing variety when elevated pressures are taken into account; phenomena like retrograde condensation (single and double) and azeotropy (normal and double) are discussed. It then gives an introduction into the relevant thermodynamic equations for fluid mixtures, including some that are rarely found in modern textbooks, and shows how they can they be used to compute phase diagrams and related properties. This chapter gives a consistent and axiomatic approach to fluid thermodynamics; it avoids using activity coefficients. Further chapters are dedicated to solid-fluid phase equilibria and global phase diagrams (systematic search for phase diagram classes). The appendix contains numerical algorithms needed for the computations. The book thus enables the reader to create or improve computer programs for the calculation of fluid phase diagrams. introduces phase diagram class...

  3. Realizing steady-state tokamak operation for fusion energy

    International Nuclear Information System (INIS)

    Luce, T. C.

    2011-01-01

    Continuous operation of a tokamak for fusion energy has clear engineering advantages but requires conditions beyond those sufficient for a burning plasma. The fusion reactions and external sources must support both the pressure and the current equilibrium without inductive current drive, leading to demands on stability, confinement, current drive, and plasma-wall interactions that exceed those for pulsed tokamaks. These conditions have been met individually, and significant progress has been made in the past decade to realize scenarios where the required conditions are obtained simultaneously. Tokamaks are operated routinely without disruptions near pressure limits, as needed for steady-state operation. Fully noninductive sustainment with more than half of the current from intrinsic currents has been obtained for a resistive time with normalized pressure and confinement approaching those needed for steady-state conditions. One remaining challenge is handling the heat and particle fluxes expected in a steady-state tokamak without compromising the core plasma performance.

  4. ARIES tokamak reactor study

    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

  5. 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

  6. Overview of Tokamak Results

    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

  7. 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

  8. 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)

  9. Free-Boundary 3D Equilibria and Resistive Wall Instabilities with Extended-MHD

    Science.gov (United States)

    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.

  10. 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...

  11. Gyrokinetic magnetohydrodynamics and the associated equilibria

    Science.gov (United States)

    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.

  12. Multiple equilibria in a simple elastocapillary system

    KAUST Repository

    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.

  13. Graphical Derivatives and Stability Analysis for Parameterized Equilibria with Conic Constraints

    Czech Academy of Sciences Publication Activity Database

    Mordukhovich, B. S.; Outrata, Jiří; Ramírez, H. C.

    2015-01-01

    Roč. 23, č. 4 (2015), s. 687-704 ISSN 1877-0533 R&D Projects: GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : Variational analysis and optimization * Parameterized equilibria * Conic constraints * Sensitivity and stability analysis * Solution maps * Graphical derivatives * Normal and tangent cones Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2015 http://library.utia.cas.cz/separaty/2015/MTR/outrata-0449259.pdf

  14. Bifurcation of equilibria between with and without a large island in the large helical device

    Energy Technology Data Exchange (ETDEWEB)

    Ohyabu, N; Narushima, Y; Nagayama, Y; Narihara, K; Morisaki, T; Komori, A [National Institute for Fusion Science, Toki, Gifu, 509-5292 (Japan)

    2005-09-01

    A rapid bifurcation of the equilibria with and without a large island (n/m = 1/1) has been observed in the medium to high beta large helical device discharges. A large island imposed by an external resonant field is suddenly suppressed nearly perfectly by the plasma effects when the beta at the {iota}/2{pi} = 1 surface exceeds a critical value. The critical beta value is nearly proportional to the externally imposed resonant field normalized by the main field strength.

  15. A thermodynamic solution model for calcium carbonate: Towards an understanding of multi-equilibria precipitation pathways

    OpenAIRE

    Donnet, Marcel; Bowen, Paul; Lemaître, Jacques

    2009-01-01

    Thermodynamic solubility calculations are normally only related to thermodynamic equilibria in solution. In this paper, we extend the use of such solubility calculations to help elucidate possible precipitation reaction pathways during the entire reaction. We also estimate the interfacial energy of particles using only solubility data by a modification of Mersmann’s approach. We have carried this out by considering precipitation reactions as a succession of small quasi-equilibrium states. Thu...

  16. High beta tokamaks

    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

  17. 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

  18. Reconnection in tokamaks

    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

  19. Research using small tokamaks

    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

  20. Research using small tokamaks

    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

  1. Compact tokamak reactors

    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

  2. Texas Experimental Tokamak

    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

  3. 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.

  4. 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)

  5. 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

  6. 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

  7. Tokamaks (Second Edition)

    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)

  8. Tokamaks (Second Edition)

    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)

  9. 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

  10. Phase equilibria for mixtures containing very many components. development and application of continuous thermodynamics for chemical process design

    International Nuclear Information System (INIS)

    Cotterman, R.L.; Bender, R.; Prausnitz, J.M.

    1984-01-01

    For some multicomponent mixtures, where detailed chemical analysis is not feasible, the compositio of the mixture may be described by a continuous distribution function of some convenient macroscopic property suc as normal boiling point or molecular weight. To attain a quantitative description of phase equilibria for such mixtures, this work has developed thermodynamic procedures for continuous systems; that procedure is called continuous thermodynamics. To illustrate, continuous thermodynamics is used to calculate dew points for natural-gas mixtures, solvent loss in a high-pressure absorber, and liquid-liquid phase equilibria in a polymer fractionation process. Continuous thermodynamics provides a rational method for calculating phase equilibria for those mixtures where complete chemical analysis is not available but where composition can be given by some statistical description. While continuous thermodynamics is only the logical limit of the well-known pseudo-component method, it is more efficient than that method because it is less arbitrary and it often requires less computer time

  11. Microinstability theory in tokamaks: a review

    International Nuclear Information System (INIS)

    Tang, W.M.

    1977-06-01

    Significant investigations in the area of tokamak microinstability theory are reviewed. Emphasis is given to the work covering the period from 1970 through 1976. Special attention is focused on low-frequency electrostatic drift-type modes, which are generally believed to be the dominant tokamak microinstabilities under normal operating conditions. The basic linear formalism including electromagnetic (finite beta) modifications is presented along with a general survey of the numerous papers investigating specific linear and nonlinear effects on these modes. Estimates of the associated anomalous transport and confinement times are discussed, and a summary of relevant experimental results is given. Studies of the nonelectrostatic and high-frequency instabilities associated with the presence of high energy ions from neutral beam injection (or with the presence of alpha particles from fusion reactions) are also surveyed

  12. Microinstability theory in tokamaks: a review

    Energy Technology Data Exchange (ETDEWEB)

    Tang, W.M.

    1977-06-01

    Significant investigations in the area of tokamak microinstability theory are reviewed. Emphasis is given to the work covering the period from 1970 through 1976. Special attention is focused on low-frequency electrostatic drift-type modes, which are generally believed to be the dominant tokamak microinstabilities under normal operating conditions. The basic linear formalism including electromagnetic (finite beta) modifications is presented along with a general survey of the numerous papers investigating specific linear and nonlinear effects on these modes. Estimates of the associated anomalous transport and confinement times are discussed, and a summary of relevant experimental results is given. Studies of the nonelectrostatic and high-frequency instabilities associated with the presence of high energy ions from neutral beam injection (or with the presence of alpha particles from fusion reactions) are also surveyed.

  13. Design of next step tokamak: Consistent analysis of plasma performance flux composition and poloidal field system

    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)

  14. 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.

  15. 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

  16. 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

  17. 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

  18. 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)

  19. 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

  20. 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

  1. Exogenous empirical-evidence equilibria in perfect-monitoring repeated games yield correlated equilibria

    KAUST Repository

    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.

  2. Exogenous empirical-evidence equilibria in perfect-monitoring repeated games yield correlated equilibria

    KAUST Repository

    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.

  3. Tokamak reactor startup power

    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

  4. 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.)

  5. 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

  6. 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)

  7. High temperature phase equilibria and phase diagrams

    CERN Document Server

    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

  8. Solid-phase equilibria on Pluto's surface

    Science.gov (United States)

    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.

  9. 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

  10. Density limits in Tokamaks

    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)

  11. Tokamak pump limiters

    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

  12. 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

  13. Tokamak pump limiters

    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.)

  14. A unifying approach to existence of Nash equilibria

    NARCIS (Netherlands)

    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

  15. Optimized profiles for improved confinement and stability in the DIII-D tokamak

    International Nuclear Information System (INIS)

    Taylor, T.S.; St. John, H.; Turnbull, A.D.

    1995-02-01

    Simultaneous achievement of high energy confinement, τ E , and high plasma beta, β, leads to an economically attractive compact tokamak fusion reactor. High confinement enhancement, H = τ E /τ E-ITER89P = 4, and high normalized beta β N = β/(I/aB) = 6%-m-T/MA, have been obtained in DIII-D experimental discharges. These improved confinement and/or improved stability limits are observed in several DIII-D high performance operational regimes: VH-mode, high ell i H-mode, second stable core, and high beta poloidal. The authors have identified several important features of the improved performance in these discharges: details of the plasma shape, toroidal rotation or ExB flow profile, q profile and current density profile, and pressure profile. From the improved physics understanding of these enhanced performance regimes, they have developed operational scenarios which maintain the essential features of the improved confinement and which increase the stability limits using localized current profile control. The stability limit is increased by modifying the interior safety factor profile to be nonmonotonic with high central q, while maintaining the edge current density consistent with the improved transport regimes and the high edge bootstrap current. They have calculated high beta equilibria with β N = 6.5, stable to ideal n = 1 kinks and stable to ideal ballooning modes. The safety factor at the 95% flux surface is 6, the central q value is 3.9 and the minimum in q is 2.6. The current density profile is maintained by the natural profile of the bootstrap current, and a modest amount of electron cyclotron current drive

  16. Theory-based model for the pedestal, edge stability and ELMs in tokamaks

    International Nuclear Information System (INIS)

    Pankin, A.Y.; Bateman, G.; Brennan, D.P.; Schnack, D.D.; Snyder, P.B.; Voitsekhovitch, I.; Kritz, A.H.; Janeschitz, G.; Kruger, S.; Onjun, T.; Pacher, G.W.; Pacher, H.D.

    2006-01-01

    An improved model for triggering edge localized mode (ELM) crashes is developed for use within integrated modelling simulations of the pedestal and ELM cycles at the edge of H-mode tokamak plasmas. The new model is developed by using the BALOO, DCON and ELITE ideal MHD stability codes to derive parametric expressions for the ELM triggering threshold. The whole toroidal mode number spectrum is studied with these codes. The DCON code applies to low mode numbers, while the BALOO code applies to only high mode numbers and the ELITE code applies to intermediate and high mode numbers. The variables used in the parametric stability expressions are the normalized pressure gradient and the parallel current density, which drive ballooning and peeling modes. Two equilibria motivated by DIII-D geometry with different plasma triangularities are studied. It is found that the stable region in the high triangularity discharge covers a much larger region of parameter space than the corresponding stability region in the low triangularity discharge. The new ELM trigger model is used together with a previously developed model for pedestal formation and ELM crashes in the ASTRA integrated modelling code to follow the time evolution of the temperature profiles during ELM cycles. The ELM frequencies obtained in the simulations of low and high triangularity discharges are observed to increase with increasing heating power. There is a transition from second stability to first ballooning mode stability as the heating power is increased in the high triangularity simulations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD

  17. Optimized profiles for improved confinement and stability in the Dill-D tokamak

    International Nuclear Information System (INIS)

    Taylor, T.S.; St John, H.; Turnbull, A.D.

    1994-01-01

    Simultaneous achievement of high energy confinement, τ E , and high plasma beta, β, leads to an economically attractive compact tokamak fusion reactor. High confinement enhancement, H τ E /τ E -ITER89P 4, and high normalized beta β N β/(I/aB) = 6%-m-T/MA. have been obtained in DIII-D experimental discharges. These improved confinement and/or improved stability limits are observed in several DIII-D high performance operational regimes: VH-mode, high l i H-mode, second stable core, and high beta poloidal. We have identified several important features of the improved performance in these discharges: details of the plasma shape, toroidal rotation or ExB flow profile, q profile and current density profile, and pressure profile. From our improved physics understanding of these enhanced performance regimes, we have developed operational scenarios which maintain the essential features of the improved confinement and which increase the stability limits using localized current profile control. The stability limit is increased by modifying the interior safety factor profile to be nonmonotonic with high central q, while maintaining the edge current density consistent with the improved transport regimes and the high edge bootstrap current. We have calculated high beta equilibria with β N 6.5, stable to ideal n=1 kinks and stable to ideal ballooning modes. The safety factor at the 95% flux surface is 6, the central q value is 3.9 and the minimum in q is 2.6. The current density profile is maintained by the natural profile of the bootstrap current, and a modest amount of electron cyclotron current drive. (Author)

  18. 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

  19. 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

  20. 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

  1. Systematic design and simulation of a tearing mode suppression feedback control system for the TEXTOR tokamak

    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)

  2. 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

  3. Equilibria of perceptrons for simple contingency problems.

    Science.gov (United States)

    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.

  4. Status of the tokamak program

    Science.gov (United States)

    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.

  5. 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

  6. The density limit in Tokamaks

    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

  7. 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)

  8. Tokamaks - Third Edition

    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

  9. 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

  10. Prediction of vapour-liquid equilibria for the kinetic study of processes based on synthesis gas

    Energy Technology Data Exchange (ETDEWEB)

    Di Serio, M.; Tesser, R.; Cozzolino, M.; Santacesaria, E. [Naples Univ., Napoli (Italy). Dept. of Chemistry

    2006-07-01

    Syngas is normally used in the production of a broad range of chemicals and fuels. In many of these processes multiphase reactors, gas-liquid or gas-liquid-solid are used. Kinetic studies in multiphase systems are often complicated by the non-ideal behaviour of reagents and/or products that are consistently partitioned between the liquid and the vapour phase. Moreover, as often kinetic data are collected in batch conditions for the liquid phase, activity coefficients of the partitioned components can consistently change during the time as a consequence of changing the composition of the reaction mixture. Therefore, it is necessary, in these cases, to known the vapor-liquid equilibria (VLE) in order to collect and to interpret correctly the kinetic data. The description of phase equilibria, at high pressures, is usually performed by means of an EOS (Equation of State) allowing the calculation of fugacity coefficients, for each component, in both phases and determining the partition coefficients but the EOS approach involves the experimental determination of the interaction parameters for all the possible binary system of the mixture. For multicomponent mixtures a complete experimental determination of vapourliquid equilibria is very hard, also considering the high pressure and temperatures used. Some predictive group contribution methods have been recently developed. In this paper, we will describe in detail the application of these methods to the methanol homologation, as an example, with the scope of determining more reliable kinetic parameters for this reaction. (orig.)

  11. 'Crescent'-shaped tokamak for compact ignition

    International Nuclear Information System (INIS)

    Yamazaki, K.; Reiersen, W.T.

    1985-12-01

    A compact high-beta tokamak configuration with ''crescent''-shaped (or ''boomerang''-shaped) cross-section is proposed as a next-generation ignition machine. This configuration with a small indentation but a large triangularity is more compact than the normal dee-shaped design because of its high-beta characteristics in the first-second transition regime of stability. This may also be a more reliable next-generation compact device than the bean-shaped design with large indentation and small triangularity, because this design dose not rely on the second stability and is easily extendable from the present dee-shaped design. (author)

  12. 'Crescent'-shaped tokamak for compact ignition

    International Nuclear Information System (INIS)

    Yamazaki, K.; Reiersen, W.T.

    1986-01-01

    A compact high-beta tokamak configuration with ''crescent''-shaped (or ''boomerang''-shaped) cross section is proposed as a next-generation ignition machine. This configuration with a small indentation but a large triangularity is more compact than the normal dee-shaped design because of its high-beta characteristics in the first-second transition regime of stability. This may also be a more reliable next-generation compact device than the bean-shaped design with large indentation and small triangularity, because this design does not rely on the second stability and is easily extendable from the present dee-shaped design. (author)

  13. 'Snowflake' H Mode in a Tokamak Plasma

    International Nuclear Information System (INIS)

    Piras, F.; Coda, S.; Duval, B. P.; Labit, B.; Marki, J.; Moret, J.-M.; Pitzschke, A.; Sauter, O.; Medvedev, S. Yu.

    2010-01-01

    An edge-localized mode (ELM) H-mode regime, supported by electron cyclotron heating, has been successfully established in a 'snowflake' (second-order null) divertor configuration for the first time in the TCV tokamak. This regime exhibits 2 to 3 times lower ELM frequency and 20%-30% increased normalized ELM energy (ΔW ELM /W p ) compared to an identically shaped, conventional single-null diverted H mode. Enhanced stability of mid- to high-toroidal-mode-number ideal modes is consistent with the different snowflake ELM phenomenology. The capability of the snowflake to redistribute the edge power on the additional strike points has been confirmed experimentally.

  14. 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

  15. 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

  16. 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

  17. 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...

  18. ITER tokamak device

    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

  19. Dust Measurements in Tokamaks

    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

  20. 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)

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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....

  6. 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)

  7. On the uniqueness of fully informative rational expectations equilibria

    OpenAIRE

    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...

  8. Research using small tokamaks

    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

  9. The effect of pressure anisotropy on ballooning modes in tokamak plasmas

    Science.gov (United States)

    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.

  10. 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

  11. 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.

  12. 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.)

  13. Alcator C-Mod Tokamak

    Data.gov (United States)

    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...

  14. 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)

  15. Preliminary Design of Alborz Tokamak

    Science.gov (United States)

    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.

  16. 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

  17. The Tokamak IST-TOK

    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

  18. 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

  19. 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

  20. 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)

  1. 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

  2. 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)

  3. 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)

  4. 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)

  5. 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)

  6. High Beta Tokamak research

    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

  7. 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

  8. Tokamak hybrid study

    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

  9. Tokamak hybrid study

    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

  10. The Compact Ignition Tokamak

    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

  11. Plasma turbulence in tokamaks

    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)

  12. Disruptions in Tokamaks

    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)

  13. ADVANCED TOKAMAK OPERATION USING THE DIII-D PLASMA CONTROL SYSTEM

    International Nuclear Information System (INIS)

    HUMPHREYS, DA; FERRON, JR; GAROFALO, AM; HYATT, AW; JERNIGAN, TC; JOHNSON, RD; LAHAYE, RJ; LEUER, JA; OKABAYASHI, M; PENAFLOR, BG; SCOVILLE, JT; STRAIT, EJ; WALKER, ML; WHYTE, DG

    2002-01-01

    A271 ADVANCED TOKAMAK OPERATION USING THE DIII-D PLASMA CONTROL SYSTEM. The principal focus of experimental operations in the DIII-D tokamak is the advanced tokamak (AT) regime to achieve, which requires highly integrated and flexible plasma control. In a high performance advanced tokamak, accurate regulation of the plasma boundary, internal profiles, pumping, fueling, and heating must be well coordinated with MHD control action to stabilize such instabilities as tearing modes and resistive wall modes. Sophisticated monitors of the operational regime must provide detection of off-normal conditions and trigger appropriate safety responses with acceptable levels of reliability. Many of these capabilities are presently implemented in the DIII-D plasma control system (PCS), and are now in frequent or routine operational use. The present work describes recent development, implementation, and operational experience with AT regime control elements for equilibrium control, MHD suppression, and off-normal event detection and response

  14. 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

  15. 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

  16. Thermodynamic Equilibria and Extrema Analysis of Attainability Regions and Partial Equilibria

    CERN Document Server

    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.

  17. Unifying dynamical and structural stability of equilibria

    Science.gov (United States)

    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.

  18. Axisymmetric plasma equilibria in a Kerr metric

    Science.gov (United States)

    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.

  19. 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

  20. 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.

  1. 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

  2. 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

  3. 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)

  4. 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)

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. Surface currents on the plasma-vacuum interface in MHD equilibria

    Science.gov (United States)

    Hanson, James

    2017-10-01

    The VMEC non-axisymmetric MHD equilibrium code can compute free-boundary equilibria. Since VMEC assumes that magnetic fields within the plasma form closed and nested flux surfaces, the plasma-vacuum interface is a flux surface, and the total magnetic field there has no normal component. VMEC imposes this condition of zero normal field using the potential formulation of Merkel, and solves a Neumann problem for the magnetic potential in the exterior region. This boundary condition necessarily admits the possibility of a surface current on the interface. While this surface current may be small in MHD equilibrium, it is readily computed in terms of the magnetic potentials in both the interior and exterior regions, evaluated on the surface. If only the external magnetic potential is known (as in VMEC), then the surface current can be computed from the discontinuity of the tangential field across the interface. Examples of the surface current for VMEC equilibria will be shown for a zero-pressure stellarator equilibrium. Field-line following of the vacuum magnetic field shows magnetic islands within the plasma region.

  10. 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

  11. 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

  12. 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

  13. 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)

  14. 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

  15. Theory of equilibria of elastic 2-braids with interstrand interaction

    Science.gov (United States)

    Starostin, E. L.; van der Heijden, G. H. M.

    2014-03-01

    Motivated by continuum models for DNA supercoiling we formulate a theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. No assumption is made on the shape of the contact curve. The theory is developed in terms of a moving frame of directors attached to one of the strands. The other strand is tracked by including in this frame the normalised closest-approach chord connecting the two strands. The kinematic constant-distance constraint is formulated at strain level through the introduction of what we call braid strains. As a result the total potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Hard contact models are used to obtain the normal contact pressure between strands that has to be non-negative for a physically realisable solution without the need for external devices such as clamps or glue to keep the strands together. The theory is first illustrated by a number of problems that can be solved analytically and then applied to several new problems that have not hitherto been treated.

  16. 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)

  17. 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...

  18. Measurement of the energy balance in ATC Tokamak

    International Nuclear Information System (INIS)

    Hsuan, H.; Bol, K.; Ellis, R.A.

    1975-01-01

    Gross properties of the energy balance in the ATC tokamak have been investigated. During the quasi-steady state phase of a normal discharge, the major part of the energy loss was found to be the limiters. Radiation and charge-exchange play minor roles during this quasi-steady state phase, but are nevertheless the dominant loss mechanisms at the termination of a discharge; and account for a substantial portion of the stored poloidal magnetic energy associated with the plasma current. (auth)

  19. Problems with the concept of plasma equilibrium in tokamaks

    International Nuclear Information System (INIS)

    Carreras, B.A.

    1992-01-01

    The equilibrium condition for a magnetically confined plasma in normally formulated in terms of macroscopic equations. In these equations, the plasma pressure is assumed to be a function of the magnetic flux with continuous derivatives. However, in three- dimensional systems this is not necessarily the case. Here, we look at the case of an intrinsically three-dimensional realistic tokamak, and we discuss the possible interconnection between the equilibrium and anomalous transport

  20. 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)

  1. 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

  2. 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.)

  3. 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)

  4. Nematic Equilibria on a Two-Dimensional Annulus

    KAUST Repository

    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.

  5. Hydrostatic Equilibria of Rotating Stars with Realistic Equation of State

    Science.gov (United States)

    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.

  6. Nematic Equilibria on a Two-Dimensional Annulus

    KAUST Repository

    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.

  7. 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

  8. 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)

  9. 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

  10. 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

  11. 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

  12. 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....

  13. 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....

  14. 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...

  15. The tokamak hybrid reactor

    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.)

  16. 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 ...

  17. Evaluation of a Mathematical Model for Single Component Adsorption Equilibria with Reference to the Prediction of Multicomponent Adsorption Equilibria

    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...

  18. EUV impurity study of the Alcator tokamak

    International Nuclear Information System (INIS)

    Terry, J.L.; Chen, K.I.; Moos, H.W.; Marmar, E.S.

    1978-01-01

    The intensity of resonance line radiation from oxygen, nitrogen, carbon and molybdenum impurities has been measured in the high-field (80kG), high-density (6x10 14 cm -3 ) discharges of the Alcator Tokamak, using a 0.4-m normal-incidence monochromator (300-1300A) with its line of sight fixed along a major radius. Total light-impurity concentrations of a few tenths of a percent have been estimated by using both a simple model and a computer code which included Pfirsch-Schlueter impurity diffusion. The resulting values of Zsub(eff), including the contributions due to both the light impurities and molybdenum, were close to one. The power lost through the impurity line radiation from the lower ionization states accounted for approximately 10% of the total Ohmic input power at high densities. (author)

  19. 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

  20. 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

  1. 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.

  2. ECRH Studies on Tokamak Plasmas.

    Science.gov (United States)

    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

  3. 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

  4. 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)

  5. An enhanced tokamak startup model

    Science.gov (United States)

    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.

  6. 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

  7. 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

  8. Evaluation of Thermodynamic Models for Predicting Phase Equilibria of CO2 + Impurity Binary Mixture

    Science.gov (United States)

    Shin, Byeong Soo; Rho, Won Gu; You, Seong-Sik; Kang, Jeong Won; Lee, Chul Soo

    2018-03-01

    For the design and operation of CO2 capture and storage (CCS) processes, equation of state (EoS) models are used for phase equilibrium calculations. Reliability of an EoS model plays a crucial role, and many variations of EoS models have been reported and continue to be published. The prediction of phase equilibria for CO2 mixtures containing SO2, N2, NO, H2, O2, CH4, H2S, Ar, and H2O is important for CO2 transportation because the captured gas normally contains small amounts of impurities even though it is purified in advance. For the design of pipelines in deep sea or arctic conditions, flow assurance and safety are considered priority issues, and highly reliable calculations are required. In this work, predictive Soave-Redlich-Kwong, cubic plus association, Groupe Européen de Recherches Gazières (GERG-2008), perturbed-chain statistical associating fluid theory, and non-random lattice fluids hydrogen bond EoS models were compared regarding performance in calculating phase equilibria of CO2-impurity binary mixtures and with the collected literature data. No single EoS could cover the entire range of systems considered in this study. Weaknesses and strong points of each EoS model were analyzed, and recommendations are given as guidelines for safe design and operation of CCS processes.

  9. 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.

  10. Stability of equilibria for a two-phase osmosis model

    NARCIS (Netherlands)

    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

  11. A Numerical Algorithm to find All Scalar Feedback Nash Equilibria

    NARCIS (Netherlands)

    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

  12. 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....

  13. 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.

  14. 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....

  15. Predicting phase equilibria in one-component systems

    Science.gov (United States)

    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.

  16. 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)

  17. 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....

  18. 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...

  19. 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...

  20. 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

  1. On Nash-Equilibria of Approximation-Stable Games

    Science.gov (United States)

    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.

  2. 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

  3. 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

  4. 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

  5. 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

  6. A cross-tokamak neural network disruption predictor for the JET and ASDEX Upgrade tokamaks

    Science.gov (United States)

    Windsor, C. G.; Pautasso, G.; Tichmann, C.; Buttery, R. J.; Hender, T. C.; EFDA Contributors, JET; ASDEX Upgrade Team

    2005-05-01

    First results are reported on the prediction of disruptions in one tokamak, based on neural networks trained on another tokamak. The studies use data from the JET and ASDEX Upgrade devices, with a neural network trained on just seven normalized plasma parameters. In this way, a simple single layer perceptron network trained solely on JET correctly anticipated 67% of disruptions on ASDEX Upgrade in advance of 0.01 s before the disruption. The converse test led to a 69% success rate in advance of 0.04 s before the disruption in JET. Only one overall time scaling parameter is allowed between the devices, which can be introduced from theoretical arguments. Disruption prediction performance based on such networks trained and tested on the same device shows even higher success rates (JET, 86%; ASDEX Upgrade, 90%), despite the small number of inputs used and simplicity of the network. It is found that while performance for networks trained and tested on the same device can be improved with more complex networks and many adjustable weights, for cross-machine testing the best approach is a simple single layer perceptron. This offers the basis of a potentially useful technique for large future devices such as ITER, which with further development might help to reduce disruption frequency and minimize the need for a large disruption campaign to train disruption avoidance systems.

  7. A cross-tokamak neural network disruption predictor for the JET and ASDEX Upgrade tokamaks

    International Nuclear Information System (INIS)

    Windsor, C.G.; Buttery, R.J.; Hender, T.C.; Pautasso, G.; Tichmann, C.

    2005-01-01

    First results are reported on the prediction of disruptions in one tokamak, based on neural networks trained on another tokamak. The studies use data from the JET and ASDEX Upgrade devices, with a neural network trained on just seven normalized plasma parameters. In this way, a simple single layer perceptron network trained solely on JET correctly anticipated 67% of disruptions on ASDEX Upgrade in advance of 0.01 s before the disruption. The converse test led to a 69% success rate in advance of 0.04 s before the disruption in JET. Only one overall time scaling parameter is allowed between the devices, which can be introduced from theoretical arguments. Disruption prediction performance based on such networks trained and tested on the same device shows even higher success rates (JET, 86%; ASDEX Upgrade, 90%), despite the small number of inputs used and simplicity of the network. It is found that while performance for networks trained and tested on the same device can be improved with more complex networks and many adjustable weights, for cross-machine testing the best approach is a simple single layer perceptron. This offers the basis of a potentially useful technique for large future devices such as ITER, which with further development might help to reduce disruption frequency and minimize the need for a large disruption campaign to train disruption avoidance systems

  8. Safety in the ARIES Tokamak Design Study

    International Nuclear Information System (INIS)

    Herring, J.S.; Wong, C.P.-C.; Cheng, E.T.; Grotz, S.

    1989-01-01

    Safety is one of the primary goals of the ARIES Tokamak Design Study. Public safety goals are the achievement passive safety which is demonstrable in tests that could precede operation and the assurance that releases from accidents be passively limited such that no evacuation plan in necessary. Strategies for safety of the plant investment are factory fabrication, short construction times and a design such that no off-normal operational transient results in damage which could not be repaired in routine maintenance. ARIES-I, the first of three 'visions' of potential tokamak reactors, will use He at 5 MPa as a blanket coolant and SiC/composite ceramic for the first wall and blanket materials. Both the coolant and the structural material were chosen for their low activation, both in the short term after accidents and for long term waste management. The breeder, Li 4 SiO 4 , was also chosen for low activation. Contemporary plasma physics and aggressive technology are used in ARIES-I, which results in very high toroidal fields (24 T maximum at the coil). The stored TF energy will be about 130 GJ. A central concern is the safe discharge of this stored energy under electrical fault conditions and prevention of a failure in the magnet set from propagating into systems containing radioactive inventories. The TF coil system consists of 16 coils, each containing two separate windings powered by two independent power supplies. Arcs and shorts between the two power supply systems and across individual windings have been modeled. In addition, delay or failure in circuit breaker opening has been modeled. The safety impacts of LOCA, LOFA and disruptive events have also been evaluated. 8 refs., 4 figs., 7 tabs

  9. 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

  10. 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)

  11. 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

  12. On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch-Schlueter diffusion

    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

  13. On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch-Schlüter diffusion

    Science.gov (United States)

    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.

  14. 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.

  15. 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

  16. 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)

  17. 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

  18. 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

  19. 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

  20. 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

  1. 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

  2. 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.)

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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.)

  9. 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

  10. 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)

  11. 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

  12. Phase diagrams and heterogeneous equilibria a practical introduction

    CERN Document Server

    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.

  13. 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...

  14. Magnetic coordinates for equilibria with a continuous symmetry

    International Nuclear Information System (INIS)

    Dewar, R.L.; Monticello, D.A.; Sy, W.N.C.

    1983-08-01

    Magnetic coordinates for hydromagnetic equilibria are defined which treat toroidal and straight helical plasmas equivalently yet exploit the existence of a continuous symmetry to derive relations between various geometrical and physical quantities. This allows the number of equilibrium quantities which must be known to be reduced to a minimal, or primitive set. Practical formulae for various quantities required in hydromagnetic stability calculations (interchange, ballooning, and global) are given in terms of this primitive set

  15. Phase equilibria and phase structures of polymer blends

    International Nuclear Information System (INIS)

    Chalykh, Anatolii E; Gerasimov, Vladimir K

    2004-01-01

    Experimental, methodical and theoretical studies dealing with phase equilibria and phase structures of polymer blends are generalised. The general and specific features of the change in solubility of polymers with changes in the molecular mass and copolymer composition and upon the formation of three-dimensional cross-linked networks are described. The results of the effect of the prehistory on the phase structure and the non-equilibrium state of polymer blends are considered in detail.

  16. Existence of equilibria in quantum Bertrand-Edgeworth duopoly game

    Science.gov (United States)

    Sekiguchi, Yohei; Sakahara, Kiri; Sato, Takashi

    2012-12-01

    Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter condition than that of the idealized one in the classical form game. This is the problem known as Edgeworth paradox in economics. In the quantum form game, however, the former converges to the latter as the measure of entanglement goes to infinity.

  17. Analysis on Θ pumping for tokamak current drive

    International Nuclear Information System (INIS)

    Miyamoto, Kenro; Naito, Osamu

    1986-01-01

    Analytical results of Θ pumping for the tokamak current drive are presented. Diffusion of externally applied oscillating electric field into the tokamak plasma is examined when the plasma is normal. When the oscillating electric field is parallel to the stationary toroidal plasma current and the induced current density by the applied electric field becomes larger than the average density of the toroidal plasma current over the plasma cross section, the radial profile of the safety factor has the extremum near the plasma boundary region and MHD instabilities are excited. It is assumed that anomalous diffusion of the induced current localized in the plasma boundary region takes place, so that the extreme value in the radial profile of the safety factor disappears. The anomalously diffused electric field due to this relaxation process has net d. c component and its non-zero value of the time average is estimated. Then the condition of the tokamak current drive by Θ pumping is derived. Some numerical results are presented for an example of a fusion grade plasma. (author)

  18. Variational-moment method for computing magnetohydrodynamic equilibria

    International Nuclear Information System (INIS)

    Lao, L.L.

    1983-08-01

    A fast yet accurate method to compute magnetohydrodynamic equilibria is provided by the variational-moment method, which is similar to the classical Rayleigh-Ritz-Galerkin approximation. The equilibrium solution sought is decomposed into a spectral representation. The partial differential equations describing the equilibrium are then recast into their equivalent variational form and systematically reduced to an optimum finite set of coupled ordinary differential equations. An appropriate spectral decomposition can make the series representing the solution coverge rapidly and hence substantially reduces the amount of computational time involved. The moment method was developed first to compute fixed-boundary inverse equilibria in axisymmetric toroidal geometry, and was demonstrated to be both efficient and accurate. The method since has been generalized to calculate free-boundary axisymmetric equilibria, to include toroidal plasma rotation and pressure anisotropy, and to treat three-dimensional toroidal geometry. In all these formulations, the flux surfaces are assumed to be smooth and nested so that the solutions can be decomposed in Fourier series in inverse coordinates. These recent developments and the advantages and limitations of the moment method are reviewed. The use of alternate coordinates for decomposition is discussed

  19. (Liquid + liquid) equilibria of perfluorocarbons with fluorinated ionic liquids

    International Nuclear Information System (INIS)

    Martinho, S.; Araújo, J.M.M.; Rebelo, L.P.N.; Pereiro, A.B.; Marrucho, I.M.

    2013-01-01

    Highlights: • (Liquid + liquid) equilibria perfluorocarbons and fluorinated ionic liquids. • Non-Random Two Liquid model was successfully applied. • Thermodynamic functions that describe the solvation process were calculated. -- Abstract: In order to evaluate the feasibility of partially replace perfluorocarbons (PFCs) with fluorinated ionic liquids (FILs) in PFCs-in-water emulsions, usually used for biomedical purposes, herein the (liquid + liquid) phase equilibria of FILs containing fluorinated chains longer than four carbons with PFCs were carried out in a wide range of temperatures. With this goal in mind, two PFCs (perfluorooctane and perfluorodecalin) were selected and the (liquid + liquid) equilibria of the binary mixtures of these PFCs and FILs were studied at atmospheric pressure in a temperature range from T (293.15 to 343.15) K. For these studies, FILs containing ammonium, pyridinium and imidazolium cations and different anions with fluorocarbon alkyl chains between 4 and 8 were included. Additionally, Non-Random Two Liquid (NRTL) thermodynamic model was successfully applied to correlate the behaviour of the PFCs + FILs binary mixtures. Moreover, thermodynamic functions that describe the solvation process were calculated from the experimental data

  20. Long-term Nash equilibria in electricity markets

    International Nuclear Information System (INIS)

    Pozo, David; Contreras, Javier; Caballero, Angel; de Andres, Antonio

    2011-01-01

    In competitive electricity markets, companies simultaneously offer their productions to obtain the maximum profits on a daily basis. In the long run, the strategies utilized by the electric companies lead to various long-term equilibria that can be analyzed with the appropriate tools. We present a methodology to find plausible long-term Nash equilibria in pool-based electricity markets. The methodology is based on an iterative market Nash equilibrium model in which the companies can decide upon their offer strategies. An exponential smoothing of the bids submitted by the companies is applied to facilitate the convergence of the iterative procedure. In each iteration of the model the companies face residual demand curves that are accurately modeled by Hermite interpolating polynomials. We introduce the concept of meta-game equilibrium strategies to allow companies to have a range of offer strategies where several pure and mixed meta-game Nash equilibria are possible. With our model it is also possible to model uncertainty or to generate price scenarios for financial models that assess the value of a generating unit by real options analysis. The application of the proposed methodology is illustrated with several realistic case studies. (author)

  1. The Pierce diode with an external circuit. I. Oscillations about nonuniform equilibria

    International Nuclear Information System (INIS)

    Lawson, W.S.

    1989-01-01

    The nonuniform (nonlinear) equilibria of the classical (short circuit) Pierce diode and the extended (series RLC external circuit) Pierce diode are described, and the spectrum of oscillations (stable and unstable) about these equilibria are worked out. It is found that only the external capacitance alters the equilibria, though all elements alter the spectrum. In particular, the introduction of an external capacitor destabilizes some equilibria that are marginally stable without the capacitor. Computer simulations are performed to test the theoretical predictions for the case of an external capacitor only. It is found that most equilibria are correctly predicted by theory, but that the continuous set of equilibria of the classical Pierce diode at Pierce parameters (α=ω/sub pL//v 0 ) that are multiples of 2π are not observed. This appears to be a failure of the simulation method under the rather singular conditions rather than a failure of the theory

  2. Development path of low aspect ratio tokamak power plants

    International Nuclear Information System (INIS)

    Stambaugh, R.D.; Chan, V.S.; Miller, R.L.

    1997-03-01

    Recent advances in tokamak physics indicate the spherical tokamak may offer a magnetic fusion development path that can be started with a small size pilot plant and progress smoothly to larger power plants. Full calculations of stability to kink and ballooning modes show the possibility of greater than 50% beta toroidal with the normalized beta as high as 10 and fully aligned 100% bootstrap current. Such beta values coupled with 2--3 T toroidal fields imply a pilot plant about the size of the present DIII-D tokamak could produce ∼ 800 MW thermal, 160 MW net electric, and would have a ratio of gross electric power over recirculating power (Q PLANT ) of 1.9. The high beta values in the ST mean that E x B shear stabilization of turbulence should be 10 times more effective in the ST than in present tokamaks, implying that the required high quality of confinement needed to support such high beta values will be obtained. The anticipated beta values are so high that the allowable neutron flux at the blanket sets the device size, not the physics constraints. The ST has a favorable size scaling so that at 2--3 times the pilot plant size the Q PLANT rises to 4--5, an economic range and 4 GW thermal power plants result. Current drive power requirements for 10% of the plasma current are consistent with the plant efficiencies quoted. The unshielded copper centerpost should have an adequate lifetime against nuclear transmutation induced resistance change and the low voltage, high current power supplies needed for the 12 turn TF coil appear reasonable. The favorable size scaling of the ST and the high beta mean that in large sizes, if the copper TF coil is replaced with a superconducting TF coil and a shield, the advanced fuel D-He 3 could be burned in a device with Q PLANT ∼ 4

  3. Magnetic confinement by Tokamak: physical aspects

    International Nuclear Information System (INIS)

    Tachon, J.

    1980-01-01

    After describing the Tokamak configuration concept, the author provides an analysis of the principal physical aspects of this type of installation and concludes by estimating that the Tokamak concept is a 'plausible candidate' as a means of producing controlled thermonuclear fusion [fr

  4. Economic evaluation of tokamak power plants

    International Nuclear Information System (INIS)

    Reid, R.L.; Steiner, D.

    1977-01-01

    This study reports the impact of plasma operating characteristics, engineering options, and technology on the capital cost trends of tokamak power plants. Tokamak power systems are compared to other advanced energy systems and found to be economically competitive. A three-phase strategy for demonstrating commercial feasibility of fusion power, based on a common-site multiple-unit concept, is presented

  5. Simulation of a major tokamak disruption

    International Nuclear Information System (INIS)

    White, R.B.; Monticello, D.A.; Rosenbluth, M.N.

    1977-08-01

    It is known that the internal tokamak disruption leads to a current profile which is flattened inside the surface where the safety factor equals unity. It is shown that such a profile can lead to m = 2 magnetic islands which grow to fill a substantial part of the tokamak cross section in a time consistent with the observations of the major disruption

  6. Diagnostics for the Rijnhuizen Tokamak Project

    NARCIS (Netherlands)

    Donne, A. J. H.

    1994-01-01

    The research program of the Rijnhuizen Tokamak Project is concentrated on the study of plasma transport processes. The RTP tokamak is therefore equipped with an extensive set of multichannel diagnostics, including a 19-channel FIR interferometer, a 20-channel heterodyne ECE system, an 80-channel

  7. MAST: a Mega Amp Spherical Tokamak

    International Nuclear Information System (INIS)

    Darke, A.C.; Harbar, J.R.; Hay, J.H.; Hicks, J.B.; Hill, J.W.; McKenzie, J.S.; Morris, A.W.; Nightingale, M.P.S.; Todd, T.N.; Voss, G.M.; Watkins, J.R.

    1995-01-01

    The highly successful tight aspect ratio tokamak research pioneered on the START machine at Culham, together with the attractive possibilities of the concept, suggest a larger device should be considered. The design of a Mega Amp Spherical Tokamak is described, operating at much higher currents and over longer pulses than START and compatible with strong additional heating. (orig.)

  8. Mercier criterion for high-β tokamaks

    International Nuclear Information System (INIS)

    Galvao, R.M.O.

    1984-01-01

    An expression, for the application of the Mercier criterion to numerical studies of diffuse high-β tokamaks (β approximatelly Σ,q approximatelly 1), which contains only leading order contributions in the high-β tokamak approximation is derived. (L.C.) [pt

  9. The ARIES-I tokamak reactor study

    International Nuclear Information System (INIS)

    1991-01-01

    This report contains an overview of the Aries-I tokamak reactor study. The following topics are discussed on this tokamak: Systems studies; equilibrium, stability, and transport; summary and conclusions; current drive; impurity control system; tritium systems; magnet engineering; fusion-power-core engineering; power conversion; Aries-I safety design and analysis; design layout and maintenance; and start-up and operations

  10. Engineering Design of KSTAR tokamak main structure

    International Nuclear Information System (INIS)

    Im, K.H.; Cho, S.; Her, N.I.

    2001-01-01

    The main components of the KSTAR (Korea Superconducting Tokamak Advanced Research) tokamak including vacuum vessel, plasma facing components, cryostat, thermal shield and magnet supporting structure are in the final stage of engineering design. Hundai Heavy Industries (HHI) has been involved in the engineering design of these components. The current configuration and the final engineering design results for the KSTAR main structure are presented. (author)

  11. Extremely fast vertical displacement event induced by a plasma βp collapse in high βp tokamak disruptions

    International Nuclear Information System (INIS)

    Nakamura, Yukiharu; Yoshino, Ryuji; Pomphrey, N.; Jardin, S.C.

    1996-05-01

    In a vertically elongated (κ ∼ 1.5), high β p (β p ∼ 1.7) tokamak with a resistive shell, extremely fast vertical displacement events (VDE's) induced by a model of strong β p collapse were found through computer simulations using the Tokamak Simulation Code. Although the plasma current quench, which had been shown to be the prime cause of VDE's in a relatively low β p tokamak (β p ∼ 0.2), was not observed during the VDE evolution, the observed growth rate of VDE's was almost five times (γ ∼ 655 sec -1 ) faster than the growth rate of the usual positional instability (γ ∼ 149 sec -1 ). The essential mechanism of the β p collapse-induced VDE was clarified to be the significant destabilization of positional instability due to a large and sudden degradation of the decay n-index in addition to a reduction of the stability index n s . It is pointed out that the shell-geometry characterizes the VDE dynamics, and that the VDE rate depends strongly both on the magnitude of the β p collapse and the n-index of the equilibria just before the β p collapse occurs. A new guide line for designing the fusion reactor is proposed with considering the impact of disruptions. (author)

  12. Bifurcated states of a rotating tokamak plasma in the presence of a static error-field

    International Nuclear Information System (INIS)

    Fitzpatrick, R.

    1998-01-01

    The bifurcated states of a rotating tokamak plasma in the presence of a static, resonant, error-field are strongly analogous to the bifurcated states of a conventional induction motor. The two plasma states are the open-quotes unreconnectedclose quotes state, in which the plasma rotates and error-field-driven magnetic reconnection is suppressed, and the open-quotes fully reconnectedclose quotes state, in which the plasma rotation at the rational surface is arrested and driven magnetic reconnection proceeds without hindrance. The response regime of a rotating tokamak plasma in the vicinity of the rational surface to a static, resonant, error-field is determined by three parameters: the normalized plasma viscosity, P, the normalized plasma rotation, Q 0 , and the normalized plasma resistivity, R. There are 11 distinguishable response regimes. The extents of these regimes are calculated in P endash Q 0 endash R space. In addition, an expression for the critical error-field amplitude required to trigger a bifurcation from the open-quotes unreconnectedclose quotes to the open-quotes fully reconnectedclose quotes state is obtained in each regime. The appropriate response regime for low-density, ohmically heated, tokamak plasmas is found to be the nonlinear constant-ψ regime for small tokamaks, and the linear constant-ψ regime for large tokamaks. The critical error-field amplitude required to trigger error-field-driven magnetic reconnection in such plasmas is a rapidly decreasing function of machine size, indicating that particular care may be needed to be taken to reduce resonant error-fields in a reactor-sized tokamak. copyright 1998 American Institute of Physics

  13. Summary report on tokamak confinement experiments

    International Nuclear Information System (INIS)

    1982-03-01

    There are currently five major US tokamaks being operated and one being constructed under the auspices of the Division of Toroidal Confinement Systems. The currently operating tokamaks include: Alcator C at the Massachusetts Institute of Technology, Doublet III at the General Atomic Company, the Impurity Studies Experiment (ISX-B) at the Oak Ridge National Laboratory, and the Princeton Large Torus (PLT) and the Poloidal Divertor Experiment (PDX) at the Princeton Plasma Physics Laboratory. The Tokamak Fusion Test Reactor (TFTR) is under construction at Princeton and should be completed by December 1982. There is one major tokamak being funded by the Division of Applied Plasma Physics. The Texas Experimental Tokamak (TEXT) is being operated as a user facility by the University of Texas. The TEXT facility includes a complete set of standard diagnostics and a data acquisition system available to all users

  14. The effects of plasma deformability on the feedback stabilization of axisymmetric modes in tokamak plasmas

    International Nuclear Information System (INIS)

    Ward, D.J.; Jardin, S.C.

    1991-09-01

    The effects of plasma deformability on the feedback stabilization of axisymmetric modes of tokamak plasmas are studied. It is seen that plasmas with strongly shaped cross sections have unstable motion different from a rigid shift. Furthermore, the placement of passive conductors is shown to modify the non-rigid components of the eigenfunction in a way that reduces the stabilizing eddy currents in these conductors. Passive feedback results using several equilibria of varying shape are presented. The eigenfunction is also modified under the effects of active feedback. This deformation is seen to depend strongly on the position of the flux loops which are used to determine plasma vertical position for the active feedback system. The variations of these non-rigid components of the eigenfunction always serve to reduce the stabilizing effect of the active feedback system by reducing the measurable poloidal flux at the flux-loop locations. Active feedback results are presented for the PBX-M tokamak configuration. (author) 19 figs., 2 tabs., 30 refs

  15. First Results from Tests of High Temperature Superconductor Magnets on Tokamak

    Energy Technology Data Exchange (ETDEWEB)

    Gryaznevich, M.; Todd, T.T., E-mail: mikhail.gryaznevich@ccfe.ac.uk [Euratom/CCFE Fusion Association, Culham Science Centre, Abingdon (United Kingdom); Svoboda, V.; Markovic, T.; Ondrej, G. [Czech Technical University, Prague (Czech Republic); Stockel, J.; Duran, I.; Kovarik, K. [IPP Prague, Czech Technical University, Prague (Czech Republic); Sykes, A.; Kingham, D. [Tokamak Solutions, Culham Science Centre, Abingdon (United Kingdom); Melhem, Z.; Ball, S.; Chappell, S. [Oxford Instruments, Abingdon (United Kingdom); Lilley, M. K.; De Grouchy, P.; Kim, H. -T. [Imperial College, London (United Kingdom)

    2012-09-15

    Full text: It has long been known that high temperature superconductors (HTS) could have an important role to play in the future of tokamak fusion research. Here we report on first results of the use of HTS in a tokamak magnet and on the progress in design and construction of the first fully-HTS tokamak. In the experiment, the two copper vertical field coils of the small tokamak GOLEM were replaced by two coils each with 6 turns of HTS (Re)BCO tape. Liquid nitrogen was used to cool the coils to below the critical temperature at which HTS becomes superconducting. Little effect on the HTS critical current has been observed for perpendicular field up to 0.5 T and superconductivity has been achieved at {approx} 90.5K during bench tests. There had been concerns that the plasma pulses and pulsed magnetic fields might cause a 'quench' in the HTS, i.e., a sudden and potentially damaging transition from superconductor to normal conductor. However, many plasma pulses were fired without any quenches even when disruptions occurred with corresponding induced electrical fields. In addition, experiments without plasma have been performed to study properties of the HTS in a tokamak environment, i.e., critical current and its dependence on magnetic and electrical fields generated in a tokamak both in DC and pulsed operations, maximum current ramp-up speed, performance of the HTS tape after number of artificially induced quenches etc. No quench has been observed at DC currents up to 200 A (1.2 kA-turns through the coil). In short pulses, current up to 1 kA through the tape (6 kA-turns) has been achieved with no subsequent degradation of the HTS performance with a current ramp rate up to 0.6 MA/s. In future experiments, increases in both the plasma current and pulse duration are planned. Considerable experience has been gained during design and fabrication of the cryostat, coils, isolation and insulation, feeds and cryosystems, and GOLEM is now routinely operated with HTS coils. The

  16. Stability and attractive basins of multiple equilibria in delayed two-neuron networks

    International Nuclear Information System (INIS)

    Huang Yu-Jiao; Zhang Hua-Guang; Wang Zhan-Shan

    2012-01-01

    Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r ≥ 1) corner points is studied. Sufficient conditions are established for checking the existence of (2r + 1) 2 equilibria in delayed recurrent neural networks. Under these conditions, (r + 1) 2 equilibria are locally exponentially stable, and (2r + 1) 2 — (r + 1) 2 — r 2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results. (general)

  17. The Pierce diode with an external circuit: II, Non-uniform equilibria

    International Nuclear Information System (INIS)

    Lawson, W.S.

    1987-01-01

    The non-uniform (non-linear) equilibria of the classical (short circuit) Pierce diode and the extended (series RLC external circuit) Pierce diode are described theoretically, and explored via computer simulation. It is found that most equilibria are correctly predicted by theory, but that the continuous set of equilibria of the classical Pierce diode at α = 2π are not observed. The stability characteristics of the non-uniform equilibria are also worked out, and are consistent with the simulations. 8 refs., 22 figs., 3 tabs

  18. A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

    Science.gov (United States)

    Heumann, Holger; Rapetti, Francesca

    2017-04-01

    Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

  19. Cluster storage for COMPASS tokamak

    Czech Academy of Sciences Publication Activity Database

    Písačka, Jan; Hron, Martin; Janky, Filip; Pánek, Radomír

    2012-01-01

    Roč. 87, č. 12 (2012), s. 2238-2241 ISSN 0920-3796. [IAEA Technical Meeting on Control, Data Acquisition, and Remote Participation for Fusion Research/8./. San Francisco, 20.06.2011-24.06.2011] R&D Projects: GA ČR GAP205/11/2470; GA MŠk 7G10072; GA MŠk(CZ) LM2011021 Institutional research plan: CEZ:AV0Z20430508 Keywords : COMPASS * Tokamak * Codac * Cluster * GlusterFS * Storage Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.842, year: 2012 http://dx.doi.org/10.1016/j.fusengdes.2012.09.006

  20. Surface tearing modes in tokamaks

    International Nuclear Information System (INIS)

    Takizuka, Tomonori; Kurita, Gen-ichi; Azumi, Masafumi; Takeda, Tatsuoki

    1985-10-01

    Surface tearing modes in tokamaks are studied numerically and analytically. The eigenvalue problem is solved to obtain the growth rate and the mode structure. We investigate in detail dependences of the growth rate of the m/n = 2/1 resistive MHD modes on the safety factor at the plasma surface, current profile, wall position, and resistivity. The surface tearing mode moves the plasma surface even when the wall is close to the surface. The stability diagram for these modes is presented. (author)

  1. Major disruption process in tokamak

    International Nuclear Information System (INIS)

    Kurita, Gen-ichi; Azumi, Masafumi; Tuda, Takashi; Takizuka, Tomonori; Tsunematsu, Toshihide; Tokuda, Shinji; Itoh, Kimitaka; Takeda, Tatsuoki

    1981-11-01

    The major disruption in a cylindrical tokamak is investigated by using the multi-helicity code, and the destabilization of the 3/2 mode by the mode coupling with the 2/1 mode is confirmed. The evolution of the magnetic field topology caused by the major disruption is studied in detail. The effect of the internal disruption on the 2/1 magnetic island width is also studied. The 2/1 magnetic island is not enhanced by the flattening of the q-profile due to the internal disruption. (author)

  2. The strongest magnetic barrier in the DIII-D tokamak and comparison with the ASDEX UG

    Science.gov (United States)

    Ali, Halima; Punjabi, Alkesh

    2013-05-01

    Magnetic perturbations in tokamaks lead to the formation of magnetic islands, chaotic field lines, and the destruction of flux surfaces. Controlling or reducing transport along chaotic field lines is a key challenge in magnetically confined fusion plasmas. A local control method was proposed by Chandre et al. [Nucl. Fusion 46, 33-45 (2006)] to build barriers to magnetic field line diffusion by addition of a small second-order control term localized in the phase space to the field line Hamiltonian. Formation and existence of such magnetic barriers in Ohmically heated tokamaks (OHT), ASDEX UG and piecewise analytic DIII-D [Luxon, J.L.; Davis, L.E., Fusion Technol. 8, 441 (1985)] plasma equilibria was predicted by the authors [Ali, H.; Punjabi, A., Plasma Phys. Control. Fusion 49, 1565-1582 (2007)]. Very recently, this prediction for the DIII-D has been corroborated [Volpe, F.A., et al., Nucl. Fusion 52, 054017 (2012)] by field-line tracing calculations, using experimentally constrained Equilibrium Fit (EFIT) [Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. This second-order approach is applied to the DIII-D tokamak to build noble irrational magnetic barriers inside the chaos created by the locked resonant magnetic perturbations (RMPs) (m, n)=(3, 1)+(4, 1), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation with amplitude δ. A piecewise, analytic, accurate, axisymmetric generating function for the trajectories of magnetic field lines in the DIII-D is constructed in magnetic coordinates from the experimental EFIT Grad-Shafranov solver [Lao, L, et al., Fusion Sci. Technol. 48, 968 (2005)] for the shot 115,467 at 3000 ms in the DIII-D. A symplectic mathematical map is used to integrate field lines in the DIII-D. A numerical algorithm [Ali, H., et al., Radiat. Eff. Def. Solids Inc. Plasma Sc. Plasma Tech. 165, 83

  3. Computation of solution equilibria: A guide to methods in potentiometry, extraction, and spectrophotometry

    International Nuclear Information System (INIS)

    Meloun, M.; Havel, J.; Hogfeldt, E.

    1988-01-01

    Although this book contains a very good review of computation methods applicable to equilibrium systems, most of the book is dedicated to the description and evaluation of computer programs available for doing such calculations. As stated in the preface, the authors (two computniks and a user of graphical and computer methods) have joined forces in order to present the reader with the points of view of both the creator and user of modern computer program tools available for the study of solution equilibria. The successful presentation of such a complicated amalgamation of concepts is greatly aided by the structure of the book, which begins with a brief but thorough discussion of equilibrium concepts in general, followed by an equally brief discussion of experimental methods used to study equilibria with potentiometric, extraction, and spectroscopic methods. These sections would not be sufficient to teach these topics to the beginner but offer an informative presentation of concepts in relation to one another to those already familiar with basic equilibrium concepts. The importance of evaluating and analyzing the suitability of data for further analysis is then presented before an in depth (by a chemist's standards) look at the individual parts that make up a detailed equilibrium analysis program. The next one-third of the book is an examination of specific equilibrium problems and the programs available to study them. These are divided into chapters devoted to potentiometric, extraction, and spectroscopic methods. The format is to discuss a variety of programs, one at a time, including the parts of the program, the types of problems to which it has been applied, and the program's limitations. A number of problems are then presented, which are representative of the type of questions that are normally addressed by research projects in the area

  4. Nuclear fusion research at Tokamak Energy Ltd

    International Nuclear Information System (INIS)

    Windridge, Melanie J.; Gryaznevich, Mikhail; Kingham, David

    2017-01-01

    Tokamak Energy's approach is close to the mainstream of nuclear fusion, and chooses a spherical tokamak, which is an economically developed form of Tokamak reactor design, as research subjects together with a high-temperature superconducting magnet. In the theoretical prediction, it is said that spherical tokamak can make tokamak reactor's scale compact compared with ITER or DEMO. The dependence of fusion energy multiplication factor on reactor size is small. According to model studies, it has been found that the center coil can be protected from heat and radiation damage even if the neutron shielding is optimized to 35 cm instead of 1 m. As a small tokamak with a high-temperature superconducting magnet, ST25 HTS, it demonstrated in 2015 continuous operation for more than 24 hours as a world record. Currently, this company is constructing a slightly larger ST40 type, and it is scheduled to start operation in 2017. ST40 is designed to demonstrate that it can realize a high magnetic field with a compact size and aims at attaining 8-10 keV (reaching the nuclear fusion reaction temperature at about 100 million degrees). This company will verify the startup and heating technology by the coalescence of spherical tokamak expected to have plasma current of 2 MA, and will also use 2 MW of neutral particle beam heating. In parallel with ST40, it is promoting a development program for high-temperature superconducting magnet. (A.O.)

  5. CAT-D-T tokamaks

    International Nuclear Information System (INIS)

    Greenspan, E.; Blue, T.; Miley, G.H.

    1981-01-01

    The domains of plasma fuel cycles bounded by the D-T and Cat-D, and by the D-T and SCD modes of operation are examined. These domains, referred to as, respectively, the Cat-D-T and SCD-T modes of operation, are characterized by the number (γ) of tritons per fusion neutron available from external (to the plasma) sources. Two external tritium sources are considered - the blankets of the Cat-D-T (SCD-T) reactors and fission reactors supported by the Cat-D-T (SCD-T) driven hybrid reactors. It is found that by using 6 Li for the active material of the control elements of the fission reactors, it is possible to achieve γ values close to unity. Cat-D-T tokamaks could be designed to have smaller size, higher power density, lower magnetic field and even lower plasma temperature than Cat-D tokamaks; the difference becomes significant for γ greater than or equal to .75. The SCD-T mode of operation appears to be even more attractive. Promising applications identified for these Cat-D-T and SCD-T modes of operation include hybrid reactors, fusion synfuel factories and fusion reactors which have difficulty in providing all their tritium needs

  6. Divertor design for the Tokamak Physics Experiment

    International Nuclear Information System (INIS)

    Hill, D.N.; Braams, B.

    1994-05-01

    In this paper we discuss the present divertor design for the planned TPX tokamak, which will explore the physics and technology of steady-state (1000s pulses) heat and particle removal in high confinement (2--4x L-mode), high beta (β N ≥ 3) divertor plasmas sustained by non-inductive current drive. The TPX device will operate in the double-null divertor configuration, with actively cooled graphite targets forming a deep (0.5 m) slot at the outer strike point. The peak heat flux on, the highly tilted (74 degrees from normal) re-entrant (to recycle ions back toward the separatrix) will be in the range of 4--6 MW/m 2 with 18 MW of neutral beams and RF heating power. The combination of active pumping and gas puffing (deuterium plus impurities), along with higher heating power (45 MW maximum) will allow testing of radiative divertor concepts at ITER-like power densities

  7. EUV impurity study of the Alcator tokamak

    International Nuclear Information System (INIS)

    Terry, J.L.; Chen, K.I.; Moos, H.W.; Marmar, E.S.

    1977-06-01

    The intensity of resonance line radiation from oxygen, nitrogen, carbon and molybdenum impurities has been measured in the high field (80 kG), high density (6 x 10 14 cm -3 ) discharges of the Alcator tokamak, using a 0.4 m normal incidence monochromator (300 to 1300 A) with its line of sight fixed along a major radius. The total light impurity concentrations were 2 x 10 -3 , 7 x 10 -4 , and 3 x 10 -3 at central electron densities of 4.5 x 10 13 cm -3 (burnout), 4.0 x 10 13 (low density plateau) and 6.0 x 10 14 (high density plateau). Both a simple model and a computer code which included Pfirsch-Schluter impurity diffusion were used to estimate oxygen influxes of 1.6 x 10 13 cm -2 sec -1 and 1.5 x 10 14 cm -2 sec -1 at the plasma edge in the low and high density emission plateaus. The resulting values of Z/sub eff/, including the contributions due to both the light impurities and molybdenum, were close to one. The power lost through the impurity line radiation accounted for approximately equal to 7 percent of the total ohmic input power at high densities

  8. Plasma position control in TCABR Tokamak

    International Nuclear Information System (INIS)

    Galvao, R.M.O.; Kuznetsov, Yu. K.; Nascimento, I.C.; Fonseca, A.M.M.; Silva, R.P. da; Ruchko, L.F.; Tuszel, A.G.; Reis, A.P. dos; Sanada, E.K.

    1998-01-01

    The plasma control position in the TCABR tokamak is described. The TCA tokamak was transferred from the Centre de Recherches en Physique des Plasmas, Lausanne, to the Institute of Physics of University of Sao Paulo, renamed TCABR (α=0.18 m, R = 0.62 m, B = 1 T,I p = 100 kA). The control system was reconstructed using mainly components obtained from the TCA tokamak. A new method of plasma position determination is used in TCABR to improve its accuracy. A more detailed theoretical analysis of the feed forward and feedback control is performed as compared with. (author)

  9. Estimation of Zeff in Novillo Tokamak

    International Nuclear Information System (INIS)

    Valencia, R.; Olayo, G.; Cruz, G.; Lopez, R.; Chavez, E.; Melendez, L.; Flores, A.; Gaytan, E.

    1996-01-01

    We estimated the Z eff in the Novillo Tokamak after having applied a HeGDC process through two different methods: anomaly factor and mass spectrometry. The first one gave a Z eff value of 2.07 for a tokamak discharge of 4350 A plasma current and 3 V of loop voltage. By mass spectrometry 30 s after the discharge had finished a Z eff of 4.19 was obtained for the same discharge. By mass spectrometry we observed that the Z eff value is a time function. Furthermore this method is helpful for evaluating the level of impurities after many discharges in Novillo Tokamak. (orig.)

  10. Global gyrokinetic simulation of tokamak transport

    International Nuclear Information System (INIS)

    Furnish, G.; Horton, W.; Kishimoto, Y.; LeBrun, M.J.; Tajima, T.

    1998-10-01

    A kinetic simulation code based on the gyrokinetic ion dynamics in global general metric (including a tokamak with circular or noncircular cross-section) has been developed. This gyrokinetic simulation is capable of examining the global and semi-global driftwave structures and their associated transport in a tokamak plasma. The authors investigate the property of the ion temperature gradient (ITG) or η i (η i ≡ ∂ ell nT i /∂ ell n n i ) driven drift waves in a tokamak plasma. The emergent semi-global drift wave modes give rise to thermal transport characterized by the Bohm scaling

  11. Fast IR diodes thermometer for tokamak

    International Nuclear Information System (INIS)

    Chen Xiangbo

    2001-01-01

    A 30 channel fast IR pyrometry array has been constructed for tokamak, which has 0.5 μs time response, 10 mm diameter spatial resolution and 5 degree C temperature resolution. The temperature measuring range is from 250 degree C to 1200 degree C. The two dimensional temperature profiles of the first wall during both major and minor disruptions can be measured with an accuracy of about 1% measuring temperature, which is adequate for tokamak experiments. This gives a very useful tool for the disruption study, especially for the divertor physics and edge heat flux research on tokamak and other magnetic confinement devices

  12. Computation of multi-region relaxed magnetohydrodynamic equilibria

    Energy Technology Data Exchange (ETDEWEB)

    Hudson, S. R.; Lazerson, S. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States); Dewar, R. L.; Dennis, G.; Hole, M. J.; McGann, M.; Nessi, G. von [Plasma Research Laboratory, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)

    2012-11-15

    We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.

  13. Helically symmetric equilibria with pressure anisotropy and incompressible plasma flow

    Science.gov (United States)

    Evangelias, A.; Kuiroukidis, A.; Throumoulopoulos, G. N.

    2018-02-01

    We derive a generalized Grad-Shafranov equation governing helically symmetric equilibria with pressure anisotropy and incompressible flow of arbitrary direction. Through the most general linearizing ansatz for the various free surface functions involved therein, we construct equilibrium solutions and study their properties. It turns out that pressure anisotropy can act either paramegnetically or diamagnetically, the parallel flow has a paramagnetic effect, while the non-parallel component of the flow associated with the electric field has a diamagnetic one. Also, pressure anisotropy and flow affect noticeably the helical current density.

  14. Phase Equilibria Relationships of High-Tc Superconductors

    International Nuclear Information System (INIS)

    Wong-Ng, Winnie

    2011-01-01

    As an integral part of a R and D program partially supported by the Electricity Delivery and Energy Reliability Office of DOE, we have determined phase equilibria data and phase diagrams for the three generations of superconductor materials: 1st generation, (Bi,Pb)-Sr-Ca- Cu-O systems; 2nd generation, Ba-R-Cu-O systems (R=lanthanides and yttrium); and 3rd generation, MgB2 systems. Our studies involved bulk materials, single crystals and thin films. This report gives a summary of our accomplishments, a list of publications, and 15 selected journal publications.

  15. The free energy of Maxwell-Vlasov equilibria

    International Nuclear Information System (INIS)

    Morrison, P.J.; Pfirsch, D.

    1989-10-01

    A previously derived expression for the energy of arbitrary perturbations about arbitrary Vlasov-Maxwell equilibria is transformed into a very compact form. The new form is also obtained by a canonical transformation method for solving Vlasov's equation, which is based on Lie group theory. This method is simpler than the one used before and provides better physical insight. Finally a procedure is presented for determining the existence of negative-energy modes. In this context the question of why there is an accessibility constraint for the particles, but not for the fields, is discussed. 16 refs

  16. Looking for multiple equilibria when geography matters : German city growth and the WWII shock

    NARCIS (Netherlands)

    Bosker, Maarten; Brakman, Steven; Garretsen, Harry; Schramm, Marc

    Based on the methodology of Davis and Weinstein, we look for multiple equilibria in German city growth. Bytaking the bombing of Germany during WWII as an example of a large, temporary shock, we analyze whether German city growth is characterized by multiple equilibria. In doing so, we allow for

  17. Computational study of the influence of mirror parameters on FRC (field-reversed configuration) equilibria:

    International Nuclear Information System (INIS)

    Fuentes, N.O.; Sakanaka, P.H.

    1990-01-01

    Field-reversed configuration equilibria are studied by solving the Grad-Shafranov equation. A multiple coil system (main coil and end mirrors) is considered to simulate the coil geometry of CNEA device. First results are presented for computed two-dimensional FRC equilibria produced varying the mirror coil current with two different mirror lenghts. (Author)

  18. How hard is it to find extreme Nash equilibria in network congestion games?

    NARCIS (Netherlands)

    Gassner, E.; Hatzl, J.; Krumke, S.O.; Sperber, H.; Woeginger, G.J.; Papadimitriou, C.; Zhang, S.

    2008-01-01

    We study the complexity of finding extreme pure Nash equilibria in symmetric (unweighted) network congestion games. In our context best and worst equilibria are those with minimum respectively maximum makespan. On series-parallel graphs a worst Nash equilibrium can be found by a Greedy approach

  19. Effect of Various EFIT NSTX Equilibria on EBW Simulations

    Czech Academy of Sciences Publication Activity Database

    Urban, Jakub; Preinhaelter, Josef; Sabbagh, S.; Pavlo, Pavol; Vahala, L.; Vahala, G.

    2006-01-01

    Roč. 51, č. 7 (2006), QPI.00027 ISSN 0003-0503. [Annual Meeting of the Division of Plasma Physics/48th./. Philadelphia, Pennsylvania , 30.10.2006-3.11.2006] Institutional research plan: CEZ:AV0Z20430508 Keywords : Conversion * Emission * Tokamaks * Electron Bernstein waves * Simulation * MAST * NSTX Subject RIV: BL - Plasma and Gas Discharge Physics http://www.aps.org/meet/DPP06/baps/all_DPP06.pdf

  20. Submillimeter wave propagation in tokamak plasmas

    International Nuclear Information System (INIS)

    Ma, C.H.; Hutchinson, D.P.; Staats, P.A.; Vander Sluis, K.L.; Mansfield, D.K.; Park, H.; Johnson, L.C.

    1985-01-01

    The propagation of submillimeter-waves (smm) in tokamak plasmas has been investigated both theoretically and experimentally to ensure successful measurements of electron density and plasma current distributions in tokamak devices. Theoretical analyses have been carried out to study the polarization of the smm waves in TFTR and ISX-B tokamaks. A multichord smm wave interferometer/polarimeter system has been employed to simultaneously measure the line electron density and poloidal field-induced Faraday rotation in the ISX-B tokamak. The experimental study on TFTR is under way. Computer codes have been developed and have been used to study the wave propagation and to reconstruct the distributions of plasma current and density from the measured data. The results are compared with other measurements

  1. Power and particle exhaust in tokamaks

    International Nuclear Information System (INIS)

    Stambaugh, R.D.

    1998-01-01

    The status of power and particle exhaust research in tokamaks is reviewed in the light of ITER requirements. There is a sound basis for ITER's nominal design positions; important directions for further research are identified

  2. Definition of total bootstrap current in tokamaks

    International Nuclear Information System (INIS)

    Ross, D.W.

    1995-01-01

    Alternative definitions of the total bootstrap current are compared. An analogous comparison is given for the ohmic and auxiliary currents. It is argued that different definitions than those usually employed lead to simpler analyses of tokamak operating scenarios

  3. Tokamak research in the Soviet Union

    International Nuclear Information System (INIS)

    Strelkov, V.S.

    1981-01-01

    Important milestones on the way to the tokamak fusion reactor are recapitulated. Soviet tokamak research concentrated at the I.V. Kurchatov Institute in Moscow, the A.F. Ioffe Institute in Leningrad and the Physical-Technical Institute in Sukhumi successfully provides necessary scientific and technological data for reactor design. Achievments include, the successful operation of the first tokamak with superconducting windings (T-7) and the gyrotron set for microwave plasma heating in the T-10 tokamak. The following problems have intensively been studied: Various methods of additional plasma heating, heat and particle transport, and impurity control. The efficiency of electron-cyclotron resonance heating was demonstrated. In the Joule heating regime, both the heat conduction and diffusion rates are anomalously high, but the electron heat conduction rate decreases with increasing plasma density. Progress in impurity control makes it possible to obtain a plasma with effective charge approaching unity. (J.U.)

  4. Neutral beam in ALVAND IIC tokamak

    International Nuclear Information System (INIS)

    Ghrannevisse, M.; Moradshahi, M.; Avakian, M.

    1992-01-01

    Neutral beams have a wide application in tokamak experiments. It used to heat; fuel; adjust electric potentials in plasmas and diagnose particles densities and momentum distributions. It may be used to sustain currents in tokamaks to extend the pulse length. A 5 KV; 500 mA ion source has been constructed by plasma physics group, AEOI and it used to produce plasma and study the plasma parameters. Recently this ion source has been neutralized and it adapted to a neutral beam source; and it used to heat a cylindrical DC plasma and the plasma of ALVAND IIC Tokamak which is a small research tokamak with a minor radius of 12.6 cm, and a major radius of 45.5 cm. In this paper we report the neutralization of the ion beam and the results obtained by injection of this neutral beam into plasmas. (author) 2 refs., 4 figs

  5. Submillimeter wave propagation in tokamak plasmas

    International Nuclear Information System (INIS)

    Ma, C.H.; Hutchinson, D.P.; Staats, P.A.; Vander Sluis, K.L.; Mansfield, D.K.; Park, H.; Johnson, L.C.

    1986-01-01

    Propagation of submillimeter waves (smm) in tokamak plasma was investigated both theoretically and experimentally to ensure successful measurements of electron density and plasma current distributions in tokamak devices. Theoretical analyses were carried out to study the polarization of the smm waves in TFTR and ISX-B tokamaks. A multichord smm wave interferometer/polarimeter system was employed to simultaneously measure the line electron density and poloidal field-induced Faraday rotation in the ISX-B tokamak. The experimental study on TFTR is under way. Computer codes were developed and have been used to study the wave propagation and to reconstruct the distributions of plasma current and density from the measured data. The results are compared with other measurements. 5 references, 2 figures

  6. Empirical scaling for present Ohmically heated tokamaks

    International Nuclear Information System (INIS)

    Daughney, C.

    1975-01-01

    Experimental results from the Adiabatic Toroidal Compressor (ATC) tokamak are used to obtain empirical scaling laws for the average electron temperature and electron energy confinement time as functions of the average electron density, the effective ion charge, and the plasma current. These scaling laws are extended to include dependence upon minor and major plasma radius and toroidal field strength through a comparison of the various tokamaks described in the literature. Electron thermal conductivity is the dominant loss process for the ATC tokamak. The parametric dependences of the observed electron thermal conductivity are not explained by present theoretical considerations. The electron temperature obtained with Ohmic heating is shown to be a function of current density - which will not be increased in the next generation of large tokamaks. However, the temperature dependence of the electron energy confinement time suggests that significant improvement in confinement time will be obtained with supplementary electron heating. (author)

  7. Research into controlled fusion in tokamaks

    International Nuclear Information System (INIS)

    Zacek, F.

    1992-01-01

    During the thirty years of tokamak research, physicists have been approaching step by step the reactor breakeven condition defined by the Lawson criterion. JET, the European Community tokamak is probably the first candidate among the world largest tokamaks to reach the ignition threshold and thus to demonstrate the physical feasibility of thermonuclear reaction. The record plasma parameters achieved in JET at H plasma modes due to powerful additional plasma heating and due to substantial reduction of plasma impurities, opened the door to the first experiment with a deuterium-tritium plasma. In the paper, the conditions and results of these tritium experiments are described in detail. The prospects of the world tokamak research and of the participation of Czechoslovak physicists are also discussed. (J.U.) 3 figs., 6 refs

  8. Robust Sliding Mode Control for Tokamaks

    Directory of Open Access Journals (Sweden)

    I. Garrido

    2012-01-01

    Full Text Available Nuclear fusion has arisen as an alternative energy to avoid carbon dioxide emissions, being the tokamak a promising nuclear fusion reactor that uses a magnetic field to confine plasma in the shape of a torus. However, different kinds of magnetohydrodynamic instabilities may affect tokamak plasma equilibrium, causing severe reduction of particle confinement and leading to plasma disruptions. In this sense, numerous efforts and resources have been devoted to seeking solutions for the different plasma control problems so as to avoid energy confinement time decrements in these devices. In particular, since the growth rate of the vertical instability increases with the internal inductance, lowering the internal inductance is a fundamental issue to address for the elongated plasmas employed within the advanced tokamaks currently under development. In this sense, this paper introduces a lumped parameter numerical model of the tokamak in order to design a novel robust sliding mode controller for the internal inductance using the transformer primary coil as actuator.

  9. Plasma equilibrium and instabilities in tokamaks

    International Nuclear Information System (INIS)

    Caldas, I.L.; Vannucci, A.

    1985-01-01

    A phenomenological introduction of some of the main theoretical and experimental features on equilibrium and instabilities in tokamaks is presented. In general only macroscopic effects are considered, being the plasma described as a fluid. (L.C.) [pt

  10. The ARIES-I tokamak reactor study

    International Nuclear Information System (INIS)

    1991-01-01

    This report discusses the following topics on the Aries-I Tokamak: Design description; systems studies and economics; reactor plasma physics; magnet engineering; fusion-power-ore engineering; and environmental and safety features

  11. Theory of incremental turbulent transport in tokamaks

    International Nuclear Information System (INIS)

    Similon, P.L.

    1991-01-01

    The goal of this research is to understand how the various aspect of turbulent transport operate in tokamaks, in the presence of low frequency fluctuations such as drift waves or trapped electron modes

  12. High temperature interdiffusion and phase equilibria in U-Mo

    International Nuclear Information System (INIS)

    Lundberg, L.B.

    1988-01-01

    Experimental data for interdiffusion and phase equilibria in the U-Mo system have been obtained over the temperature range 1400 to 1525 K as a fallout from compatibility experiments in which UO 2 was decomposed by lithium in closed molybdenum capsules. Composition-position, x-ray diffraction and microstructural data from the interdiffusion zones indicate that the intermediate phase U 2 Mo is found in this temperature range, contrary to the currently accepted equilibrium U-Mo phase diagram. The U-Mo interdiffusion data are in good agreement with published values. Inclusion of the U 2 Mo phase in a theoretical correlation of interdiffusion and phase equilibria data using Darken's equation indicate that high temperature interdiffusion of uranium and molybdenum follows the usual thermodynamic rules. Significant changes in the value of the thermodynamic based Darken factor near the U 2 Mo phase boundary on the high uranium side are indicated from both the new and published interdiffusion data. 9 refs., 10 figs., 3 tabs

  13. Phase equilibria of the Mo-Al-Ho ternary system

    Energy Technology Data Exchange (ETDEWEB)

    Li, Yitai; Chen, Xiaoxian; Liu, Hao [Guangxi Univ., Nanning (China). College of Materials Science and Engineering; Guangxi Univ., Nanning (China). Guangxi Key Laboratory of Processing for Non-ferrous Metal and Featured Materials; Zhan, Yongzhong [Guangxi Univ., Nanning (China). College of Materials Science and Engineering; Guangxi Univ., Nanning (China). Guangxi Key Laboratory of Processing for Non-ferrous Metal and Featured Materials; Guangxi Univ., Nanning (China). Center of Ecological Collaborative Innovation for Aluminum Industry

    2017-08-15

    Investigation into the reactions and phase equilibria of transition metal elements (i.e. Mo, Zr, Cr, V and Ti), Al and rare earths is academically and industrially important for the development of both refractory alloys and lightweight high-temperature materials. In this work, the equilibria of the Mo-Al-Ho ternary system at 773 K have been determined by using X-ray powder diffraction and scanning electron microscopy equipped with energy dispersive X-ray analysis. A new ternary phase Al{sub 4}Mo{sub 2}Ho has been found and the other ternary phase Al{sub 43}Mo{sub 4}Ho{sub 6} is observed. Ten binary phases in the Al-Mo and Al-Ho systems, including Al{sub 17}Mo{sub 4} rather than Al{sub 4}Mo, have been determined to exist at 773 K. The homogeneity ranges of AlMo{sub 3} and Al{sub 8}Mo{sub 3} phase are 7.5 at.% and 1 at.%, respectively. According to the phase-disappearing method, the maximum solubility of Al in Mo is about 16 at.%.

  14. Electronic structure and phase equilibria in ternary substitutional alloys

    International Nuclear Information System (INIS)

    Traiber, A.J.S.; Allen, S.M.; Waterstrat, R.M.

    1996-01-01

    A reliable, consistent scheme to study phase equilibria in ternary substitutional alloys based on the tight-binding approximation is presented. With electronic parameters from linear muffin-tin orbital calculations, the computed density of states and band structures compare well with those from more accurate abinitio calculations. Disordered alloys are studied within the tight-binding coherent-potential approximation extended to alloys; energetics of ordered systems are obtained through effective pair interactions computed with the general perturbation method; and partially ordered alloys are studied with a novel simplification of the molecular coherent-potential approximation combined with the general perturbation method. The formalism is applied to bcc-based Zr-Ru-Pd alloys which are promising candidates for medical implant devices. Using energetics obtained from the above scheme, we apply the cluster- variation method to study phase equilibria for particular pseudo- binary alloys and show that results are consistent with observed behavior of electronic specific heat coefficient with composition for Zr 0.5 (Ru, Pd) 0.5

  15. Kinetic description of linear theta-pinch equilibria

    International Nuclear Information System (INIS)

    Batchelor, D.B.; Davidson, R.C.

    1975-01-01

    Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (o/x=0) Vlasov-Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field Bsub(z)sup(ext)esub(z). Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the th component distribution function (Hsub(perpendicular), Psub(theta), upsilonsub(z) depends on perpendicular energy H and canonical angular momentum Psub(theta), exclusively through the linear combination Hsub(perpendicular)-ωsub(j)Psub(theta), where ω;=const.=angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on Hsub(perpendicular)-ωsub(j)Psub(theta) in circumstances, where the density profile or magnetic field profile is specified. (author)

  16. Phase equilibria in the niobium-vanadium-hydrogen system

    Energy Technology Data Exchange (ETDEWEB)

    Bethin, J. (Grumman Aerospace Corp., Bethpage, NY (USA)); Welch, D.O. (Brookhaven National Lab., Upton, NY (USA)); Pick, M.A. (Commission of the European Communities, Abingdon (UK). JET Joint Undertaking)

    1990-01-01

    The effect of vanadium additions to niobium on the metal-hydrogen phase equilibria has been studied. Measurements of the equilibrium H{sub 2}(D{sub 2}) pressure-composition-temperature isotherms for Nb{sub 1-x}V{sub x} alloys with 0{le}x<0.2 were used to determine the depression of the {alpha} - {alpha}' critical temperature with increasing vanadium concentration. A simple lattice-fluid model guided reduction of the data. Changes in the triple point temperature as well as the shift of the {zeta} {yields} {epsilon} phase transition were determined by differential scanning calorimetry measurements. A rapid overall depression was found, of the order of 7 K (at.% substituted V){sup -1}, for the metal-hydrogen (deuterium) phase boundary structure when compared with the Nb-H system in the hydrogen concentration range of interest. The results explain the enhanced terminal solubility of hydrogen in this system found previously by other authors. The changes in the phase equilibria are discussed in terms of the effect of hydrogen trapping and compared with the results of a cluster-variation calculation for random-field systems of previous authors, taking into account a distribution of H-site energies due to alloying. (author).

  17. Numerical simulation of edge plasma in tokamak

    International Nuclear Information System (INIS)

    Chen Yiping; Qiu Lijian

    1996-02-01

    The transport process and transport property of plasma in edge layer of Tokamak are simulated by solving numerically two-dimensional and multi-fluid plasma transport equations using suitable simulation code. The simulation results can show plasma parameter distribution characteristics in the area of edge layer, especially the characteristics near the first wall and divertor target plate. The simulation results play an important role in the design of divertor and first wall of Tokamak. (2 figs)

  18. Plasma diagnostics using synchrotron radiation in tokamaks

    International Nuclear Information System (INIS)

    Fidone, I.; Giruzzi, G.; Granata, G.

    1995-09-01

    This report deal with the use of synchrotron radiation in tokamaks. The main advantage of this new method is that it enables to overcome several deficiencies, caused by cut-off, refraction, and harmonic overlap. It also makes it possible to enhance the informative contents of the familiar low harmonic scheme. The basic theory of the method is presented and illustrated by numerical applications, for plasma parameters of relevance in present and next step tokamaks. (TEC). 10 refs., 13 figs

  19. The ETE spherical Tokamak project. IAEA report

    Energy Technology Data Exchange (ETDEWEB)

    Ludwig, Gerson Otto; Del Bosco, E.; Berni, L.A.; Ferreira, J.G.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Barroso, J.J.; Castro, P.J.; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma]. E-mail: ludwig@plasma.inpe.br

    2002-07-01

    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 historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and operating conditions as of October, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)

  20. Electric conductivity and bootstrap current in tokamak

    International Nuclear Information System (INIS)

    Mao Jianshan; Wang Maoquan

    1996-12-01

    A modified Ohm's law for the electric conductivity calculation is presented, where the modified ohmic current can be compensated by the bootstrap current. A comparison of TEXT tokamak experiment with the theories shows that the modified Ohm's law is a more close approximation to the tokamak experiments than the classical and neoclassical theories and can not lead to the absurd result of Z eff <1, and the extended neoclassical theory would be not necessary. (3 figs.)

  1. Erosion of the first wall of Tokamaks

    International Nuclear Information System (INIS)

    Guseva, M.I.; Ionova, E.S.; Martynenko, Yu.V.

    1980-01-01

    An estimate of the rate of erosion of the wall due to sputtering and blistering requires knowledge of the fluxes and energies of the particles which go from the plasma to the wall, of the sputtering coefficients S, and of the erosion coefficients S* for blistering. The overall erosion coefficient is equal to the sum of the sputtering coefficient and the erosion coefficient for blistering. Here the T-20 Tokamak is examined as an example of a large-scale Tokamak. 18 refs

  2. Advanced tokamak physics in DIII-D

    Energy Technology Data Exchange (ETDEWEB)

    Petty, C.C.; Luce, T.C.; Politzer, P.A.; Bray, B.; Burrell, K.H.; Chu, M.S.; Ferron, J.R.; Gohil, P.; Greenfield, C.M.; Hsieh, C.-L.; Hyatt, A.W.; La Haye, R.J.; Lao, L.L.; Leonard, A.W.; Lin-Liu, Y.R.; Lohr, J.; Mahdavi, M.A.; Petrie, T.W.; Pinsker, R.I.; Prater, R.; Scoville, J.T.; Staebler, G.M.; Strait, E.J.; Taylor, T.S.; West, W.P. [General Atomics, PO Box 85608, San Diego, CA (United States); Wade, M.R.; Lazarus, E.A.; Murakami, M. [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Allen, S.L.; Casper, T.A.; Jayakumar, R.; Lasnier, C.J.; Makowski, M.A.; Rice, B.W.; Wolf, N.S. [Lawrence Livermore National Laboratory, Livermore, CA (United States); Austin, M.E. [University of Texas, Austin, TX (United States); Fredrickson, E.D.; Gorelov, I.; Johnson, L.C.; Okabayashi, M.; Wong, K.-L. [Princeton Plasma Physics Laboratory, Princeton, NJ (United States); Garofalo, A.M.; Navratil, G.A. [Columbia University, New York (United States); Heidbrink, W. [University of California, Irvine, CA (United States); Kinsey, J.E. [Leheigh University, Bethlehem, PA (United States); McKee, G.R. [University of Wisconsin, Madison, WI (United States); Rettig, C.L.; Rhodes, T.L. [University of California, Los Angeles, CA (United States); Watkins, J.G. [Sandia National Laboratories, Albuquerque, NM (United States)

    2000-12-01

    Advanced tokamaks seek to achieve a high bootstrap current fraction without sacrificing fusion power density or fusion gain. Good progress has been made towards the DIII-D research goal of demonstrating a high-{beta} advanced tokamak plasma in steady state with a relaxed, fully non-inductive current profile and a bootstrap current fraction greater than 50%. The limiting factors for transport, stability, and current profile control in advanced operating modes are discussed in this paper. (author)

  3. Optimization design for SST-1 Tokamak insulators

    International Nuclear Information System (INIS)

    Zhang Yuanbin; Pan Wanjiang

    2012-01-01

    With the help of ANSYS FEA technique, high voltage and cryogenic proper- ties of the SST-1 Tokamak insulators were obtained, and the structure of the insulators was designed and modified by taking into account the simulation results. The simulation results indicate that the optimization structure has better high voltage insulating property and cryogenic mechanics property, and also can fulfill the qualification criteria of the SST-1 Tokamak insulators. (authors)

  4. Preliminary results of the TBR small tokamak

    International Nuclear Information System (INIS)

    Nascimento, I.C.; Fagundes, A.N.; Da Silva, R.P.; Galvao, R.M.O.; Del Bosco, E.; Vuolo, J.H.; Sanada, E.K.; Dellaqua, R.

    1982-01-01

    The paper gives a short description of the TBR - small Brazilian tokamak and the first results obtained for plasma formation and equilibrium. Measured breakdown curves for hydrogen are shown to be confined within analytically calculated limits and to depend strongly on stray vertical magnetic fields. Time profiles of plasma current in equilibrium are shown and compared with the predictions of a simple analytical model for tokamak discharges. Reasonable agreement is obtained taking Zsub(eff) as a free parameter. (author)

  5. Full power in the European tokamak

    International Nuclear Information System (INIS)

    Lallia, P.P.; Hugon, M.

    1987-01-01

    A new research campaign begins at Jet (Abingdon, UK). At this occasion, authors review and compare the performances of the three big Tokamaks that are currently in competition: Jet, JT60 and TFTR, insisting upon the European one. Conditions of ignition are reviewed together and energy losses are specified. Magnetic configurations used in tokamaks are shown, together with the technological responses brought these last years

  6. Facility approach to tokamak operation

    International Nuclear Information System (INIS)

    Edmonds, P.H.; Gabbard, W.A.

    1981-01-01

    In anticipation of the appearance of more advanced tokamaks and other fusion relevant experiments, program has been established at ORNL to systemically identify the requirements of an effective machine operations group. This program is presently applied to the ISX-B experiment. With its continuing development, it is expected to provide major support in the identification of potential problem areas and to assist in the generation of the necessary procedures for forthcoming devices. The present and future generations of large plasma devices will function as facilities, operated by an operations group as service to the plasma physicists and diagnosticians. The purpose of the program discussed here is to develop and to encourage an orderly transition to the facility-like style of operation

  7. Developments in tokamak transport modeling

    International Nuclear Information System (INIS)

    Houlberg, W.A.; Attenberger; Lao, L.L.

    1981-01-01

    A variety of numerical methods for solving the time-dependent fluid transport equations for tokamak plasmas is presented. Among the problems discussed are techniques for solving the sometimes very stiff parabolic equations for particle and energy flow, treating convection-dominated energy transport that leads to large cell Reynolds numbers, optimizing the flow of a code to reduce the time spent updating the particle and energy source terms, coupling the one-dimensional (1-D) flux-surface-averaged fluid transport equations to solutions of the 2-D Grad-Shafranov equation for the plasma geometry, handling extremely fast transient problems such as internal MHD disruptions and pellet injection, and processing the output to summarize the physics parameters over the potential operating regime for reactors. Emphasis is placed on computational efficiency in both computer time and storage requirements

  8. Simulation models for tokamak plasmas

    International Nuclear Information System (INIS)

    Dimits, A.M.; Cohen, B.I.

    1992-01-01

    Two developments in the nonlinear simulation of tokamak plasmas are described: (A) Simulation algorithms that use quasiballooning coordinates have been implemented in a 3D fluid code and a 3D partially linearized (Δf) particle code. In quasiballooning coordinates, one of the coordinate directions is closely aligned with that of the magnetic field, allowing both optimal use of the grid resolution for structures highly elongated along the magnetic field as well as implementation of the correct periodicity conditions with no discontinuities in the toroidal direction. (B) Progress on the implementation of a likeparticle collision operator suitable for use in partially linearized particle codes is reported. The binary collision approach is shown to be unusable for this purpose. The algorithm under development is a complete version of the test-particle plus source-field approach that was suggested and partially implemented by Xu and Rosenbluth

  9. Burn Control Mechanisms in Tokamaks

    Science.gov (United States)

    Hill, M. A.; Stacey, W. M.

    2015-11-01

    Burn control and passive safety in accident scenarios will be an important design consideration in future tokamak reactors, in particular fusion-fission hybrid reactors, e.g. the Subcritical Advanced Burner Reactor. We are developing a burning plasma dynamics code to explore various aspects of burn control, with the intent to identify feedback mechanisms that would prevent power excursions. This code solves the coupled set of global density and temperature equations, using scaling relations from experimental fits. Predictions of densities and temperatures have been benchmarked against DIII-D data. We are examining several potential feedback mechanisms to limit power excursions: i) ion-orbit loss, ii) thermal instability density limits, iii) MHD instability limits, iv) the degradation of alpha-particle confinement, v) modifications to the radial current profile, vi) ``divertor choking'' and vii) Type 1 ELMs. Work supported by the US DOE under DE-FG02-00ER54538, DE-FC02-04ER54698.

  10. Tokamak plasma interaction with limiters

    International Nuclear Information System (INIS)

    Pitcher, C.S.

    1987-11-01

    The importance of plasma purity is first discussed in terms of the general requirements of controlled thermonuclear fusion. The tokamak approach to fusion and its inherent problem of plasma contamination are introduced. A main source of impurities is due to the bombardment of the limiter by energetic particles and thus the three main aspects of the plasma-limiter interaction are reviewed, boundary plasma conditions, fuelling/recycling and impurity production. The experiments, carried out on the DITE tokamak at Culham Laboratory, UK, investigated these three topics and the results are compared with predicted behaviour; new physical phenomena are presented in all three areas. Simple one-dimensional fluid equations are found to adequately describe the SOL plasma, except in regard to the pre-sheath electric field and ambipolarity; that is, the electric field adjacent to the limiter surface appears to be weak and the associated plasma flow can be non-ambipolar. Recycling of fuel particles from the limiter is observed to be near unity at all times. The break-up behaviour of recycled and gas puffed D 2 molecules is dependent on the electron temperature, as expected. Impurity production at the limiter is chemical erosion of graphite being negligible. Deposition of limiter and wall-produced impurities is found on the limiter. The spatial distributions of impurities released from the limiter are observed and are in good agreement with a sputtered atom transport code. Finally, preliminary experiments on the transport of impurity ions along field lines away from the limiter have been performed and compared with simple analytic theory. The results suggest that the pre-sheath electric field in the SOL is much weaker than the simple fluid model would predict

  11. Social Interactions under Incomplete Information: Games, Equilibria, and Expectations

    Science.gov (United States)

    Yang, Chao

    My dissertation research investigates interactions of agents' behaviors through social networks when some information is not shared publicly, focusing on solutions to a series of challenging problems in empirical research, including heterogeneous expectations and multiple equilibria. The first chapter, "Social Interactions under Incomplete Information with Heterogeneous Expectations", extends the current literature in social interactions by devising econometric models and estimation tools with private information in not only the idiosyncratic shocks but also some exogenous covariates. For example, when analyzing peer effects in class performances, it was previously assumed that all control variables, including individual IQ and SAT scores, are known to the whole class, which is unrealistic. This chapter allows such exogenous variables to be private information and models agents' behaviors as outcomes of a Bayesian Nash Equilibrium in an incomplete information game. The distribution of equilibrium outcomes can be described by the equilibrium conditional expectations, which is unique when the parameters are within a reasonable range according to the contraction mapping theorem in function spaces. The equilibrium conditional expectations are heterogeneous in both exogenous characteristics and the private information, which makes estimation in this model more demanding than in previous ones. This problem is solved in a computationally efficient way by combining the quadrature method and the nested fixed point maximum likelihood estimation. In Monte Carlo experiments, if some exogenous characteristics are private information and the model is estimated under the mis-specified hypothesis that they are known to the public, estimates will be biased. Applying this model to municipal public spending in North Carolina, significant negative correlations between contiguous municipalities are found, showing free-riding effects. The Second chapter "A Tobit Model with Social

  12. Kinetic equilibrium reconstruction for the NBI- and ICRH-heated H-mode plasma on EAST tokamak

    Science.gov (United States)

    Zhen, ZHENG; Nong, XIANG; Jiale, CHEN; Siye, DING; Hongfei, DU; Guoqiang, LI; Yifeng, WANG; Haiqing, LIU; Yingying, LI; Bo, LYU; Qing, ZANG

    2018-04-01

    The equilibrium reconstruction is important to study the tokamak plasma physical processes. To analyze the contribution of fast ions to the equilibrium, the kinetic equilibria at two time-slices in a typical H-mode discharge with different auxiliary heatings are reconstructed by using magnetic diagnostics, kinetic diagnostics and TRANSP code. It is found that the fast-ion pressure might be up to one-third of the plasma pressure and the contribution is mainly in the core plasma due to the neutral beam injection power is primarily deposited in the core region. The fast-ion current contributes mainly in the core region while contributes little to the pedestal current. A steep pressure gradient in the pedestal is observed which gives rise to a strong edge current. It is proved that the fast ion effects cannot be ignored and should be considered in the future study of EAST.

  13. D-D tokamak reactor assessment

    International Nuclear Information System (INIS)

    Baxter, D.C.; Dabiri, A.E.

    1983-01-01

    A quantitative comparison of the physics and technology requirements, and the cost and safety performance of a d-d tokamak relative to a d-t tokamak has been performed. The first wall/blanket and energy recovery cycle for the d-d tokamak is simpler, and has a higher efficiency than the d-t tokamak. In most other technology areas (such as magnets, RF, vacuum, etc.) d-d requirements are more severe and the systems are more complex, expensive and may involve higher technical risk than d-t tokamak systems. Tritium technology for processing the plasma exhaust, and tritium refueling technology are required for d-d reactors, but no tritium containment around the blanket or heat transport system is needed. Cost studies show that for high plasma beta and high magnetic field the cost of electricity from d-d and d-t tokamaks is comparable. Safety analysis shows less radioactivity in a d-d reactor but larger amounts of stored energy and thus higher potential for energy release. Consequences of all postulated d-d accidents are significantly smaller than those from d-t reactor tritium releases

  14. Stability of tokamaks with elongated cross section

    International Nuclear Information System (INIS)

    An, C.H.; Bateman, G.

    1978-08-01

    Fixed boundary n = 1 MHD instabilities are studied computationally as a function of diamagnetism (β/sub pol/) and current profile in elongated toroidal equilibria (1 2) or a diamagnetic plasma (β/sub pol/ > 1) with only a mildly elongated cross section

  15. Disassembly of JT-60 tokamak device and ancillary facilities for JT-60 tokamak

    International Nuclear Information System (INIS)

    Okano, Fuminori; Ichige, Hisashi; Miyo, Yasuhiko; Kaminaga, Atsushi; Sasajima, Tadayuki; Nishiyama, Tomokazu; Yagyu, Jun-ichi; Ishige, Youichi; Suzuki, Hiroaki; Komuro, Kenichi; Sakasai, Akira; Ikeda, Yoshitaka

    2014-03-01

    The disassembly of JT-60 tokamak device and its peripheral equipments, where the total weight was about 5400 tons, started in 2009 and accomplished in October 2012. This disassembly was required process for JT-60SA project, which is the Satellite Tokamak project under Japan-EU international corroboration to modify the JT-60 to the superconducting tokamak. This work was the first experience of disassembling a large radioactive fusion device based on Radiation Hazard Prevention Act in Japan. The cutting was one of the main problems in this disassembly, such as to cut the welded parts together with toroidal field coils, and to cut the vacuum vessel into two. After solving these problems, the disassembly completed without disaster and accident. This report presents the outline of the JT-60 disassembly, especially tokamak device and ancillary facilities for tokamak device. (author)

  16. Development of a tokamak plasma optimized for stability and confinement

    International Nuclear Information System (INIS)

    Politzer, P.A.

    1995-02-01

    Design of an economically attractive tokamak fusion reactor depends on producing steady-state plasma operation with simultaneous high energy density (β) and high energy confinement (τ E ); either of these, by itself, is insufficient. In operation of the DIII-D tokamak, both high confinement enhancement (H≡ τ E /τ ITER-89P = 4) and high normalized β (β N ≡ β/(I/aB) = 6%-m-T/MA) have been obtained. For the present, these conditions have been produced separately and in transient discharges. The DIII-D advanced tokamak development program is directed toward developing an understanding of the characteristics which lead to high stability and confinement, and to use that understanding to demonstrate stationary, high performance operation through active control of the plasma shape and profiles. The authors have identified some of the features of the operating modes in DIII-D that contribute to better performance. These are control of the plasma shape, control of both bulk plasma rotation and shear in the rotation and Er profiles, and particularly control of the toroidal current profiles. In order to guide their future experiments, they are developing optimized scenarios based on their anticipated plasma control capabilities, particularly using fast wave current drive (on-axis) and electron cyclotron current drive (off-axis). The most highly developed model is the second-stable core VH-mode, which has a reversed magnetic shear safety factor profile [q(O) = 3.9, q min = 2.6, and q 95 = 6]. This model plasma uses profiles which the authors expect to be realizable. At β N ≥ 6, it is stable to n=l kink modes and ideal ballooning modes, and is expected to reach H ≥ 3 with VH-mode-like confinement

  17. Clarifying Normalization

    Science.gov (United States)

    Carpenter, Donald A.

    2008-01-01

    Confusion exists among database textbooks as to the goal of normalization as well as to which normal form a designer should aspire. This article discusses such discrepancies with the intention of simplifying normalization for both teacher and student. This author's industry and classroom experiences indicate such simplification yields quicker…

  18. Thermodynamic foundations of applications of ab initio methods for determination of the adsorbate equilibria: hydrogen at the GaN(0001) surface.

    Science.gov (United States)

    Kempisty, Pawel; Strąk, Paweł; Sakowski, Konrad; Kangawa, Yoshihiro; Krukowski, Stanisław

    2017-11-08

    Thermodynamic foundations of ab initio modeling of vapor-solid and vapor-surface equilibria are introduced. The chemical potential change is divided into enthalpy and entropy terms. The enthalpy path passes through vapor-solid transition at zero temperature. The entropy path avoids the singular point at zero temperature passing a solid-vapor transition under normal conditions, where evaporation entropy is employed. In addition, the thermal changes are calculated. The chemical potential difference contribution of the following terms: vaporization enthalpy, vaporization entropy, the temperature-entropy related change, the thermal enthalpy change and mechanical pressure is obtained. The latter term is negligibly small for the pressure typical for epitaxy. The thermal enthalpy change is two orders smaller than the first three terms which have to be taken into account explicitly. The configurational vaporization entropy change is derived for adsorption processes. The same formulation is derived for vapor-surface equilibria using hydrogen at the GaN(0001) surface as an example. The critical factor is the dependence of the enthalpy of evaporation (desorption energy) on the pinning of the Fermi level bringing a drastic change of the value from 2.24 eV to -2.38 eV. In addition it is shown that entropic contributions considerable change the hydrogen equilibrium pressure over the GaN(0001) surface by several orders of magnitude. Thus a complete and exact formulation of vapor-solid and vapor-surface equilibria is presented.

  19. The Spectral Web of stationary plasma equilibria. II. Internal modes

    Science.gov (United States)

    Goedbloed, J. P.

    2018-03-01

    The new method of the Spectral Web to calculate the spectrum of waves and instabilities of plasma equilibria with sizeable flows, developed in the preceding Paper I [Goedbloed, Phys. Plasmas 25, 032109 (2018)], is applied to a collection of classical magnetohydrodynamic instabilities operating in cylindrical plasmas with shear flow or rotation. After a review of the basic concepts of the complementary energy giving the solution path and the conjugate path, which together constitute the Spectral Web, the cylindrical model is presented and the spectral equations are derived. The first example concerns the internal kink instabilities of a cylindrical force-free magnetic field of constant α subjected to a parabolic shear flow profile. The old stability diagram and the associated growth rate calculations for static equilibria are replaced by a new intricate stability diagram and associated complex growth rates for the stationary model. The power of the Spectral Web method is demonstrated by showing that the two associated paths in the complex ω-plane nearly automatically guide to the new class of global Alfvén instabilities of the force-free configuration that would have been very hard to predict by other methods. The second example concerns the Rayleigh-Taylor instability of a rotating theta-pinch. The old literature is revisited and shown to suffer from inconsistencies that are remedied. The most global n = 1 instability and a cluster sequence of more local but much more unstable n =2 ,3 ,…∞ modes are located on separate solution paths in the hydrodynamic (HD) version of the instability, whereas they merge in the MHD version. The Spectral Web offers visual demonstration of the central position the HD flow continuum and of the MHD Alfvén and slow magneto-sonic continua in the respective spectra by connecting the discrete modes in the complex plane by physically meaningful curves towards the continua. The third example concerns the magneto-rotational instability

  20. Hermite Polynomials and the Inverse Problem for Collisionless Equilibria

    Science.gov (United States)

    Allanson, O.; Neukirch, T.; Troscheit, S.; Wilson, F.

    2017-12-01

    It is long established that Hermite polynomial expansions in either velocity or momentum space can elegantly encode the non-Maxwellian velocity-space structure of a collisionless plasma distribution function (DF). In particular, Hermite polynomials in the canonical momenta naturally arise in the consideration of the 'inverse problem in collisionless equilibria' (IPCE): "for a given macroscopic/fluid equilibrium, what are the self-consistent Vlasov-Maxwell equilibrium DFs?". This question is of particular interest for the equilibrium and stability properties of a given macroscopic configuration, e.g. a current sheet. It can be relatively straightforward to construct a formal solution to IPCE by a Hermite expansion method, but several important questions remain regarding the use of this method. We present recent work that considers the necessary conditions of non-negativity, convergence, and the existence of all moments of an equilibrium DF solution found for IPCE. We also establish meaningful analogies between the equations that link the microscopic and macrosopic descriptions of the Vlasov-Maxwell equilibrium, and those that solve the initial value problem for the heat equation. In the language of the heat equation, IPCE poses the pressure tensor as the 'present' heat distribution over an infinite domain, and the non-Maxwellian features of the DF as the 'past' distribution. We find sufficient conditions for the convergence of the Hermite series representation of the DF, and prove that the non-negativity of the DF can be dependent on the magnetisation of the plasma. For DFs that decay at least as quickly as exp(-v^2/4), we show non-negativity is guaranteed for at least a finite range of magnetisation values, as parameterised by the ratio of the Larmor radius to the gradient length scale. 1. O. Allanson, T. Neukirch, S. Troscheit & F. Wilson: From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials, Journal of Plasma Physics, 82

  1. On the HL-1M tokamak plasma confinement time

    International Nuclear Information System (INIS)

    Qin Yunwen

    2001-01-01

    Emphasizing that the tokamak plasma confinement time is the plasma particle or thermal energy loss characteristic time, the relevant physical concept and HL-1M tokamak experimental data analyses are reviewed

  2. Oscillations and Multiple Equilibria in Microvascular Blood Flow.

    Science.gov (United States)

    Karst, Nathaniel J; Storey, Brian D; Geddes, John B

    2015-07-01

    We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through a combination of analytic and numeric techniques, we predict in a series of two-parameter bifurcation diagrams a range of dynamical behaviors, including multiple equilibria flow configurations, simple oscillations in volumetric flow rate, and multiple coexistent limit cycles at physically realizable parameters. We show that complexity in network topology is not necessary for complex behaviors to arise and that nonlinear rheology, in particular the plasma skimming effect, is sufficient to support oscillatory dynamics similar to those observed in vivo.

  3. Dynamic data evaluation for solid-liquid equilibria

    DEFF Research Database (Denmark)

    Cunico, Larissa; Ceriani, Roberta; Kang, Jeong Won

    The accuracy and reliability of the measured data sets to be used in regression of model parameters is an important issue related to modeling of phase equilibria. It is clear that good parameters for any model cannot be obtained from low quality data. A thermodynamic consistency test for solid...... and parameter regression. The paper will highlight the data collection, the data analysis for SLE data and the thermodynamic model performance (such as NRTL, UNIQUAC and original UNIFAC)....... studies considering the methodology proposed for SLE thermodynamic consistency tests and data from open literature and databases such as NIST-TDE®, DIPPR® and DECHEMA® are presented. The SLE consistency test and data evaluation is performed in a software containing option for data analysis, model analysis...

  4. Modified Poisson eigenfunctions for electrostatic Bernstein--Greene--Kruskal equilibria

    International Nuclear Information System (INIS)

    Ling, K.; Abraham-Shrauner, B.

    1981-01-01

    The stability of an electrostatic Bernstein--Greene--Kruskal equilibrium by Lewis and Symon's general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh--Ritz method, and (iii) a method based on a Hill's equation. In the fluid limit the Rayleigh--Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically

  5. Gas hydrate phase equilibria measurement techniques and phase rule considerations

    International Nuclear Information System (INIS)

    Beltran, Juan G.; Bruusgaard, Hallvard; Servio, Phillip

    2012-01-01

    Highlights: → Inconsistencies found in hydrate literature. → Clarification to the number of variables needed to satisfy and justify equilibrium data. → Application of phase rule to mixed hydrate systems. → Thermodynamically consistent format to present data. - Abstract: A brief review of the Gibbs phase rule for non-reacting systems and its correct application to clathrate hydrates is presented. Clarification is provided for a common mistake found in hydrate phase-equilibria literature, whereby initial compositions are used as intensive variables to satisfy the Gibbs phase rule instead of the equilibrium values. The system of (methane + carbon dioxide + water) under (hydrate + liquid + vapor) equilibrium is used as a case study to illustrate key points and suggestions to improve experimental techniques are proposed.

  6. A new transiently chaotic flow with ellipsoid equilibria

    Science.gov (United States)

    Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

    2018-03-01

    In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

  7. Metamorphism and partial melting of ordinary chondrites: Calculated phase equilibria

    Science.gov (United States)

    Johnson, T. E.; Benedix, G. K.; Bland, P. A.

    2016-01-01

    Constraining the metamorphic pressures (P) and temperatures (T) recorded by meteorites is key to understanding the size and thermal history of their asteroid parent bodies. New thermodynamic models calibrated to very low P for minerals and melt in terrestrial mantle peridotite permit quantitative investigation of high-T metamorphism in ordinary chondrites using phase equilibria modelling. Isochemical P-T phase diagrams based on the average composition of H, L and LL chondrite falls and contoured for the composition and abundance of olivine, ortho- and clinopyroxene, plagioclase and chromite provide a good match with values measured in so-called equilibrated (petrologic type 4-6) samples. Some compositional variables, in particular Al in orthopyroxene and Na in clinopyroxene, exhibit a strong pressure dependence when considered over a range of several kilobars, providing a means of recognising meteorites derived from the cores of asteroids with radii of several hundred kilometres, if such bodies existed at that time. At the low pressures (recorders of peak conditions. The intersection of isopleths of these variables may allow pressures to be quantified, even at low P, permitting constraints on the minimum size of parent asteroid bodies. The phase diagrams predict the onset of partial melting at 1050-1100 °C by incongruent reactions consuming plagioclase, clinopyroxene and orthopyroxene, whose compositions change abruptly as melting proceeds. These predictions match natural observations well and support the view that type 7 chondrites represent a suprasolidus continuation of the established petrologic types at the extremes of thermal metamorphism. The results suggest phase equilibria modelling has potential as a powerful quantitative tool in investigating, for example, progressive oxidation during metamorphism, the degree of melting and melt loss or accumulation required to produce the spectrum of differentiated meteorites, and whether the onion shell or rubble pile

  8. Phase equilibria and molecular interaction studies on (naphthols + vanillin) systems

    International Nuclear Information System (INIS)

    Gupta, Preeti; Agrawal, Tanvi; Das, Shiva Saran; Singh, Nakshatra Bahadur

    2012-01-01

    Highlights: ► Phase equilibria of (naphthol + vanillin) systems have been studied for the first time. ► Eutectic type phase diagrams are obtained. ► Eutectic mixtures show nonideal behaviour. ► There is a weak molecular interaction between the components in the eutectic mixtures. ► α-Naphthol–vanillin eutectic is more stable as compared to β-naphthol–vanillin. - Abstract: Phase equilibria between (α-naphthol + vanillin) and (β-naphthol + vanillin) systems have been studied by thaw-melt method and the results show the formation of simple eutectic mixtures. Crystallization velocities of components and eutectic mixtures were determined at different stages under cooling. With the help of differential scanning calorimeter (DSC), the enthalpy of fusion of components and eutectic mixtures was determined and from the values excess thermodynamic functions viz., excess Gibbs free energy (G E ), excess entropy (S E ), excess enthalpy (H E ) of hypo-, hyper- and eutectic mixtures were calculated. Flexural strength measurements were made in order to understand the non-ideal nature of eutectics. FT-IR spectral studies indicate the formation of hydrogen bond in the eutectic mixture. Anisotropic and isotropic microstructural studies of components, hypo-, hyper- and eutectic mixtures were made. Jackson’s roughness parameter was calculated and found to be greater than 2 suggesting the faceted morphology with irregular structures. The overall results have shown that there is a weak molecular interaction between the components in the eutectic mixtures and the (α-naphthol + vanillin) eutectic is more stable as compared to the (β-naphthol + vanillin) eutectic system.

  9. Electromagnetic effects on trace impurity transport in tokamak plasmas

    Science.gov (United States)

    Hein, T.; Angioni, C.

    2010-01-01

    The impact of electromagnetic effects on the transport of light and heavy impurities in tokamak plasmas is investigated by means of an extensive set of linear gyrokinetic numerical calculations with the code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and of analytical derivations with a fluid model. The impurity transport is studied by appropriately separating diffusive and convective contributions, and conditions of background microturbulence dominated by both ion temperature gradient (ITG) and trapped electron modes (TEMs) are analyzed. The dominant contribution from magnetic flutter transport turns out to be of pure convective type. However it remains small, below 10% with respect to the E ×B transport. A significant impact on the impurity transport due to an increase in the plasma normalized pressure parameter β is observed in the case of ITG modes, while for TEM the overall effect remains weak. In realistic conditions of high β plasmas in the high confinement (H-) mode with dominant ITG turbulence, the impurity diffusivity is found to decrease with increasing β in qualitative agreement with recent observations in tokamaks. In contrast, in these conditions, the ratio of the total off-diagonal convective velocity to the diagonal diffusivity is not strongly affected by an increase in β, particularly at low impurity charge, due to a compensation between the different off-diagonal contributions.

  10. Analysis of tokamak plasma confinement modes using the fast

    Indian Academy of Sciences (India)

    The Fourier analysis is a satisfactory technique for detecting plasma confinement modes in tokamaks. The confinement mode of tokamak plasma was analysed using the fast Fourier transformation (FFT). For this purpose, we used the data of Mirnov coils that is one of the identifying tools in the IR-T1 tokamak, with and ...

  11. Comparative studies of stellarator and tokamak transport

    Energy Technology Data Exchange (ETDEWEB)

    Stroth, U; Burhenn, R; Geiger, J; Giannone, L.; Hartfuss, H J; Kuehner, G; Ledl, L; Simmet, E E; Walter, H [Max-Planck-Inst. fuer Plasmaphysik, IPP-Euratom Association, Garching (Germany); ECRH Team; W7-AS Team

    1997-09-01

    Transport properties in the W7-AS stellarator and in tokamaks are compared. The parameter dependences and the absolute values of the energy confinement time are similar. Indications are found that the density dependence, which is usually observed in stellarator confinement, can vanish above a critical density. The density dependence in stellarators seems to be similar to that in the linear ohmic confinement regime, which, in small tokamaks, extends to high density values, too. Because of the similarity in the gross confinement properties, transport in stellarators and tokamaks should not be dominated by the parameters which are very different in the two concepts, i.e. magnetic shear, major rational values of the rotational transform and plasma current. A difference in confinement is that there exists evidence for pinches in the particle and, possibly, energy transport channels in tokamaks whereas in stellarators no pinches have been observed, so far. In order to study the effect of plasma current and toroidal electric fields, stellarator discharges were carried out with an increasing amount of plasma current. From these experiments, no clear evidence of a connection of pinches with these parameters is found. The transient response in W7-AS plasmas can be described in terms of a non-local model. As in tokamaks, also cold pulse experiments in W7-AS indicate the importance of non-local transport. (author). 8 refs, 5 figs.

  12. Three novel tokamak plasma regimes in TFTR

    International Nuclear Information System (INIS)

    Furth, H.P.

    1985-10-01

    Aside from extending ''standard'' ohmic and neutral beam heating studies to advanced plasma parameters, TFTR has encountered a number of special plasma regimes that have the potential to shed new light on the physics of tokamak confinement and the optimal design of future D-T facilities: (1) High-powered, neutral beam heating at low plasma densities can maintain a highly reactive hot-ion population (with quasi-steady-state beam fueling and current drive) in a tokamak configuration of modest bulk-plasma confinement requirements. (2) Plasma displacement away from limiter contact lends itself to clarification of the role of edge-plasma recycling and radiation cooling within the overall pattern of tokamak heat flow. (3) Noncentral auxiliary heating (with a ''hollow'' power-deposition profile) should serve to raise the central tokamak plasma temperature without deterioration of central region confinement, thus facilitating the study of alpha-heating effects in TFTR. The experimental results of regime (3) support the theory that tokamak profile consistency is related to resistive kink stability and that the global energy confinement time is determined by transport properties of the plasma edge region

  13. Edge plasma diagnostics on Tore Supra tokamak

    International Nuclear Information System (INIS)

    Fujita, Junji

    1991-01-01

    From 1988 to 1991, the international scientific research 'Diagnosis of peripheral plasma in Tore Supra tokamak' was carried out as a three-year plan receiving the support of the scientific research expense of the Ministry of Education. This is to apply the method of measuring electron density distribution by neutral lithium beam probe spectroscopy to the measurement of the electron density distribution in the peripheral plasma in Tore Supra Tokamak in France. Among many tokamaks in operation doing respective characteristics researches, the Tore Supra generates the toroidal magnetic field by using superconducting coils, and aims at the long time discharge for 30 sec. for the time being, and for 300 sec. in future. In the plasma generators for long time discharge like this, the technology of particle control is a large problem. For this purpose, a divertor was added to the Tore Supra. In order to advance the research on particle control, it is necessary to examine the behavior of plasma in the peripheral part in detail. The measurement of peripheral plasma in tokamaks, beam probe spectroscopy, the Tore Supra tokamak, the progress of the joint research, the problems in the joint research and the perspective of hereafter are reported. (K.I.)

  14. Electron thermal transport in tokamak plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Konings, J A

    1994-11-30

    The process of fusion of small nuclei thereby releasing energy, as it occurs continuously in the sun, is essential for the existence of mankind. The same process applied in a controlled way on earth would provide a clean and an abundant energy source, and be the long term solution of the energy problem. Nuclear fusion requires an extremely hot (10{sup 8} K) ionized gas, a plasma, that can only be maintained if it is kept insulated from any material wall. In the so called `tokamak` this is achieved by using magnetic fields. The termal insulation, which is essential if one wants to keep the plasma at the high `fusion` temperature, can be predicted using basic plasma therory. A comparison with experiments in tokamaks, however, showed that the electron enery losses are ten to hundred times larger than this theory predicts. This `anomalous transport` of thermal energy implies that, to reach the condition for nuclear fusion, a fusion reactor must have very large dimensions. This may put the economic feasibility of fusion power in jeopardy. Therefore, in a worldwide collaboration, physicists study tokamak plasmas in an attempt to understand and control the energy losses. From a scientific point of view, the mechanisms driving anomalous transport are one of the challenges in fudamental plasma physics. In Nieuwegein, a tokamak experiment (the Rijnhuizen Tokamak Project, RTP) is dedicated to the study of anomalous transport, in an international collaboration with other laboratories. (orig./WL).

  15. CASTOR: Normal-mode analysis of resistive MHD plasmas

    NARCIS (Netherlands)

    Kerner, W.; Goedbloed, J. P.; Huysmans, G. T. A.; Poedts, S.; Schwarz, E.

    1998-01-01

    The CASTOR (complex Alfven spectrum of toroidal plasmas) code computes the entire spectrum of normal-modes in resistive MHD for general tokamak configurations. The applied Galerkin method, in conjunction with a Fourier finite-element discretisation, leads to a large scale eigenvalue problem A (x)

  16. Alfven Eigenmodes in spherical tokamaks

    International Nuclear Information System (INIS)

    Gryaznevich, Mikhail P.; Sharapov, Sergei E.; Berk, Herbert L.; Pinches, Simon D.

    2005-01-01

    Electromagnetic instabilities are often excited by fast super-Alfvenic ions produced by neutral beam injection (NBI) in plasmas of the spherical tokamaks START and MAST (toroidal magnetic confinement devices in which the minor a and major R 0 radii of the torus are comparable, R 0 /a≅1.2/1.8). These instabilities are seen as discrete weakly-damped toroidal and elliptical Alfven Eigenmodes (TAEs and EAEs) with frequencies tracing in time the Alfven scaling with the equilibrium magnetic field and plasma density, or as energetic particle modes (EPMs) whose frequencies don't start from TAE-frequency and sweep down in time faster than the equilibrium parameters change. In some discharges the beam drives Aflvenic-type modes that start from the TAE frequency and sweep in both up- and down- directions. Such electromagnetic perturbations are interpreted as 'hole-clump' long-living nonlinear fluctuations of the fast ion distribution function predicted by Berk-Breizman-Petviashvili [Phys. Lett. A238 (1998) 408]. It is found on both START and MAST that the Alfven instabilities weaken in their mode amplitude and in the number of unstable modes as the pressure of the thermal plasma increases, in agreement with increased thermal ion Landau damping and the pressure effect on core-localised TAEs. (author)

  17. The collaborative tokamak control room

    International Nuclear Information System (INIS)

    Schissel, D.P.

    2006-01-01

    Magnetic fusion experiments keep growing in size and complexity resulting in a concurrent growth in collaborations between experimental sites and laboratories worldwide. In the US, the National Fusion Collaboratory Project is developing a persistent infrastructure to enable scientific collaboration for all aspects of magnetic fusion energy research by creating a robust, user-friendly collaborative environment and deploying this to the more than 1000 US fusion scientists in 40 institutions who perform magnetic fusion research. This paper reports on one aspect of the project which is the development of the collaborative tokamak control room to enhance both collocated and remote scientific participation in experimental operations. This work includes secured computational services that can be scheduled as required, the ability to rapidly compare experimental data with simulation results, a means to easily share individual results with the group by moving application windows to a shared display, and the ability for remote scientists to be fully engaged in experimental operations through shared audio, video, and applications. The project is funded by the USDOE Office of Science, Scientific Discovery through Advanced Computing (SciDAC) Program and unites fusion and computer science researchers to directly address these challenges

  18. Tokamak rotation and charge exchange

    International Nuclear Information System (INIS)

    Hazeltine, R.D.; Rowan, W.L.; Solano, E.R.; Valanju, P.M.

    1991-01-01

    In the absence of momentum input, tokamak toroidal rotation rates are typically small - no larger in particular than poloidal rotation - even when the radial electric field is strong, as near the plasma edge. This circumstance, contradicting conventional neoclassical theory, is commonly attributed to the rotation damping effect of charge exchange, although a detailed comparison between charge-exchange damping theory and experiment is apparently unavailable. Such a comparison is attempted here in the context of recent TEXT experiments, which compare rotation rates, both poloidal and toroidal, in helium and hydrogen discharges. The helium discharges provide useful data because they are nearly free of ion-neutral charge exchange; they have been found to rotate toroidally in reasonable agreement with neoclassical predictions. The hydrogen experiments show much smaller toroidal motion as usual. The theoretical calculation uses the full charge-exchange operator and assumes plateau collisionality, roughly consistent with the experimental conditions. The authors calculate the ion flow as a function of v cx /v c , where v cx is the charge exchange rate and v c the Coulomb collision frequency. The results are in reasonable accord with the observations. 1 ref

  19. Progress of the ECH·ECCD experiments. Research progress of the ECH·ECCD experiments in tokamaks and spherical tokamaks

    International Nuclear Information System (INIS)

    Isayama, Akihiko; Tanaka, Hitoshi

    2009-01-01

    Recent progress in the ECH·ECCD study in tokamak and spherical tokamak devices is described. As for the tokamak study, results on the control of neoclassical tearing modes and sawtooth oscillations, the current profile, the internal transport barrier, the plasma start-up and the discharge cleaning are given. As for the spherical tokamak study, the plasma start-up by ECH·ECCD and the electron-Bernstein-wave heating and the current drive are described. (T.I.)

  20. A thermodynamic solution model for calcium carbonate: Towards an understanding of multi-equilibria precipitation pathways.

    Science.gov (United States)

    Donnet, Marcel; Bowen, Paul; Lemaître, Jacques

    2009-12-15

    Thermodynamic solubility calculations are normally only related to thermodynamic equilibria in solution. In this paper, we extend the use of such solubility calculations to help elucidate possible precipitation reaction pathways during the entire reaction. We also estimate the interfacial energy of particles using only solubility data by a modification of Mersmann's approach. We have carried this out by considering precipitation reactions as a succession of small quasi-equilibrium states. Thus possible equilibrium precipitation pathways can be evaluated by calculating the evolution of surface charge, particle size and/or interfacial energy during the ongoing reaction. The approach includes the use of the Kelvin's law to express the influence of particle size on the solubility constant of precipitates, the use of Nernst's law to calculate surface potentials from solubility calculations and relate this to experimentally measured zeta potentials. Calcium carbonate precipitation and zeta potential measurements of well characterised high purity calcite have been used as a model system to validate the calculated values. The clarification of the change in zeta potential on titration illustrates the power of this approach as a tool for reaction pathway prediction and hence knowledge based tailoring of precipitation reactions.