Progress on accelerated calculation of 3D MHD equilibrium with the PIES code
Raburn, Daniel; Reiman, Allan; Monticello, Donald
2016-10-01
Continuing progress has been made in accelerating the 3D MHD equilibrium code, PIES, using an external numerical wrapper. The PIES code (Princeton Iterative Equilibrium Solver) is capable of calculating 3D MHD equilibria with islands. The numerical wrapper has been demonstrated to greatly improve the rate of convergence in numerous cases corresponding to equilibria in the TFTR device where magnetic islands are present; the numerical wrapper makes use of a Jacobian-free Newton-Krylov solver along with adaptive preconditioning and a sophisticated subspace-restricted Levenberg backtracking algorithm. The wrapper has recently been improved by automation which combines the preexisting backtracking algorithm with insights gained from the stability of the Picard algorithm traditionally used with PIES. Improved progress logging and stopping criteria have also been incorporated in to the numerical wrapper.
Nakamura, Y.; Matsumoto, T.; Wakatani, M. [Kyoto Univ. (Japan). Plasma Physics Lab.; Galkin, S.A.; Drozdov, V.V.; Martynov, A.A.; Poshekhonov, Yu.Yu. [Keldysh Institute of Applied Mathematics, Moscow (Russian Federation); Ichiguchi, K. [National Institute for Fusion Science, Nagoya (Japan); Garcia, L. [Universidad Carlos III de Madrid (Spain); Carreras, B.A. [Oak Ridge National Lab., TN (United States)] [and others
1995-04-01
A particular configuration of the LHD stellarator with an unusually flat pressure profile has been chosen to be a test case for comparison of the MHD stability property predictions of different three-dimensional and averaged codes for the purpose of code comparison and validation. In particular, two relatively localized instabilities, the fastest growing modes with toroidal mode number n = 2 and n = 3 were studied using several different codes, with the good agreement that has been found providing justification for the use of any of them for equilibria of the type considered.
Galkowski, A. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad`s ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs.
MHD equilibrium and stability in heliotron plasmas
Ichiguchi, Katsuji [National Inst. for Fusion Science, Toki, Gifu (Japan)
1999-09-01
Recent topics in the theoretical magnetohydrodynamic (MHD) analysis in the heliotron configuration are overviewed. Particularly, properties of three-dimensional equilibria, stability boundary of the interchange mode, effects of the net toroidal current including the bootstrap current and the ballooning mode stability are focused. (author)
Modified NASA-Lewis Chemical Equilibrium Code for MHD applications
Sacks, R. A.; Geyer, H. K.; Grammel, S. J.; Doss, E. D.
1979-12-01
A substantially modified version of the NASA-Lewis Chemical Equilibrium Code has recently been developed. The modifications were designed to extend the power and convenience of the Code as a tool for performing combustor analysis for MHD systems studies. This report describes the effect of the programming details from a user point of view, but does not describe the Code in detail.
MHD Turbulent Mixing Layers: Equilibrium Cooling Models
Esquivel, A; Cho, J; Lazarian, A; Leitner, S N
2006-01-01
We present models of turbulent mixing at the boundaries between hot (T~10^{6-7} K) and warm material (T~10^4 K) in the interstellar medium, using a three-dimensional magnetohydrodynamical code, with radiative cooling. The source of turbulence in our simulations is a Kelvin-Helmholtz instability, produced by shear between the two media. We found, that because the growth rate of the large scale modes in the instability is rather slow, it takes a significant amount of time (~1 Myr) for turbulence to produce effective mixing. We find that the total column densities of the highly ionized species (C IV, N V, and O VI) per interface (assuming ionization equilibrium) are similar to previous steady-state non-equilibrium ionization models, but grow slowly from log N ~10^{11} to a few 10^{12} cm^{-2} as the interface evolves. However, the column density ratios can differ significantly from previous estimates, with an order of magnitude variation in N(C IV)/N(O VI) as the mixing develops.
Hall MHD Equilibrium of Accelerated Compact Toroids
Howard, S. J.; Hwang, D. Q.; Horton, R. D.; Evans, R. W.; Brockington, S. J.
2007-11-01
We examine the structure and dynamics of the compact toroid's magnetic field. The compact toroid is dramatically accelerated by a large rail-gun Lorentz force density equal to j xB. We use magnetic data from the Compact Toroid Injection Experiment to answer the question of exactly where in the system j xB has nonzero values, and to what extent we can apply the standard model of force-free equilibrium. In particular we present a method of analysis of the magnetic field probe signals that allows direct comparison to the predictions of the Woltjer-Taylor force-free model and Turner's generalization of magnetic relaxation in the presence of a non-zero Hall term and fluid vorticity.
A numerical code for a three-dimensional magnetospheric MHD equilibrium model
Voigt, G.-H.
1992-01-01
Two dimensional and three dimensional MHD equilibrium models were begun for Earth's magnetosphere. The original proposal was motivated by realizing that global, purely data based models of Earth's magnetosphere are inadequate for studying the underlying plasma physical principles according to which the magnetosphere evolves on the quasi-static convection time scale. Complex numerical grid generation schemes were established for a 3-D Poisson solver, and a robust Grad-Shafranov solver was coded for high beta MHD equilibria. Thus, the effects were calculated of both the magnetopause geometry and boundary conditions on the magnetotail current distribution.
Investigations on application of multigrid method to MHD equilibrium analysis
Ikuno, Soichiro [Faculty of Engineering Science, School of Engineering, Tokyo Univ. of Technology, Tokyo (Japan)
2000-06-01
The potentiality of application for Multi-grid method to MHD equilibrium analysis is investigated. The nonlinear eigenvalue problem often appears when the MHD equilibria are determined by solving the Grad-Shafranov equation numerically. After linearization of the equation, the problem is solved by use of the iterative method. Although the Red-Black SOR method or Gauss-Seidel method is often used for the solution of the linearized equation, it takes much CPU time to solve the problem. The Multi-grid method is compared with the SOR method for the Poisson Problem. The results of computations show that the CPU time required for the Multi-grid method is about 1000 times as small as that for the SOR method. (author)
Hybrid Method for Tokamak MHD Equilibrium Configuration Reconstruction
HE Hong-Da; DONG Jia-Qi; ZHANG Jin-Hua; JIANG Hai-Bin
2007-01-01
A hybrid method for tokamak MHD equilibrium configuration reconstruction is proposed and employed in the modified EFIT code. This method uses the free boundary tokamak equilibrium configuration reconstruction algorithm with one boundary point fixed. The results show that the position of the fixed point has explicit effects on the reconstructed divertor configurations. In particular, the separatrix of the reconstructed divertor configuration precisely passes the required position when the hybrid method is used in the reconstruction. The profiles of plasma parameters such as pressure and safety factor for reconstructed HL-2A tokamak configurations with the hybrid and the free boundary methods are compared. The possibility for applications of the method to swing the separatrix strike point on the divertor target plate is discussed.
Equilibrium calculations of firework mixtures
Hobbs, M.L. [Sandia National Labs., Albuquerque, NM (United States); Tanaka, Katsumi; Iida, Mitsuaki; Matsunaga, Takehiro [National Inst. of Materials and Chemical Research, Tsukuba, Ibaraki (Japan)
1994-12-31
Thermochemical equilibrium calculations have been used to calculate detonation conditions for typical firework components including three report charges, two display charges, and black powder which is used as a fuse or launch charge. Calculations were performed with a modified version of the TIGER code which allows calculations with 900 gaseous and 600 condensed product species at high pressure. The detonation calculations presented in this paper are thought to be the first report on the theoretical study of firework detonation. Measured velocities for two report charges are available and compare favorably to predicted detonation velocities. However, the measured velocities may not be true detonation velocities. Fast deflagration rather than an ideal detonation occurs when reactants contain significant amounts of slow reacting constituents such as aluminum or titanium. Despite such uncertainties in reacting pyrotechnics, the detonation calculations do show the complex nature of condensed phase formation at elevated pressures and give an upper bound for measured velocities.
李莉; 刘悦; 许欣洋; 夏新念
2012-01-01
A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Linearized resistivity MHD equations with plasma viscosity are adopted to describe our model, and the equations are solved numerically as an initial value problem. Some of the results are used as benchmark tests for the code, and then a series of equilibrium current profiles are used to simulate the bootstrap current profiles in actual experiments with a bump on tail. Thus the effects of these kinds of profiles on MHD instabilities in tokamaks are revealed. From the analysis of the numerical results, it is found that more plasma can be confined when the center of the current bump is closer to the plasma surface, and a higher and narrower current bump has a better stabilizing effect on the MHD instabilities.
Numerical Calculation of the Output Power of a MHD Generator
Adrian CARABINEANU
2014-12-01
Full Text Available Using Lazăr Dragoş’s analytic solution for the electric potential we perform some numerical calculations in order to find the characteristics of a Faraday magnetohydrodymamics (MHD power generator (total power, useful power and Joule dissipation power.
Calculation of three-dimensional MHD equilibria with islands and stochastic regions
Reiman, A.; Greenside, H.
1986-08-01
A three-dimensional MHD equilibrium code is described that does not assume the existence of good surfaces. Given an initial guess for the magnetic field, the code proceeds by calculating the pressure-driven current and then by updating the field using Ampere's law. The numerical algorithm to solve the magnetic differential equation for the pressure-driven current is described, and demonstrated for model fields having islands and stochastic regions. The numerical algorithm which solves Ampere's law in three dimensions is also described. Finally, the convergence of the code is illustrated for a particular stellarator equilibrium with no large islands.
Willensdorfer, M; Strumberger, E; Suttrop, W; Vanovac, B; Brida, D; Cavedon, M; Classen, I; Dunne, M; Fietz, S; Fischer, R; Kirk, A; Laggner, F M; Liu, Y Q; Odstrcil, T; Ryan, D A; Viezzer, E; Zohm, H; Luhmann, I C
2016-01-01
The plasma response from an external n = 2 magnetic perturbation field in ASDEX Upgrade has been measured using mainly electron cyclotron emission (ECE) diagnostics and a rigid rotating field. To interpret ECE and ECE-imaging (ECE-I) measurements accurately, forward modeling of the radiation transport has been combined with ray tracing. The measured data is compared to synthetic ECE data generated from a 3D ideal magnetohydrodynamics (MHD) equilibrium calculated by VMEC. The measured amplitudes of the helical displacement in the midplane are in reasonable agreement with the one from the synthetic VMEC diagnostics. Both exceed the vacuum field calculations and indicate the presence of an amplified kink response at the edge. Although the calculated magnetic structure of this edge kink peaks at poloidal mode numbers larger than the resonant components |m| > |nq|, the displacement measured by ECE-I is almost resonant |m| ~ |nq|. This is expected from ideal MHD in the proximity of rational surfaces. VMEC and MARS-...
Non-Equilibrium Properties from Equilibrium Free Energy Calculations
Pohorille, Andrew; Wilson, Michael A.
2012-01-01
Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.
Resonant behaviour of MHD waves on magnetic flux tubes. III - Effect of equilibrium flow
Goossens, Marcel; Hollweg, Joseph V.; Sakurai, Takashi
1992-01-01
The Hollweg et al. (1990) analysis of MHD surface waves in a stationary equilibrium is extended. The conservation laws and jump conditions at Alfven and slow resonance points obtained by Sakurai et al. (1990) are generalized to include an equilibrium flow, and the assumption that the Eulerian perturbation of total pressure is constant is recovered as the special case of the conservation law for an equilibrium with straight magnetic field lines and flow along the magnetic field lines. It is shown that the conclusions formulated by Hollweg et al. are still valid for the straight cylindrical case. The effect of curvature is examined.
Stabilization of the SIESTA MHD Equilibrium Code Using Rapid Cholesky Factorization
Hirshman, S. P.; D'Azevedo, E. A.; Seal, S. K.
2016-10-01
The SIESTA MHD equilibrium code solves the discretized nonlinear MHD force F ≡ J X B - ∇p for a 3D plasma which may contain islands and stochastic regions. At each nonlinear evolution step, it solves a set of linearized MHD equations which can be written r ≡ Ax - b = 0, where A is the linearized MHD Hessian matrix. When the solution norm | x| is small enough, the nonlinear force norm will be close to the linearized force norm | r| 0 obtained using preconditioned GMRES. In many cases, this procedure works well and leads to a vanishing nonlinear residual (equilibrium) after several iterations in SIESTA. In some cases, however, | x|>1 results and the SIESTA code has to be restarted to obtain nonlinear convergence. In order to make SIESTA more robust and avoid such restarts, we have implemented a new rapid QR factorization of the Hessian which allows us to rapidly and accurately solve the least-squares problem AT r = 0, subject to the condition | x|QR method is based on a pairwise row factorization of the tri-diagonal Hessian. It provides a complete Cholesky factorization while preserving the memory allocation of A. This work was supported by the U.S. D.O.E. contract DE-AC05-00OR22725.
Yang, H.; Bhattacharjee, A.; Forbes, T. G.
2008-12-01
It has long been suggested that eruptive phenomena such as coronal mass ejections, prominence eruptions, and large flares might be caused by a loss of equilibrium in a coronal flux rope (Van Tend and Kuperus, 1978). Forbes et al. (1994) developed an analytical two-dimensional model in which eruptions occur due to a catastrophic loss of equilibrium and relaxation to a lower-energy state containing a thin current sheet. Magnetic reconnection then intervenes dynamically, leading to the release of magnetic energy and expulsion of a plasmoid. We have carried out high-Lundquist-number simulations to test the loss-of equilibrium mechanism, and demonstrated that it does indeed occur in the quasi-ideal limit. We have studied the subsequent dynamical evolution of the system in resistive and Hall MHD models for single as well as multiple arcades. The typical parallel electric fields are super-Dreicer, which makes it necessary to include collisionless effects via a generalized Ohm's law. It is shown that the nature of the local dissipation mechanism has a significant effect on the global geometry and dynamics of the magnetic configuration. The presence of Hall currents is shown to alter the length of the current sheet and the jets emerging from the reconnection site, directed towards the chromosphere. Furthermore, Hall MHD effects break certain symmetries of resistive MHD dynamics, and we explore their observational consequences.
High resolution equilibrium calculations of pedestal and SOL plasma in tokamaks
Medvedev, S. Yu; Martynov, A. A.; Drozdov, V. V.; Ivanov, A. A.; Poshekhonov, Yu Yu
2017-02-01
For integrated modeling of equilibrium, stability and dynamics of the divertor tokamak plasma with scrape-off layer (SOL) high resolution equilibrium calculations are needed. A new version of the CAXE equilibrium code computes the tokamak equilibrium on a numerical grid adaptive to magnetic surfaces both in the plasma region with closed flux surfaces and in the SOL region with open magnetic lines. The plasma profiles can be prescribed independently in each region with nested flux surfaces, and realistic SOL profiles with very short pressure drop off length can be accurately treated. The influence of the finite current density in SOL on the connection length is studied. From the point of view of the MHD equilibrium and stability modeling, self-consistent calculations of diverted tokamak configurations with finite current density at the separatrix require taking into account plasma outside the separatrix. Calculated high resolution equilibria provide an input to new versions of the ideal MHD stability codes treating tokamak plasma with SOL. The study of the influence of the pressure gradient profile in the pedestal plasma inside and outside the separatrix on the pedestal height limit set by external kink-ballooning mode stability is presented. Another possible application of the high resolution pedestal and SOL equilibrium code is a coupling to the SOLPS code with a purpose to increase equilibrium accuracy and support self-consistent plasma flow/equilibrium modeling.
Group Contribution Methods for Phase Equilibrium Calculations.
Gmehling, Jürgen; Constantinescu, Dana; Schmid, Bastian
2015-01-01
The development and design of chemical processes are carried out by solving the balance equations of a mathematical model for sections of or the whole chemical plant with the help of process simulators. For process simulation, besides kinetic data for the chemical reaction, various pure component and mixture properties are required. Because of the great importance of separation processes for a chemical plant in particular, a reliable knowledge of the phase equilibrium behavior is required. The phase equilibrium behavior can be calculated with the help of modern equations of state or g(E)-models using only binary parameters. But unfortunately, only a very small part of the experimental data for fitting the required binary model parameters is available, so very often these models cannot be applied directly. To solve this problem, powerful predictive thermodynamic models have been developed. Group contribution methods allow the prediction of the required phase equilibrium data using only a limited number of group interaction parameters. A prerequisite for fitting the required group interaction parameters is a comprehensive database. That is why for the development of powerful group contribution methods almost all published pure component properties, phase equilibrium data, excess properties, etc., were stored in computerized form in the Dortmund Data Bank. In this review, the present status, weaknesses, advantages and disadvantages, possible applications, and typical results of the different group contribution methods for the calculation of phase equilibria are presented.
TEA: A Code Calculating Thermochemical Equilibrium Abundances
Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver
2016-07-01
We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature-pressure pairs. We tested the code against the method of Burrows & Sharp, the free thermochemical equilibrium code Chemical Equilibrium with Applications (CEA), and the example given by Burrows & Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.
Experimental and theoretical studies of the effects of nonuniformities in equilibrium MHD generators
Rosenbaum, M.; Shamma, S.E.; Louis, J.F.
1980-01-01
An experimental study of the effects of thermal and velocity nonuniformities is performed in an equilibrium plasma for a range of Hall parameters. An electrodeless MHD disk generator with radial flow is chosen as the ideal geometry for these experiments. By introducing equally spaced cold blades in the flow, it is possible to create well defined two-dimensional wake nonuniformities with strong variations of the plasma properties in the direction normal to the magnetic field and the flow. This type of nonuniformity is predicted to provide the strongest reduction of Hall coefficient and effective conductivity for high values of Hall parameter. This degradation is controlled by both the level of nonuniformities and the value of the ideal Hall parameter. The former is dependent upon the number of blades (root mean square deviation of the conductivity), and the latter is dependent upon the values of the magnetic field intensities. The results provide basic quantitative information about the effects of conductivity and velocity nonuniformities on the performance of equilibrium MHD generators over a wide range of Hall coefficients, between 2 and 7. Reduction formulae are established between the effective and ideal Hall parameters for different levels of nonuniformities intensities. Theoretical predictions are derived from a detailed two-dimensional electrodynamic analysis and a simplified engineering model based on a generalization of Rosa's layer model. These experiments validate the analytical studies and support the use of the theoretical layer models in describing the effect of boundary layers on the performance of linear generators.
Held, E.D. [Univ. of Wisconsin, Madison, WI (United States). Center for Plasma Theory and Computation; Leboeuf, J.N.; Carreras, B.A. [Oak Ridge National Lab., TN (United States). Fusion Energy Div.
1998-07-01
The linear and nonlinear stability of a nonmonotonic q profile is examined using a reduced set of magnetohydrodynamic (MHD) equations with an equilibrium, sheared toroidal flow. The reversed shear profile is shown to be unstable to a rich variety of resistive MHD modes including pressure-driven instabilities and tearing instabilities possessing a tearing/interchange character at low Lundquist number, S, and taking on a double/triple tearing structure at high S. Linear calculations show that the destabilizing effect of toroidal velocity shear on tearing modes is enhanced at finite pressure seen previously for tearing modes at high S. Nonlinear calculations show the generation of a large, m = 1, n = 0, Reynolds-stress-driven poloidal flow in the absence of significant flow damping. Calculations in which the poloidal flow was heavily damped show that sub-Alfvenic, sheared toroidal flows have a minimal effect on weakly-coupled, localized instabilities.
Hirshman, S. P.; Shafer, M. W.; Seal, S. K.; Canik, J. M.
2016-04-01
> The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces) of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.
Kobayashi, H.; Okuno, Y.; Kabashima, S. [Tokyo Institute of Technology, Tokyo (Japan)
1995-08-20
The performance of non-equilibrium MHD disk generator with segmented loads is examined with {gamma}-{theta} two dimensional numerical simulations. The use of segmented loads is found to improve the generator performance when a low electron temperature plasma is introduced to the channel. The simulation results reveal the desired values of load resistances connected in upstream and downstream regions, respectively. The concept of the segmented loads is considered to be superior to rearranging seed fractions and load resistances. 10 refs., 6 figs., 2 tabs.
Merkle Peterkin, Laurence D., Jr.
1997-11-01
The time-dependent location of the critical surface of laser absorption is studied numerically, using the general purpose two-dimensional finite-difference MHD software uc(Mach2.) This software, which is based on an arbitrary Lagrangian-Eulerian fluid algorithm, includes models for partial laser absorption in underdense plasmas via inverse brehmsstrahlung, as well as total laser absorption at a critical surface. The simulations conducted are of a laboratory experiment in which a plasma is generated by a mode-locked laser interacting with a solid copper target (G.K. Chawla and C.W. von Rosenberg, Jr., IEEE Conference Record --- Abstracts, 1997 IEEE International Conference on Plasma Science). The location of the critical surface is a function of the number density of free electrons. Consequently, calculations must carefully consider the energy budget. Because of large opacities in hot regions, a non-equilibrium radiation diffusion model is employed. Adequate energy conservation in such simulations is possible only with careful attention to numerical aspects, such as time steps and flux limits. Simulations are performed for both 90^circ and 45^circ incident beams. The former are carried out using both cylindrical and plane-parallel geometries, while the latter require a plane-parallel geometry.
Non-local thermodynamic equilibrium inversions from a 3D MHD chromospheric model
Rodríguez, Jaime de la Cruz; Carlsson, Mats; Leenaarts, Jorrit
2012-01-01
The structure of the solar chromosphere is believed to be governed by magnetic fields, even in quiet-Sun regions that have a relatively weak photospheric field. During the past decade inversion methods have emerged as powerful tools for analyzing the chromosphere of active regions. The applicability of inversions to infer the stratification of the physical conditions in a dynamic 3D solar chromosphere has not yet been studied in detail. This study aims to establish the diagnostic capabilities of non-local thermodynamical equilibrium (NLTE) inversion techniques of Stokes profiles induced by the Zeeman effect in the Ca II 8542 line. We computed the Ca II atomic level populations in a snapshot from a 3D radiation-MHD simulation of the quiet solar atmosphere in non-LTE using the 3D radiative transfer code Multi3d. These populations were used to compute synthetic full-Stokes profiles in the Ca II 8542 line using 1.5D radiative transfer and the inversion code Nicole. The profiles were then spectrally degraded to ac...
Calculation of individual isotope equilibrium constants for geochemical reactions
Thorstenson, D.C.; Parkhurst, D.L.
2004-01-01
Theory is derived from the work of Urey (Urey H. C. [1947] The thermodynamic properties of isotopic substances. J. Chem. Soc. 562-581) to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by ?? = (Kex)1/n, where n is the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example 13C16O18O and 1H2H18O. The equilibrium constants of the isotope exchange reactions can be expressed as ratios of individual isotope equilibrium constants for geochemical reactions. Knowledge of the equilibrium constant for the dominant isotopic species can then be used to calculate the individual isotope equilibrium constants. Individual isotope equilibrium constants are calculated for the reaction CO2g = CO2aq for all species that can be formed from 12C, 13C, 16O, and 18O; for the reaction between 12C18 O2aq and 1H218Ol; and among the various 1H, 2H, 16O, and 18O species of H2O. This is a subset of a larger number of equilibrium constants calculated elsewhere (Thorstenson D. C. and Parkhurst D. L. [2002] Calculation of individual isotope equilibrium constants for implementation in geochemical models. Water-Resources Investigation Report 02-4172. U.S. Geological Survey). Activity coefficients, activity-concentration conventions for the isotopic variants of H2O in the solvent 1H216Ol, and salt effects on isotope fractionation have been included in the derivations. The effects of nonideality are small because of the chemical similarity of different isotopic species of the same molecule or ion. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation
Methane on Mars: Thermodynamic Equilibrium and Photochemical Calculations
Levine, J. S.; Summers, M. E.; Ewell, M.
2010-01-01
The detection of methane (CH4) in the atmosphere of Mars by Mars Express and Earth-based spectroscopy is very surprising, very puzzling, and very intriguing. On Earth, about 90% of atmospheric ozone is produced by living systems. A major question concerning methane on Mars is its origin - biological or geological. Thermodynamic equilibrium calculations indicated that methane cannot be produced by atmospheric chemical/photochemical reactions. Thermodynamic equilibrium calculations for three gases, methane, ammonia (NH3) and nitrous oxide (N2O) in the Earth s atmosphere are summarized in Table 1. The calculations indicate that these three gases should not exist in the Earth s atmosphere. Yet they do, with methane, ammonia and nitrous oxide enhanced 139, 50 and 12 orders of magnitude above their calculated thermodynamic equilibrium concentration due to the impact of life! Thermodynamic equilibrium calculations have been performed for the same three gases in the atmosphere of Mars based on the assumed composition of the Mars atmosphere shown in Table 2. The calculated thermodynamic equilibrium concentrations of the same three gases in the atmosphere of Mars is shown in Table 3. Clearly, based on thermodynamic equilibrium calculations, methane should not be present in the atmosphere of Mars, but it is in concentrations approaching 30 ppbv from three distinct regions on Mars.
Calculation of Ion Equilibrium Temperature in Ultracold Neutral Plasmas
李金星; 曹明涛; 韩亮; 齐越蓉; 张首刚; 高宏; 李福利; T.C.Killian
2011-01-01
We provide a fast iteration method to calculate the ion equilibrium temperature in an ultracold neutral plasma (UNP). The temperature as functions of electron initial temperature and ion density is obtained and compared with the recent UNP experimental data. The theoretical predictions agree with the experimental results very well. The calculated ion equilibrium temperature by this method can be applied to study the UNP expansion process more effectively.%We provide a fast iteration method to calculate the ion equilibrium temperature in an ultracold neutral plasma (UNP).The temperature as functions of electron initial temperature and ion density is obtained and compared with the recent UNP experimental data.The theoretical predictions agree with the experimental results very well.The calculated ion equilibrium temperature by this method can be applied to study the UNP expansion process more effectively.
TEA: A Code for Calculating Thermochemical Equilibrium Abundances
Blecic, Jasmina; Bowman, M Oliver
2015-01-01
We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. (1958) and Eriksson (1971). It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature-pressure pairs. We tested the code against the method of Burrows & Sharp (1999), the free thermochemical equilibrium code CEA (Chemical Equilibrium with Applications), and the example given by White et al. (1958). Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is ...
Reyes Labarta, Juan Antonio; Olaya López, María del Mar; Gómez Siurana, Amparo; Marcilla Gomis, Antonio
1999-01-01
Póster presentado en el congreso EQUIFASE 99 (Vigo, del 20 al 24 de Junio de 1999). Resumen publicado en el libro de actas del Congreso An algebraic correlation method to calculate equilibrium data for ternary vapor-liquid equilibrium and quaternary liquid-liquid equilibrium has been proposed. The proposed method allows the calculation of the conjugated phase in equilibrium with a given phase, and the calculation of the two phases in equilibrium from the composition of a heterogeneous glob...
Isochronous Cyclotron Closed Equilibrium Orbit Calculation Program Description
Kian, I N; Tarashkevich, R
2003-01-01
The Equilibrium Orbit Research Program - EORP, written in C++ with the use of Visual C++ is described. The program is intended for the calculation of the particle rotation frequency and particle kinetic energy in the closed equilibrium orbits of an isochronous cyclotron, where the closed equilibrium orbits are described through the radius and particle momentum angle: r_{eo}(\\theta) and \\varphi_{p}(\\theta). The program algorithm was developed on the basis of articles, lecture notes and original analytic calculations. The results of calculations by the EORP were checked and confirmed by using the results of calculations by the numerical methods. The discrepancies between the EORP results and the numerical method results for the calculations of the particle rotation frequency and particle kinetic energy are within the limits of \\pm1\\cdot10^{-4}. The EORP results and the numerical method results for the calculations of r_{eo}(\\theta) and \\varphi_{p}(\\theta) practically coincide. All this proves the accuracy of ca...
Computer program for equilibrium calculation and diffusion simulation
无
2000-01-01
A computer program called TKCALC(thermodynamic and kinetic calculation) has been successfully developedfor the purpose of phase equilibrium calculation and diffusion simulation in ternary substitutional alloy systems. The program was subsequently applied to calculate the isothermal sections of the Fe-Cr-Ni system and predict the concentrationprofiles of two γ/γ single-phase diffusion couples in the Ni-Cr-Al system. The results are in excellent agreement withTHERMO-CALC and DICTRA software packages. Detailed mathematical derivation of some important formulae involvedis also elaborated
Opacity Calculations for Non-Local Thermodynamic Equilibrium Mixtures
吴泽清; 韩国兴; 逄锦桥
2002-01-01
Based on the average atom model, a non-local thermodynamic equilibrium (non-LTE) model is developed to calculate opacity for mixtures. This model could be applied to high-Z problems. The mean ionization degrees of SiO2 of the present calculation are slightly higher compared with another model for mixtures. As an example, the opacity of Au and Nd mixture is calculated. The results show concrete non-LTE effects and the increase in opacity of the mixture is shown clearly.
NON-EQUILIBRIUM HELIUM IONIZATION IN AN MHD SIMULATION OF THE SOLAR ATMOSPHERE
Golding, Thomas Peter; Carlsson, Mats [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo (Norway); Leenaarts, Jorrit, E-mail: thomas.golding@astro.uio.no, E-mail: mats.carlsson@astro.uio.no, E-mail: jorrit.leenaarts@astro.su.se [Institute for Solar Physics, Department of Astronomy, Stockholm University, AlbaNova University Centre, SE-106 91 Stockholm (Sweden)
2016-02-01
The ionization state of the gas in the dynamic solar chromosphere can depart strongly from the instantaneous statistical equilibrium commonly assumed in numerical modeling. We improve on earlier simulations of the solar atmosphere that only included non-equilibrium hydrogen ionization by performing a 2D radiation-magnetohydrodynamics simulation featuring non-equilibrium ionization of both hydrogen and helium. The simulation includes the effect of hydrogen Lyα and the EUV radiation from the corona on the ionization and heating of the atmosphere. Details on code implementation are given. We obtain helium ion fractions that are far from their equilibrium values. Comparison with models with local thermodynamic equilibrium (LTE) ionization shows that non-equilibrium helium ionization leads to higher temperatures in wavefronts and lower temperatures in the gas between shocks. Assuming LTE ionization results in a thermostat-like behavior with matter accumulating around the temperatures where the LTE ionization fractions change rapidly. Comparison of DEM curves computed from our models shows that non-equilibrium ionization leads to more radiating material in the temperature range 11–18 kK, compared to models with LTE helium ionization. We conclude that non-equilibrium helium ionization is important for the dynamics and thermal structure of the upper chromosphere and transition region. It might also help resolve the problem that intensities of chromospheric lines computed from current models are smaller than those observed.
Linear stability of ideal MHD configurations. II. Results for stationary equilibrium configurations
Demaerel, T.; Keppens, R.
2016-12-01
In this paper, we continue exploring the consequences of the general equation of motion (EOM) governing all Lagrangian perturbations ξ about a time-dependent, ideal magnetohydrodynamic (MHD) configuration, which includes self-gravity, external gravity, pressure gradients, compressibility, inertial effects, and anisotropic Lorentz force. We here address the specific case of MHD stability for 3D stationary equilibria, where the perturbed EOM features a symmetric operator F and an antisymmetric Doppler-Coriolis operator v . ∇ . For this case, we state and prove the general properties for the solutions ξ of the governing dynamical system. For axisymmetric perturbations about axisymmetric equilibria with purely toroidal, or purely poloidal magnetic fields, specific stability theorems can be formulated. We derive a useful integral expression for the quadratic quantity given by the inner product ⟨ ξ , F [ ξ ] ⟩ . For deriving stability statements on MHD states where self-gravity is involved as well, we provide an upper bound on the perturbed self-gravitational energy associated with the displacement ξ . The resulting expression elucidates the role of potentially stabilizing versus destabilizing contributions and shows the role of gravity, entropy gradients, velocity shear, currents, Lorentz forces, inertia, and pressure gradients in offering many routes to unstable behavior in flowing gases and plasmas. These have historically mostly been studied for static v = 0 configurations, looking at stability of exactly force-balanced states, or by assuming stationarity similar to our approach here (i.e., ∂ t ≡ 0 for the state we perturb), but typically in combination with some reduced dimensionality on the configuration of interest (translational or axisymmetry). We show that in these limits, we find and generalize expressions well-known from, e.g., the study of ideal MHD stability of tokamak plasmas or from Schwarzschild's criteria controlling convection in
A subdivision algorithm for phase equilibrium calculations at high pressures
M. L. Corazza
2007-12-01
Full Text Available Phase equilibrium calculations at high pressures have been a continuous challenge for scientists and engineers. Traditionally, this task has been performed by solving a system of nonlinear algebraic equations originating from isofugacity equations. The reliability and accuracy of the solutions are strongly dependent on the initial guess, especially due to the fact that the phase equilibrium problems frequently have multiple roots. This work is focused on the application of a subdivision algorithm for thermodynamic calculations at high pressures. The subdivision algorithm consists in the application of successive subdivisions at a given initial interval (rectangle of variables and a systematic test to verify the existence of roots in each subinterval. If the interval checked passes in the test, then it is retained; otherwise it is discharged. The algorithm was applied for vapor-liquid, solid-fluid and solid-vapor-liquid equilibrium as well as for phase stability calculations for binary and multicomponent systems. The results show that the proposed algorithm was capable of finding all roots of all high-pressure thermodynamic problems investigated, independent of the initial guess used.
A general framework for ion equilibrium calculations in compacted bentonite
Birgersson, Martin
2017-03-01
An approach for treating chemical equilibrium between compacted bentonite and aqueous solutions is presented. The treatment is based on conceptualizing bentonite as a homogeneous mixture of water and montmorillonite, and assumes Gibbs-Donnan membrane equilibrium across interfaces to external solutions. An equation for calculating the electrostatic potential difference between bentonite and external solution (Donnan potential) is derived and solved analytically for some simple systems. The solutions are furthermore analyzed in order to illuminate the general mechanisms of ion equilibrium and their relation to measurable quantities. A method is suggested for estimating interlayer activity coefficients based on the notion of an interlayer ionic strength. Using this method, several applications of the framework are presented, giving a set of quantitative predictions which may be relatively simply tested experimentally, e.g.: (1) the relative amount of anions entering the bentonite depends approximately on the square-root of the external concentration for a 1:2 salt (e.g. CaCl2). For a 1:1 salt (e.g. NaCl) the dependence is approximately linear, and for a 1:2 salt (e.g. Na2SO4) the dependence is approximately quadratic. (2) Bentonite contains substantially more nitrate as compared to chloride if equilibrated with the two salt solutions at equal external concentration. (3) Potassium bentonite generally contains more anions as compared to sodium bentonite if equilibrated at the same external concentration. (4) The anion concentration ratio in two bentonite samples of different cations (but with the same density and cation exchange capacity) resembles the ion exchange selectivity coefficient for that specific cation pair. The results show that an adequate treatment of chemical equilibrium between interlayers and bulk solutions are essential when modeling compacted bentonite, and that activity corrections generally are required for relevant ion equilibrium calculations. It
Simplified method for calculation of equilibrium plasma composition
Rydalevskaya, Maria A.
2017-06-01
In this work, a simplified method for the evaluation of equilibrium composition of plasmas consisted of monoatomic species is proposed. Multicomponent gas systems resulting from thermal ionization of spatially uniform mixtures are assumed enough rarefied to be treated as ideal gases even after multiple ionization steps. The method developed for the calculation of equilibrium composition of these mixtures makes use of the fundamental principles of statistical physics. Equilibrium concentrations of mixture components are determined by integration of distribution functions over the space of momentum and summation over electronic energy levels. These functions correspond to the entropy maximum. To determine unknown parameters, the systems of equations corresponding to the normalization conditions are derived. It is shown that the systems may be reduced to one algebraic equation if the equilibrium temperature is known. Numeral method to solve this equation is proposed. Special attention is given to the ionized mixtures, generated from the atoms of a single chemical species and the situations, when in the gas only the first- or the first- and second-order ionization are possible.
Non-equilibrium helium ionization in an MHD simulation of the solar atmosphere
Golding, Thomas Peter; Carlsson, Mats
2015-01-01
The ionization state of the gas in the dynamic solar chromosphere can depart strongly from the instantaneous statistical equilibrium commonly assumed in numerical modeling. We improve on earlier simulations of the solar atmosphere that only included non-equilbrium hydrogen ionization by performing a 2D radiation-magneto-hydrodynamics simulation featuring non-equilibrium ionization of both hydrogen and helium. The simulation includes the effect of hydrogen Lyman-$\\alpha$ and the EUV radiation from the corona on the ionization and heating of the atmosphere. Details on code implementation are given. We obtain helium ion fractions that are far from their equilibrium values. Comparison with models with LTE ionization shows that non-equilibrium helium ionization leads to higher temperatures in wave fronts and lower temperatures in the gas between shocks. Assuming LTE ionization results in a thermostat-like behaviour with matter accumulating around the temperatures where the LTE ionization fractions change rapidly. ...
Opacity calculations for Non-Local-Thermodynamic-Equilibrium plasmas
PANG Jin-qiao; WU Ze-qing; YAN Jun; HAN Guo-xing
2004-01-01
In this paper, we presented a method to calculate the spectral-resolved opacity for Non-Local-Thermodynamic-Equilibrium (non-LTE) plasmas. By solving the rate equations, we get the population. In the rate equations, configuration-averaged rate coefficients are used and the cross sections are calculated based on the first-perturbation theory. Using the detailed configuration accounting with the term structures treated by the unresolved transition array model, we calculated the spectral-resolved opacity of Al plasmas. The results are compared with those of other theoretical models. From the comparison, we can see that the present results fit well with other models for low-Z plasmas. For high-Z plasmas, we will give detailed discussion in the future.
Chen, J.; Zhuang, G., E-mail: ge-zhuang@hust.edu.cn; Li, Q.; Liu, Y.; Gao, L.; Zhou, Y. N.; Jian, X.; Xiong, C. Y.; Wang, Z. J. [State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074 (China); Brower, D. L.; Ding, W. X. [Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095 (United States)
2014-11-15
A high-performance Faraday-effect polarimeter-interferometer system has been developed for the J-TEXT tokamak. This system has time response up to 1 μs, phase resolution < 0.1° and minimum spatial resolution ∼15 mm. High resolution permits investigation of fast equilibrium dynamics as well as magnetic and density perturbations associated with intrinsic Magneto-Hydro-Dynamic (MHD) instabilities and external coil-induced Resonant Magnetic Perturbations (RMP). The 3-wave technique, in which the line-integrated Faraday angle and electron density are measured simultaneously by three laser beams with specific polarizations and frequency offsets, is used. In order to achieve optimum resolution, three frequency-stabilized HCOOH lasers (694 GHz, >35 mW per cavity) and sensitive Planar Schottky Diode mixers are used, providing stable intermediate-frequency signals (0.5–3 MHz) with S/N > 50. The collinear R- and L-wave probe beams, which propagate through the plasma poloidal cross section (a = 0.25–0.27 m) vertically, are expanded using parabolic mirrors to cover the entire plasma column. Sources of systematic errors, e.g., stemming from mechanical vibration, beam non-collinearity, and beam polarization distortion are individually examined and minimized to ensure measurement accuracy. Simultaneous density and Faraday measurements have been successfully achieved for 14 chords. Based on measurements, temporal evolution of safety factor profile, current density profile, and electron density profile are resolved. Core magnetic and density perturbations associated with MHD tearing instabilities are clearly detected. Effects of non-axisymmetric 3D RMP in ohmically heated plasmas are directly observed by polarimetry for the first time.
Thermodynamic equilibrium calculation on preparation of copper oxalate precursor powder
FAN You-qi; ZHANG Chuan-fu; ZHAN Jing; WU Jian-hui
2008-01-01
According to the principles of simultaneous equilibrium and mass balance, a series of thermodynamic equilibrium equations of Cu2+ -C2O2-4 -NH3-NH4+-H2O system at ambient temperature were deduced theoretically and the logarithm concentration versus pH value (lg[Cu2+]T-pH) diagrams at different solution compositions were drawn. The results show that when pH is below 5.0, copper ion reacts with C2O42- directly and the morphology of copper precursor powder is of pie-shape; when pH is above 5.0, copper ion coordinates with ammonia, and the precipitation proceeds slowly accompanying with the release of copper ions from the multi-coordinated Cu(NH3)n2+ (n =1, 2, …, 5) and the morphologies of copper precursor powder are respectively of rod aggregation shape (when 5.0＜pH＜8.0) and of rod-shape (when pH＞8.0). Some experiments were performed to confirm the relation between the total concentration of copper ion and pH value. It is shown that the thermodynamic mathematical model is correct and the calculated values are basically accurate.
Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry
Furukawa, M
2016-01-01
Simulated annealing (SA) is applied for three-dimensional (3D) equilibrium calculation of ideal, low-beta reduced MHD in cylindrical geometry. The SA is based on the theory of Hamiltonian mechanics. The dynamical equation of the original system, low-beta reduced MHD in this study, is modified so that the energy changes monotonically while preserving the Casimir invariants in the artificial dynamics. An equilibrium of the system is given by an extremum of the energy, therefore SA can be used as a method for calculating ideal MHD equilibrium. Previous studies demonstrated that the SA succeeds to lead to various MHD equilibria in two dimensional rectangular domain. In this paper, the theory is applied to 3D equilibrium of ideal, low-beta reduced MHD. An example of equilibrium with magnetic islands, obtained as a lower energy state, is shown. Several versions of the artificial dynamics are developed that can effect smoothing.
Schnack, Dalton D.
In this lecture we will examine some simple examples of MHD equilibrium configurations. These will all be in cylindrical geometry. They form the basis for more complicated equilibrium states in toroidal geometry.
Extraproximal approach to calculating equilibriums in pure exchange models
Antipin, A. S.
2006-10-01
Models of economic equilibrium are a powerful tool of mathematical modeling of various markets. However, according to many publications, there are as yet no universal techniques for finding equilibrium prices that are solutions to such models. A technique of this kind that is a natural implementation of the Walras idea of tatonnements (i.e., groping for equilibrium prices) is proposed, and its convergence is proved.
MHD Calculation of halo currents and vessel forces in NSTX VDEs
Breslau, J. A.; Strauss, H. R.; Paccagnella, R.
2012-10-01
Research tokamaks such as ITER must be designed to tolerate a limited number of disruptions without sustaining significant damage. It is therefore vital to have numerical tools that can accurately predict the effects of these events. The 3D nonlinear extended MHD code M3D [1] can be used to simulate disruptions and calculate the associated wall currents and forces. It has now been validated against halo current data from NSTX experiments in which vertical displacement events (VDEs) were deliberately induced by turning off vertical feedback control. The results of high-resolution numerical simulations at realistic Lundquist numbers show reasonable agreement with the data, supporting a model in which the most dangerously asymmetric currents and heat loads, and the largest horizontal forces, arise in situations where a fast-growing ideal 2,1 external kink mode is destabilized by the scraping-off of flux surfaces with safety factor q>2 during the course of the VDE. [4pt] [1] W. Park, et al., Phys. Plasmas 6 (1999) 1796.
Dellinger, T. C.; Hnat, J. G.; Marston, C. H.
1979-01-01
A parametric study of the performance of the MHD generator and combustor components of potential early commercial open-cycle MHD/steam power plants is presented. Consideration is given to the effects of air heater system concept, MHD combustor type, coal type, thermal input power, oxygen enrichment of the combustion, subsonic and supersonic generator flow and magnetic field strength on coupled generator and combustor performance. The best performance is found to be attained with a 3000 F, indirectly fired air heater, no oxygen enrichment, Illinois no. 6 coal, a two-stage cyclone combustor with 85% slag rejection, a subsonic generator, and a magnetic field configuration yielding a constant transverse electric field of 4 kV/m. Results indicate that optimum net MHD generator power is generally compressor-power-limited rather than electric-stress-limited, with optimum net power a relatively weak function of operating pressure.
Clouds in Super-Earth Atmospheres: Chemical Equilibrium Calculations
Mbarek, Rostom; Kempton, Eliza M.-R.
2016-08-01
Recent studies have unequivocally proven the existence of clouds in super-Earth atmospheres. Here we provide a theoretical context for the formation of super-Earth clouds by determining which condensates are likely to form under the assumption of chemical equilibrium. We study super-Earth atmospheres of diverse bulk composition, which are assumed to form by outgassing from a solid core of chondritic material, following Schaefer & Fegley. The super-Earth atmospheres that we study arise from planetary cores made up of individual types of chondritic meteorites. They range from highly reducing to oxidizing and have carbon to oxygen (C:O) ratios that are both sub-solar and super-solar, thereby spanning a range of atmospheric composition that is appropriate for low-mass exoplanets. Given the atomic makeup of these atmospheres, we minimize the global Gibbs free energy of formation for over 550 gases and condensates to obtain the molecular composition of the atmospheres over a temperature range of 350-3000 K. Clouds should form along the temperature-pressure boundaries where the condensed species appear in our calculation. We find that the composition of condensate clouds depends strongly on both the H:O and C:O ratios. For the super-Earth archetype GJ 1214b, KCl and ZnS are the primary cloud-forming condensates at solar composition, in agreement with previous work. However, for oxidizing atmospheres, K2SO4 and ZnO condensates are favored instead, and for carbon-rich atmospheres with super-solar C:O ratios, graphite clouds appear. For even hotter planets, clouds form from a wide variety of rock-forming and metallic species.
Module description of TOKAMAK equilibrium code MEUDAS
Suzuki, Masaei; Hayashi, Nobuhiko; Matsumoto, Taro; Ozeki, Takahisa [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2002-01-01
The analysis of an axisymmetric MHD equilibrium serves as a foundation of TOKAMAK researches, such as a design of devices and theoretical research, the analysis of experiment result. For this reason, also in JAERI, an efficient MHD analysis code has been developed from start of TOKAMAK research. The free boundary equilibrium code ''MEUDAS'' which uses both the DCR method (Double-Cyclic-Reduction Method) and a Green's function can specify the pressure and the current distribution arbitrarily, and has been applied to the analysis of a broad physical subject as a code having rapidity and high precision. Also the MHD convergence calculation technique in ''MEUDAS'' has been built into various newly developed codes. This report explains in detail each module in ''MEUDAS'' for performing convergence calculation in solving the MHD equilibrium. (author)
Implementation of a 3-D nonlinear MHD calculation on the Intel hypercube
Drake, J.B.; Lawkins, W.F.; Carreras, B.A.; Hicks, H.R.
1987-08-01
As part of an exploratory study of the suitability of hypercube multiprocessors for scientific computations, the non-linear magnetohydrodynamics (MHD) code RSF was parallelized for use on an Intel iPSC hypercube. This report presents the numerical algorithm of RSF and the techniques used to obtain parallelism without sacrificing the numerical properties of the serial algorithm. Timing results are presented for a sample problem.
Clouds in Super-Earth Atmospheres: Chemical Equilibrium Calculations
Mbarek, Rostom
2016-01-01
Recent studies have unequivocally proven the existence of clouds in super-Earth atmospheres (Kreidberg et al. 2014). Here we provide a theoretical context for the formation of super-Earth clouds by determining which condensates are likely to form under the assumption of chemical equilibrium. We study super-Earth atmospheres of diverse bulk composition, which are assumed to form by outgassing from a solid core of chondritic material, following Schaefer & Fegley (2010). The super-Earth atmospheres that we study arise from planetary cores made up of individual types of chondritic meteorites. They range from highly reducing to oxidizing and have carbon to oxygen (C:O) ratios that are both subsolar and super-solar, thereby spanning a range of atmospheric composition that is appropriate for low-mass exoplanets. Given the atomic makeup of these atmospheres, we minimize the global Gibbs free energy of formation for over 550 gases and condensates to obtain the molecular composition of the atmospheres over a temper...
Chen, J; Zhuang, G; Li, Q; Liu, Y; Gao, L; Zhou, Y N; Jian, X; Xiong, C Y; Wang, Z J; Brower, D L; Ding, W X
2014-11-01
A high-performance Faraday-effect polarimeter-interferometer system has been developed for the J-TEXT tokamak. This system has time response up to 1 μs, phase resolution dynamics as well as magnetic and density perturbations associated with intrinsic Magneto-Hydro-Dynamic (MHD) instabilities and external coil-induced Resonant Magnetic Perturbations (RMP). The 3-wave technique, in which the line-integrated Faraday angle and electron density are measured simultaneously by three laser beams with specific polarizations and frequency offsets, is used. In order to achieve optimum resolution, three frequency-stabilized HCOOH lasers (694 GHz, >35 mW per cavity) and sensitive Planar Schottky Diode mixers are used, providing stable intermediate-frequency signals (0.5-3 MHz) with S/N > 50. The collinear R- and L-wave probe beams, which propagate through the plasma poloidal cross section (a = 0.25-0.27 m) vertically, are expanded using parabolic mirrors to cover the entire plasma column. Sources of systematic errors, e.g., stemming from mechanical vibration, beam non-collinearity, and beam polarization distortion are individually examined and minimized to ensure measurement accuracy. Simultaneous density and Faraday measurements have been successfully achieved for 14 chords. Based on measurements, temporal evolution of safety factor profile, current density profile, and electron density profile are resolved. Core magnetic and density perturbations associated with MHD tearing instabilities are clearly detected. Effects of non-axisymmetric 3D RMP in ohmically heated plasmas are directly observed by polarimetry for the first time.
无
2007-01-01
A new numerical approach has been developed for vapor solid equilibrium calculations and for predicting vapor solid equilibrium constant and composition of vapor and solid phases in gas hydrate formation. Equation of state methods generally do a good job of determining vapor phase properties,but for solid phase it is much more difficult and inaccurate. This proposed new model calculates vapor solid equilibrium constant and vapor and solid phase composition as a function of temperature and partial pressure. The results of this proposed numerical approach, for vapor solid equilibrium, have a good agreement with the available reported data. This new numerical model also has an advantage to tune coefficients, to cover different sets of experimental data accurately.
Two-dimensional coupled fluid and electrodynamic calculations for a MHD DCW channel with slag layers
Liu, B. L.
1982-01-01
A fully coupled, two dimensional numerical method of modeling linear, coal-fired MHD generators is developed for the case of a plasma flow bounded by a slag layer on the channel walls. The governing partial differential equations for the plasma flow, slag layer and electrodynamics are presented and their coupling discussed. An iterative, numerical procedure employing non-uniform computational meshes and appropriate tridiagonal matrix solution schemes for the equations is presented. The method permits the investigation of the mutual plasma flow-slag layer development for prescribed wall temperatures, electrode geometry, slag properties and channel loading. In particular, the slag layer-plasma interface properties which require prior specification in an uncoupled analysis comprise part of the solution in the present approach. Results are presented for a short diagonally connected generator channel and include contour plots of the electric potential and current stream function as well as transverse and axial profiles of pertinent plasma properties. The results indicate that a thin electrode slag layer can be maintained in the presence of reasonable current density levels.
Semelsberger, Troy A.; Borup, Rodney L.
The production of a hydrogen-rich fuel-cell feed by dimethyl ether (DME) steam reforming was investigated using calculations of thermodynamic equilibrium as a function of steam-to-carbon ratio (0.00-4.00), temperature (100-600 °C), pressure (1-5 atm), and product species. Species considered were acetone, acetylene, carbon dioxide, carbon monoxide, dimethyl ether, ethane, ethanol, ethylene, formaldehyde, formic acid, hydrogen, isopropanol, methane, methanol, methyl-ethyl ether, n-propanol and water. Thermodynamic equilibrium calculations of DME steam reforming indicate complete conversion of dimethyl ether to hydrogen, carbon monoxide and carbon dioxide at temperatures greater than 200 °C and steam-to-carbon ratios greater than 1.25 at atmospheric pressure ( P = 1 atm). Increasing the operating pressure shifts the equilibrium toward the reactants; increasing the pressure from 1 to 5 atm decreases the conversion of dimethyl ether from 99.5 to 76.2%. The trend of thermodynamically stable products in decreasing mole fraction is methane, ethane, isopropyl alcohol, acetone, n-propanol, ethylene, ethanol, methyl-ethyl ether and methanol-formaldehyde, formic acid, and acetylene were not observed. Based on the equilibrium calculations, the optimal processing conditions for dimethyl ether steam reforming occur at a steam-to-carbon ratio of 1.50, a pressure of 1 atm, and a temperature of 200 °C. These thermodynamic equilibrium calculations show dimethyl ether processed with steam will produce hydrogen-rich fuel-cell feeds—with hydrogen concentrations exceeding 70%. The conversion of dimethyl ether via hydrolysis (considering methanol as the only product) is limited by thermodynamic equilibrium. Equilibrium conversion increases with temperature and steam-to-carbon ratio. A maximum dimethyl ether conversion of 62% is achieved at a steam-to-carbon ratio of 5.00 and a processing temperature of 600 °C.
Gordon, Sanford; Mcbride, Bonnie J.
1994-01-01
This report presents the latest in a number of versions of chemical equilibrium and applications programs developed at the NASA Lewis Research Center over more than 40 years. These programs have changed over the years to include additional features and improved calculation techniques and to take advantage of constantly improving computer capabilities. The minimization-of-free-energy approach to chemical equilibrium calculations has been used in all versions of the program since 1967. The two principal purposes of this report are presented in two parts. The first purpose, which is accomplished here in part 1, is to present in detail a number of topics of general interest in complex equilibrium calculations. These topics include mathematical analyses and techniques for obtaining chemical equilibrium; formulas for obtaining thermodynamic and transport mixture properties and thermodynamic derivatives; criteria for inclusion of condensed phases; calculations at a triple point; inclusion of ionized species; and various applications, such as constant-pressure or constant-volume combustion, rocket performance based on either a finite- or infinite-chamber-area model, shock wave calculations, and Chapman-Jouguet detonations. The second purpose of this report, to facilitate the use of the computer code, is accomplished in part 2, entitled 'Users Manual and Program Description'. Various aspects of the computer code are discussed, and a number of examples are given to illustrate its versatility.
Cranfill, C.W.
1983-08-01
This manual describes MIXPAC, a subroutine package for calculating equations of state (i.e., thermodynamic and transport properties) for plasmas composed of equilibrium mixtures of materials. The package is vectorized for the Los Alamos Cray-1 computers and uses EOSPAC, another vectorized subroutine package, to access the Los Alamos Sesame EOS data library. Each mixture is forced to be in equilibrium through the constraints that all its constituents have the same values for two state functions (e.g., temperature and pressure). The desired equations of state (including first partial derivatives) are then calculated for the mixture consistent with these constraints. All equations of state available for pure materials through EOSPAC are available for equilibrium mixtures through MIXPAC.
Zhilkin, A G; Mason, P A; 10.1134/S1063772912040087
2012-01-01
We performed 3D MHD calculations of stream accretion in cataclysmic variable stars for which the white dwarf primary star possesses a strong and complex magnetic field. These calculations are motivated by observations of polars; cataclysmic variables containing white dwarfs with magnetic fields sufficiently strong to prevent the formation of an accretion disk. So an accretion stream flows from the L1 point and impacts directly onto one or more spots on the surface of the white dwarf. Observations indicate that the white dwarf, in some binaries, possesses a complex (non-dipolar) magnetic field. We perform simulations of 10 polars or equivalently one asynchronous polar at 10 different beat phases. Our models have an aligned dipole plus quadrupole magnetic field centered on the white dwarf primary. We find that for a sufficiently strong quadrupole component an accretion spot occurs near the magnetic equator for slightly less than half of our simulations while a polar accretion zone is active for most of the rest...
Belkadi, Abdelkrim; Yan, Wei; Moggia, Elsa;
2013-01-01
architecture makes the implementation and evaluation of new ideas and concepts easy. Tests on several 2-D and 3-D gas injection examples indicate that with an efficient implementation of the thermodynamic package and the conventional stability analysis algorithm, the speed can be increased by several folds......Compositional reservoir simulations are widely used to simulate reservoir processes with strong compositional effects, such as gas injection. The equations of state (EoS) based phase equilibrium calculation is a time consuming part in this type of simulations. The phase equilibrium problem can...... be either decoupled from or coupled with the transport problem. In the former case, flash calculation is required, which consists of stability analysis and subsequent phase split calculation; in the latter case, no explicit phase split calculation is required but efficient stability analysis and optimized...
Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan
2017-05-01
Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.
Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan
2017-05-01
Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.
Pawlowski, F; Jorgensen, P; Olsen, Jeppe
2002-01-01
-Fock vibration-rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD(T) energy. The most accurate vibration-rotation interaction constants are those calculated at the CCSD(T)/cc-pVQZ level. The equilibrium bond distances determined from these interaction...
The CHEASE code for toroidal MHD equilibria
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.
Leal, Allan; Saar, Martin
2016-04-01
Computational methods for geochemical and reactive transport modeling are essential for the understanding of many natural and industrial processes. Most of these processes involve several phases and components, and quite often requires chemical equilibrium and kinetics calculations. We present an overview of novel methods for multiphase equilibrium calculations, based on both the Gibbs energy minimization (GEM) approach and on the solution of the law of mass-action (LMA) equations. We also employ kinetics calculations, assuming partial equilibrium (e.g., fluid species in equilibrium while minerals are in disequilibrium) using automatic time stepping to improve simulation efficiency and robustness. These methods are developed specifically for applications that are computationally expensive, such as reactive transport simulations. We show how efficient the new methods are, compared to other algorithms, and how easy it is to use them for geochemical modeling via a simple script language. All methods are available in Reaktoro, a unified open-source framework for modeling chemically reactive systems, which we also briefly describe.
Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method
Rasouli, C.; Abbasi Davani, F.; Rokrok, B.
2016-08-01
Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.
Solution-large molecules method for calculating the equilibrium composition of heterogeneous systems
Alemasov, V.E.; Gruzdeva, Z.KH.; Dregalin, A.A.; Dregalin, A.F.
1985-01-01
A refined method for calculating the equilibrium composition of heterogeneous systems is presented which combines the advantages of the large-molecule method and of the model of an ideal solution of condensed phases. It is shown that the new method provides better convergence and requires less computational effort than either of the above approaches. Results are presented for the combustion products of O2 + BeH2 fuel.
The principal moments of inertia calculated with the hydrostatic equilibrium figure of the Earth
Chengjun Liu
2017-05-01
Full Text Available As an indication of the Earth's mass distribution, the principal moments of inertia (PMOI, i.e., A, B, C of the Earth are the basic parameters in studies of the global dynamics of the earth, like earth nutation, and the geophysics. From the aspect of observation, the PMOI can be calculated from the spherical coefficients of observed gravity field. In this paper, the PMOI are calculated directly according to its definition with the figures of the Earth's interior derived by a generalized theory of the hydrostatic equilibrium figure of the Earth. We obtain that the angle between the principal axis of the maximum moment of PMOI and the rotational axis is 0.184°, which means that the other two principal axes are very closely in the equatorial plane. Meanwhile, B-A is 1.60 × 10−5 MR2, and the global dynamical flattening (H is calculated to be 3.29587 × 10−3, which is 0.67% different from the latest observation derived value Hobs(3.273795 × 10−3 (Petit and Luzum, 2010, and this is a significant improvement from the 1.1% difference between the value of H derived from traditional theories of the figure of the Earth and the value of Hobs. It shows that we can calculate the PMOI and H with an appropriate accuracy by a generalized theory of the hydrostatic equilibrium figure of the Earth.
Seif-Eddeen K. Fateen
2014-01-01
Full Text Available The search for reliable and efficient global optimization algorithms for solving phase stability and phase equilibrium problems in applied thermodynamics is an ongoing area of research. In this study, we evaluated and compared the reliability and efficiency of eight selected nature-inspired metaheuristic algorithms for solving difficult phase stability and phase equilibrium problems. These algorithms are the cuckoo search (CS, intelligent firefly (IFA, bat (BA, artificial bee colony (ABC, MAKHA, a hybrid between monkey algorithm and krill herd algorithm, covariance matrix adaptation evolution strategy (CMAES, magnetic charged system search (MCSS, and bare bones particle swarm optimization (BBPSO. The results clearly showed that CS is the most reliable of all methods as it successfully solved all thermodynamic problems tested in this study. CS proved to be a promising nature-inspired optimization method to perform applied thermodynamic calculations for process design.
MHD thrust vectoring of a rocket engine
Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic
2016-09-01
In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.
Dzifcakova, Elena
2013-01-01
New data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian kappa-distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The kappa-distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII--XIV. The results are supplied in electronic form compatible with the CHIANTI database.
Calculation of NARM's equilibrium with Peng-Robinson equation of state
Li, Tingxun; Guo, Kaihua; Wang, Ruzhu; Fan, Shuanshi
2001-04-01
The liquid molar volumes of nonazeotropic refrigerant mixtures (NARM), calculated with Peng Robinson (PR) equation, were compared with vapor -liquid equilibrium experimental data in this paper. Provided with co-reaction coefficient k ij , the discrepancies of liquid molar volume data for R22+R114 and R22+R142b using PR equation are 7.7% and 8.1%, respectively. When HBT (Hankinson-Brobst-Thomson) equation was joined with PR equation, the deviations are reduced to less than 1.5% for both R22+R114 and R22+R142b.
Calculation of NARM's Equilibrium with Peng-Robinson Equation of State
LI Tingxun; GUO Kaihua; WANG Ruzhu; FAN Shuanshi
2001-01-01
The liquid molar volumes of nonazeotropic refrigerant mixtures (NARM), calculated with Peng Robinson (PR)equation, were compared with vapor -liquid equilibrium experimental data in this paper. Provided with coreaction coefficient kij, the discrepancies of liquid molar volume data for R22+Rl14 and R22+R142b using PR equation are 7.7% and 8.1% , respectively. When HBT (Hankinson-Brobst-Thomson) equation was joined with PR equation, the deviations are reduced to less than 1.5% for both R22+Rl14 and R22+R142b.
1983-07-08
CALCULATE Sinii.ItrmEMISSION AND TRANSMISSION OF INFRARED Sinii.Itrm RADIATION THROUGH NON-EQUILIBRIUM G. PERFORMING O1G. REPORT NUMBER ATMOSPHERES ERP ...8217 669.726-3 .9144J.1. *S4!468E+14 .S6d36E*14 .99414E414 *669.7265 .695eOE.1. .921910E+14 .94616E+14 .97342E414 ’ Saa hit.tZi!tt f.73 1Eti- .IMU1 -4 SIACIF+±4
Toroidal Energy Principle (TEP) and perturbed equilibrium code STB
Zakharov, Leonid; Hu, Di
2016-10-01
The MHD energy principle TEP is presented in terms of perturbations of the vector potential, rather than plasma displacement. This form makes TEP capable to discribe both the ideal plasmas stability and the perturbed equilibria. The functional is expressed in two terms. The first one represents the energy of magnetic field and is calculated using working equilibrium coordinate system. The second term, containing plasma displacement is expressed in the compact form using Hamada coordinates. This representation uses the same combinations of metric coefficients as in the equilibrium calculations. The STB code implements the TEP for both ideal MHD and perturbed equilibria. In the first case, it uses the matching conditions of the ideal MHD. In the second case, the 2-D equilibrium islands are introduced in order to resolve the singularity and match the solutions across the resonant surfaces Partially by (a) US DoE Contract No. DE-AC02-09-CH11466, (b) General Fusion Inc.
Fully Parallel MHD Stability Analysis Tool
Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang
2015-11-01
Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Results of MARS parallelization and of the development of a new fix boundary equilibrium code adapted for MARS input will be reported. Work is supported by the U.S. DOE SBIR program.
Density functional calculation of equilibrium geometry and electronic structure of pyrite
邱冠周; 肖奇; 胡岳华; 徐竞
2001-01-01
The equilibrium geometry and electronic structure of pyrite has been studied using self-consistent density-functional theory within the local density approximation (LDA). The optimum bulk geometry is in good agreement with crystallographic data. The calculated band structure and density of states in the region around the Fermi energy show that valence-band maximum (VBM) is at X (100), and the conduction-band minimum (CBM) is at G (000). The indirect and direct band gaps are 0.6eV and 0.74eV, respectively. The calculated contour map of difference of charge density shows excess charge in nonbonding d electron states on the Fe sites. The density increases between sulfur nuclei and between iron and sulfur nuclei qualitatively reveal that S-S bond and Fe-S bond are covalent binding.
Calculation of Design Parameters for an Equilibrium LEU Core in the NBSR
Hanson, A.L.; Diamond, D.
2011-09-30
A plan is being developed for the conversion of the NIST research reactor (NBSR) from high-enriched uranium (HEU) fuel to low-enriched uranium (LEU) fuel. Previously, the design of the LEU fuel had been determined in order to provide the users of the NBSR with the same cycle length as exists for the current HEU fueled reactor. The fuel composition at different points within an equilibrium fuel cycle had also been determined. In the present study, neutronics parameters have been calculated for these times in the fuel cycle for both the existing HEU and the proposed LEU equilibrium cores. The results showed differences between the HEU and LEU cores that would not lead to any significant changes in the safety analysis for the converted core. In general the changes were reasonable except that the figure-of-merit for neutrons that can be used by experimentalists shows there will be a 10% reduction in performance. The calculations included kinetics parameters, reactivity coefficients, reactivity worths of control elements and abnormal configurations, and power distributions.
Xie, Min; Qi, Yajing; Hu, Yongjun
2011-04-14
2-Phenylethylamine (PEA) is the simplest aromatic amine neurotransmitter, as well as one of the most important. In this work, the conformational equilibrium and hydrogen bonding in liquid PEA were studied by means of Raman spectroscopy and theoretical calculations (DFT/MP2). By changing the orientation of the ethyl and the NH(2) group, nine possible conformers of PEA were found, including four degenerate conformers. Comparison of the experimental Raman spectra of liquid PEA and the calculated Raman spectra of the five typical conformers in selected regions (550-800 and 1250-1500 cm(-1)) revealed that the five conformers can coexist in conformational equilibrium in the liquid. The NH(2) stretching mode of the liquid is red-shifted by ca. 30 cm(-1) relative to that of an isolated PEA molecule (measured previously), implying that intermolecular N-H···N hydrogen bonds play an important role in liquid PEA. The relative intensity of the Raman band at 762 cm(-1) was found to increase with increasing temperature, indicating that the anti conformer might be favorable in liquid PEA at room temperature. The blue shift of the band for the bonded N-H stretch with increasing temperature also provides evidence of the existence of intermolecular N-H···N hydrogen bonds.
2009-10-01
Beattie - Bridgeman Virial expansion The above equations are suitable for moderate pressures and are usually based on either empirical constants...CR 2010-013 October 2009 A Review of Equation of State Models, Chemical Equilibrium Calculations and CERV Code Requirements for SHS Detonation...Defence R&D Canada. A Review of Equation of State Models, Chemical Equilibrium Calculations and CERV Code Requirements for SHS Detonation
Numerical Study of Turbulent Mixing Layers with Non-Equilibrium Ionization Calculations
Kwak, Kyujin
2010-01-01
Highly ionized species such as C IV, N V, and O VI, are commonly observed in diffuse gas in various places in the universe, such as in our Galaxy's disk and halo, high velocity clouds (HVCs), external galaxies, and the intergalactic medium. One possible mechanism for producing high ions is turbulent mixing of cool gas with hotter gas in locations where these gases slide past each other. By using hydrodynamic simulations with radiative cooling and non-equilibrium ionization (NEI) calculations, we investigate the physical properties of turbulent mixing layers and the production of high ions. We find that most of the mixing occurs on the hot side of the hot/cool interface and that the mixed region separates into a tepid zone containing radiatively cooled, C IV-rich gas and a hotter zone which is rich in C IV, N V, and O VI. Mixing occurs faster than ionization or recombination, making the mixed gas a better source of C IV, N V, and O VI in our NEI simulations than in our collisional ionization equilibrium (CIE) ...
Nguyen, H.D.
1991-11-01
Several of the technologies being evaluated for the treatment of waste material involve chemical reactions. Our example is the in situ vitrification (ISV) process where electrical energy is used to melt soil and waste into a ``glass like`` material that immobilizes and encapsulates any residual waste. During the ISV process, various chemical reactions may occur that produce significant amounts of products which must be contained and treated. The APOLLO program was developed to assist in predicting the composition of the gases that are formed. Although the development of this program was directed toward ISV applications, it should be applicable to other technologies where chemical reactions are of interest. This document presents the mathematical methodology of the APOLLO computer code. APOLLO is a computer code that calculates the products of both equilibrium and kinetic chemical reactions. The current version, written in FORTRAN, is readily adaptable to existing transport programs designed for the analysis of chemically reacting flow systems. Separate subroutines EQREACT and KIREACT for equilibrium ad kinetic chemistry respectively have been developed. A full detailed description of the numerical techniques used, which include both Lagrange multiplies and a third-order integrating scheme is presented. Sample test problems are presented and the results are in excellent agreement with those reported in the literature.
Nguyen, H.D.
1991-11-01
Several of the technologies being evaluated for the treatment of waste material involve chemical reactions. Our example is the in situ vitrification (ISV) process where electrical energy is used to melt soil and waste into a glass like'' material that immobilizes and encapsulates any residual waste. During the ISV process, various chemical reactions may occur that produce significant amounts of products which must be contained and treated. The APOLLO program was developed to assist in predicting the composition of the gases that are formed. Although the development of this program was directed toward ISV applications, it should be applicable to other technologies where chemical reactions are of interest. This document presents the mathematical methodology of the APOLLO computer code. APOLLO is a computer code that calculates the products of both equilibrium and kinetic chemical reactions. The current version, written in FORTRAN, is readily adaptable to existing transport programs designed for the analysis of chemically reacting flow systems. Separate subroutines EQREACT and KIREACT for equilibrium ad kinetic chemistry respectively have been developed. A full detailed description of the numerical techniques used, which include both Lagrange multiplies and a third-order integrating scheme is presented. Sample test problems are presented and the results are in excellent agreement with those reported in the literature.
Marchand, Pierre; Chabrier, Gilles; Hennebelle, Patrick; Commerçon, Benoit; Vaytet, Neil
2016-01-01
We develop a detailed chemical network relevant to the conditions characteristic of prestellar core collapse. We solve the system of time-dependent differential equations to calculate the equilibrium abundances of molecules and dust grains, with a size distribution given by size-bins for these latter. These abundances are used to compute the different non-ideal magneto-hydrodynamics resistivities (ambipolar, Ohmic and Hall), needed to carry out simulations of protostellar collapse. For the first time in this context, we take into account the evaporation of the grains, the thermal ionisation of Potassium, Sodium and Hydrogen at high temperature, and the thermionic emission of grains in the chemical network, and we explore the impact of various cosmic ray ionisation rates. All these processes significantly affect the non-ideal magneto-hydrodynamics resistivities, which will modify the dynamics of the collapse. Ambipolar diffusion and Hall effect dominate at low densities, up to n_H = 10^12 cm^-3, after which Oh...
Magnetic stresses in ideal MHD plasmas
Jensen, V.O.
1995-01-01
and it is shown that the resulting magnetic forces on a finite volume element can be obtained by integrating the magnetic stresses over the surface of the element. The concept is used to rederive and discuss the equilibrium conditions for axisymmetric toroidal plasmas, including the virial theorem......The concept of magnetic stresses in ideal MHD plasma theory is reviewed and revisited with the aim of demonstrating its advantages as a basis for calculating and understanding plasma equilibria. Expressions are derived for the various stresses that transmit forces in a magnetized plasma...
Tornow, Sabine; Tong, Ning-Hua; Bulla, Ralf
2006-07-01
We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.
Tornow, Sabine [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany); Tong, Ning-Hua [Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, 76128 Karlsruhe (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany)
2006-07-05
We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.
Theoretical calculation of equilibrium copper (I) isotope fractionations in ore-forming fluid
Seo, J.; Lee, I.; Lee, S.
2006-05-01
Equilibrium isotope fractionation of Cu (I) complexes in hydrothermal ore-forming fluid is calculated. Ab-initio quantum calculation of molecular structures and vibrational frequencies is conducted by Density Functional Theory (DFT) and Hartree-Fock Self Consistent Field (HF-SCF) method. Cu isotope (65Cu, 63Cu) exchange is expressed as reduced partition function ratios, 103·ln(β65-63), for liquid phase complexes (copper chlorides, copper hydrosulfides), and vapor phase complexes (hydrated copper chloride). Isodensity Polarizable Continuum Model (IPCM) is applied to the liquid complexes, whereas the vapor complexes are calculated in vacuo. Large fractionation (more than 2‰ at 25°C) is predicted between coexisting phases without changing oxidation state. CuCl(H2O)2 (vapor phase) is enriched in 65Cu better than any other studied complexes, whereas [CuCl3]2- (liquid phase) is mostly depleted. Heavy copper isotope is favor to partition into vapor phase complexes than coexisting liquid phase complexes. In the sea-floor hydrothermal system, after separation of phases into vapor and brine, vapor phase (CuCl(H2O)2) and chlorine-rich brine ([CuCl3]2-) will show +0.418‰ and -0.688‰ deviation from [CuCl2]1- at 150°C, respectively. However, most of the dominant copper-bearing species in hydrothermal condition, [CuCl2]1- and [Cu(HS)2]1-, fractionate at almost the same degree. Possible ranges of copper isotope ratio, δ65Cu, can be constrained from the calculated equilibrium isotope fractionation. Changes of oxidation state in low-temperature (e.g. supergene formation) have been thought to trigger most copper isotope fractionations, so far. However, measurable Cu isotope fractionation (1.106‰ at 150°C and 0.615‰ at 300°C) in hydrothermal ore-forming fluid is predicted within +1 valence state by theoretical study. Molecular structures and vibrational frequencies are compared with measured data. However, there is no experimental or theoretical work of some molecules
MHD Energy Bypass Scramjet Engine
Mehta, Unmeel B.; Bogdanoff, David W.; Park, Chul; Arnold, Jim (Technical Monitor)
2001-01-01
Revolutionary rather than evolutionary changes in propulsion systems are most likely to decrease cost of space transportation and to provide a global range capability. Hypersonic air-breathing propulsion is a revolutionary propulsion system. The performance of scramjet engines can be improved by the AJAX energy management concept. A magneto-hydro-dynamics (MHD) generator controls the flow and extracts flow energy in the engine inlet and a MHD accelerator downstream of the combustor accelerates the nozzle flow. A progress report toward developing the MHD technology is presented herein. Recent theoretical efforts are reviewed and ongoing experimental efforts are discussed. The latter efforts also include an ongoing collaboration between NASA, the US Air Force Research Laboratory, US industry, and Russian scientific organizations. Two of the critical technologies, the ionization of the air and the MHD accelerator, are briefly discussed. Examples of limiting the combustor entrance Mach number to a low supersonic value with a MHD energy bypass scheme are presented, demonstrating an improvement in scramjet performance. The results for a simplified design of an aerospace plane show that the specific impulse of the MHD-bypass system is better than the non-MHD system and typical rocket over a narrow region of flight speeds and design parameters. Equilibrium ionization and non-equilibrium ionization are discussed. The thermodynamic condition of air at the entrance of the engine inlet determines the method of ionization. The required external power for non-equilibrium ionization is computed. There have been many experiments in which electrical power generation has successfully been achieved by magneto-hydrodynamic (MHD) means. However, relatively few experiments have been made to date for the reverse case of achieving gas acceleration by the MHD means. An experiment in a shock tunnel is described in which MHD acceleration is investigated experimentally. MHD has several
Moffat, Harry K.; Jove-Colon, Carlos F.
2009-06-01
In this report, we summarize our work on developing a production level capability for modeling brine thermodynamic properties using the open-source code Cantera. This implementation into Cantera allows for the application of chemical thermodynamics to describe the interactions between a solid and an electrolyte solution at chemical equilibrium. The formulations to evaluate the thermodynamic properties of electrolytes are based on Pitzer's model to calculate molality-based activity coefficients using a real equation-of-state (EoS) for water. In addition, the thermodynamic properties of solutes at elevated temperature and pressures are computed using the revised Helgeson-Kirkham-Flowers (HKF) EoS for ionic and neutral aqueous species. The thermodynamic data parameters for the Pitzer formulation and HKF EoS are from the thermodynamic database compilation developed for the Yucca Mountain Project (YMP) used with the computer code EQ3/6. We describe the adopted equations and their implementation within Cantera and also provide several validated examples relevant to the calculations of extensive properties of electrolyte solutions.
Cismondi, Martin; Michelsen, Michael Locht
2007-01-01
of critical lines. Each calculated point is analysed for stability by means of the tangent plane distance, and the occurrence of an unstable point is used to determine a critical endpoint (CEP). The critical endpoint, in turn, is used as the starting point for constructing the three-phase line. The equations...... for the critical endpoint, as well as for points on the three-phase line, are also solved using Newton's method with temperature, molar volume and composition as the independent variables. The different calculations are integrated into a general procedure that allows us to automatically trace critical lines......, critical endpoints and three-phase lines for binary mixtures with phase diagrams of types from I to V without advance knowledge of the type of phase diagram. The procedure requires a thermodynamic model in the form of a pressure-explicit EOS but is not specific to a particular equation of state. (C) 2006...
Haskins, Justin; Kinaci, Alper; Sevik, Cem; Cagin, Tahir
2012-01-01
It is widely known that graphene and many of its derivative nanostructures have exceedingly high reported thermal conductivities (up to 4000 W/mK at 300 K). Such attractive thermal properties beg the use of these structures in practical devices; however, to implement these materials while preserving transport quality, the influence of structure on thermal conductivity should be thoroughly understood. For graphene nanostructures, having average phonon mean free paths on the order of one micron, a primary concern is how size influences the potential for heat conduction. To investigate this, we employ a novel technique to evaluate the lattice thermal conductivity from the Green-Kubo relations and equilibrium molecular dynamics in systems where phonon-boundary scattering dominates heat flow. Specifically, the thermal conductivities of graphene nanoribbons and carbon nanotubes are calculated in sizes up to 3 microns, and the relative influence of boundary scattering on thermal transport is determined to be dominant at sizes less than 1 micron, after which the thermal transport largely depends on the quality of the nanostructure interface. The method is also extended to carbon nanostructures (fullerenes) where phonon confinement, as opposed to boundary scattering, dominates, and general trends related to the influence of curvature on thermal transport in these materials are discussed.
R Baldik; H Aytekin; E Tel
2013-02-01
In this study, the pre-equilibrium and equilibrium calculations of cross-sections of 89Y(, ), 90Zr$(p, xn)$ and 94Mo(, ) reactions, which were used for the production of 89Zr, 90Nb and 94Tc positron-emitting radioisotopes, have been investigated. Pre-equilibrium calculations have been performed at different proton incident energies by using the hybrid, geometry-dependent-hybrid and full exciton models. The Weisskopf–Ewing model is used for calculating the equilibrium effects at the same incident energies. The calculated results have been discussed and compared with the experimental results.
Lim, S.; Oh, M. [Hongik University, Seoul (Republic of Korea). School of Chemical Engineering
2007-09-15
In slagging gasifiers, slag foaming can cause serious operational problems, so there is a need for investigation into the conditions causing slag foaming. Viscosity experiments were carried out examining viscosity, extent of swelling and Fe formation. Although extensive swelling was not observed, FeO reduction was observed under an N{sub 2}/CO gas atmosphere, but not under CO{sub 2}/CO. In order to predict FeO reduction conditions in the gasifier, a model for an adiabatic equilibrium gasifier was developed. The gas composition, the amount of gas to slag, and PO{sub 2} were calculated for a slurry-feed gasifier, and the results of the calculation were used to predict the reduction of FeO in slag by using FactSage. Under typical gasification conditions for Denisovsky coal, the predicted -O{sub 2} in the gasifier was not low enough to cause FeO reduction. The FactSage simulation for the viscometer conditions predicted no FeO reduction under a CO/CO{sub 2} atmosphere, but did predict Fe formation under CO/N{sub 2} conditions. At a 20% CO concentration, FeO reduction starts at temperatures above 1,600{sup o}C. Since the slag has a low viscosity at 1,600{sup o}C, the oxygen bubble may have escaped as it formed. Therefore, slag foaming, caused by FeO reduction in the slag, can only occur when the right conditions of viscosity and oxygen partial pressure are met.
Calculation of simultaneous chemical and phase equilibrium by the methodof Lagrange multipliers
Tsanas, Christos; Stenby, Erling Halfdan; Yan, Wei
2017-01-01
iteration in the inner loop and non-ideality updated in the outer loop, thus giving an overall linear convergence rate. Stability analysis is used to introduce additional phases sequentially so as to obtain the final multiphase solution. The procedure was successfully tested on vapor-liquid equilibrium (VLE......) and vapor-liquid-liquid equilibrium (VLLE) of reaction systems....
1981-11-01
Program accomplishments in a continuing effort to demonstrate the feasibility of direct coal fired, closed cycle, magnetohydrodynamic power generation are detailed. These accomplishments relate to all system aspects of a CCMHD power generation system including coal combustion, heat transfer to the MHD working fluid, MHD power generation, heat and cesium seed recovery and overall systems analysis. Direct coal firing of the combined cycle has been under laboratory development in the form of a high slag rejection, regeneratively air cooled cyclone coal combustor concept, originated within this program. A hot bottom ceramic regenerative heat exchanger system was assembled and test fired with coal for the purposes of evaluating the catalytic effect of alumina on NO/sub x/ emission reduction and operability of the refractory dome support system. Design, procurement, fabrication and partial installation of a heat and seed recovery flow apparatus was accomplished and was based on a stream tube model of the full scale system using full scale temperatures, tube sizes, rates of temperature change and tube geometry. Systems analysis capability was substantially upgraded by the incorporation of a revised systems code, with emphasis on ease of operator interaction as well as separability of component subroutines. The updated code was used in the development of a new plant configuration, the Feedwater Cooled (FCB) Brayton Cycle, which is superior to the CCMHD/Steam cycle both in performance and cost. (WHK)
Khaikin, L. S.; Tikhonov, D. S.; Grikina, O. E.; Rykov, A. N.; Stepanov, N. F.
2014-05-01
The equilibrium molecular structure of 2-methyl-1,4-naphthoquinone (vitamin K3) having C s symmetry is experimentally characterized for the first time by means of gas-phase electron diffraction using quantum-chemical calculations and data on the vibrational spectra of related compounds.
Two-Fluid Equilibrium for Transonic Poloidal Flows
Guazzotto, Luca; Betti, Riccardo
2012-03-01
Much analytical and numerical work has been done in the past on ideal MHD equilibrium in the presence of macroscopic flow. In recent years, several authors have worked on equilibrium formulations for a two-fluid system, in which inertial ions and massless electrons are treated as distinct fluids. In this work, we present our approach to the formulation of the two-fluid equilibrium problem. Particular attention is given to the relation between the two-fluid equations and the equilibrium equations for the single-fluid ideal MHD system. Our purpose is to reconsider the results of one-fluid calculation with the more accurate two-fluid model, referring in particular to the so-called transonic discontinuities, which occur when the poloidal velocity spans a range crossing the poloidal sound speed (i.e., the sound speed reduced by a factor Bp/B). It is expected that the one-fluid discontinuity will be resolved into a sharp gradient region by the two-fluid model. Also, contrary to the ideal MHD case, in the two-fluid model the equations governing the equilibrium are elliptic in the whole range of interest for transonic equilibria. The numerical solution of the two-fluid system of equations is going to be based on a code built on the structure of the existing ideal-MHD code FLOW.
C. Wang
2017-06-01
Full Text Available Gas–particle partitioning governs the distribution, removal, and transport of organic compounds in the atmosphere and the formation of secondary organic aerosol (SOA. The large variety of atmospheric species and their wide range of properties make predicting this partitioning equilibrium challenging. Here we expand on earlier work and predict gas–organic and gas–aqueous phase partitioning coefficients for 3414 atmospherically relevant molecules using COSMOtherm, SPARC Performs Automated Reasoning in Chemistry (SPARC, and poly-parameter linear free-energy relationships. The Master Chemical Mechanism generated the structures by oxidizing primary emitted volatile organic compounds. Predictions for gas–organic phase partitioning coefficients (KWIOM/G by different methods are on average within 1 order of magnitude of each other, irrespective of the numbers of functional groups, except for predictions by COSMOtherm and SPARC for compounds with more than three functional groups, which have a slightly higher discrepancy. Discrepancies between predictions of gas–aqueous partitioning (KW/G are much larger and increase with the number of functional groups in the molecule. In particular, COSMOtherm often predicts much lower KW/G for highly functionalized compounds than the other methods. While the quantum-chemistry-based COSMOtherm accounts for the influence of intra-molecular interactions on conformation, highly functionalized molecules likely fall outside of the applicability domain of the other techniques, which at least in part rely on empirical data for calibration. Further analysis suggests that atmospheric phase distribution calculations are sensitive to the partitioning coefficient estimation method, in particular to the estimated value of KW/G. The large uncertainty in KW/G predictions for highly functionalized organic compounds needs to be resolved to improve the quantitative treatment of SOA formation.
Chen, J.; Zhuang, G.; Li, Q.; Liu, Y.; Gao, L.; Zhou, Y. N.; Jian, X.; Xiong, C. Y.; Wang, Z. J.; Brower, D. L.; Ding, W. X.
2014-11-01
A high-performance Faraday-effect polarimeter-interferometer system has been developed for the J-TEXT tokamak. This system has time response up to 1 μs, phase resolution dynamics as well as magnetic and density perturbations associated with intrinsic Magneto-Hydro-Dynamic (MHD) instabilities and external coil-induced Resonant Magnetic Perturbations (RMP). The 3-wave technique, in which the line-integrated Faraday angle and electron density are measured simultaneously by three laser beams with specific polarizations and frequency offsets, is used. In order to achieve optimum resolution, three frequency-stabilized HCOOH lasers (694 GHz, >35 mW per cavity) and sensitive Planar Schottky Diode mixers are used, providing stable intermediate-frequency signals (0.5-3 MHz) with S/N > 50. The collinear R- and L-wave probe beams, which propagate through the plasma poloidal cross section (a = 0.25-0.27 m) vertically, are expanded using parabolic mirrors to cover the entire plasma column. Sources of systematic errors, e.g., stemming from mechanical vibration, beam non-collinearity, and beam polarization distortion are individually examined and minimized to ensure measurement accuracy. Simultaneous density and Faraday measurements have been successfully achieved for 14 chords. Based on measurements, temporal evolution of safety factor profile, current density profile, and electron density profile are resolved. Core magnetic and density perturbations associated with MHD tearing instabilities are clearly detected. Effects of non-axisymmetric 3D RMP in ohmically heated plasmas are directly observed by polarimetry for the first time.
Stationary MHD equilibria describing azimuthal rotations in symmetric plasmas
da Silva, Sidney T.; Viana, Ricardo L.
2016-12-01
We consider the stationary magnetohydrodynamical (MHD) equilibrium equation for an axisymmetric plasma undergoing azimuthal rotations. The case of cylindrical symmetry is treated, and we present two semi-analytical solutions for the stationary MHD equilibrium equations, from which a number of physical properties of the magnetically confined plasma are derived.
Nonlinear helical MHD instability
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
Nevinitsa, V. A.; Dudnikov, A. A.; Blandinskiy, V. Yu.; Balanin, A. L.; Alekseev, P. N.; Titarenko, Yu. E.; Batyaev, V. F.; Pavlov, K. V.; Titarenko, A. Yu.
2015-12-01
A subcritical molten salt reactor with an external neutron source is studied computationally as a facility for incineration and transmutation of minor actinides from spent nuclear fuel of reactors of VVER-1000 type and for producing 233U from 232Th. The reactor configuration is chosen, the requirements to be imposed on the external neutron source are formulated, and the equilibrium isotopic composition of heavy nuclides and the key parameters of the fuel cycle are calculated.
Nevinitsa, V. A., E-mail: Neviniza-VA@nrcki.ru; Dudnikov, A. A.; Blandinskiy, V. Yu.; Balanin, A. L.; Alekseev, P. N. [National Research Centre Kurchatov Institute (Russian Federation); Titarenko, Yu. E.; Batyaev, V. F.; Pavlov, K. V.; Titarenko, A. Yu., E-mail: yuri.titarenko@itep.ru [Institute for Theoretical and Experimental Physics (Russian Federation)
2015-12-15
A subcritical molten salt reactor with an external neutron source is studied computationally as a facility for incineration and transmutation of minor actinides from spent nuclear fuel of reactors of VVER-1000 type and for producing {sup 233}U from {sup 232}Th. The reactor configuration is chosen, the requirements to be imposed on the external neutron source are formulated, and the equilibrium isotopic composition of heavy nuclides and the key parameters of the fuel cycle are calculated.
Dongre, B.; Wang, T.; Madsen, G. K. H.
2017-07-01
Different molecular dynamics methods like the direct method, the Green-Kubo (GK) method and homogeneous non-equilibrium molecular dynamics (HNEMD) method have been widely used to calculate lattice thermal conductivity ({κ }{\\ell }). While the first two methods have been used and compared quite extensively, there is a lack of comparison of these methods with the HNEMD method. Focusing on the underlying computational parameters, we present a detailed comparison of the GK and HNEMD methods for both bulk and vacancy Si using the Stillinger-Weber potential. For the bulk calculations, we find both methods to perform well and yield {κ }{\\ell } within acceptable uncertainties. In case of the vacancy calculations, HNEMD method has a slight advantage over the GK method as it becomes computationally cheaper for lower {κ }{\\ell } values. This study could promote the application of HNEMD method in {κ }{\\ell } calculations involving other lattice defects like nanovoids, dislocations, interfaces.
Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example
Bouchet, Freddy; Gawȩdzki, Krzysztof; Nardini, Cesare
2016-06-01
In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory (Freidlin and Wentzell, Random perturbations of dynamical systems, 2012). In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory (Bertini et al., arXiv:1404.6466 URL"/> , 2014), which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to 1/√{N}, where N is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter λ , starting from a known quasi-potential for λ =0. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner (Stochastics 20:247-308, 1987; Stochastic differential systems, vol 96, pp 1-10, 1987). Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators (Prog Theoret Phys 75:1105-1110, [74
Non-Equilibrium Green's Function Calculation for Electron Transport through Magnetic Tunnel Junction
Sara Nobakht
2014-06-01
Full Text Available In this paper non-equilibrium Green's function method –dependent electron transport through non magnetic layer (insulator has been studied in one dimension .electron transport in multi-layer (magnetic/non magnetic/ magneticlayers is studied as quantum .the result show increasing the binding strength of the electrical insulator transition probability density case , the electron density , broad levels of disruption increases. Broad band connection increases the levels of disruption to electrical insulation and show non- conductive insulating state to semiconductor stat and even conductor
Bursik, J. W.; Hall, R. M.
1980-01-01
The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.
Ideal MHD Stability Prediction and Required Power for EAST Advanced Scenario
陈均杰; 李国强; 钱金平; 刘子奚
2012-01-01
The Experimental Advanced Superconducting Tokamak (EAST) is the first fully superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. The ideal magnetohydrodynamic (MHD) stability and required power for the EAST advanced tokamak (AT) scenario with negative central shear and double transport barrier (DTB) are investigated. With the equilibrium code TOQ and stability code GATO, the ideal MHD stability is analyzed. It is shown that a moderate ratio of edge transport barriers' (ETB) height to internal transport barriers' (ITBs) height is beneficial to ideal MHD stability. The normalized beta/3N limit is about 2.20 (without wall) and 3.70 (with ideal wall). With the scaling law of energy confinement time, the required heating power for EAST AT scenario is calculated. The total heating power Pt increases as the toroidal magnetic field BT or the normalized beta βN is increased.
Quantum chemical calculation of the equilibrium structures of small metal atom clusters
Kahn, L. R.
1982-01-01
Metal atom clusters are studied based on the application of ab initio quantum mechanical approaches. Because these large 'molecular' systems pose special practical computational problems in the application of the quantum mechanical methods, there is a special need to find simplifying techniques that do not compromise the reliability of the calculations. Research is therefore directed towards various aspects of the implementation of the effective core potential technique for the removal of the metal atom core electrons from the calculations.
Study of extended MHD effects on interchange modes in spheromak equilibria
Howell, E. C.; Sovinec, C. R.
2014-10-01
A study of extended MHD effects on linear interchange modes is performed using the NIMROD code [Sovinec & King JCP 2010]. A linear cylindrical equilibrium model is adapted from [Jardin NF 1982] to allow finite toroidal current at the edge. These equilibria are representative of SSPX discharges where currents are driven on the open field to keep the safety factor above 1/2 across the profile [McLean et al., POP 2006]. These spheromaks have weak magnetic shear, and interchange stability is an important consideration. The Suydam parameter, D, is scaled to study resistive and ideal interchange modes. The calculated MHD growth rate increases with D. The resistive interchange scaling γ ~η 1 / 3 is observed for D <1/4 . Calculations using the full extended MHD model are performed for a range of hall parameters Λ. This model includes gyro-viscosity, the hall term, equilibrium diamagnetic flows, and the cross-field diamagnetic heat flux. Two fluid effects in the full model are always destabilizing at large Λ. However, some cases exhibit a range of Λ where the growth rate for the full model is reduced relative to the MHD growth rate. Work supported by US DOE.
Pusateri, Elise N.; Morris, Heidi E.; Nelson, Eric; Ji, Wei
2016-10-01
Atmospheric electromagnetic pulse (EMP) events are important physical phenomena that occur through both man-made and natural processes. Radiation-induced currents and voltages in EMP can couple with electrical systems, such as those found in satellites, and cause significant damage. Due to the disruptive nature of EMP, it is important to accurately predict EMP evolution and propagation with computational models. CHAP-LA (Compton High Altitude Pulse-Los Alamos) is a state-of-the-art EMP code that solves Maxwell's equations for gamma source-induced electromagnetic fields in the atmosphere. In EMP, low-energy, conduction electrons constitute a conduction current that limits the EMP by opposing the Compton current. CHAP-LA calculates the conduction current using an equilibrium ohmic model. The equilibrium model works well at low altitudes, where the electron energy equilibration time is short compared to the rise time or duration of the EMP. At high altitudes, the equilibration time increases beyond the EMP rise time and the predicted equilibrium ionization rate becomes very large. The ohmic model predicts an unphysically large production of conduction electrons which prematurely and abruptly shorts the EMP in the simulation code. An electron swarm model, which implicitly accounts for the time evolution of the conduction electron energy distribution, can be used to overcome the limitations exhibited by the equilibrium ohmic model. We have developed and validated an electron swarm model previously in Pusateri et al. (2015). Here we demonstrate EMP damping behavior caused by the ohmic model at high altitudes and show improvements on high-altitude, upward EMP modeling obtained by integrating a swarm model into CHAP-LA.
Water-Aromatic Liquid-Liquid-Vapour Equilibrium Calculation Using a Cubic Equation of State
无
1994-01-01
This paper presents an extension of the procedure developed in the case of water-alkane binaries to mixtures of water and benzene or toluene or xylene or ethylbenzene or diethylbenzene.The method used to calculate the equilibria is based on the Peng-Robinson cubic equation of state modified as regards the coefficient α(Tr)and on the use of a binary interaction coefficient kiw specific to binaries containing water.
Calculations of Gas-liquid Equilibrium in Wellbore with High Carbon dioxide Flow
Zhang, Jiaming; Wu, Xiaodong; Wang, Bo; Liu, Kai; Gao, Yue
2014-05-01
Carbon dioxide injection not only enhances the oil recovery dramatically, but also it will reduce the greenhouse effect, therefore, Carbon dioxide injection technique is applied extensively. During the process of carbon dioxide displacement, when carbon dioxide breaks though into oil production wells, carbon dioxide content will impacts the phase state and physical properties of the mixed liquor in the wellbore, as a result, it will affect the calculation of temperature and pressure in oil production wells. Applying the conventional black-oil model to calculate the phase state of the miscible fluids is unacceptable. To tackle the problem, this paper uses the gas-liquid flash theory and component model to program software, so that the phase state (gas, liquid or gas-liquid) and physical properties of the mixed liquor (including hydrogen sulfide, carbon dioxide and hydrocarbon) under initial conditions is calculated, moreover, the impact of carbon dioxide content on the physical properties(mainly including density, viscosity, specific heat at const pressure, surface tension, etc) of mixed liquor in oil production wells is analyzed in this paper. The comparison of the results shows that this model can meet the engineering needs with high accuracy.
Bryans, P; Savin, D W
2008-01-01
We have reanalyzed SUMER observations of a parcel of coronal gas using new collisional ionization equilibrium (CIE) calculations. These improved CIE fractional abundances were calculated using state-of-the-art electron-ion recombination data for K-shell, L-shell, Na-like, and Mg-like ions of all elements from H through Zn and, additionally, Al- through Ar-like ions of Fe. Improved CIE calculations based on these data are presented here. We have also developed a new systematic method for determining the average emission measure (EM) and electron temperature (T_e) of an emitting plasma. With our new CIE data and our new approach for determining the average EM and T_e we have reanalyzed SUMER observations of the solar corona. We have compared our results with those of previous studies and found some significant differences for the derived EM and T_e. We have also calculated the enhancement of coronal elemental abundances compared to their photospheric abundances, using the SUMER observations themselves to determ...
Andrade, Maria Celia Ramos; Ludwig, Gerson Otto [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma]. E-mail: mcr@plasma.inpe.br
2004-07-01
Different bootstrap current formulations are implemented in a self-consistent equilibrium calculation obtained from a direct variational technique in fixed boundary tokamak plasmas. The total plasma current profile is supposed to have contributions of the diamagnetic, Pfirsch-Schlueter, and the neoclassical Ohmic and bootstrap currents. The Ohmic component is calculated in terms of the neoclassical conductivity, compared here among different expressions, and the loop voltage determined consistently in order to give the prescribed value of the total plasma current. A comparison among several bootstrap current models for different viscosity coefficient calculations and distinct forms for the Coulomb collision operator is performed for a variety of plasma parameters of the small aspect ratio tokamak ETE (Experimento Tokamak Esferico) at the Associated Plasma Laboratory of INPE, in Brazil. We have performed this comparison for the ETE tokamak so that the differences among all the models reported here, mainly regarding plasma collisionality, can be better illustrated. The dependence of the bootstrap current ratio upon some plasma parameters in the frame of the self-consistent calculation is also analysed. We emphasize in this paper what we call the Hirshman-Sigmar/Shaing model, valid for all collisionality regimes and aspect ratios, and a fitted formulation proposed by Sauter, which has the same range of validity but is faster to compute than the previous one. The advantages or possible limitations of all these different formulations for the bootstrap current estimate are analysed throughout this work. (author)
Phase Equilibrium Calculations for Multi-Component Polar Fluid Mixtures with tPC-PSAFT
Karakatsani, Eirini; Economou, Ioannis
2007-01-01
The truncated Perturbed-Chain Polar Statistical Associating Fluid Theory (tPC-PSAFT) is applied to a number of different mixtures, including binary, ternary and quaternary mixtures of components that differ substantially in terms of intermolecular interactions and molecular size. In contrast...... to most other SAFT versions, tPC-PSAFT accounts explicitly for polar forces. Three pure-component parameters are required for non-polar and non-associating compounds, two additional parameters characterize the association contribution and one parameter is needed to account for polar interactions....... The experimental dipole and/or quadrupole moment and/or polarizability of the component are used to calculate polar interactions. Using a temperature-independent interaction parameter kij for each binary system, tPC-PSAFT provides accurate prediction of multi-component phase behavior over a wide range...
Thermodynamic equilibrium calculations of sulfur poisoning in Ce-O-S and La-O-S systems
Karjalainen, Heidi; Lassi, Ulla; Rahkamaa-Tolonen, Katariina; Kroeger, Virpi; Keiski, Riitta L. [University of Oulu, Department of Process and Environmental Engineering, P.O. Box 4300, FIN-90014 Oulu (Finland)
2005-02-28
Sulfur poisoning is still a problem in many application areas of exhaust gas catalysts despite the fact that the sulfur levels, e.g. in gasoline are being continuously reduced. The aim of this study was to calculate thermodynamic equilibrium compositions of sulfur in Ce-O-S and La-O-S systems in the presence of precious metals (Pt, Pd, and Rh), which all were considered as bulk materials, in order to understand the experimentally observed sulfur poisoning under the real applications of exhaust gas catalysts. Depending on temperature and oxygen partial pressure, sulfur can be present in the form of sulfates, sulfides and oxysulfides. It is thermodynamically favorable that cerium oxide reacts with SO{sub 2} to form cerium sulfate at low temperatures and cerium oxysulfides at high temperatures. Lanthanum oxide reacts with SO{sub 2} to form sulfate under oxidizing conditions and sulfides under reducing conditions.
K-alpha X-rays from cosmic ray oxygen. [Detection and calculation of equilibrium charge fractions
Pravdo, S. H.; Boldt, E. A.
1975-01-01
Equilibrium charge fractions are calculated for subrelativistic cosmic ray oxygen ions in the interstellar medium. These are used to determine the expected flux of K-alpha rays arising from atomic processes for a number of different postulated interstellar oxygen spectra. Relating these results to the diffuse X-ray background measured at the appropriate energy level suggests an observable line feature. If the flux of low energy cosmic ray oxygen is sufficiently large, K-alpha X-ray line emission from these nuclei will comprise a significant fraction of the total diffuse flux at approximately 0.6 keV. A satellite borne detector with a resolution greater than 30 percent could observe this feature if the subrelativistic interstellar cosmic ray oxygen spectrum is as large as certain theoretical estimates expressed in the text.
Long, Luping; Liu, Wensheng; Ma, Yunzhu; Liu, Ye; Liu, Shuhua
2015-10-01
Electron beam melting (EBM) technology has been considered as one of the key steps for preparing high purity tungsten, and reasonable setting of process parameters is the premise. In this paper, the optimum process parameters obtained from thermal equilibrium calculation and evaporation loss control of tungsten are presented. Effective power is closely related to melting temperature, and the required power for maintaining the superheating melt linearly increases with the increase of melt superheat temperature. The evaporation loss behavior of tungsten is significantly influenced by melting rate and melting temperature. Analysis of experiments show that the best results are realized at melting rate of 1.82 g/s, melting temperature of 4200 K, and the corresponding melting power of 130 kW, in which the main impurity elements in tungsten, such as As, Cd, Mg and Sn, present high removal ratio of 90%, 95%, 85.7% and 90%, respectively.
Flow stabilization of the ideal MHD resistive wall mode^1
Smith, S. P.; Jardin, S. C.; Freidberg, J. P.; Guazzotto, L.
2009-05-01
We demonstrate for the first time in a numerical calculation that for a typical circular cylindrical equilibrium, the ideal MHD resistive wall mode (RWM) can be completely stabilized by bulk equilibrium plasma flow, V, for a window of wall locations without introducing additional dissipation into the system. The stabilization is due to a resonance between the RWM and the Doppler shifted ideal MHD sound continuum. Our numerical approach introduces^2 u=φξ+ iV .∇ξ and the perturbed wall current^3 as variables, such that the eigenvalue, φ, only appears linearly in the linearized stability equations, which allows for the use of standard eigenvalue solvers. The wall current is related to the plasma displacement at the boundary by a Green's function. With the introduction of the resistive wall, we find that it is essential that the finite element grid be highly localized around the resonance radius where the parallel displacement, ξ, becomes singular. We present numerical convergence studies demonstrating that this singular behavior can be approached in a limiting sense. We also report on progress toward extending this calculation to an axisymmetric toroidal geometry. ^1Work supported by a DOE FES fellowship through ORISE and ORAU. ^2L.Guazzotto, J.P Freidberg, and R. Betti, Phys.Plasmas 15, 072503 (2008). ^3S.P. Smith and S. C. Jardin, Phys. Plasmas 15, 080701 (2008).
Integral Constraints and MHD Stability
Jensen, T. H.
2003-10-01
Determining stability of a plasma in MHD equilibrium, energetically isolated by a conducting wall, requires an assumption on what governs the dynamics of the plasma. One example is the assumption that the plasma obeys ideal MHD, leading to the well known ``δ W" criteria [I. Bernstein, et al., Proc. Roy. Soc. London A244, 17 (1958)]. A radically different approach was used by Taylor [J.B. Taylor, Rev. Mod. Phys. 58, 741 (1986)] in assuming that the dynamics of the plasma is restricted only by the requirement that helicity, an integral constant associated with the plasma, is conserved. The relevancy of Taylor's assumption is supported by the agreement between resulting theoretical results and experimental observations. Another integral constraint involves the canonical angular momentum of the plasma particles. One consequence of using this constraint is that tokamak plasmas have no poloidal current in agreement with some current hole tokamak observations [T.H. Jensen, Phys. Lett. A 305, 183 (2002)].
J Gong; L Thompson; G Li
2016-01-01
A semi-analytical model for determining the equi-librium configuration and the radial breathing mode (RBM) frequency of single-wall carbon nanotubes (CNTs) is pre-sented. By taking advantage of the symmetry characteristics, a CNT structure is represented by five independent vari-ables. A line search optimization procedure is employed to determine the equilibrium values of these variables by minimizing the potential energy. With the equilibrium con-figuration obtained, the semi-analytical model enables an efficient calculation of the RBM frequency of the CNTs. The radius and radial breathing mode frequency results obtained from the semi-analytical approach are compared with those from molecular dynamics (MD) and ab initio calculations. The results demonstrate that the semi-analytical approach offers an efficient and accurate way to determine the equilib-rium structure and radial breathing mode frequency of CNTs.
Gong, J.; Thompson, L.; Li, G.
2016-12-01
A semi-analytical model for determining the equilibrium configuration and the radial breathing mode (RBM) frequency of single-wall carbon nanotubes (CNTs) is presented. By taking advantage of the symmetry characteristics, a CNT structure is represented by five independent variables. A line search optimization procedure is employed to determine the equilibrium values of these variables by minimizing the potential energy. With the equilibrium configuration obtained, the semi-analytical model enables an efficient calculation of the RBM frequency of the CNTs. The radius and radial breathing mode frequency results obtained from the semi-analytical approach are compared with those from molecular dynamics (MD) and ab initio calculations. The results demonstrate that the semi-analytical approach offers an efficient and accurate way to determine the equilibrium structure and radial breathing mode frequency of CNTs.
Wong, Kin-Yiu; Xu, Yuqing; York, Darrin M
2014-06-30
Detailed understandings of the reaction mechanisms of RNA catalysis in various environments can have profound importance for many applications, ranging from the design of new biotechnologies to the unraveling of the evolutionary origin of life. An integral step in the nucleolytic RNA catalysis is self-cleavage of RNA strands by 2'-O-transphosphorylation. Key to elucidating a reaction mechanism is determining the molecular structure and bonding characteristics of transition state. A direct and powerful probe of transition state is measuring isotope effects on biochemical reactions, particularly if we can reproduce isotope effect values from quantum calculations. This article significantly extends the scope of our previous joint experimental and theoretical work in examining isotope effects on enzymatic and nonenzymatic 2'-O-transphosphorylation reaction models that mimic reactions catalyzed by RNA enzymes (ribozymes), and protein enzymes such as ribonuclease A (RNase A). Native reactions are studied, as well as reactions with thio substitutions representing chemical modifications often used in experiments to probe mechanism. Here, we report and compare results from eight levels of electronic-structure calculations for constructing the potential energy surfaces in kinetic and equilibrium isotope effects (KIE and EIE) computations, including a "gold-standard" coupled-cluster level of theory [CCSD(T)]. In addition to the widely used Bigeleisen equation for estimating KIE and EIE values, internuclear anharmonicity and quantum tunneling effects were also computed using our recently developed ab initio path-integral method, that is, automated integration-free path-integral method. The results of this work establish an important set of benchmarks that serve to guide calculations of KIE and EIE for RNA catalysis. Copyright © 2014 Wiley Periodicals, Inc.
Lim, Gerald H W; Huber, Greg
2009-03-18
Constrained minimization of energy functionals is a central part, and usually the difficult part, of solving problems in the equilibrium mechanics of biological and biomimetic membranes. The inherent difficulties of the conventional variational-calculus approach prevents the numerical calculation involved from being made routine in the analyses of experimental results. We have developed a simulated annealing-based computational technique for routinizing the task of constrained minimization of energy functionals governing whole, or small patches of whole, fluid membranes with axisymmetry, spherical topology, and no domains of inhomogeneity. In this article, we describe the essential principles of the technique and apply it to five examples to demonstrate its versatility. It gives membrane shapes that are automatically stable to axisymmetric perturbations. Presently, it can account for constraints on 1), the membrane area or the effective membrane tension; 2), the enclosed volume or the effective pressure difference across the membrane thickness; and 3), the axial end-to-end distance or the applied axial point force.
Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas
Piovesan, P.; Bonfiglio, D.; Cianciosa, M.; Luce, T. C.; Taylor, N. Z.; Terranova, D.; Turco, F.; Wilcox, R. S.; Wingen, A.; Cappello, S.; Chrystal, C.; Escande, D. F.; Holcomb, C. T.; Marrelli, L.; Paz-Soldan, C.; Piron, L.; Predebon, I.; Zaniol, B.; DIII-D, The; RFX-Mod Teams
2017-07-01
Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. In this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8-1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.
Calculation of continuum damping of Alfv\\'en eigenmodes in 2D and 3D cases
Bowden, G W; Könies, A
2015-01-01
In ideal MHD, shear Alfv\\'{e}n eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfv\\'{e}n continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfv\\'{e}n eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD code CKA . ...
MHD Turbulence and Magnetic Dynamos
Shebalin, John V
2014-01-01
Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much
Pessôa Filho P. A.
2004-01-01
Full Text Available Mixtures containing compounds that undergo hydrogen bonding show large deviations from ideal behavior. These deviations can be accounted for through chemical theory, according to which the formation of a hydrogen bond can be treated as a chemical reaction. This chemical equilibrium needs to be taken into account when applying stability criteria and carrying out phase equilibrium calculations. In this work, we illustrate the application of the stability criteria to establish the conditions under which a liquid-phase split may occur and the subsequent calculation of liquid-liquid equilibrium using a chemical-theory-modified Flory-Huggins equation to describe the non ideality of aqueous two-phase systems composed of poly(ethylene glycol and dextran. The model was found to be able to correlate ternary liquid-liquid diagrams reasonably well by simple adjustment of the polymer-polymer binary interaction parameter.
2006-09-01
Aerospace Applications, AIAA-Paper 96-2355, New Orleans, 1996 2. V.A.Bityurin, A.N.Bocharov, J.Lineberry, MHD Aerospace Applications, Invited Lecture ...Paper 2003- 4303, Orlando, FL 8. V.A.Bityurin, Prospective of MHD Interaction in Hypersonic and Propulsion Technologies, In: von Karman Series : Lectures ...Efforts in MHD AeoSpace Applications, In: von Karman Series : Lectures , Introduction of Magneto-Fluid Dynamics for AeroSpace Applications, von Karman
Nagapetyan, Tigran
2011-01-01
In this work we widespread statistical physics (chemical kinetic stochastic) approach to the investigation of macrosystems, arise in economic, sociology and traffic flow theory. The main line is a definition of equilibrium of macrosystem as most probable macrostate of invariant measure of Markov dynamic (corresponds to the macrosystem). We demonstrate new dynamical interpretations for the well known static model of correspondence matrix calculation. Based on this model we propose a best response dynamics for the Beckmann's traffic flow distribution model. We prove that this "natural" dynamic under quite general conditions converges to the Nash-Wardrop's equilibrium. After that we consider two interesting demonstration examples.
Dipole Alignment in Rotating MHD Turbulence
Shebalin, John V.; Fu, Terry; Morin, Lee
2012-01-01
We present numerical results from long-term CPU and GPU simulations of rotating, homogeneous, magnetohydrodynamic (MHD) turbulence, and discuss their connection to the spherically bounded case. We compare our numerical results with a statistical theory of geodynamo action that has evolved from the absolute equilibrium ensemble theory of ideal MHD turbulence, which is based on the ideal MHD invariants are energy, cross helicity and magnetic helicity. However, for rotating MHD turbulence, the cross helicity is no longer an exact invariant, although rms cross helicity becomes quasistationary during an ideal MHD simulation. This and the anisotropy imposed by rotation suggests an ansatz in which an effective, nonzero value of cross helicity is assigned to axisymmetric modes and zero cross helicity to non-axisymmetric modes. This hybrid statistics predicts a large-scale quasistationary magnetic field due to broken ergodicity , as well as dipole vector alignment with the rotation axis, both of which are observed numerically. We find that only a relatively small value of effective cross helicity leads to the prediction of a dipole moment vector that is closely aligned (less than 10 degrees) with the rotation axis. We also discuss the effect of initial conditions, dissipation and grid size on the numerical simulations and statistical theory.
Zeiner, T. [Technical University of Dortmund, Lehrstuhl fuer Fluidverfahrenstechnik, Emil-Figge Str. 70, 44227 Dortmund (Germany); Browarzik, C. [Technical University of Berlin, Institut fuer Prozess- und Verfahrenstechnik (TK7), Fachgebiet Thermodynamik und thermische Verfahrenstechnik, Strasse des 17, Juni 135, 10623 Berlin (Germany); Browarzik, D., E-mail: dieter.browarzik@chemie.uni-halle.de [Martin-Luther University Halle-Wittenberg, Institut fuer Chemie/Physikalische Chemie, 06099 Halle (Germany); Enders, S. [Technical University of Berlin, Institut fuer Prozess- und Verfahrenstechnik (TK7), Fachgebiet Thermodynamik und thermische Verfahrenstechnik, Strasse des 17, Juni 135, 10623 Berlin (Germany)
2011-12-15
Highlights: > The (liquid + liquid) equilibrium of hyperbranched polyester solutions is calculated. > The solvents are n-alkanes, propan-1-ol, and butan-1-ol. > The lattice-cluster theory is combined with a chemical association model. > The solvent molecules are assumed to be linear chains of segments. > The calculations agree reasonably well with the experimental data. - Abstract: The (liquid + liquid) equilibrium of solutions of hyperbranched polyesters is calculated with the lattice-cluster theory (LCT) combined with a chemical association model. The considered solvents are n-alkanes as well as propan-1-ol and butan-1-ol. The structure of the solvents is also considered in the framework of the LCT, assuming the solvent molecules as linear chains of several segments. For polymer solutions with the non-associating n-alkanes only the self association of the hyperbranched polymer molecules has to be considered by the chemical association lattice model (CALM). For the solutions of the type alcohol + hyperbranched polymer additionally the cross association is taken into account by a modified version of the extended chemical association lattice model (ECALM). The association effects are proved to influence strongly the phase equilibrium. Calculating the cloud-point curve and the critical point the polydispersity of the polymer samples is neglected. There is a reasonable agreement of the calculated curves with the experimental data taken from the literature.
Tokamak magnetohydrodynamic equilibrium states with axisymmetric boundary and a 3D helical core.
Cooper, W A; Graves, J P; Pochelon, A; Sauter, O; Villard, L
2010-07-16
Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.
Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg; Saar, Martin O.
2016-10-01
We present an extended law of mass-action (xLMA) method for multiphase equilibrium calculations and apply it in the context of reactive transport modeling. This extended LMA formulation differs from its conventional counterpart in that (i) it is directly derived from the Gibbs energy minimization (GEM) problem (i.e., the fundamental problem that describes the state of equilibrium of a chemical system under constant temperature and pressure); and (ii) it extends the conventional mass-action equations with Lagrange multipliers from the Gibbs energy minimization problem, which can be interpreted as stability indices of the chemical species. Accounting for these multipliers enables the method to determine all stable phases without presuming their types (e.g., aqueous, gaseous) or their presence in the equilibrium state. Therefore, the here proposed xLMA method inherits traits of Gibbs energy minimization algorithms that allow it to naturally detect the phases present in equilibrium, which can be single-component phases (e.g., pure solids or liquids) or non-ideal multi-component phases (e.g., aqueous, melts, gaseous, solid solutions, adsorption, or ion exchange). Moreover, our xLMA method requires no technique that tentatively adds or removes reactions based on phase stability indices (e.g., saturation indices for minerals), since the extended mass-action equations are valid even when their corresponding reactions involve unstable species. We successfully apply the proposed method to a reactive transport modeling problem in which we use PHREEQC and GEMS as alternative backends for the calculation of thermodynamic properties such as equilibrium constants of reactions, standard chemical potentials of species, and activity coefficients. Our tests show that our algorithm is efficient and robust for demanding applications, such as reactive transport modeling, where it converges within 1-3 iterations in most cases. The proposed xLMA method is implemented in Reaktoro, a
LI Yiwen; LI Yinghong; LU Haoyu; ZHU Tao; ZHANG Bailing; CHEN Feng; ZHAO Xiaohu
2011-01-01
This paper presents a preliminary experimental investigation on magnetohydrodynamic (MHD) power generation using seeded supersonic argon flow as working fluid.Helium and argon are used as driver and driven gas respectively in a shock tunnel.Equilibrium contact surface operating mode is used to obtain high temperature gas,and the conductivity is obtained by adding seed K2CO3 powder into the driven section.Under the conditions of nozzle inlet total pressure being 0.32 MPa,total temperature 6 504 K,magnetic field density about 0.5 T and nozzle outlet velocity 1 959 m/s,induction voltage and short-circuit current of the segmentation MHD power generation channel are measured,and the experimental results agree with theoretical calculations; the average conductivity is about 20 S/m calculated from characteristics of voltage and current.When load factor is 0.5,the maximum power density of the MHD power generation channel reaches 4.797 1 MW/m3,and the maximum enthalpy extraction rate is 0.34%.Finally,the principle and method of indirect testing for gas state parameters are derived and analyzed.
Passive stabilization in a linear MHD stability code
Todd, A.M.M.
1980-03-01
Utilizing a Galerkin procedure to calculate the vacuum contribution to the ideal MHD Lagrangian, the implementation of realistic boundary conditions are described in a linear stability code. The procedure permits calculation of the effect of arbitrary conducting structure on ideal MHD instabilities, as opposed to the prior use of an encircling shell. The passive stabilization of conducting coils on the tokamak vertical instability is calculated within the PEST code and gives excellent agreement with 2-D time dependent simulations of PDX.
Gülfen, Mustafa; Özdemir, Abdil; Lin, Jung-Lee; Chen, Chung-Hsuan
2017-10-01
In this study, the dissociation and formation equilibrium constants of Na(I)-insulin and K(I)-insulin complexes have been calculated after the quantifying them on ESI mass spectrometer. The ESI-MS spectra of the complexes were measured by using the solvents as 50% MeOH in water and 100% water. The effect of pH on the Na(I)-insulin and K(I)-insulin complex formation were examined. Serial binding of Na(I) and K(I) ions to the insulin molecule were observed in the ESI-MS measurements. The first formation equilibrium constants were calculated as Kf1: 5.48×10(3) 1/M for Na(I)-insulin complex and Kf1: 4.87×10(3) 1/M for K(I)-insulin in water. The binding capability of Na(I) ions to insulin molecule is higher than the capability of K(I) ions. In case of a comparison together with Ca(II)-insulin and Mg(II)-insulin, the formation equilibrium constants (Kf1) are in order of Ca(II)-insulin>Mg(II)-insulin>Na(I)-insulin>K(I)-insulin in water. The results showed that Na(I) and K(I) ions are involved in the formation of the non-covalent complexes with insulin molecule, since high extracellular and intracellular concentrations of them in the body. Copyright © 2017 Elsevier B.V. All rights reserved.
Yasuda, H.; Kubis, T.; Hosako, I.; Hirakawa, K.
2012-04-01
We theoretically investigated GaN-based resonant phonon terahertz-quantum cascade laser (QCL) structures for possible high-temperature operation by using the non-equilibrium Green's function method. It was found that the GaN-based THz-QCL structures do not necessarily have a gain sufficient for lasing, even though the thermal backfilling and the thermally activated phonon scattering are effectively suppressed. The main reason for this is the broadening of the subband levels caused by a very strong interaction between electrons and longitudinal optical (LO) phonons in GaN.
Alexakis, A.
2009-04-01
Most astrophysical and planetary systems e.g., solar convection and stellar winds, are in a turbulent state and coupled to magnetic fields. Understanding and quantifying the statistical properties of magneto-hydro-dynamic (MHD) turbulence is crucial to explain the involved physical processes. Although the phenomenological theory of hydro-dynamic (HD) turbulence has been verified up to small corrections, a similar statement cannot be made for MHD turbulence. Since the phenomenological description of Hydrodynamic turbulence by Kolmogorov in 1941 there have been many attempts to derive a similar description for turbulence in conducting fluids (i.e Magneto-Hydrodynamic turbulence). However such a description is going to be based inevitably on strong assumptions (typically borrowed from hydrodynamics) that do not however necessarily apply to the MHD case. In this talk I will discuss some of the properties and differences of the energy and helicity cascades in turbulent MHD and HD flows. The investigation is going to be based on the analysis of direct numerical simulations. The cascades in MHD turbulence appear to be a more non-local process (in scale space) than in Hydrodynamics. Some implications of these results to turbulent modeling will be discussed
MHD Equilibria and Triggers for Prominence Eruption
Fan, Yuhong
2015-01-01
Magneto-hydrodynamic (MHD) simulations of the emergence of twisted magnetic flux tubes from the solar interior into the corona are discussed to illustrate how twisted and sheared coronal magnetic structures (with free magnetic energy), capable of driving filament eruptions, can form in the corona in emerging active regions. Several basic mechanisms that can disrupt the quasi-equilibrium coronal structures and trigger the release of the stored free magnetic energy are discussed. These include both ideal processes such as the onset of the helical kink instability and the torus instability of a twisted coronal flux rope structure and the non-ideal process of the onset of fast magnetic reconnections in current sheets. Representative MHD simulations of the non-linear evolution involving these mechanisms are presented.
MHD equilibria with diamagnetic effects
Tessarotto, M.; Zorat, R.; Johnson, J. L.; White, R. B.
1997-11-01
An outstanding issue in magnetic confinement is the establishment of MHD equilibria with enhanced flow shear profiles for which turbulence (and transport) may be locally effectively suppressed or at least substantially reduced with respect to standard weak turbulence models. Strong flows develop in the presence of equilibrium E× B-drifts produced by a strong radial electric field, as well as due to diamagnetic contributions produced by steep equilibrium radial profiles of number density, temperature and the flow velocity itself. In the framework of a kinetic description, this generally requires the construction of guiding-center variables correct to second order in the relevant expansion parameter. For this purpose, the Lagrangian approach developed recently by Tessarotto et al. [1] is adopted. In this paper the conditions of existence of such equilibria are analyzed and their basic physical properties are investigated in detail. 1 - M. Pozzo, M. Tessarotto and R. Zorat, in Theory of fusion Plasmas, E.Sindoni et al. eds. (Societá Italiana di Fisica, Editrice Compositori, Bologna, 1996), p.295.
Goossens, Marcel; Hollweg, Joseph V.
1993-01-01
Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.
Shargatov, V. A.
2016-11-01
We examined the approximate method to calculate composition and thermodynamic parameters of hydrocarbons-air nonequilibrium explosion products based on the assumption of the existence of a partial chemical equilibrium. With excellent accuracy of calculating thermodynamic properties and species mass fraction the respective stiff system of detailed kinetics differential equations can be replaced by the one differential equation or the two differential equations and a system of algebraic equations. This method is always consistent with the detailed kinetic mechanism. The constituent equations of the method were derived and the respective computer code written. We examine the applicability of the method by solving the test problem. The proposed method simulation results are in excellent agreement with the detailed kinetics model results corresponding the stiff ordinary differential equation solver including NO time histories.
Jaffe, Richard L.
1987-01-01
Specific heat data for high-temperature air species are needed to compute the temperature and enthalpy of gas mixtures in aerothermodynamics flowfield calculations. Accurate data are known only for temperatures under 6000 K, but are required for temperatures exceeding 25,000 K. In the present study, CP data are computed for N2, O2 and NO. The calculations are based on summations over all the vibration-rotation energy levels for all known bound electronic states. Estimates are made for the error introduced by the neglect of possible additional high-lying electronic states. In addition, a scheme for the partitioning of the internal energy into vibrational, rotational and electronic contributions is presented which consistently accounts for the nonseparable nature of the various energy modes. The multitemperature specific heat data are recommended for use in nonequilibrium flowfield models.
Hanson A. L.; Diamond D.
2014-06-30
A plan is being developed for the conversion of the NIST research reactor (NBSR) from high-enriched uranium (HEU) fuel to low-enriched uranium (LEU) fuel. The LEU fuel may be a monolithic foil (LEUm) of U10Mo (10% molybdenum by weight in an alloy with uranium) or a dispersion of U7Mo in aluminum (LEUd). A previous report provided neutronic calculations for the LEUm fuel and this report presents the neutronics parameters for the LEUd fuel. The neutronics parameters for the LEUd fuel are compared to those previously obtained for the present HEU fuel and the proposed LEUm fuel. The results show no significant differences between the LEUm and the LEUd other than the LEUd fuel requires slightly less uranium than the LEUm fuel due to less molybdenum being present. The calculations include kinetics parameters, reactivity coefficients, reactivity worths of control elements and abnormal configurations, and power distributions under normal operation and with misloaded fuel elements.
Kim, Ki Chul; Kulkarni, Anant D; Johnson, J Karl; Sholl, David S
2011-04-21
Systematic thermodynamics calculations based on density functional theory-calculated energies for crystalline solids have been a useful complement to experimental studies of hydrogen storage in metal hydrides. We report the most comprehensive set of thermodynamics calculations for mixtures of light metal hydrides to date by performing grand canonical linear programming screening on a database of 359 compounds, including 147 compounds not previously examined by us. This database is used to categorize the reaction thermodynamics of all mixtures containing any four non-H elements among Al, B, C, Ca, K, Li, Mg, N, Na, Sc, Si, Ti, and V. Reactions are categorized according to the amount of H(2) that is released and the reaction's enthalpy. This approach identifies 74 distinct single step reactions having that a storage capacity >6 wt.% and zero temperature heats of reaction 15 ≤ΔU(0)≤ 75 kJ mol(-1) H(2). Many of these reactions, however, are likely to be problematic experimentally because of the role of refractory compounds, B(12)H(12)-containing compounds, or carbon. The single most promising reaction identified in this way involves LiNH(2)/LiH/KBH(4), storing 7.48 wt.% H(2) and having ΔU(0) = 43.6 kJ mol(-1) H(2). We also examined the complete range of reaction mixtures to identify multi-step reactions with useful properties; this yielded 23 multi-step reactions of potential interest.
Semelsberger, Troy A.; Borup, Rodney L.
-to-carbon ratio of 0.00 in the temperature range of 400 °C-500 °C. Increasing the system pressure shifts the equilibrium toward ammonia and hydrogen cyanide.
Oh, Suk Yung; Bae, Young Chan
2010-07-15
The method presented in this paper was developed to predict liquid-liquid equilibria in ternary liquid mixtures by using a combination of a thermodynamic model and molecular dynamics simulations. In general, common classical thermodynamic models have many parameters which are determined by fitting a model with experimental data. This proposed method, however, provides a simple procedure for calculating liquid-liquid equilibria utilizing binary interaction parameters and molecular size parameters determined from molecular dynamics simulations. This method was applied to mixtures containing water, hydrocarbons, alcohols, chlorides, ketones, acids, and other organic liquids over various temperature ranges. The predicted results agree well with the experimental data without the use of adjustable parameters.
Walters, Wendell W.; Michalski, Greg
2016-10-01
The oxygen stable isotope composition (δ18O) of nitrogen oxides [NOx = nitric oxide (NO) + nitrogen dioxide (NO2)] and their oxidation products (NOy = NOx + nitric acid (HNO3) + particulate nitrate (p-NO3-) + nitrate radical (NO3) + dinitrogen pentoxide (N2O5) + nitrous acid (HONO) + …) have been shown to be a useful tool for inferring the proportion of NOx that is oxidized by ozone (O3). However, isotopic fractionation processes may have an influence on δ18O of various NOy molecules and other atmospheric O-bearing molecules pertinent to NOx oxidation chemistry. Here we have evaluated the impacts of O isotopic exchange involving NOy molecules, the hydroxyl radical (radOH), and water (H2O) using reduced partition function ratios (xβ) calculated by hybrid density functional theory. Assuming atmospheric isotopic equilibrium is achieved between NO and NO2 during the daytime, and NO2, NO3, and N2O5 during the nighttime, δ18O-δ15N compositions were predicted for the major atmospheric nitrate formation pathways using our calculated exchange fractionation factors and isotopic mass-balance. Our equilibrium model predicts that various atmospheric nitrate formation pathways, including NO2 + radOH → HNO3, N2O5 + H2O + surface → 2HNO3, and NO3 + R → HNO3 + Rrad will yield distinctive δ18O-δ15N compositions. Our calculated δ18O-δ15N compositions match well with previous atmospheric nitrate measurements, and will potentially help better understand the role oxidation chemistry plays on the N and O isotopic composition of atmospheric nitrate.
3D MHD Simulations of Tokamak Disruptions
Woodruff, Simon; Stuber, James
2014-10-01
Two disruption scenarios are modeled numerically by use of the CORSICA 2D equilibrium and NIMROD 3D MHD codes. The work follows the simulations of pressure-driven modes in DIII-D and VDEs in ITER. The aim of the work is to provide starting points for simulation of tokamak disruption mitigation techniques currently in the CDR phase for ITER. Pressure-driven instability growth rates previously observed in simulations of DIIID are verified; Halo and Hiro currents produced during vertical displacements are observed in simulations of ITER with implementation of resistive walls in NIMROD. We discuss plans to exercise new code capabilities and validation.
Application of ADER Scheme in MHD Simulation
ZHANG Yanyan; FENG Xueshang; JIANG Chaowei; ZHOU Yufen
2012-01-01
The Arbitrary accuracy Derivatives Riemann problem method（ADER） scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions： （ⅰ） Brio-Wu shock tube problem,（ⅱ） Dai-Woodward shock tube problem,（ⅲ） Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.
F. Álvarez-Velarde
2012-01-01
Full Text Available A fast numerical method for the calculation in a zero-dimensional approach of the equilibrium isotopic composition of an iteratively used transmutation system in an advanced fuel cycle, based on the Banach fixed point theorem, is described in this paper. The method divides the fuel cycle in successive stages: fuel fabrication, storage, irradiation inside the transmutation system, cooling, reprocessing, and incorporation of the external material into the new fresh fuel. The change of the fuel isotopic composition, represented by an isotope vector, is described in a matrix formulation. The resulting matrix equations are solved using direct methods with arbitrary precision arithmetic. The method has been successfully applied to a double-strata fuel cycle with light water reactors and accelerator-driven subcritical systems. After comparison to the results of the EVOLCODE 2.0 burn-up code, the observed differences are about a few percents in the mass estimations of the main actinides.
Nieto Solana, Hector; Sandholt, Inge; Aguado, Inmaculada
2010-01-01
and validate the vapour pressure models. Finally air temperature and vapour pressure were combined to calculate the EMC for dead fuels and the transfer of errors of these estimates have been assessed with ground meteorological data for three different EMC models. Promising results were obtained, with mean......In this study we propose to use remote sensing data to estimate hourly meteorological data and then assess the moisture content of dead fuels. Three different models to estimate the equilibrium moisture content (EMC) were applied together with remotely sensed retrieved air temperature and relative......-Vegetation Index (TVX) algorithm. This algorithm exploits the inverse linear relationship between the land surface temperature and the vegetation fractional cover. This relationship was evaluated in a spatial window where the meteorological forcing is assumed to be constant. To estimate the vapour pressure...
张志禹; 胡中桥; 杨基础; 李以圭
2002-01-01
Three calculational models, statistical associating fluid theory (SAFT), modified SAFT, and Boublík-Alder-Chen-Kreglewshi (BACK) are compared for supercritical CO2-C2H5OH using a set of van der Waals type mixing rules for both the BACK equation of state (EOS) and the SAFT EOS. Equations are presented for the residual Helmholtz free energy, residual chemical potentials, and compressibilty factor for mixtures. A comparison with experimental vapor-liquid equilibrium (VLE) data reveals that the BACK EOS together with the suggested mixing rules provides more accurate prediction of the binary system than the SAFT or the modified SAFT model with no adjustable binary parameters. The correlation results are improved with an adjustable parameter.
Renata Bellová
2016-07-01
Full Text Available Hydrogen sulfide is presented in textbooks as toxic, environmentally unacceptable species, however some positive effects in human metabolism were discovered in the last decades. It is important to offer students also some new information about this compound. As didactic tool in this case may serve serial precipitation of Cd2+, Cu2+, Zn2+, Mn2+ and Pb2+ ions forming various colored sulfides in bubblers with chemically generated hydrogen sulfide stream. This experiment has strong and diverse color effect for enhancing the visual perception to motivate students to understand more abstract and complex information about hydrogen sulfide. It also may be helpful in analytical chemistry courses for conditional precipitation equilibrium teaching and calculations.
Proceedings of the workshop on nonlinear MHD and extended MHD
NONE
1998-12-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
Wolery, T.J.
1979-02-01
The newly developed EQ/36 software package computes equilibrium models of aqueous geochemical systems. The package contains two principal programs: EQ3 performs distribution-of-species calculations for natural water compositions; EQ6 uses the results of EQ3 to predict the consequences of heating and cooling aqueous solutions and of irreversible reaction in rock--water systems. The programs are valuable for studying such phenomena as the formation of ore bodies, scaling and plugging in geothermal development, and the long-term disposal of nuclear waste. EQ3 and EQ6 are compared with such well-known geochemical codes as SOLMNEQ, WATEQ, REDEQL, MINEQL, and PATHI. The data base allows calculations in the temperature interval 0 to 350{sup 0}C, at either 1 atm-steam saturation pressures or a constant 500 bars. The activity coefficient approximations for aqueous solutes limit modeling to solutions of ionic strength less than about one molal. The mathematical derivations and numerical techniques used in EQ6 are presented in detail. The program uses the Newton--Raphson method to solve the governing equations of chemical equilibrium for a system of specified elemental composition at fixed temperature and pressure. Convergence is aided by optimizing starting estimates and by under-relaxation techniques. The minerals present in the stable phase assemblage are found by several empirical methods. Reaction path models may be generated by using this approach in conjunction with finite differences. This method is analogous to applying high-order predictor--corrector methods to integrate a corresponding set of ordinary differential equations, but avoids propagation of error (drift). 8 figures, 9 tables.
Frutos-Alfaro, Francisco
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a code that can be used as a seed for a MHD code for numerical applications. As an example, we present part of output of our programs for Cartesian coordinates and how to do the discretization.
Course 1: Accretion and Ejection-Related MHD
Heyvaerts, Jean
This lecture is an introduction to MHD. Relevant equations, both in the classical and special-relativistic regimes are derived. The magnetic field evolution is considered both in the perfect-MHD limit and when weak resistivity is present, giving rise to reconnection flows. A short section gives a flavour of dynamo theory. Examples of simple stationnary flows and equilibria are then presented. Stationnary, axisymmetric, rotating perfect-MHD winds and jets are discussed in some more detail. Their asymptotic structure is described. The last sections deal with small motions about an equilibrium and stability. These issues are illustrated by a few classical examples. The last section discusses linear aspects of the magneto-rotationnal instability.
Lectures in magnetohydrodynamics. With an appendix on extended MHD
Schnack, Dalton D. [Wisconsin Univ., Madison, WI (United States). Dept. Physics
2009-07-01
This concise and self-contained primer is based on class-tested notes for an advanced graduate course in MHD. The broad areas chosen for presentation are the derivation and properties of the fundamental equations, equilibrium, waves and instabilities, self-organization, turbulence, and dynamos. The latter topics require the inclusion of the effects of resistivity and nonlinearity. Together, these span the range of MHD issues that have proven to be important for understanding magnetically confined plasmas as well as in some space and astrophysical applications. The combined length and style of the thirty-eight lectures are appropriate for complete presentation in a single semester. An extensive appendix on extended MHD is included as further reading. (orig.)
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
Frutos-Alfaro, Francisco; Carboni-Mendez, Rodrigo
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a c...
G. García Segura
2000-01-01
Full Text Available Se presenta un escenario auto consistente para explicar la morfolog a de las nebulosas planetarias. El escenario es consistente con la distribuci on Gal actica de los diferentes tipos morfol ogicos. Este trabajo resuelve, por medio de efectos MHD, algunas de las caracter sticas controversiales que aparecen en las nebulosas planetarias. Estas caracter sticas incluyen la presencia de ujos axisim etricos y colimados, con una cinem atica que aumenta linealmente con la distancia y la existencia de morfolog as asim etricas tales como las de las nebulosas con simetr a de punto.
Retallick, F.D.
1978-04-01
This document establishes criteria to be utilized for the design of a pilot-scale (150 to 300 MW thermal) open cycle, coal-fired MHD/steam plant. Criteria for this Engineering Test Facility (ETF) are presented relative to plant siting, plant engineering and operations, MHD-ETF testing, costing and scheduling.
MHD turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, that spectral properties of distributed chaos in MHD turbulence with zero mean magnetic field are similar to those of hydrodynamic turbulence. An exception is MHD spontaneous breaking of space translational symmetry, when the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ has $\\beta=4/7$.
Mohammed, H. E. Abu-Sei'leek
2011-01-01
A non-relativistic microscopic mean field theory of finite nuclei is investigated where the nucleus is described as a collection of nucleons and delta resonances. The ground state properties of 90Zr nucleus have been investigated at equilibrium and large amplitude compression using a realistic effective baryon-baryon Hamiltonian based on Reid Soft Core (RSC) potential. The sensitivity of the ground state properties is studied, such as binding energy, nuclear radius, radial density distribution, and single particle energies to the degree of compression. It is found that the most of increasing in the nuclear energy generated under compression is used to create the massive Δ particles. For 90Zr nucleus under compression at 2.5 times density of the normal nuclear density, the excited nucleons to Δ's are increased sharply up to 14% of the total number of constituents. This result is consistent with the values extracted from relativistic heavy-ion collisions. The single particle energy levels are calculated and their behaviors under compression are examined too. A good agreement between results with effective Hamiltonian and the phenomenological shell model for the low lying single-particle spectra is obtained. A considerable reduction in compressibility for the nucleus, and softening of the equation of state with the inclusion of the Δ's in the nuclear dynamics are suggested by the results.
Preliminary Analysis of Liquid Metal MHD Pressure Drop in the Blanket for the FDS
王红艳; 吴宜灿; 何晓雄
2002-01-01
Preliminary analysis and calculation of liquid metal Li17Pb83 magnetohydrodynamic (MHD) pressure drop in the blanket for the FDS have been presented to evaluate the significance of MHD effects on the thermal-hydraulic design of the blanket. To decrease the liquid metal MHD pressure drop, Al2O3 is applied as an electronically insulated coating onto the inner surface of the ducts. The requirement for the insulated coating to reduce the additional leakage pressure drop caused by coating imperfections has been analyzed. Finally, the total liquid metal MHD pressure drop and magnetic pump power in the FDS blanket have been given.
M. Schüssler
Full Text Available Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere ('convective collapse' are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10^{5} G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.
Key words. Solar physics · astrophysics and astronomy (photosphere and chromosphere; stellar interiors and dynamo theory; numerical simulation studies.
Study of MHD activities in the plasma of SST-1
Dhongde, Jasraj; Bhandarkar, Manisha; Pradhan, Subrata, E-mail: pradhan@ipr.res.in; Kumar, Sameer
2016-10-15
Highlights: • An account of MHD activity in the plasma of SST-1 • Observation of MHD instabilities with mode m = 2, n = 1 in SST-1 plasma. • MHD instabilities study of characteristic growth time, growth rate of island and island width etc. in SST-1 plasma. - Abstract: Steady State Superconducting Tokamak (SST-1) is a medium size Tokamak in operation at the Institute for Plasma Research, India. SST-1 has been consistently producing plasma currents in excess of 60 kA, with plasma durations above 400 ms and a central magnetic field of 1.5 T over last few experimental campaigns of 2014. Investigation of these experimental data suggests the presence of MHD activity in the SST-1 plasma. Further analysis clearly explains the behavior of MHD instabilities observed (i.e. tearing modes with m = 2, n = 1), estimating the growth rate and the island width in the SST-1 plasma. Poloidal magnetic field and Toroidal magnetic field fluctuations in SST-1 are observed using Mirnov coils. Onsets of disruptions in connection with MHD activities have been correlated with other diagnostics such as ECE, Density and Hα etc. The observations have been cross compared with the theoretical calculations and are found to be in good agreement.
Preliminary Study of Ideal Operational MHD Beta Limit in HL-2A Tokamak Plasmas
SHEN Yong; DONG Jiaqi; HE Hongda; A. D. TURNBULL
2009-01-01
Magnetohydrodynamic (MHD) n=1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q0 both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of βcN=2.56 for a typical HL-2A discharge with a plasma current Ip=0.245 MA, and the scaling of βcN～constant is confirmed.
Monique Florenzano
2008-09-01
Full Text Available General equilibrium is a central concept of economic theory. Unlike partial equilibrium analysis which study the equilibrium of a particular market under the clause “ceteris paribus” that revenues and prices on the other markets stay approximately unaffected, the ambition of a general equilibrium model is to analyze the simultaneous equilibrium in all markets of a competitive economy. Definition of the abstract model, some of its basic results and insights are presented. The important issues of uniqueness and local uniqueness of equilibrium are sketched; they are the condition for a predictive power of the theory and its ability to allow for statics comparisons. Finally, we review the main extensions of the general equilibrium model. Besides the natural extensions to infinitely many commodities and to a continuum of agents, some examples show how economic theory can accommodate the main ideas in order to study some contexts which were not thought of by the initial model
Smith, S. P.; Jardin, S. C.; Freidberg, J. P.; Guazzotto, L.
2008-11-01
The ideal MHD linear stability normal modes and frequencies for a circular cylindrical plasma (having an arbitrary equilibrium flow) interacting with a resistive wall are calculated. Projections of the plasma displacement are expanded as finite elements, using a Galerkin approach to form the inner products. A Green's function approach is taken to couple the perturbed wall currents to the plasma surface perturbations. The standard linear form, φAx=B x, is obtained by introducing an auxiliary variable, u=φξ+iV .∇ξ, and an additional degree of freedom representing the perturbed current in the resistive wall. It is shown that having projections aligned with (or perpendicular to) the equilibrium magnetic field is more important for correctly calculating the slow wave part of the spectrum than having a higher order finite element expansion with non-field-aligned projections. Investigations into the effects of axial and azimuthal flows on the resistive wall mode are also presented.
3-D nonlinear evolution of MHD instabilities
Bateman, G.; Hicks, H. R.; Wooten, J. W.
1977-03-01
The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed.
Magnetorotational Instability of Dissipative MHD Flows
HERRON, ISOM H
2010-07-10
Executive summary Two important general problems of interest in plasma physics that may be addressed successfully by Magnetohydrodynamics (MHD) are: (1) Find magnetic field configurations capable of confining a plasma in equilibrium. (2) Study the stability properties of each such an equilibrium. It is often found that the length scale of many instabilities and waves that are able to grow or propagate in a system, are comparable with plasma size, such as in magnetically confined thermonuclear plasmas or in astrophysical accretion disks. Thus MHD is able to provide a good description of such large-scale disturbances. The Magnetorotational instability (MRI) is one particular instance of a potential instability. The project involved theoretical work on fundamental aspects of plasma physics. Researchers at the Princeton Plasma Physics Laboratory (PPPL) began to perform a series of liquid metal Couette flow experiments between rotating cylinders. Their purpose was to produce MRI, which they had predicted theoretically 2002, but was only observed in the laboratory since this project began. The personnel on the project consisted of three persons: (1) The PI, who was partially supported on the budget during each of four summers 2005-2008. (2) Two graduate research assistants, who worked consecutively on the project throughout the years 2005-2009. As a result, the first student, Fritzner Soliman, obtained an M.S. degree in 2006; the second student, Pablo Suarez obtained the Ph.D. degree in 2009. The work was in collaboration with scientists in Princeton, periodic trips were made by the PI as part of the project. There were 4 peer-reviewed publications and one book produced.
Eigenanalysis of Ideal Hall MHD Turbulence
Fu, T.; Shebalin, J. V.
2011-12-01
Ideal, incompressible, homogeneous, Hall magnetohydrodynamic (HMHD) turbulence may be investigated through a Fourier spectral method. In three-dimensional periodic geometry, the independent Fourier coefficients represent a canonical ensemble described by a Gaussian probability density. The canonical ensemble is based on the conservation of three invariants: total energy, generalized helicity, and magnetic helicity. Generalized helicity in HMHD takes the place of cross helicity in MHD. The invariants determine the modal probability density giving the spectral structure and equilibrium statistics of ideal HMHD, which are compared to known MHD results. New results in absolute equilibrium ensemble theory are derived using a novel approach that involves finding the eigenvalues of a Hermitian covariance matrix for each modal probability density. The associated eigenvectors transform the original phase space variables into eigenvariables through a special unitary transformation. These are the normal modes which facilitate the analysis of ideal HMHD non-linear dynamics. The eigenanalysis predicts that the low wavenumber modes with very small eigenvalues may have mean values that are large compared to their standard deviations, contrary to the ideal ensemble prediction of zero mean values. (Expectation values may also be relatively large at the highest wave numbers, but the addition of even small levels of dissipation removes any relevance this may have for real-world turbulence.) This behavior is non-ergodic over very long times for a numerical simulation and is termed 'broken ergodicity'. For fixed values of the ideal invariants, the effect is seen to be enhanced with increased numerical grid size. Broken ergodicity at low wave number modes gives rise to large-scale, quasi-stationary, coherent structure. Physically, this corresponds to plasma relaxation to force-free states. For real HMHD turbulence with dissipation, broken ergodicity and coherent structure are still
MHD computations for stellarators
Johnson, J.L.
1985-12-01
Considerable progress has been made in the development of computational techniques for studying the magnetohydrodynamic equilibrium and stability properties of three-dimensional configurations. Several different approaches have evolved to the point where comparison of results determined with different techniques shows good agreement. 55 refs., 7 figs.
Equilibrium statistical mechanics
Mayer, J E
1968-01-01
The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t
Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow
Dimitrov, Z D; Hristov, T S; Mishonov, T M
2011-01-01
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space.
Annular MHD Physics for Turbojet Energy Bypass
Schneider, Steven J.
2011-01-01
The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated assuming weakly ionized flows obtained from pulsed nanosecond discharges. The equations for a 1-D, axisymmetric MHD generator/accelerator are derived and numerically integrated to determine the generator/accelerator performance characteristics. The concept offers a shockless means of interacting with high speed inlet flows and potentially offers variable inlet geometry performance without the complexity of moving parts simply by varying the generator loading parameter. The cycle analysis conducted iteratively with a spike inlet and turbojet flying at M = 7 at 30 km altitude is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at an aggressive 2200 deg K. The annular MHD Hall generator/accelerator is L = 3 m in length with a B(sub r) = 5 Tesla magnetic field and a conductivity of sigma = 5 mho/m for the generator and sigma= 1.0 mho/m for the accelerator. The calculated isentropic efficiency for the generator is eta(sub sg) = 84 percent at an enthalpy extraction ratio, eta(sub Ng) = 0.63. The calculated isentropic efficiency for the accelerator is eta(sub sa) = 81 percent at an enthalpy addition ratio, eta(sub Na) = 0.62. An assessment of the ionization fraction necessary to achieve a conductivity of sigma = 1.0 mho/m is n(sub e)/n = 1.90 X 10(exp -6), and for sigma = 5.0 mho/m is n(sub e)/n = 9.52 X 10(exp -6).
郭兰兰; 孔祥强; 王默晗
2013-01-01
在冷凝法油气回收过程中,油气组分和含量不断变化,热物性如焓、熵、粘度、比热容等也相应发生改变.为了正确计算动态参数,给出了油气的相平衡计算模型.该模型由物料平衡条件方程组、热力学平衡条件方程组和状态方程结构体系3部分构成,并通过VC++语言编程求解.利用实际气体PR状态方程计算某油气成分在三级冷凝温度4℃、-50℃、110℃下的相平衡特性,与Aspen软件计算结果相比误差不大,可以作为后续流程模拟计算的基础.%In the condensate oil and gas recovery process, components and contents of oil and gas change constantly and thermo-physical properties such as enthalpy, entropy, viscosity and specific heat also change accordingly. To correctly calculate these dynamic parameters, a phase equilibrium calculation model for oil and gas is given. This model consists of material equilibrium condition equation set, thermodynamic equilibrium condition equation set and state equation structure system and is resolved using VC++ language programming. PR state equation of actual gas is used to calculate phase equilibrium feature of a oil and gas component at three condensing temperatures such as 4℃, -50℃ and -110℃. The feature is closed to calculation results of Aspen software, so it can be taken as the basis of follow-up process simulation calculation.
Using Faraday Rotation to Probe MHD Instabilities in Intracluster Media
Bogdanovic, Tamara; Massey, Richard
2010-01-01
It has recently been suggested that conduction-driven magnetohydrodynamic (MHD) instabilities may operate at all radii within an intracluster medium (ICM), and profoundly affect the structure of a cluster's magnetic field. Where MHD instabilities dominate the dynamics of an ICM, they will re-orient magnetic field lines perpendicular to the temperature gradient inside a cooling core, or parallel to the temperature gradient outside it. This characteristic structure of magnetic field could be probed by measurements of polarized radio emission from background sources. Motivated by this possibility we have constructed 3-d models of a magnetized cooling core cluster and calculated Faraday rotation measure (RM) maps in the plane of the sky under realistic observing conditions. We compare a scenario in which magnetic field geometry is characterized by conduction driven MHD instabilities to that where it is determined by the turbulent motions. We find that future high-sensitivity spectro-polarimetric measurements of R...
3D Equilibrium Effects Due to RMP Application on DIII-D
S. Lazerson, E. Lazarus, S. Hudson, N. Pablant and D. Gates
2012-06-20
The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon [1]. Vacuum calculations suggest the formation of edge islands and stochastic regions when RMPs are applied to the axisymmetric equilibria. Self-consistent calculations of the plasma equilibrium with the VMEC [2] and SPEC [3] codes have been performed for an up-down symmetric shot (142603) in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nested family of flux surfaces is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete "ideal-interfaces" at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.
3D Equilibrium Effects Due to RMP Application on DIII-D
Lazerson, S.; Lazarus, E.; Hudson, S.; Pablant, N.; Gates, D.
2012-06-20
The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon. Vacuum calculations suggest the formation of edge islands and stochastic regions when RMPs are applied to the axisymmetric equilibria. Self-consistent calculations of the plasma equilibrium with the VMEC and SPEC codes have been performed for an up-down symmetric shot in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nested family of flux surfaces is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete "ideal-interfaces" at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.
Shim, Irene; Pelino, Mario; Gingerich, Karl A.
1992-01-01
, and they hardly contribute to the bonding. The chemical bond in the YC molecule is polar with charge transfer from Y to C giving rise to a dipole moment of 3.90 D at 3.9 a.u. in the 4PI ground state. Mass spectrometric equilibrium investigations in the temperature range 2365-2792 K have resulted...
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
Formation and collimation of relativistic MHD jets - simulations and radio maps
Fendt, Christian; Sheikhnezami, Somayeh
2013-01-01
We present results of magnetohydrodynamic (MHD) simulations of jet formation and propagation, discussing a variety of astrophysical setups. In the first approach we consider simulations of relativistic MHD jet formation, considering jets launched from the surface of a Keplerian disk, demonstrating numerically - for the first time - the self-collimating ability of relativistic MHD jets. We obtain Lorentz factors up to about 10 while acquiring a high degree of collimation of about 1 degree. We then present synchrotron maps calculated from the intrinsic jet structure derived from the MHD jet formation simulation. We finally present (non-relativistic) MHD simulations of jet lauching, treating the transition between accretion and ejection. These setups include a physical magnetic diffusivity which is essential for loading the accretion material onto the outflow. We find relatively high mass fluxes in the outflow, of the order of 20-40 % of the accretion rate.
MHD Energy Bypass Scramjet Performance with Real Gas Effects
Park, Chul; Mehta, Unmeel B.; Bogdanoff, David W.
2000-01-01
The theoretical performance of a scramjet propulsion system incorporating an magneto-hydro-dynamic (MHD) energy bypass scheme is calculated. The one-dimensional analysis developed earlier, in which the theoretical performance is calculated neglecting skin friction and using a sudden-freezing approximation for the nozzle flow, is modified to incorporate the method of Van Driest for turbulent skin friction and a finite-rate chemistry calculation in the nozzle. Unlike in the earlier design, in which four ramp compressions occurred in the pitch plane, in the present design the first two ramp compressions occur in the pitch plane and the next two compressions occur in the yaw plane. The results for the simplified design of a spaceliner show that (1) the present design produces higher specific impulses than the earlier design, (2) skin friction substantially reduces thrust and specific impulse, and (3) the specific impulse of the MHD-bypass system is still better than the non-MHD system and typical rocket over a narrow region of flight speeds and design parameters. Results suggest that the energy management with MHD principles offers the possibility of improving the performance of the scramjet. The technical issues needing further studies are identified.
Generation of sheet currents by high frequency fast MHD waves
Núñez, Manuel, E-mail: mnjmhd@am.uva.es
2016-07-01
The evolution of fast magnetosonic waves of high frequency propagating into an axisymmetric equilibrium plasma is studied. By using the methods of weakly nonlinear geometrical optics, it is shown that the perturbation travels in the equatorial plane while satisfying a transport equation which enables us to predict the time and location of formation of shock waves. For plasmas of large magnetic Prandtl number, this would result into the creation of sheet currents which may give rise to magnetic reconnection and destruction of the original equilibrium. - Highlights: • Regular solutions of quasilinear hyperbolic systems may evolve into shocks. • The shock location is found for high frequency fast MHD waves. • The result is applied to static axisymmetric equilibria. • The previous process may lead to the formation of sheet currents and destruction of the equilibrium.
Nieto Solana, Hector; Sandholt, Inge; Aguado, Inmaculada; Chuvieco, Emilio
2010-01-01
Udgivelsesdato: 2010 In this study we propose to use remote sensing data to estimate hourly meteorological data and then assess the moisture content of dead fuels. Three different models to estimate the equilibrium moisture content (EMC) were applied together with remotely sensed retrieved air temperature and relative humidity. The input data were acquired by the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor, on board the Meteosat Second Generation (MSG) satellite, from whi...
Lulit Mitik
2008-01-01
Full Text Available The effects of trade liberalization on female labor depend on a country′s socio-economic and employment sector characteristics. A Gender-aware computable general equilibrium model is applied to Ethiopia and South Africa from a comparative perspective. Tariff reduction results in opposite outcomes regarding gender-based wage and labor market participation inequalities in the two countries due to their structural differences in men′s and women′s employment.
McBride, Bonnie J.; Gordon, Sanford
1996-01-01
This users manual is the second part of a two-part report describing the NASA Lewis CEA (Chemical Equilibrium with Applications) program. The program obtains chemical equilibrium compositions of complex mixtures with applications to several types of problems. The topics presented in this manual are: (1) details for preparing input data sets; (2) a description of output tables for various types of problems; (3) the overall modular organization of the program with information on how to make modifications; (4) a description of the function of each subroutine; (5) error messages and their significance; and (6) a number of examples that illustrate various types of problems handled by CEA and that cover many of the options available in both input and output. Seven appendixes give information on the thermodynamic and thermal transport data used in CEA; some information on common variables used in or generated by the equilibrium module; and output tables for 14 example problems. The CEA program was written in ANSI standard FORTRAN 77. CEA should work on any system with sufficient storage. There are about 6300 lines in the source code, which uses about 225 kilobytes of memory. The compiled program takes about 975 kilobytes.
Roussel-Dupre, R.
1979-01-01
Non-Maxwellian electron velocity distribution functions, previously computed for Dupree's model of the solar transition region are used to calculate ionization rates for ions of carbon, nitrogen, and oxygen. Ionization equilibrium populations for these ions are then computed and compared with similar calculations assuming Maxwellian distribution functions for the electrons. The results show that the ion populations change (compared to the values computed with a Maxwellian) in some cases by several orders of magnitude depending on the ion and its temperature of formation.
Problems in nonlinear resistive MHD
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Magnetohydrodynamic (MHD) channel corner seal
Spurrier, Francis R.
1980-01-01
A corner seal for an MHD duct includes a compressible portion which contacts the duct walls and an insulating portion which contacts the electrodes, sidewall bars and insulators. The compressible portion may be a pneumatic or hydraulic gasket or an open-cell foam rubber. The insulating portion is segmented into a plurality of pieces of the same thickness as the electrodes, insulators and sidewall bars and aligned therewith, the pieces aligned with the insulator being of a different size from the pieces aligned with the electrodes and sidewall bars to create a stepped configuration along the corners of the MHD channel.
MHD stability limits in the TCV Tokamak
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
observed decrease of this limit with elongation is also in qualitative agreement with ideal MHD theory. Edge localised modes (ELMs), occurring in TCV Ohmic high-confinement mode discharges, were observed to be preceded by coherent magnetic oscillations. The detected poloidal and toroidal mode structures are consistent with a resonant flux surface close to the plasma edge. Unlike conventional MHD modes, these precursors start at a random toroidal location and then grow in amplitude and toroidal extent until they encompass the whole toroidal circumference. Thus, the asymmetry causing and maintaining the toroidal localisation of the ELM precursor must be intrinsic to the plasma. Soft X-ray measurements show that the localised precursor always coincides with a central m = 1 mode, which can usually be associated with the sawtooth pre- or postcursor mode. A comparison of the phases indicates a correlation with the maximum of the central mode preceding the toroidal location of the ELM precursor and, therefore, a hitherto unobserved coupling between central modes and ELMs. Highly elongated plasmas promise several advantages, among them higher current and beta limits. During TCV experiments dedicated to an increasing of the plasma elongation, a new disruptive current limit, at values well below the conventional current limit corresponding to q{sub a} > 2, was encountered for {kappa} > 2.3. This limit, which is preceded by a kink-type mode, is found to be consistent with ideal MHD stability calculations. The TCV observations, therefore, provide the first experimental confirmation of a deviation of the linear Troyon-scaling of the ideal beta limit with normalised current at high elongation, which was predicted over 10 years ago. Neoclassical tearing modes (NTMs), which have been observed to limit the achievable beta in a number of tokamaks, arise from a helical perturbation of the bootstrap current caused by an existing seed island. Neoclassical m/n = 2/1 tearing modes have been
朱贵凤; 邹杨; 李明海; 严睿; 彭红花; 徐洪杰
2015-01-01
The burnup calculation code PBRE coupling MCNP5 and ORIGEN2 was developed for pebble‐bed high temperature reactor at equilibrium state ,and it can be used to analyze the neutronic performance of equilibrium core .The iteration method was optimized in order to save Monte Carlo calculation time ,and the convergence can be reached in 10 iterative steps .The average discharged burnup for HTR‐10 is consistent with literature ,and it indicates that the PBRE is suitable to analyze the burnup for pebble‐bed reactor at equilibrium state .%基于MCNP5和ORIGEN2耦合方法，开发了平衡态下球床高温堆的燃耗计算程序PBRE ，用于堆的性能价值分析。为节省蒙特卡罗计算时间，对迭代收敛的方法进行优化，使之可在10个迭代步内收敛。使用PBRE对清华大学H T R‐10进行建模计算，得到的平均卸料燃耗深度与文献报道值一致，表明PBRE程序适用于球床堆平衡态的燃耗分析。
Neutrino oscillations in MHD supernova explosions
Kawagoe, S; Kotake, K [Division of Theoretical Astronomy, National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588 (Japan); Takiwaki, T, E-mail: shio.k@nao.ac.j [Center for Computational Astrophysics, National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588 (Japan)
2010-01-01
We calculate the neutrino oscillations numerically in magnetohydrodynamic (MHD) explosion models to see how asphericity has impacts on neutrino spectra. Magneto-driven explosions are one of the most attracting scenarios for producing large scale departures from spherical symmetric geometry, that are reported by many observational data. We find that the event rates at Super-Kamiokande (SK) seen from the polar direction (e.g., the rotational axis of the supernovae) decrease when the shock wave is propagating through H-resonance. In addition, we find that L-resonance in this situation becomes non-adiabatic, and the effect of L-resonance appears in the neutrino signal, because the MHD shock can propagate to the stellar surface without shock-stall after core bounce, and the shock reaches the L-resonance at earlier stage than the conventional spherical supernova explosion models. Our results suggest that we may obtain the observational signatures of the two resonances in SK for Galactic supernova.
张志禹; 胡中桥; 杨基础; 李以圭
2002-01-01
The statistical associating fluid theory (SAFT)-Boublík-Alder-Chen- Kreglewshi(BACK) equation of state is employed to correlate vapor-liquid equilibria of 16 binary mixtures composed of supercritical fluids with other fluids at elevated pressures. The van der Waals mixing rules are used and the binary parameters are adjusted to experimental data. The SAFT-BACK equation of state provides a better correlation of vapor-liquid equilibrium than the original BACK equation. Consequently, the binary parameters computed from the data sets can be used to accurately predict the saturated densities of the vapor and liquid phases.
Turbulent MHD transport coefficients - An attempt at self-consistency
Chen, H.; Montgomery, D.
1987-01-01
In this paper, some multiple scale perturbation calculations of turbulent MHD transport coefficients begun in earlier papers are first completed. These generalize 'alpha effect' calculations by treating the velocity field and magnetic field on the same footing. Then the problem of rendering such calculations self-consistent is addressed, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg for the Navier-Stokes case. The method also borrows from Kraichnan's direct interaction approximation. The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous 'alpha effect' and 'beta effect' coefficients emerge as limiting cases. A treatment of the inertial range can also be given, consistent with a -5/3 energy spectrum power law. In the Navier-Stokes limit, a value of 1.72 is extracted for the Kolmogorov constant. Further applications to MHD are possible.
Using ant colony algorithm to calculate the chemical equilibrium of complex system%利用蚁群算法计算复杂体系化学平衡
胡元; 李尚勇; 谢刚
2012-01-01
基于Gibbs自由能最小原理,本文利用蚁群算法构建了一个复杂体系化学平衡计算的数值计算模型.该模型嵌入局部搜索算法以提高计算精度,通过蚁群移动以获取全局最优解.通过算法验证计算表明,该模型能够作为一种复杂体系化学平衡计算的方法.%Based on the Gibbs free energy minimization method, we use ant colony algorithm to build a numerical calculation model of chemical equilibrium calculations of complex system. The model is embedded into the local search algorithm to improve precision in calculation and through the colony moved to obtain global optimal solution. Algorithm validation results show that the model can be used as a method of chemical equilibrium calculations of complex system.
Three-dimensional fluid and electrodynamic modeling for MHD DCW channels
Liu, B. L.; Lineberry, J. T.; Schmidt, H. J.
1983-01-01
A three dimensional, numerical solution for modeling diagonal conducting wall (DCW) magnetohydrodynamic (MHD) generators is developed and discussed. Cross plane gasdynamic and electrodynamic profiles are computed considering coupled MHD flow and electrical phenomena. A turbulent transport model based on the mixing length theory is used to deal with wall roughness generated turbulence effects. The infinitely fine electrode segmentation formulation is applied to simplify the governing electrical equations. Calculations show the development of distorted temperature and velocity profiles under influence of magnetohydrodynamic interaction. Since both sidewall and electrode wall boundary losses are treated, the results furnish a realistic representation of MHD generator behavior.
于慎波; 陈仕彬
2012-01-01
A novel search method was presented to calculate the steady-state equilibrium position of a tilting pad journal bearing in motorized spindle for solving the problem of difficult search of equilibrium position from the nonlinear hydrodynamic force. It is found that the slight variations in fulcrum position of pads will have a great influence on the 8 hydrodynamic coefficients during the calculation. With the proposed methods,the steady-state equilibrium position can be calculated in multiple directions search in motion polar coordinate system. The calculated results show that the stability is improved by increasing the difference between outside diameter of pad and inner diameter of bearing bracket. Never- ending loop in process of search is avoided effectively by using of the novel search method. The method can also be applied to other forms of hydrodynamic bearings.%提出一种计算电主轴用可倾瓦滑动轴承稳态平衡位置的新搜索方法,解决了油膜力非线性导致的平衡位置难以搜索的问题.在计算过程中,发现瓦背支点位置的微小变化会在很大程度上影响可倾瓦轴承的8个动力系数.用该搜索方法,采用运动极坐标系同时对多个方向进行搜索,计算出稳态平衡位置.计算结果表明,适当增大瓦背与轴承座的半径差会提高可倾瓦轴承的稳定性;新搜索方法可以有效避免搜索中的死循环,且可用于其他形式的滑动轴承.
van der Burg, W.; van Willigenburg, T.
1998-01-01
The basic idea of reflective equilibrium, as a method for theory construction and decision making in ethics, is that we should bring together a broad variety of moral and non-moral beliefs and, through a process of critical scrutiny and mutual adjustment, combine these into one coherent belief syste
van der Burg, W.; van Willigenburg, T.
1998-01-01
The basic idea of reflective equilibrium, as a method for theory construction and decision making in ethics, is that we should bring together a broad variety of moral and non-moral beliefs and, through a process of critical scrutiny and mutual adjustment, combine these into one coherent belief syste
Nieto Solana, Hector; Sandholt, Inge; Aguado, Inmaculada;
2010-01-01
In this study we propose to use remote sensing data to estimate hourly meteorological data and then assess the moisture content of dead fuels. Three different models to estimate the equilibrium moisture content (EMC) were applied together with remotely sensed retrieved air temperature and relative...... humidity. The input data were acquired by the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor, on board the Meteosat Second Generation (MSG) satellite, from which air temperature and relative humidity were estimated every 15 min. Air temperature estimations are based on the Temperature......-Vegetation Index (TVX) algorithm. This algorithm exploits the inverse linear relationship between the land surface temperature and the vegetation fractional cover. This relationship was evaluated in a spatial window where the meteorological forcing is assumed to be constant. To estimate the vapour pressure...
MHD control in burning plasmas MHD control in burning plasmas
Donné, Tony; Liang, Yunfeng
2012-07-01
Fusion physics focuses on the complex behaviour of hot plasmas confined by magnetic fields with the ultimate aim to develop a fusion power plant. In the future generation of tokamaks like ITER, the power generated by the fusion reactions substantially exceeds the external input power (Pfusion}/Pin >= 10). When this occurs one speaks of a burning plasma. Twenty per cent of the generated fusion power in a burning plasma is carried by the charged alpha particles, which transfer their energy to the ambient plasma in collisions, a process called thermalization. A new phenomenon in burning plasmas is that the alpha particles, which form a minority but carry a large fraction of the plasma kinetic energy, can collectively drive certain types of magneto-hydrodynamic (MHD) modes, while they can suppress other MHD modes. Both types of MHD modes can have desirable effects on the plasma, as well as be detrimental to the plasma. For example, the so-called sawtooth instability, on the one hand, is largely responsible for the transport of the thermalized alpha particles out of the core, but, on the other hand, may result in the loss of the energetic alphas before they have fully thermalized. A further undesirable effect of the sawtooth instability is that it may trigger other MHD modes such as neoclassical tearing modes (NTMs). These NTMs, in turn, are detrimental to the plasma confinement and in some cases may even lead to disruptive termination of the plasma. At the edge of the plasma, finally, so-called edge localized modes or ELMs occur, which result in extremely high transient heat and particle loads on the plasma-facing components of a reactor. In order to balance the desired and detrimental effects of these modes, active feedback control is required. An additional complication occurs in a burning plasma as the external heating power, which is nowadays generally used for plasma control, is small compared to the heating power of the alpha particles. The scientific challenge
Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.
2017-09-01
The Hamiltonian structure of ideal translationally symmetric extended MHD (XMHD) is obtained by employing a method of Hamiltonian reduction on the three-dimensional noncanonical Poisson bracket of XMHD. The existence of the continuous spatial translation symmetry allows the introduction of Clebsch-like forms for the magnetic and velocity fields. Upon employing the chain rule for functional derivatives, the 3D Poisson bracket is reduced to its symmetric counterpart. The sets of symmetric Hall, Inertial, and extended MHD Casimir invariants are identified, and used to obtain energy-Casimir variational principles for generalized XMHD equilibrium equations with arbitrary macroscopic flows. The obtained set of generalized equations is cast into Grad-Shafranov-Bernoulli (GSB) type, and special cases are investigated: static plasmas, equilibria with longitudinal flows only, and Hall MHD equilibria, where the electron inertia is neglected. The barotropic Hall MHD equilibrium equations are derived as a limiting case of the XMHD GSB system, and a numerically computed equilibrium configuration is presented that shows the separation of ion-flow from electro-magnetic surfaces.
Expected IPS variations due to a disturbance described by a 3-D MHD model
Tappin, S. J.; Dryer, M.; Han, S. M.; Wu, S. T.
1988-01-01
The variations of interplanetary scintillation due to a disturbance described by a three-dimensional, time-dependent, MHD model of the interplanetary medium are calculated. The resulting simulated IPS maps are compared with observations of real disturbances and it is found that there is some qualitative agreement. It is concluded that the MHD model with a more realistic choice of input conditions would probably provide a useful description of many interplanetary disturbances.
Toward 3D MHD modeling of neoclassical tearing mode suppression by ECCD
Westerhof E.
2012-09-01
Full Text Available We propose a framework to extend the magnetohydrodynamic (MHD equations to include electron cyclotron current drive (ECCD and discuss previous models proposed by Giruzzi et al. [2] and by Hegna and Callen [3]. To model neoclassical tearing mode (NTM instabilities and study the growth of magnetic islands as NTMs evolve, we employ the nonlinear reduced-MHD simulation JOREK. We present tearing-mode growth-rate calculations from JOREK simulations.
Variational Integration for Ideal MHD with Built-in Advection Equations
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Burby, J. W. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2014-08-05
Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
Magnetic levitation and MHD propulsion
Tixador, P.
1994-04-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried out in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ...) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. Depuis quelques années nous assistons à un redémarrage de programmes concernant la lévitation et la propulsion supraconductrices. Différents systèmes supraconducteurs de lévitation et de propulsion seront décrits en examinant plus particulièrement l'aspect électromagnétique. Quelques programmes à travers le monde seront abordés. Les trains à sustentation magnétique pourraient constituer un nouveau mode de transport terrestre à vitesse élevée (500 km/h) pour le 21^e siècle. Les japonais n'ont cessé de s'intéresser à ce système avec bobine supraconductrice. Ils envisagent un stade préindustriel avec la construction d'une ligne de 43 km. En 1991 un programme américain pour une durée de six ans a été lancé pour évaluer les performances des systèmes à lévitation pour le transport aux Etats Unis. La MHD (Magnéto- Hydro-Dynamique) présente des avantages intéressants pour la propulsion navale et un regain d'intérêt apparaît à l'heure actuelle. Le japon se situe là encore à la pointe des d
Chau, Nancy H.
2009-01-01
This paper presents a capability-augmented model of on the job search, in which sweatshop conditions stifle the capability of the working poor to search for a job while on the job. The augmented setting unveils a sweatshop equilibrium in an otherwise archetypal Burdett-Mortensen economy, and reconciles a number of oft noted yet perplexing features of sweatshop economies. We demonstrate existence of multiple rational expectation equilibria, graduation pathways out of sweatshops in complete abs...
Lemon, C. L.; Crabtree, C. E.; Chen, M.; Guild, T. B.
2015-12-01
Modeling the progression of the magnetotail configuration during a substorm growth phase is challenging because the current sheet becomes very thin, and is difficult to resolve while keeping the problem computationally tractable. Magnetohydrodynamics (MHD) models have dealt with this problem in various ways, and many claim to be driven by physical rather than numerical considerations. The Rice Convection Model-Equilibrium (RCM-E) is not an MHD model, and has advantages and disadvantages compared to MHD. The notable advantages are the characterization of the full energy distribution of the plasma (including the associated gradient/curvature drift), as well as its generally more comprehensive treatment of the electrodynamics of magnetosphere-ionosphere coupling. The disadvantages include the bounce-averaging of plasma drift, which limits the domain to closed field lines, and the assumption of slow flow relative to the Alfvén speed. The RCM-E has been used in the past to model a substorm growth phase, but its assumptions do not allow it to properly treat the onset mechanism or the formation of x-lines. It can simulate the approach to onset, but is limited by its ability to resolve the thinning current sheet. In this presentation, we present advances in the technique used to calculate the self-consistent magnetic field, which allows us to resolve thinner current sheets than were previously possible. We combine this with a generalized ballooning mode analysis of specific flux tubes in order to assess the stability of the magnetotail to substorm onset.
Equilibrium modeling of the TFCX poloidal field coil system
Strickler, D.J.; Miller, J.B.; Rothe, K.E.; Peng, Y.K.M.
1984-04-01
The Toroidal Fusion Core Experiment (TFCX) isproposed to be an ignition device with a low safety factor (q approx. = 2.0), rf or rf-assisted startup, long inductive burn pulse (approx. 300 s), and an elongated plasma cross section (kappa = 1.6) with moderate triangularity (delta = 0.3). System trade studies have been carried out to assist in choosing an appropriate candidate for TFCX conceptual design. This report describes an important element in these system studies - the magnetohydrodynamic (MHD) equilibrium modeling of the TFCX poloidal field (PF) coil system and its impact on the choice of machine size. Reference design points for the all-super-conducting toroidal field (TF) coil (TFCX-S) and hybrid (TFCX-H) options are presented that satisfy given PF system criteria, including volt-second requirements during burn, mechanical configuration constraints, maximum field constraints at the superconducting PF coils, and plasma shape parameters. Poloidal coil current waveforms for the TFCX-S and TFCX-H reference designs consistent with the equilibrium requirements of the plasma startup, heating, and burn phases of a typical discharge scenario are calculated. Finally, a possible option for quasi-steady-state operation is discussed.
MHD rotation of electrically conducting media in crossed fields
Nikitin, N.V.
1978-01-01
A nonlinear scheme is developed for calculating the hydrodynamic characteristics of MHD flow in a cylindrical vessel of finite dimensions, in an electric field and a magnetic field crossing each other. The incompressible fluid is assumed to have a constant viscosity and electrical conductivity. The solution to the complete system of MHD equations is expanded in a series with respect to the magnetic Reynolds number, for a large hydrodynamic Reynolds number. And rather simple engineering formulas for calculating the velocity field and the pressure field are derived by the Karman-Pohlhausen method of integral relations. The results are compared with experimental data pertaining to a model helium-xenon discharge chamber with distribution of the Lorentz force causing the plasma to rotate as a quasi-solid. 15 references, 5 figures, 1 table.
Birzvalk, Yu.
1978-01-01
The shunting ratio and the local shunting ratio, pertaining to currents induced by a magnetic field in a flow channel, are properly defined and systematically reviewed on the basis of the Lagrange criterion. Their definition is based on the energy balance and related to dimensionless parameters characterizing an MHD flow, these parameters evolving from the Hartmann number and the hydrodynamic Reynolds number as well as the magnetic Reynolds number, and the Lundquist number. These shunting ratios, of current density in the core of a stream (uniform) or equivalent mean current density to the short-circuit (maximum) current density, are given here for a slot channel with nonconducting or conducting walls, for a conduction channel with heavy side rails, and for an MHD-flow around bodies. 5 references, 1 figure.
Extended MHD Modeling of Tearing-Driven Magnetic Relaxation
Sauppe, Joshua
2016-10-01
Driven plasma pinch configurations are characterized by the gradual accumulation and episodic release of free energy in discrete relaxation events. The hallmark of this relaxation in a reversed-field pinch (RFP) plasma is flattening of the parallel current density profile effected by a fluctuation-induced dynamo emf in Ohm's law. Nonlinear two-fluid modeling of macroscopic RFP dynamics has shown appreciable coupling of magnetic relaxation and the evolution of plasma flow. Accurate modeling of RFP dynamics requires the Hall effect in Ohm's law as well as first order ion finite Larmor radius (FLR) effects, represented by the Braginskii ion gyroviscous stress tensor. New results find that the Hall dynamo effect from / ne can counter the MHD effect from - in some of the relaxation events. The MHD effect dominates these events and relaxes the current profile toward the Taylor state, but the opposition of the two dynamos generates plasma flow in the direction of equilibrium current density, consistent with experimental measurements. Detailed experimental measurements of the MHD and Hall emf terms are compared to these extended MHD predictions. Tracking the evolution of magnetic energy, helicity, and hybrid helicity during relaxation identifies the most important contributions in single-fluid and two-fluid models. Magnetic helicity is well conserved relative to the magnetic energy during relaxation. The hybrid helicity is dominated by magnetic helicity in realistic low-beta pinch conditions and is also well conserved. Differences of less than 1 % between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution through ion FLR effects, which have not been included in contemporary relaxation theories. The kinetic energy driven by relaxation in the computations is dominated by velocity components perpendicular to the magnetic field, an effect that had not been predicted. Work performed at University of Wisconsin
Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria
Bowden, G. W.; Hole, M. J. [Plasma Theory and Modelling, Research School of Physics and Engineering, Australian National University, Acton 2601, Australian Capital Territory (Australia); Könies, A. [Max-Planck-Institut für Plasmaphysik, EURATOM-Association, D-17491 Greifswald (Germany)
2015-09-15
In an ideal magnetohydrodynamic (MHD) plasma, shear Alfvén eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfvén continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD Code for Kinetic Alfvén waves. In this paper, we discuss the application of the complex contour technique to calculate the continuum damping of global modes in tokamak as well as torsatron, W7-X and H-1NF stellarator cases. To the authors' knowledge, these stellarator calculations represent the first calculation of continuum damping for eigenmodes in fully three-dimensional equilibria. The continuum damping of global modes in W7-X and H-1NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics.
Hot self-similar relativistic MHD flows
Zakamska, Nadia L; Blandford, Roger D
2008-01-01
We consider axisymmetric relativistic jets with a toroidal magnetic field and an ultrarelativistic equation of state, with the goal of studying the lateral structure of jets whose pressure is matched to the pressure of the medium through which they propagate. We find all self-similar steady-state solutions of the relativistic MHD equations for this setup. One of the solutions is the case of a parabolic jet being accelerated by the pressure gradient as it propagates through a medium with pressure declining as p(z)\\propto z^{-2}. As the jet material expands due to internal pressure gradients, it runs into the ambient medium resulting in a pile-up of material along the jet boundary, while the magnetic field acts to produce a magnetic pinch along the axis of the jet. Such jets can be in a lateral pressure equilibrium only if their opening angle \\theta_j at distance z is smaller than about 1/\\gamma, where \\gamma is the characteristic bulk Lorentz-factor at this distance; otherwise, different parts of the jet canno...
A three dimensional MHD model of the earth's magnetosphere
Wu, C. C.; Walker, R. J.; Dawson, J. M.
1981-01-01
The results of a global MHD calculation of the steady state solar wind interaction with a dipole magnetic field are presented. The computer code used, being much faster than previous codes, makes it possible to increase the number of grid points in the system by an order of magnitude. The resulting model qualitatively reproduces many of the observed features of the quiet time magnetosphere including the bow shock, magnetopause, and plasma sheet.
Self-excitation of a diagonal MHD channel
Doperchuk, I.I.; Koneyev, S.M.A.
1982-01-01
Questions are examined of self-excitation of a diagonal MHD channel. Conditions are obtained for self-excitation using 0-dimensional approximation. An algorithm is presented for calculating the optimal self-exciting diagonal channel with regard for development and separation of the boundary layers, presence of near-electrode drops in voltage. Graphs are presented for the transitional regimes of channel operation with intermediate point of connection of the excitation winding.
Non-Radial Oscillations in an Axisymmetric MHD Incompressible Fluid
A. Satya Narayanan
2000-09-01
It is well known from Helioseismology that the Sun exhibits oscillations on a global scale, most of which are non-radial in nature. These oscillations help us to get a clear picture of the internal structure of the Sun as has been demonstrated by the theoretical and observational (such as GONG) studies. In this study we formulate the linearised equations of motion for non-radial oscillations by perturbing the MHD equilibrium solution for an axisymmetric incompressible fluid. The fluid motion and the magnetic field are expressed as scalars , , and , respectively. In deriving the exact solution for the equilibrium state, we neglect the contribution due to meridional circulation. The perturbed quantities *, *, *, * are written in terms of orthogonal polynomials. A special case of the above formulation and its stability is discussed.
Shim, Irene; Kingcade, Joseph E. , Jr.; Gingerich, Karl A.
1986-01-01
In the present work we present all-electron ab initio Hartree–Fock (HF) and configuration interaction (CI) calculations of six electronic states of the PdGe molecule. The molecule is predicted to have a 3Pi ground state and two low-lying excited states 3Sigma− and 1Sigma+. The electronic structure...
Denis-Petit, David; Gosselin, Gilbert; Hannachi, Fazia; Tarisien, Medhi; Bonnet, Thomas; Comet, Maxime; Gobet, Franck; Versteegen, Maud; Morel, Pascal; Méot, Vincent; Matea, Iolanda
2017-08-01
One promising candidate for the first detection of nuclear excitation in plasma is the 463-keV, 20.26-min-lifetime isomeric state in 84Rb, which can be excited via a 3.5-keV transition to a higher lying state. According to our preliminary calculations, under specific plasma conditions, nuclear excitation by electron transition (NEET) may be its strongest excitation process. Evaluating a reliable NEET rate requires, in particular, a thorough examination of all atomic transitions contributing to the rate under plasma conditions. We report the results of a detailed evaluation of the NEET rate based on multiconfiguration Dirac Fock (MCDF) atomic calculations, in a rubidium plasma at local thermodynamic equilibrium with a temperature of 400 eV and a density of 10-2g /cm3 and based on a more precise energy measurement of the nuclear transition involved in the excitation.
Ferreira, J
2006-01-01
This is a doctorate level lecture on the physics of accretion discs driving magnetically self-confined jets, usually referred to in the literature as disc winds. I will first review the governing magnetohydrodynamic equations and then discuss their physical content. At that level, necessary conditions to drive jets from keplerian accretion discs can already be derived. These conditions are validated with self-similar calculations of accretion-ejection structures. In a second part, I will critically discuss the biases introduced when using self-similarity as well as some other questions such as: Are these systems really unstable? Can a standard accretion disc provide the conditions to launch jets in its innermost parts? What is the difference between X-winds and disc-winds? Finally, the magnetic interaction between a protostar and its circumstellar disc will be discussed with a focus on stellar spin down.
Bollerslev, Tim; Sizova, Natalia; Tauchen, George
Stock market volatility clusters in time, carries a risk premium, is fractionally inte- grated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast......, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes....
Equilibrium reconstruction in the TCA/Br tokamak; Reconstrucao do equilibrio no tokamak TCA/BR
Sa, Wanderley Pires de
1996-12-31
The accurate and rapid determination of the Magnetohydrodynamic (MHD) equilibrium configuration in tokamaks is a subject for the magnetic confinement of the plasma. With the knowledge of characteristic plasma MHD equilibrium parameters it is possible to control the plasma position during its formation using feed-back techniques. It is also necessary an on-line analysis between successive discharges to program external parameters for the subsequent discharges. In this work it is investigated the MHD equilibrium configuration reconstruction of the TCA/BR tokamak from external magnetic measurements, using a method that is able to fast determine the main parameters of discharge. The thesis has two parts. Firstly it is presented the development of an equilibrium code that solves de Grad-Shafranov equation for the TCA/BR tokamak geometry. Secondly it is presented the MHD equilibrium reconstruction process from external magnetic field and flux measurements using the Function Parametrization FP method. this method. This method is based on the statistical analysis of a database of simulated equilibrium configurations, with the goal of obtaining a simple relationship between the parameters that characterize the equilibrium and the measurements. The results from FP are compared with conventional methods. (author) 68 refs., 31 figs., 16 tabs.
Purgel, Mihály; Takács, Zoltán; Jonsson, Caroline M; Nagy, Lajos; Andersson, Ingegärd; Bányai, István; Pápai, Imre; Persson, Per; Sjöberg, Staffan; Tóth, Imre
2009-11-01
The stoichiometries and stability constants of a series of Al(3+)-N-phosponomethyl glycine (PMG/H(3)L) complexes have been determined in acidic aqueous solution using a combination of precise potentiometric titration data, quantitative (27)Al and (31)P NMR spectra, ATR-FTIR spectrum and ESI-MS measurements (0.6M NaCl, 25 degrees C). Besides the mononuclear AlH(2)L(2+), Al(H(2)L)(HL), Al(HL)(2)(-) and Al(HL)L(2-), dimeric Al(2)(HL)L(+) and trinuclear Al(3)H(5)L(4)(2+) complexes have been postulated. (1)H and (31)P NMR data show that different isomers co-exist in solution and the isomerization reactions are slow on the (31)P NMR time scale. The geometries of monomeric and dimeric complexes likely double hydroxo bridged and double phosphonate bridged isomers have been optimized using DFT ab initio calculations starting from rational structural proposals. Energy calculations using the PCM solvation method also support the co-existence of isomers in solutions.
de Oliveira, Mário J
2017-01-01
This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Néel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This new edit...
Oliveira, Mário J
2013-01-01
This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Néel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This textbo...
Varzandeh, Farhad; Stenby, Erling Halfdan; Yan, Wei
2017-01-01
Accurate description of thermodynamic properties of natural gas systems is of great significance in the oil and gas industry. For this application, non-cubic equations of state (EoSs) are advantageous due to their better density and compressibility description. Among the non-cubic models, GERG-2008......S is another model that despite its empirical nature, provides accurate density description even around the critical point. It is much simpler than GERG-2008 and easier to handle and generalize to reservoir oil fluids. This study presents a comprehensive comparison between GERG-2008 and other cubic (SRK and PR......) and noncubic EoSs (Soave-BWR and PC-SAFT) with a focus on Soave-BWR in description of pure components density and compressibility in a wide temperature and pressure range, calculation of binary Vapor- Liquid-Equilibria (VLE) and density, prediction of multicomponent phase envelopes and gas compressibility...
MHD Driving of Relativistic Jets
Arieh Königl
2007-01-01
Full Text Available Paulatinamente se ha ido reconociendo que los campos magnéticos juegan un papel dominante en la producción y colimación de chorros astrofísicos. Demostramos aquí, usando soluciones semianalíticas exactas para las ecuaciones de MHD ideal en relatividad especial, que un disco de acreción altamente magnetizado (con un campo magnético principalmente poloidal o azimutal alrededor de un agujero negro es capaz de acelerar un flujo de protones y electrones a los factores de Lorentz y energías cinéticas asociadas a fuentes de destellos de rayos gama y nucleos activos de galaxias. También se discuten las contribuciones a la aceleración provenientes de efectos térmicos (por presión de radiación y pares electrón-positrón y de MHD no ideal. Notamos que la aceleración por MHD se caracteriza por ser extendida espacialmente, y esta propiedad se manifesta más claramente en flujos relativistas. Las indicaciones observacionales de que la aceleración de movimientos superlumínicos en chorros de radio ocurre sobre escalas mucho más grandes que las del agujero negro propiamente, apoyan la idea de que la producción de chorros es principalmente un fenómeno magnético. Presentamos resultados preliminares de un modelo global que puede utilizarse para probar esta interpretación.
Global MHD model of the earth's magnetosphere
Wu, C. C.
1983-01-01
A global MHD model of the earth's magnetosphere is defined. An introduction to numerical methods for solving the MHD equations is given with emphasis on the shock-capturing technique. Finally, results concerning the shape of the magnetosphere and the plasma flows inside the magnetosphere are presented.
MHD Turbulence, Turbulent Dynamo and Applications
Beresnyak, Andrey
2014-01-01
MHD Turbulence is common in many space physics and astrophysics environments. We first discuss the properties of incompressible MHD turbulence. A well-conductive fluid amplifies initial magnetic fields in a process called small-scale dynamo. Below equipartition scale for kinetic and magnetic energies the spectrum is steep (Kolmogorov -5/3) and is represented by critically balanced strong MHD turbulence. In this paper we report the basic reasoning behind universal nonlinear small-scale dynamo and the inertial range of MHD turbulence. We measured the efficiency of the small-scale dynamo $C_E=0.05$, Kolmogorov constant $C_K=4.2$ and anisotropy constant $C_A=0.63$ for MHD turbulence in high-resolution direct numerical simulations. We also discuss so-called imbalanced or cross-helical MHD turbulence which is relevant for in many objects, most prominently in the solar wind. We show that properties of incompressible MHD turbulence are similar to the properties of Alfv\\'enic part of MHD cascade in compressible turbul...
An MHD model of the earth's magnetosphere
Wu, C. C.
1985-01-01
It is pointed out that the earth's magnetosphere arises from the interaction of the solar wind with the earth's geomagnetic field. A global magnetohydrodynamics (MHD) model of the earth's magnetosphere has drawn much attention in recent years. In this model, MHD equations are used to describe the solar wind interaction with the magnetosphere. In the present paper, some numerical aspects of the model are considered. Attention is given to the ideal MHD equations, an equation of state for the plasma, the model as an initial- and boundary-value problem, the shock capturing technique, computational requirements and techniques for global MHD modeling, a three-dimensional mesh system employed in the global MHD model, and some computational results.
李继安; 张凯
2011-01-01
Radium and radon equilibrium coefficient is an important recifying parameter for resources/reserves estimation. Starting with the the reason analysi about radium and radon balance on sandstone type uranium deposits, the authors discussed the calculation means of radium and radon equilibrium coefficient and their difference. This corrected parameter provide scientific evidence for correction of radioactivity logging, division of cut - off grade and resources/reserves estimation.%从分析在砂岩型铀矿中镭氡平衡破坏的原因出发,探讨了镭氡平衡系数的计算方法,并对不同的计算方法进行了讨论.该系数的取得,为十红滩铀矿床北带放射性测井数据的修正、矿体边界的划分、铀矿资源量的计算提供了科学依据.
Feasibility of MHD submarine propulsion
Doss, E.D. (ed.) (Argonne National Lab., IL (United States)); Sikes, W.C. (ed.) (Newport News Shipbuilding and Dry Dock Co., VA (United States))
1992-09-01
This report describes the work performed during Phase 1 and Phase 2 of the collaborative research program established between Argonne National Laboratory (ANL) and Newport News Shipbuilding and Dry Dock Company (NNS). Phase I of the program focused on the development of computer models for Magnetohydrodynamic (MHD) propulsion. Phase 2 focused on the experimental validation of the thruster performance models and the identification, through testing, of any phenomena which may impact the attractiveness of this propulsion system for shipboard applications. The report discusses in detail the work performed in Phase 2 of the program. In Phase 2, a two Tesla test facility was designed, built, and operated. The facility test loop, its components, and their design are presented. The test matrix and its rationale are discussed. Representative experimental results of the test program are presented, and are compared to computer model predictions. In general, the results of the tests and their comparison with the predictions indicate that thephenomena affecting the performance of MHD seawater thrusters are well understood and can be accurately predicted with the developed thruster computer models.
Electron MHD: dynamics and turbulence
Lyutikov, Maxim
2013-01-01
(Abridged) We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron MHD (EMHD). We argue there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact non-linear solutions; (ii) co-linear whistlers do not interact (including counter-propagating); (iii) waves with the same value of the wave vector, $k_1=k_2$, do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero-mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfven turbulence cannot be transferred to the E...
Further validation of liquid metal MHD code for unstructured grid based on OpenFOAM
Feng, Jingchao; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; He, Qingyun; Ye, Minyou
2015-11-15
Highlights: • Specific correction scheme has been adopted to revise the calculating result for non-orthogonal meshes. • The developed MHD code based on OpenFOAM platform has been validated by benchmark cases under uniform and non-uniform magnetic field in round and rectangular ducts. • ALEX experimental results have been used to validate the MHD code based on OpenFOAM. - Abstract: In fusion liquid metal blankets, complex geometries involving contractions, expansions, bends, manifolds are very common. The characteristics of liquid metal flow in these geometries are significant. In order to extend the magnetohydrodynamic (MHD) solver developed on OpenFOAM platform to be applied in the complex geometry, the MHD solver based on unstructured meshes has been implemented. The adoption of non-orthogonal correction techniques in the solver makes it possible to process the non-orthogonal meshes in complex geometries. The present paper focused on the validation of the code under critical conditions. An analytical solution benchmark case and two experimental benchmark cases were conducted to validate the code. Benchmark case I is MHD flow in a circular pipe with arbitrary electric conductivity of the walls in a uniform magnetic field. Benchmark cases II and III are experimental cases of 3D laminar steady MHD flow under fringing magnetic field. In all these cases, the numerical results match well with the benchmark cases.
王金勋; 李士伦; 刘玉慧
2001-01-01
Continuation ( or Homotopy) method was applied to calculate thedew-point pressures of four gas condensate systems under reservoir temperatures in comparing with Newton iterative method and Broyden method. The effects of initial iteration pressures on the convergence of dew-point pressures were studied based on the results from the three different methods. The Peng and Robinson equation of state was used for all calculations. The results showed that continuation method is an efficient algorithm for the phase equilibrium calculations of reservoir fluids.%用延拓法、经典的Newton算法和Broyden算法分别计算了四个实际油气体系的露点(用PR方程)，对同一体系的重馏分使用同样的临界参数，对比不同压力初值下这三种方法的迭代收敛情况。对同一体系同样的压力初值对比了改变重馏分的临界参数拟合实验露点时这三种算法的适应性。结果表明延拓法对初值要求低，是油藏流体相平衡计算的一种有效算法。
MHD stability limits in the TCV Tokamak
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
observed decrease of this limit with elongation is also in qualitative agreement with ideal MHD theory. Edge localised modes (ELMs), occurring in TCV Ohmic high-confinement mode discharges, were observed to be preceded by coherent magnetic oscillations. The detected poloidal and toroidal mode structures are consistent with a resonant flux surface close to the plasma edge. Unlike conventional MHD modes, these precursors start at a random toroidal location and then grow in amplitude and toroidal extent until they encompass the whole toroidal circumference. Thus, the asymmetry causing and maintaining the toroidal localisation of the ELM precursor must be intrinsic to the plasma. Soft X-ray measurements show that the localised precursor always coincides with a central m = 1 mode, which can usually be associated with the sawtooth pre- or postcursor mode. A comparison of the phases indicates a correlation with the maximum of the central mode preceding the toroidal location of the ELM precursor and, therefore, a hitherto unobserved coupling between central modes and ELMs. Highly elongated plasmas promise several advantages, among them higher current and beta limits. During TCV experiments dedicated to an increasing of the plasma elongation, a new disruptive current limit, at values well below the conventional current limit corresponding to q{sub a} > 2, was encountered for {kappa} > 2.3. This limit, which is preceded by a kink-type mode, is found to be consistent with ideal MHD stability calculations. The TCV observations, therefore, provide the first experimental confirmation of a deviation of the linear Troyon-scaling of the ideal beta limit with normalised current at high elongation, which was predicted over 10 years ago. Neoclassical tearing modes (NTMs), which have been observed to limit the achievable beta in a number of tokamaks, arise from a helical perturbation of the bootstrap current caused by an existing seed island. Neoclassical m/n = 2/1 tearing modes have been
Wall ablation of heated compound-materials into non-equilibrium discharge plasmas
Wang, Weizong; Kong, Linghan; Geng, Jinyue; Wei, Fuzhi; Xia, Guangqing
2017-02-01
The discharge properties of the plasma bulk flow near the surface of heated compound-materials strongly affects the kinetic layer parameters modeled and manifested in the Knudsen layer. This paper extends the widely used two-layer kinetic ablation model to the ablation controlled non-equilibrium discharge due to the fact that the local thermodynamic equilibrium (LTE) approximation is often violated as a result of the interaction between the plasma and solid walls. Modifications to the governing set of equations, to account for this effect, are derived and presented by assuming that the temperature of the electrons deviates from that of the heavy particles. The ablation characteristics of one typical material, polytetrafluoroethylene (PTFE) are calculated with this improved model. The internal degrees of freedom as well as the average particle mass and specific heat ratio of the polyatomic vapor, which strongly depends on the temperature, pressure and plasma non-equilibrium degree and plays a crucial role in the accurate determination of the ablation behavior by this model, are also taken into account. Our assessment showed the significance of including such modifications related to the non-equilibrium effect in the study of vaporization of heated compound materials in ablation controlled arcs. Additionally, a two-temperature magneto-hydrodynamic (MHD) model accounting for the thermal non-equilibrium occurring near the wall surface is developed and applied into an ablation-dominated discharge for an electro-thermal chemical launch device. Special attention is paid to the interaction between the non-equilibrium plasma and the solid propellant surface. Both the mass exchange process caused by the wall ablation and plasma species deposition as well as the associated momentum and energy exchange processes are taken into account. A detailed comparison of the results of the non-equilibrium model with those of an equilibrium model is presented. The non-equilibrium results
E. Bolaños-Reynoso
2004-01-01
Full Text Available Se ha analizado el efecto de la presión en destilación flash con soluciones múltiples aplicando cálculos de equilibrio instantáneo y equilibrio entre fases. La metodología establece la localización de soluciones múltiples en función de la temperatura (de burbuja a rocío y de la presión, mediante el empleo de dos herramientas de cálculo termodinámico, basadas en los métodos de Rachford y Rice y de la minimización de la energía libre de Gibbs. Los resultados determinan que si la presión en el sistema se incrementa, el intervalo de composición es minimizado y una de las soluciones múltiples tiende a no ser observable. Se concluye que las soluciones múltiples son termodinámicamente factibles y que ambas soluciones sólo coexisten en el estado estacionario, si no existen grandes cambios en la presión del sistemaThe effect of the pressure on flash distillation with multiple solutions was analyzed, applying calculations for instantaneous equilibrium and phase equilibrium. The methodology establishes the localization of multiple solutions as a function of the temperature (from bubble to dew and of the pressure, employing two thermodynamic calculation methods, based on those of Rachford and Rice and that of the minimization of the Gibb´s free energy. The results suggested that if the pressure in the system is increased, the composition range is minimized and one of the multiple solutions tends to not be observable. It is concluded that the multiple solutions are thermodynamically feasible and that both solutions only coexist in the stationary state, if there are no major changes in pressure in the system
Alfven Wave Tomography for Cold MHD Plasmas
I.Y. Dodin; N.J. Fisch
2001-09-07
Alfven waves propagation in slightly nonuniform cold plasmas is studied by means of ideal magnetohydrodynamics (MHD) nonlinear equations. The evolution of the MHD spectrum is shown to be governed by a matrix linear differential equation with constant coefficients determined by the spectrum of quasi-static plasma density perturbations. The Alfven waves are shown not to affect the plasma density inhomogeneities, as they scatter off of them. The application of the MHD spectrum evolution equation to the inverse scattering problem allows tomographic measurements of the plasma density profile by scanning the plasma volume with Alfven radiation.
MHD Integrated Topping Cycle Project
1992-07-01
This seventeenth quarterly technical progress report of the MHD Integrated Topping Cycle Project presents the accomplishments during the period August 1, 1991 to October 31, 1991. Manufacturing of the prototypical combustor pressure shell has been completed including leak, proof, and assembly fit checking. Manufacturing of forty-five cooling panels was also completed including leak, proof, and flow testing. All precombustor internal components (combustion can baffle and swirl box) were received and checked, and integration of the components was initiated. A decision was made regarding the primary and backup designs for the 1A4 channel. The assembly of the channel related prototypical hardware continued. The cathode wall electrical wiring is now complete. The mechanical design of the diffuser has been completed.
Cosmological AMR MHD with Enzo
Xu, Hao [Los Alamos National Laboratory; Li, Hui [Los Alamos National Laboratory; Li, Shengtai [Los Alamos National Laboratory
2009-01-01
In this work, we present EnzoMHD, the extension of the cosmological code Enzoto include magnetic fields. We use the hyperbolic solver of Li et al. (2008) for the computation of interface fluxes. We use constrained transport methods of Balsara & Spicer (1999) and Gardiner & Stone (2005) to advance the induction equation, the reconstruction technique of Balsara (2001) to extend the Adaptive Mesh Refinement of Berger & Colella (1989) already used in Enzo, though formulated in a slightly different way for ease of implementation. This combination of methods preserves the divergence of the magnetic field to machine precision. We use operator splitting to include gravity and cosmological expansion. We then present a series of cosmological and non cosmologjcal tests problems to demonstrate the quality of solution resulting from this combination of solvers.
Numerical simulation study of disk MHD generator for nonequilibrium plasma (NPG) system
Tsunoda, Kazumi [Shibaura Institute of Technology, Tokyo (Japan); Harada, Nob [Nagaoka Univ. of Technology (Japan)
1995-12-31
Design and performance prediction of a disk-shaped magnetohydrodynamic (MHD) generator, which is applied to the nonequilibrium plasma generator (NPG) system, have been carried out by means of a quasi-one-dimensional numerical simulation. The calculations have been performed for generator with constant height which is planned to be used for NPG-MHD disk generator pulse power demonstration. A maximum enthalpy extraction ratio obtained from the present calculation reached up to 20%, and, in this case, the electron temperature of working plasma fluctuated in the unstable regime against ionization instability. Taking into account this phenomenon, in order to obtain much higher generator performance, the MHD channel, in which electron temperature was kept at 5000 K, was designed. With this channel, enthalpy extraction ratio of 40% and output power of 7.2 MW were achieved without major modification of the supersonic nozzle, the inlet swirl vanes and the configuration of magnet system.
Sub-atmospheric disk generators for coal-fired MHD/steam combined cycle power plant
Messerle, H.K.; Fang, Y.; Simpson, S.W.; Marty, S.M. (Sydney Univ. (Australia). School of Electrical Engineering)
1989-01-01
A coal fired MHD disk generator in a combined cycle MHD/steam power generation system with a diffuser operating at sub-atmospheric pressure is proposed. The effects of pressure on the performance of a radial outflow MHD disk generator and other system components are analysed. Using a previous study as a reference case, preliminary calculations show that, in such a sub-atmospheric system, improved power station efficiency can be achieved. In addition, operation at reduced values of magnetic field strength would be feasible. Calculations have also been carried out for a 30 MW{sub th} experimental disk generator operating at reduced pressure with a magnetic field strength of 2 T. Flow conditions at sub-atmospheric pressure would provide an improved simulation of a full-scale generator operating at normal pressures. (author).
Ambipolar diffusion in low-mass star formation. I. General comparison with the ideal MHD case
Masson, Jacques; Hennebelle, Patrick; Vaytet, Neil; Commerçon, Benoit
2015-01-01
In this paper, we provide a more accurate description of the evolution of the magnetic flux redistribution during prestellar core collapse by including resistive terms in the magnetohydrodynamics (MHD) equations. We focus more particularly on the impact of ambipolar diffusion. We use the adaptive mesh refinement code RAMSES to carry out such calculations. The resistivities required to calculate the ambipolar diffusion terms were computed using a reduced chemical network of charged, neutral and grain species. The inclusion of ambipolar diffusion leads to the formation of a magnetic diffusion barrier in the vicinity of the core, preventing accumulation of magnetic flux in and around the core and amplification of the field above 0.1G. The mass and radius of the first Larson core remain similar between ideal and non-ideal MHD models. This diffusion plateau has crucial consequences on magnetic braking processes, allowing the formation of disk structures. Magnetically supported outflows launched in ideal MHD models...
Coupled simulation of kinetic pedestal growth and MHD ELM crash
Park, G [Courant Institute of Mathematical Sciences, New York University (United States); Cummings, J [California Institute of Technology (United States); Chang, C S [Courant Institute of Mathematical Sciences, New York University (United States); Podhorszki, N [Univ. California at Davis (United States); Klasky, S [ORNL (United States); Ku, S [Courant Institute of Mathematical Sciences, New York University (United States); Pankin, A [Lehigh Univ. (United States); Samtaney, R [Princeton Plasma Physics Laboratory (United States); Shoshani, A [LBNL (United States); Snyder, P [General Atomics (United States); Strauss, H [Courant Institute of Mathematical Sciences, New York University (United States); Sugiyama, L [MIT (United States)
2007-07-15
Edge pedestal height and the accompanying ELM crash are critical elements of ITER physics yet to be understood and predicted through high performance computing. An entirely self-consistent first principles simulation is being pursued as a long term research goal, and the plan is planned for completion in time for ITER operation. However, a proof-of-principle work has already been established using a computational tool that employs the best first principles physics available at the present time. A kinetic edge equilibrium code XGC0, which can simulate the neoclassically dominant pedestal growth from neutral ionization (using a phenomenological residual turbulence diffusion motion superposed upon the neoclassical particle motion) is coupled to an extended MHD code M3D, which can perform the nonlinear ELM crash. The stability boundary of the pedestal is checked by an ideal MHD linear peeling-ballooning code, which has been validated against many experimental data sets for the large scale (type I) ELMs onset boundary. The coupling workflow and scientific results to be enabled by it are described.
MHD Forces in Quasi-Static Evolution, Catastrophe, and ``Failed'' Eruption of Solar Flux Ropes
Chen, James
2017-08-01
This paper presents the first unified theoretical model of flux rope dynamics---a single set of flux-rope equations in ideal MHD---to describe as one dynamical process the quasi-static evolution, catastrophic transition to eruption, cessation (``failure'') of eruption, and the post-eruption quasi-equilibria. The model is defined by the major radial {\\it and} minor radial equations of motion including pressure. The initial equilibrium is a flux rope in a background plasma with pressure $p_c(Z)$ and an overlying magnetic field $B_c(Z)$. The flux rope is initially force-free, but theevolution is not required to be force- free. A single quasi-static control parameter, the rate of increase in poloidal flux, is used for the entire process. As this parameter is slowly increased, the flux rope rises, following a sequence of quasi-static equilibria. As the apex of the flux rope rises past a critical height $Z_{crt}$, it expands on a dynamical (Alfvénic) timescale. The eruption rapidly ceases, as the stored magnetic energy of eruption is exhausted, and a new equilibrium is established at height $Z_1 > Z_{crt}$. The calculated velocity profile resembles the observed velocity profiles in ``failed'' eruptions including a damped oscillation. In the post-eruption equilibria, the outward hoop force is balanced by the tension of the toroidal self magnetic field and pressure gradient force. Thus, the flux rope does not evolve in a force-free manner. The flux rope may also expand without reaching a new equilibrium, provided a sufficient amount of poloidal flux is injected on the timescale of eruption. This scenario results in a full CME eruption. It is shown that the minor radial expansion critically couples the evolution of the toroidal self-field and pressure gradient force. No parameter regime is found in which the commonly used simplifications---near-equilibrium minor radial expansion, force-free expansion, and constant aspect ratio $R/a$ (e.g., the torus instability equation
Characteristics of laminar MHD fluid hammer in pipe
Huang, Z.Y.; Liu, Y.J., E-mail: yajun@scut.edu.cn
2016-01-01
As gradually wide applications of MHD fluid, transportation as well as control with pumps and valves is unavoidable, which induces MHD fluid hammer. The paper attempts to combine MHD effect and fluid hammer effect and to investigate the characteristics of laminar MHD fluid hammer. A non-dimensional fluid hammer model, based on Navier–Stocks equations, coupling with Lorentz force is numerically solved in a reservoir–pipe–valve system with uniform external magnetic field. The MHD effect is represented by the interaction number which associates with the conductivity of the MHD fluid as well as the external magnetic field and can be interpreted as the ratio of Lorentz force to Joukowsky force. The transient numerical results of pressure head, average velocity, wall shear stress, velocity profiles and shear stress profiles are provided. The additional MHD effect hinders fluid motion, weakens wave front and homogenizes velocity profiles, contributing to obvious attenuation of oscillation, strengthened line packing and weakened Richardson annular effect. Studying the characteristics of MHD laminar fluid hammer theoretically supplements the gap of knowledge of rapid-transient MHD flow and technically provides beneficial information for MHD pipeline system designers to better devise MHD systems. - Highlights: • Characteristics of laminar MHD fluid hammer are discussed by simulation. • MHD effect has significant influence on attenuation of wave. • MHD effect strengthens line packing. • MHD effect inhibits Richardson annular effect.
Nabert, Christian; Othmer, Carsten; Glassmeier, Karl-Heinz
2017-05-01
The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD) simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms) magnetosheath data to estimate Earth's dipole moment.
MHD activity in the ISX-B tokamak: experimental results and theoretical interpretation
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.
Analysis of Linear MHD Power Generators
Witalis, E.A.
1965-02-15
The finite electrode size effects on the performance of an infinitely long MHD power generation duct are calculated by means of conformal mapping. The general conformal transformation is deduced and applied in a graphic way. The analysis includes variations in the segmentation degree, the Hall parameter of the gas and the electrode/insulator length ratio as well as the influence of the external circuitry and loading. A general criterion for a minimum of the generator internal resistance is given. The same criterion gives the conditions for the occurrence of internal current leakage between adjacent electrodes. It is also shown that the highest power output at a prescribed efficiency is always obtained when the current is made to flow between exactly opposed electrodes. Curves are presented showing the power-efficiency relations and other generator properties as depending on the segmentation degree and the Hall parameter in the cases of axial and transverse power extraction. The implications of limiting the current to flow between a finite number of identical electrodes are introduced and combined with the condition for current flow between opposed electrodes. The characteristics of generators with one or a few external loads can then be determined completely and examples are given in a table. It is shown that the performance of such generators must not necessarily be inferior to that of segmented generators with many independent loads. However, the problems of channel end losses and off-design loading have not been taken into consideration.
Aerospace Applications of Non-Equilibrium Plasma
Blankson, Isaiah M.
2016-01-01
Nonequilibrium plasma/non-thermal plasma/cold plasmas are being used in a wide range of new applications in aeronautics, active flow control, heat transfer reduction, plasma-assisted ignition and combustion, noise suppression, and power generation. Industrial applications may be found in pollution control, materials surface treatment, and water purification. In order for these plasma processes to become practical, efficient means of ionization are necessary. A primary challenge for these applications is to create a desired non-equilibrium plasma in air by preventing the discharge from transitioning into an arc. Of particular interest is the impact on simulations and experimental data with and without detailed consideration of non-equilibrium effects, and the consequences of neglecting non-equilibrium. This presentation will provide an assessment of the presence and influence of non-equilibrium phenomena for various aerospace needs and applications. Specific examples to be considered will include the forward energy deposition of laser-induced non-equilibrium plasmoids for sonic boom mitigation, weakly ionized flows obtained from pulsed nanosecond discharges for an annular Hall type MHD generator duct for turbojet energy bypass, and fundamental mechanisms affecting the design and operation of novel plasma-assisted reactive systems in dielectric liquids (water purification, in-pipe modification of fuels, etc.).
Open Boundary Conditions for Dissipative MHD
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Resistive MHD jet simulations with large resistivity
Cemeljic, Miljenko; Vlahakis, Nektarios; Tsinganos, Kanaris
2009-01-01
Axisymmetric resistive MHD simulations for radially self-similar initial conditions are performed, using the NIRVANA code. The magnetic diffusivity could occur in outflows above an accretion disk, being transferred from the underlying disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We introduce, in addition to the classical magnetic Reynolds number Rm, which measures the importance of resistive effects in the induction equation, a new number Rb, which measures the importance of the resistive effects in the energy equation. We find two distinct regimes of solutions in our simulations. One is the low-resistivity regime, in which results do not differ much from ideal-MHD solutions. In the high-resistivity regime, results seem to show some periodicity in time-evolution, and depart significantly from the ideal-MHD case. Whether this departure is caused by numerical or physical reasons is of considerable interest for nu...
Hamiltonian and action formalisms for two-dimensional gyroviscous MHD
Morrison, P J; Acevedo, R
2014-01-01
A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD) model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.
Equations of state for self-excited MHD generator studies
Rogers, F.J.; Ross, M.; Haggin, G.L.; Wong, L.K.
1980-02-26
We have constructed a state-of-the-art equation of state (EOS) for argon covering the temperature density range attainable by currently proposed self-excited MHD generators. The EOS for conditions in the flow channel was obtained primarily by a non-ideal plasma code (ACTEX) that is based on a many body activity expansion. For conditions in the driver chamber the EOS was primarily obtained from a fluid code (HDFP) that calculates the fluid properties from perturbation theory based on the insulator interatomic pair potential but including electronic excitations. The results are in agreement with several sets of experimental data in the 0.6 - 91 GPa pressure range.
Porting a Hall MHD Code to a Graphic Processing Unit
Dorelli, John C.
2011-01-01
We present our experience porting a Hall MHD code to a Graphics Processing Unit (GPU). The code is a 2nd order accurate MUSCL-Hancock scheme which makes use of an HLL Riemann solver to compute numerical fluxes and second-order finite differences to compute the Hall contribution to the electric field. The divergence of the magnetic field is controlled with Dedner?s hyperbolic divergence cleaning method. Preliminary benchmark tests indicate a speedup (relative to a single Nehalem core) of 58x for a double precision calculation. We discuss scaling issues which arise when distributing work across multiple GPUs in a CPU-GPU cluster.
MHD-effects in a turbulent medium of nonuniform density
Vaynshteyn, S.I.
1978-01-01
Turbulence in a medium of nonuniform density, such as the convective solar layer, is analyzed with the assumption that Del rho = rho lambda (exponential stratification). Considered are first the simplest case of a quasi-isotropic turbulence, then addition of a scalar factor such as the temperature, and finally anisotropic turbulence. The magnetic field and MHD-effects are then calculated without diffusion, and with two-dimensional turbulence as a special case. Also the values of the essential parameters in this problem are estimated. 7 references.
国义军; 代光月; 桂业伟; 童福林; 邱波; 刘骁
2015-01-01
A detailed description of the methods used to evaluate the non-equilibrium and catalytic surface effects on thermal environment of the reentry vehicles is presented.There are lots of engineering prediction models for non-equilibrium effects since 1950s,most of them based on the hypothesis that the boundary layer is frozen and recombination of the dissociated gases only occurs at the wall surface depending on the wall catalytic properties.Five widely used meth-ods for one same question are selected and compared,and their results are quite different from one another.Based on recently numerical results and theoretical analysis,a new model which takes chemical reactions both in boundary layer and on body surface into account simultaneously is proposed in this paper.It is shown that the chemical state of the boundary layer is controlled mainly by the recombination that takes place near the wall,which suggests representing the gas-phase reaction by an equivalent surface reaction with all state variables specified by surface conditions.The equivalent surface reaction method then can be extended to the case in which the surface has an arbitrary catalytic.The results obtained by this proposed model agree quite well with the flying test data of STS-2 space shuttle.From the calculation results,the non-equilibri-um effect often appears when the vehicle flight altitude is above 50 km at atmosphere accompa-nied by the rarefied flow effects,and the non-equilibrium effect mainly occurs near the nosetip regions.At the place far down the nosetip,the chemical state of the boundary layer will transfer to equilibrium.%综合比较了现有的非平衡热环境工程计算方法，发现采用不同方法给出的计算结果相互之间差别较大。本文基于边界层中的原子复合反应主要发生在靠近壁面薄层内的特点，将边界层中的气相反应等价到表面上，建立了同时考虑边界层内非平衡反应和表面催化特性的非平衡边界层气
The role of pressure flattening in calculating tearing mode stability
Ham, C. J.; Connor, J. W.; Cowley, S. C.; Hastie, R. J.; Hender, T. C.; Liu, Y. Q.
2013-12-01
Calculations of tearing mode stability in tokamaks split conveniently into one in an external region, where marginally stable ideal magnetohydrodynamics (MHD) is applicable, and one in a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter Δ‧. Axisymmetric pressure and current perturbations localized around the rational surface significantly alter Δ‧. Equations governing the changes in the external solution and Δ‧ are derived for arbitrary perturbations in axisymmetric toroidal geometry. These equations can be used in two ways: (i) the Δ‧ can be calculated for a physically occurring perturbation to the pressure or current; (ii) alternatively we can use these equations to calculate Δ‧ for profiles with a pressure gradient at the rational surface in terms of the value when the perturbation removes this gradient. It is the second application we focus on here since resistive magnetohydrodynamics (MHD) codes do not contain the appropriate layer physics and therefore cannot predict stability for realistic hot plasma directly. They can, however, be used to calculate Δ‧. Existing methods (Ham et al 2012 Plasma Phys. Control. Fusion 54 025009) for extracting Δ‧ from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface and favourable average curvature because of the Glasser stabilizing effect (Glasser et al 1975 Phys. Fluids 18 875). To overcome this difficulty we introduce a specific artificial pressure flattening function that allows the earlier approach to be used. The technique is first tested numerically in cylindrical geometry with an artificial favourable curvature. Its application to toroidal geometry is then demonstrated using the toroidal tokamak tearing mode stability code T7 (Fitzpatrick et al 1993 Nucl. Fusion 33 1533) which employs an approximate analytic equilibrium. The prospects for applying this
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
He, Qingyun; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; Feng, Jingchao
2015-12-15
Highlights: • A 3D PISO-MHD was implemented on Kepler-class graphics processing units (GPUs) using CUDA technology. • A consistent and conservative scheme is used in the code which was validated by three basic benchmarks in a rectangular and round ducts. • Parallelized of CPU and GPU acceleration were compared relating to single core CPU in MHD problems and non-MHD problems. • Different preconditions for solving MHD solver were compared and the results showed that AMG method is better for calculations. - Abstract: The pressure-implicit with splitting of operators (PISO) magnetohydrodynamics MHD solver of the couple of Navier–Stokes equations and Maxwell equations was implemented on Kepler-class graphics processing units (GPUs) using the CUDA technology. The solver is developed on open source code OpenFOAM based on consistent and conservative scheme which is suitable for simulating MHD flow under strong magnetic field in fusion liquid metal blanket with structured or unstructured mesh. We verified the validity of the implementation on several standard cases including the benchmark I of Shercliff and Hunt's cases, benchmark II of fully developed circular pipe MHD flow cases and benchmark III of KIT experimental case. Computational performance of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms and meshes. The resulted showed that a GPU (GTX 770) can outperform a server-class 4-core, 8-thread CPU (Intel Core i7-4770k) by a factor of 2 at least.
MHD Field Line Resonances and Global Modes in Three-Dimensional Magnetic Fields
C.Z. Cheng
2002-05-30
By assuming a general isotropic pressure distribution P = P (y,a), where y and a are three-dimensional scalar functions labeling the field lines with B = -y x -a, we have derived a set of MHD eigenmode equations for both global MHD modes and field line resonances (FLR). Past MHD theories are restricted to isotropic pressures with P = P (y only). The present formulation also allows the plasma mass density to vary along the field line. The linearized ideal-MHD equations are cast into a set of global differential equations from which the field line resonance equations of the shear Alfvin waves and slow magnetosonic modes are naturally obtained for general three-dimensional magnetic field geometries with flux surfaces. Several new terms associated with the partial derivative of P with respect to alpha are obtained. In the FLR equations, a new term is found in the shear Alfvin FLR equation due to the geodesic curvature and the pressure gradient in the poloidal flux surface. The coupling between the shear Alfvin waves and the magnetosonic waves is through the combined effects of geodesic magnetic field curvature and plasma pressure as previously derived. The properties of the FLR eigenfunctions at the resonance field lines are investigated, and the behavior of the FLR wave solutions near the FLR surface are derived. Numerical solutions of the FLR equations for three-dimensional magnetospheric fields in equilibrium with high plasma pressure will be presented in a future publication.
Initial Studies of Validation of MHD Models for MST Reversed Field Pinch Plasmas
Jacobson, C. M.; Almagri, A. F.; Craig, D.; McCollam, K. J.; Reusch, J. A.; Sauppe, J. P.; Sovinec, C. R.; Triana, J. C.
2015-11-01
Quantitative validation of visco-resistive MHD models for RFP plasmas takes advantage of MST's advanced diagnostics. These plasmas are largely governed by MHD relaxation activity, so that a broad range of validation metrics can be evaluated. Previous nonlinear simulations using the visco-resistive MHD code DEBS at Lundquist number S = 4 ×106 produced equilibrium relaxation cycles in qualitative agreement with experiment, but magnetic fluctuation amplitudes b~ were at least twice as large as in experiment. The extended-MHD code NIMROD previously suggested that a two-fluid model may be necessary to produce b~ in agreement with experiment. For best comparisons with DEBS and to keep computational expense tractable, NIMROD is run in single-fluid mode at low S. These simulations are complemented by DEBS at higher S in cylindrical geometry, which will be used to examine b~ as a function of S. Experimental measurements are used with results from these simulations to evaluate validation metrics. Convergence tests of previous high S DEBS simulations are also discussed, along with benchmarking of DEBS and NIMROD with the SPECYL and PIXIE3D codes. Work supported by U.S. DOE and NSF.
Cosmic-ray pitch-angle scattering in imbalanced MHD turbulence simulations
Weidl, Martin S; Teaca, Bogdan; Schlickeiser, Reinhard
2015-01-01
Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.
The entropy production at the multi-fluid MHD solar wind termination shock
Fahr, Hans Joerg; Siewert, Mark [Argelander Institut fuer Astronomie, Universitaet Bonn, Auf dem Huegel 71, 53121 Bonn (Germany)
2014-07-01
It has become evident meanwhile that the MHD solar wind termination shock needs a multifluid theoretical approach to adequately describe the intertwisted physical complexity in the interaction between fields and particles. In this approach here we treat the passage of three separate fluids over the MHD shock, namely solar wind protons, pickup protons and electrons. Connected with the different downstream pressures of three fluids we also calculate the different fluid entropies that are produced at the shock passage. As we can show the most relevant contribution to the total particle entropy is connected with the electron pressure which actually by far dominates the downstream plasma pressure.
Absence of complete finite-Larmor-radius stabilization in extended MHD.
Zhu, P; Schnack, D D; Ebrahimi, F; Zweibel, E G; Suzuki, M; Hegna, C C; Sovinec, C R
2008-08-22
The dominant finite-Larmour-radius (FLR) stabilization effects on interchange instability can be retained by taking into account the ion gyroviscosity or the generalized Ohm's law in an extended MHD model. However, recent simulations and theoretical calculations indicate that complete FLR stabilization of the interchange mode may not be attainable by ion gyroviscosity or the two-fluid effect alone in the framework of extended MHD. For a class of plasma equilibria in certain finite-beta or nonisentropic regimes, the critical wave number for complete FLR stabilization tends toward infinity.
MHD Jets in inhomogeneous media
S. O´Sullivan
2002-01-01
Full Text Available Presentamos simulaciones de la propagaci on de jets moleculares no-adiab aticos en un medio ambiente inhomog eneo. Los jets tienen condiciones descritos por un modelo de jet MHD en el cual la forma de las l neas magn eticas se prescribe cerca de la fuente. Per les de densidad ambiental fueron elegidos para representar la zona de transici on entre las regiones exteriores de una nube molecular y el medio interestelar. Escalamos las tasas de enfriamiento at omico y molecular a niveles apropriados para resolver todas las escalas espaciales apropriadas. Con la inclusi on de variabilidad de la fuente, las simulaciones reproducen varias caracter sticas observacionales de jets moleculares, entre ellas las cavidades moleculares. Adicionalmente, encontramos similitudes entre teor a y observaci on para la fracci on de ionizaci on a lo largo del jet. Encontramos que la extensi on lateral de las super cies de trabajo internas son sensibles al medio ambiente. Tambi en presentamos resultados preliminares para un m etodo de calcular mapas de emisi on en l neas usando solamente variables fundamentales de estado que parecen reproducir la emisi on lamentosa de Balmer en frentes de choque.
MHD Integrated Topping Cycle Project
1992-02-01
This fourteenth quarterly technical progress report of the MHD Integrated Topping Cycle Project presents the accomplishments during the period November 1, 1990 to January 31, 1991. Testing of the High Pressure Cooling Subsystem electrical isolator was completed. The PEEK material successfully passed the high temperature, high pressure duration tests (50 hours). The Combustion Subsystem drawings were CADAM released. The procurement process is in progress. An equipment specification and RFP were prepared for the new Low Pressure Cooling System (LPCS) and released for quotation. Work has been conducted on confirmation tests leading to final gas-side designs and studies to assist in channel fabrication.The final cathode gas-side design and the proposed gas-side designs of the anode and sidewall are presented. Anode confirmation tests and related analyses of anode wear mechanisms used in the selection of the proposed anode design are presented. Sidewall confirmation tests, which were used to select the proposed gas-side design, were conducted. The design for the full scale CDIF system was completed. A test program was initiated to investigate the practicality of using Avco current controls for current consolidation in the power takeoff (PTO) regions and to determine the cause of past current consolidation failures. Another important activity was the installation of 1A4-style coupons in the 1A1 channel. A description of the coupons and their location with 1A1 channel is presented herein.
Nonlinear tearing mode study using the almost ideal magnetohydrodynamics (MHD) constraint
Ren, C.; Callen, J.D. [Univ. of Wisconsin, Madison, WI (United States); Jensen, T.H. [General Atomics, San Diego, CA (United States)
1998-12-31
The tearing mode is an important resistive magnetohydrodynamics (MHD) mode. It perturbs the initial equilibrium magnetic flux surfaces through magnetic field line reconnection to form new flux surfaces with magnetic islands. In the study of the tearing mode, usually the initial equilibria are one dimensional with two ignorable coordinates and the perturbed equilibria are two dimensional with one ignorable coordinate. The tearing mode can be linearly unstable and its growth saturates at a fine amplitude. The neoclassical tearing mode theory shows that the mode can be nonlinearly driven by the bootstrap current even when it is linearly stable to the classical tearing mode. It is important to study the nonlinear behavior of the tearing mode. As an intrinsically nonlinear approach, the use of the almost ideal MHD constraint is suited to study the nonlinear properties of the tearing mode. In this paper, as a validation of the method, the authors study two characteristics of the tearing mode using the almost ideal MHD constraint: (1) the linear stability condition for the initial one dimensional equilibrium; and (2) the final saturation level for the unstable case. In this work, they only consider the simplest case where no gradient of pressure or current density exists at the mode resonant surface.
A New MHD Code with Adaptive Mesh Refinement and Parallelization for Astrophysics
Jiang, R L; Chen, P F
2012-01-01
A new code, named MAP, is written in Fortran language for magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for computing the MHD part, namely, modified Mac Cormack Scheme (MMC), Lax-Friedrichs scheme (LF) and weighted essentially non-oscillatory (WENO) scheme. All of them are second order, two-step, component-wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann solvers are also equipped. A high resolution can be achieved by the hierarchical block-structured AMR mesh. We use the extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced by the scheme in the magnetic induction equation. The numerical algorithms for the non-ideal terms, e.g., the resistivity and the thermal conduction, are also equipped in the MAP code. The details of the AMR and MPI algorithms are d...
Non-linear interaction between high energy ions and MHD-modes
Bergkvist, Tommy
2001-12-01
When heating a fusion plasma with ICRE or NBI a non-Maxwellian distribution function with high energy ions is created. Ions which are in resonance with a MHD mode will interact with the electric field from the mode and in some circumstances energy will flow from the particles to the mode or opposite. A quasi-linear model for the interaction between high energy ions and a MHD mode has been developed. To solve the time evolution of the MHD mode a module has been implemented into the Monte Carlo code FIDO, which is used for calculating a 3-dimensional distribution function. The model has been tested for an internal kink mode during fishbone oscillations.
Intensity contrast from MHD simulations and from HINODE observations
Afram, N; Solanki, S K; Schuessler, M; Lagg, A; Voegler, A
2010-01-01
Changes in the solar surface area covered by small-scale magnetic elements are thought to cause long-term changes in the solar spectral irradiance, which are important for determining the impact on Earth's climate. To study the effect of small-scale magnetic elements on total and spectral irradiance, we derive their contrasts from 3-D MHD simulations of the solar atmosphere. Such calculations are necessary since measurements of small-scale flux tube contrasts are confined to a few wavelengths and suffer from scattered light and instrument defocus, even for space observations. To test the contrast calculations, we compare rms contrasts from simulations with those obtained with the broad-band filter imager mounted on the Solar Optical Telescope (SOT) onboard the Hinode satellite and also analyse centre-to-limb variations (CLV). The 3-D MHD simulations include the interaction between convection and magnetic flux tubes. They have been run with non-grey radiative transfer using the MURaM code. Simulations have an ...
3D Equilibrium Reconstructions in DIII-D
Lao, L. L.; Ferraro, N. W.; Strait, E. J.; Turnbull, A. D.; King, J. D.; Hirshman, H. P.; Lazarus, E. A.; Sontag, A. C.; Hanson, J.; Trevisan, G.
2013-10-01
Accurate and efficient 3D equilibrium reconstruction is needed in tokamaks for study of 3D magnetic field effects on experimentally reconstructed equilibrium and for analysis of MHD stability experiments with externally imposed magnetic perturbations. A large number of new magnetic probes have been recently installed in DIII-D to improve 3D equilibrium measurements and to facilitate 3D reconstructions. The V3FIT code has been in use in DIII-D to support 3D reconstruction and the new magnetic diagnostic design. V3FIT is based on the 3D equilibrium code VMEC that assumes nested magnetic surfaces. V3FIT uses a pseudo-Newton least-square algorithm to search for the solution vector. In parallel, the EFIT equilibrium reconstruction code is being extended to allow for 3D effects using a perturbation approach based on an expansion of the MHD equations. EFIT uses the cylindrical coordinate system and can include the magnetic island and stochastic effects. Algorithms are being developed to allow EFIT to reconstruct 3D perturbed equilibria directly making use of plasma response to 3D perturbations from the GATO, MARS-F, or M3D-C1 MHD codes. DIII-D 3D reconstruction examples using EFIT and V3FIT and the new 3D magnetic data will be presented. Work supported in part by US DOE under DE-FC02-04ER54698, DE-FG02-95ER54309 and DE-AC05-06OR23100.
Linear Two-Dimensional MHD of Accretion Disks: Crystalline structure and Nernst coefficient
Montani, Giovanni
2009-01-01
We analyse the two-dimensional MHD configurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline structure outlined in Coppi (2005), dealing with a local model too, when a specific accretion rate is taken into account. We limit our attention to the linearised MHD formulation of the electromagnetic back-reaction characterising the equilibrium, by fixing the structure of the radial, vertical and azimuthal profiles. Since we deal with toroidal currents only, the consistency of the model is ensured by the presence of a small collisional effect, phenomenologically described by a non-zero constant Nernst coefficient (thermal power of the plasma). Such an effect provides a proper balance of the electron force equation via non zero temperature gradients, related directly to the radial and vertical velocity components. We show that the obtained profile has the typical oscillating feat...
Extension of the MURaM radiative MHD code for coronal simulations
Rempel, Matthias
2016-01-01
We present a new version of the MURaM radiative MHD code that allows for simulations spanning from the upper convection zone into the solar corona. We implemented the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction and an equilibrium ionization equation of state. We artificially limit the coronal Alfv{\\'e}n and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantify the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be...
Preliminary evaluation of the role of K2S in MHD hot stream seed recovery
Bennett, J. E.; Kohl, F. J.
1979-01-01
Results are presented for recent analytical and experimental studies of the role of K2S in MHD hot stream seed recovery. The existing thermodynamic data base was found to contain large uncertainties and to be nonexistent for vapor phase K2S. Knudsen cell mass spectrometric experiments were undertaken to determine the vapor species in equilibrium with K2S(c). K atoms and S2 molecules ere found to be the major vapor phase species in vacuum, accounting for greater than 99 percent of the vapor phase. Combustion gas deposition studies using No. 2 Diesel fuel were also undertaken and revealed that condensed phase K2SO3 may potentially be an important compound in the MHD stream at near-stoichiometric combustion.
Radiation-driven MHD systems for space applications
Lee, J. H.; Jalufka, N. W.
High-power radiation such as concentrated solar or high-power laser radiation is considered as a driver for magnetohydrodynamic (MHD) systems which could be developed for efficient power generation and propulsion in space. Eight different systems are conceivable since the MHD systems can be classified in two: plasma and liquid-metal MHD's. Each of these systems is reviewed and solar- (or laser-) driven MHD thrusters are proposed.
The mathematical theory of reduced MHD models for fusion plasmas
Guillard, Hervé
2015-01-01
The derivation of reduced MHD models for fusion plasma is here formulated as a special instance of the general theory of singular limit of hyperbolic system of PDEs with large operator. This formulation allows to use the general results of this theory and to prove rigorously that reduced MHD models are valid approximations of the full MHD equations. In particular, it is proven that the solutions of the full MHD system converge to the solutions of an appropriate reduced model.
Simulation of wave interactions with MHD
Batchelor, D; Bernholdt, D; Berry, L; Elwasif, W; Jaeger, E; Keyes, D; Klasky, S [Oak Ridge National Laboratory, Oak Ridge, TN 37331 (United States); Alba, C; Choi, M [General Atomics, San Diego, CA 92186 (United States); Bateman, G [Lehigh University, Bethlehem, PA 18015 (United States); Bonoli, P [Plasma Science and Fusion Center, MTT, Cambridge, MA 02139 (United States); Bramley, R [Indiana University, Bloomington, IN 47405 (United States); Breslau, J; Chance, M; Chen, J; Fu, G; Jardin, S [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Harvey, R [CompX, Del Mar, CA 92014 (United States); Jenkins, T [University of Wisconsin, Madison, WI 53706 (United States); Kruger, S [Tech-X, Boulder, CO 80303 (United States)], E-mail: batchelordb@ornl.gov (and others)
2008-07-15
The broad scientific objectives of the SWIM (Simulation 01 Wave Interaction with MHD) project are twofold: (1) improve our understanding of interactions that both radio frequency (RF) wave and particle sources have on extended-MHD phenomena, and to substantially improve our capability for predicting and optimizing the performance of burning plasmas in devices such as ITER: and (2) develop an integrated computational system for treating multiphysics phenomena with the required flexibility and extensibility to serve as a prototype for the Fusion Simulation Project. The Integrated Plasma Simulator (IPS) has been implemented. Presented here are initial physics results on RP effects on MHD instabilities in tokamaks as well as simulation results for tokamak discharge evolution using the IPS.
Simulation of wave interactions with MHD
Batchelor, Donald B [ORNL; Abla, G [General Atomics, San Diego; Bateman, Glenn [Lehigh University, Bethlehem, PA; Bernholdt, David E [ORNL; Berry, Lee A [ORNL; Bonoli, P. [Massachusetts Institute of Technology (MIT); Bramley, R [Indiana University; Breslau, J. [Princeton Plasma Physics Laboratory (PPPL); Chance, M. [Princeton Plasma Physics Laboratory (PPPL); Chen, J. [Princeton Plasma Physics Laboratory (PPPL); Choi, M. [General Atomics; Elwasif, Wael R [ORNL; Fu, GuoYong [Princeton Plasma Physics Laboratory (PPPL); Harvey, R. W. [CompX, Del Mar, CA; Jaeger, Erwin Frederick [ORNL; Jardin, S. C. [Princeton Plasma Physics Laboratory (PPPL); Jenkins, T [University of Wisconsin; Keyes, David E [Columbia University; Klasky, Scott A [ORNL; Kruger, Scott [Tech-X Corporation; Ku, Long-Poe [Princeton Plasma Physics Laboratory (PPPL); Lynch, Vickie E [ORNL; McCune, Douglas [Princeton Plasma Physics Laboratory (PPPL); Ramos, J. [Massachusetts Institute of Technology (MIT); Schissel, D. [General Atomics; Schnack, [University of Wisconsin; Wright, J. [Massachusetts Institute of Technology (MIT)
2008-07-01
The broad scientific objectives of the SWIM (Simulation of Wave Interaction with MHD) project are twofold: (1) improve our understanding of interactions that both radio frequency (RF) wave and particle sources have on extended-MHD phenomena, and to substantially improve our capability for predicting and optimizing the performance of burning plasmas in devices such as ITER: and (2) develop an integrated computational system for treating multiphysics phenomena with the required flexibility and extensibility to serve as a prototype for the Fusion Simulation Project. The Integrated Plasma Simulator (IPS) has been implemented. Presented here are initial physics results on RF effects on MHD instabilities in tokamaks as well as simulation results for tokamak discharge evolution using the IPS.
Vogt, Natalja; Khaikin, Leonid S; Grikina, Olga E; Rykov, Anatolii N; Vogt, Jürgen
2008-08-21
Thymine is one of the nucleobases which forms the nucleic acid (NA) base pair with adenine in DNA. The study of molecular structure and dynamics of nucleobases can help to understand and explain some processes in biological systems and therefore it is of interest. Because the scattered intensities on the C, N, and O atoms as well as some bond lengths in thymine are close to each other the structural problem cannot been solved by the gas phase electron diffraction (GED) method alone. Therefore the rotational constants from microvawe (MW) studies and differences in the groups of N-C, C=O, N-H, and C-H bond lengths from MP2 (full)/cc-pVQZ calculations were used as supplementary data. The analysis of GED data was based on the C(s) molecular symmetry according to results of the structure optimizations at the MP2 (full) level using 6-311G (d,p), cc-pVTZ, and cc-pVQZ basis sets confirmed by vibrational frequency calculations with 6-311G (d,p) and cc-pVTZ basis sets. Mean-square amplitudes as well as harmonic and anharmonic vibrational corrections to the internuclear distances (r(e)-r(a)) and to the rotational constants (B(e)(k)-B(0)(k), where k = A, B, C) were calculated from the quadratic (MP2 (full)/cc-pVTZ) and cubic (MP2 (full)/6-311G (d,p)) force constants (the latter were used only for anharmonic corrections). The harmonic force field was scaled using published IR and Raman spectra of the parent and N1,N3-dideuterated species, which were for the first time completely assigned in the present work. The main equilibrium structural parameters of the thymine molecule determined from GED data supplemented by MW rotational constants and results of MP2 calculations are the following (bond lengths in Angstroms and bond angles in degrees with 3sigma in parentheses): r(e) (C5=C6) = 1.344 (16), r(e) (C5-C9) = 1.487 (8), r(e) (N1-C6) = 1.372 (3), r(e) (N1-C2) = 1.377 (3), r(e) (C2-N3) = 1.378 (3), r(e) (N3-C4) = 1.395 (3), r(e) (C2=O7) = 1.210 (1), r(e) (C4=O8) = 1.215 (1
Equilibrium Tail Distribution Due to Touschek Scattering
Nash,B.; Krinsky, S.
2009-05-04
Single large angle Coulomb scattering is referred to as Touschek scattering. In addition to causing particle loss when the scattered particles are outside the momentum aperture, the process also results in a non-Gaussian tail, which is an equilibrium between the Touschek scattering and radiation damping. Here we present an analytical calculation for this equilibrium distribution.
An experimentally constrained MHD model for a collisional, rotating plasma column
Wright, A. M.; Qu, Z. S.; Caneses, J. F.; Hole, M. J.
2017-02-01
A steady-state single fluid MHD model which describes the equilibrium of plasma parameters in a collisional, rotating plasma column with temperature gradients and a non-uniform externally applied magnetic field is developed. Two novel methods of simplifying the governing equations are introduced. Specifically, a ‘radial transport constraint’ and an ordering argument are applied. The reduced system is subsequently solved to yield the equilibrium of macroscopic plasma parameters in the bulk region of the plasma. The model is benchmarked by comparing these solutions to experimental measurements of axial velocity and density for a hydrogen plasma in the converging-field experiment MAGPIE and overall a good agreement is observed. The plasma equilibrium is determined by the interaction of a density gradient, due to a temperature gradient, with an electric field. The magnetic field and temperature gradient are identified as key parameters in determining the flow profile, which may be important considerations in other applications.
Euler potentials for the MHD Kamchatnov-Hopf soliton solution
Semenov, VS; Korovinski, DB; Biernat, HK
2002-01-01
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invarian
Safety and reliability in superconducting MHD magnets
Laverick, C.; Powell, J.; Hsieh, S.; Reich, M.; Botts, T.; Prodell, A.
1979-07-01
This compilation adapts studies on safety and reliability in fusion magnets to similar problems in superconducting MHD magnets. MHD base load magnet requirements have been identified from recent Francis Bitter National Laboratory reports and that of other contracts. Information relevant to this subject in recent base load magnet design reports for AVCO - Everett Research Laboratories and Magnetic Corporation of America is included together with some viewpoints from a BNL workshop on structural analysis needed for superconducting coils in magnetic fusion energy. A summary of design codes used in large bubble chamber magnet design is also included.
Explosively-driven magnetohydrodynamic (MHD) generator studies
Agee, F.J.; Lehr, F.M. [Phillips Lab., Kirtland AFB, NM (United States); Vigil, M.; Kaye, R. [Sandia National Labs., Albuquerque, NM (United States); Gaudet, J.; Shiffler, D. [New Mexico Univ., Albuquerque, NM (United States)
1995-08-01
Plasma jet generators have been designed and tested which used an explosive driver and shocktube with a rectangular cross section that optimize the flow velocity and electrical conductivity. The latest in a series of designs has been tested using a reactive load to diagnose the electrical properties of the MHD generator/electromagnet combination. The results of these tests indicate that the plasma jet/MHD generator design does generate a flow velocity greater than 25 km/s and produces several gigawatts of pulsed power in a very small package size. A larger, new generator design is also presented.
Summary report for ITER Task-T19: MHD pressure drop and heat transfer study for liquid metal systems
Reed, Claude B.; Hua, Thanh Q.; Natesan, Ken; Kirillov, Igor R.; Vitkovski, Ivan V.; Anisimov, Aleksandr M.
1995-03-01
A key feasibility issue for the ITER Vanadium/Lithium breeding blanket is the question of insulator coatings. Design calculations show that an electrically insulating layer is necessary to maintain an acceptably low MHD pressure drop. To begin experimental investigations of the MHD performance of candidate insulator materials and the technology for putting them in place, a new test section was prepared. Aluminum oxide was chosen as the first candidate insulating material because it may be used in combination with NaK in the ITER vacuum vessel and/or the divertor. Details on the methods used to produce the aluminum oxide layer as well as the microstructures of the coating and the aluminide sublayer are presented and discussed. The overall MHD pressure drop, local MHD pressure gradient, local transverse MHD pressure difference, and surface voltage distributions in both the circumferential and the axial directions are reported and discussed. The positive results obtained here for high-temperature NaK have two beneficial implications for ITER. First, since NaK may be used in the vacuum vessel and/or the divertor, these results support the design approach of using electrically insulating coatings to substantially reduce MHD pressure drop. Secondly, while Al2O3/SS is not the same coating/base material combination which would be used in the advanced blanket, this work nonetheless shows that it is possible to produce a viable insulating coating which is stable in contact with a high temperature alkali metal coolant.
Towards a Scalable Fully-Implicit Fully-coupled Resistive MHD Formulation with Stabilized FE Methods
Shadid, J N; Pawlowski, R P; Banks, J W; Chacon, L; Lin, P T; Tuminaro, R S
2009-06-03
This paper presents an initial study that is intended to explore the development of a scalable fully-implicit stabilized unstructured finite element (FE) capability for low-Mach-number resistive MHD. The discussion considers the development of the stabilized FE formulation and the underlying fully-coupled preconditioned Newton-Krylov nonlinear iterative solver. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by the Newton linearization, fully-coupled algebraic multilevel preconditioners are employed. Verification results demonstrate the expected order-of-acuracy for the stabilized FE discretization of a 2D vector potential form for the steady and transient solution of the resistive MHD system. In addition, this study puts forth a set of challenging prototype problems that include the solution of an MHD Faraday conduction pump, a hydromagnetic Rayleigh-Bernard linear stability calculation, and a magnetic island coalescence problem. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.
Effects of water molecules of Ar-Cs MHD disk generator operated with strong MHD interaction
Ishikawa, M.; Kosugi, A.; Inui, Y.; Kabashima, S.
1998-07-01
Effects of water molecule impurity are studied on performance of a disk type MHD generator operated with Ar-Cs weakly ionized plasma. To reveal phenomena for a wide range of operation conditions, time-dependent one-dimensional analyses are carried out, where an up-wind, second order Chakravarthy TVD scheme is applied for the gasdynamics, while a Galerkin FEM is used for the electrodynamics. A simplified model is used for the water molecule impurity, where total effects of nonelastic collision between electrons and water molecules are estimated by the collision loss factor of electrons and also the electron momentum-transfer collision frequency is taken into account. The collision loss factor of electrons and the electron momentum-transfer collision frequency are taken from references, and the loss factor is assumed to be 700 independently of the electron temperature. On the Fuji-1 facilities at Tokyo Institute Technology, Japan, series of experiment A4105 were carried out with the Disk F-4 generator. Ar was heated with the heat-exchanger heated by the natural gas-air combustion and the metal cesium was used as the seeding material, while SCM maintained the magnetic field of 4.7 T at the center of disk and the very strong MHD interaction was realized. The thermal input was about 3 MW, the electrical output was about 500 kW with the enthalpy extraction ratio of about 17%. The numerical analyses have shown that the water molecule enhances the ionization instability at the low voltage loading because of insufficient Joule heating for electrons. The generator performance is degraded and the strong MHD interaction between the unstable plasma and the flow field induces slow and fast moving shock waves, leading to the very complicated flow field. The fast and slow moving shocks collide with each other, merge into a sharp shock moving downward, and then the shock front moves back slightly to maintain the pressure balance, collides again with another weak moving shock, and
Ion exchange equilibrium constants
Marcus, Y
2013-01-01
Ion Exchange Equilibrium Constants focuses on the test-compilation of equilibrium constants for ion exchange reactions. The book first underscores the scope of the compilation, equilibrium constants, symbols used, and arrangement of the table. The manuscript then presents the table of equilibrium constants, including polystyrene sulfonate cation exchanger, polyacrylate cation exchanger, polymethacrylate cation exchanger, polysterene phosphate cation exchanger, and zirconium phosphate cation exchanger. The text highlights zirconium oxide anion exchanger, zeolite type 13Y cation exchanger, and
Pressure, Chaotic Magnetic Fields and MHD Equilibria
S.R. Hudson & N. Nakajima
2010-05-12
Analyzes of plasma behavior often begin with a description of the ideal magnetohydrodynamic equilibrium, this being the simplest model capable of approximating macroscopic force balance. Ideal force balance is when the pressure gradient is supported by the Lorentz force, ∇p = j x B. We discuss the implications of allowing for a chaotic magnetic field on the solutions to this equation. We argue that the solutions are pathological and not suitable for numerical calculations. If the pressure and magnetic Field are continuous, the only non-trivial solutions have an uncountable infinity of discontinuities in the pressure gradient and current. The problems arise from the arbitrarily small length scales in the structure of the field, and the consequence of ideal force balance that the pressure is constant along the Field-lines, B • ∇p = 0. A simple method to ameliorate the singularities is to include a small but Finite perpendicular diffusion. A self-consistent set of equilibrium equations is described and some algorithmic approaches aimed at solving these equations are discussed.
On the characterization of magnetic reconnection in global MHD simulations
T. V. Laitinen
2006-11-01
Full Text Available The conventional definition of reconnection rate as the electric field parallel to an x-line is problematic in global MHD simulations for several reasons: the x-line itself may be hard to find in a non-trivial geometry such as at the magnetopause, and the lack of realistic resistivity modelling leaves us without reliable non-convective electric field. In this article we describe reconnection characterization methods that avoid those problems and are practical to apply in global MHD simulations. We propose that the reconnection separator line can be identified as the region where magnetic field lines of different topological properties meet, rather than by local considerations. The global convection associated with reconnection is then quantified by calculating the transfer of mass, energy or magnetic field across the boundary of closed and open field line regions. The extent of the diffusion region is determined from the destruction of electromagnetic energy, given by the divergence of the Poynting vector. Integrals of this energy conversion provide a way to estimate the total reconnection efficiency.
Two-fluid MHD Regime of Drift Wave Instability
Yang, Shang-Chuan; Zhu, Ping; Xie, Jin-Lin; Liu, Wan-Dong
2015-11-01
Drift wave instabilities contribute to the formation of edge turbulence and zonal flows, and thus are believed to play essential roles in the anomalous transport processes in tokamaks. Whereas drift waves are generally assumed to be local and electrostatic, experiments have often found regimes where the spatial scales and the magnetic components of drift waves approach those of magnetohydrodynamic (MHD) processes. In this work we study such a drift wave regime in a cylindrical magnetized plasma using a full two-fluid MHD model implemented in the NIMROD code. The linear dependency of growth rates on resistivity and the dispersion relation found in the NIMROD calculations qualitatively agree with theoretical analysis. As the azimuthal mode number increases, the drift modes become highly localized radially; however, unlike the conventional local approximation, the radial profile of the drift mode tends to shift toward the edge away from the center of the density gradient slope, suggesting the inhomogeneity of two-fluid effects. Supported by National Natural Science Foundation of China Grant 11275200 and National Magnetic Confinement Fusion Science Program of China Grant 2014GB124002.
Hodograph method in MHD orthogonal fluid flows
P. V. Nguyen
1992-01-01
Full Text Available Equations for steady plane MHD orthogonal flows of a viscous incompressible fluid of finite electrical conductivity are recast in the hodograph plane by using the Legendre transform function of the streamfunction. Three examples are studied to illustrate the developed theory. Solutions and geometries for these examples are determined.
Principal characteristics of SFC type MHD generator
Kayukawa, Naoyuki; Oikawa, Shun-ichi; Aoki, Yoshiaki; Seidou, Tadashi; Okinaka, Noriyuki
1988-02-01
This paper describes the experimental and analytical results obtained for an MHD channel with a two dimensionally shaped magnetic field configuration called 'the SFC-type'. The power generating performance was examined under various load conditions and B-field intensities with a 2 MWt shock tunnel MHD facility. It is demonstrated that the power output performance and the enthalpy extraction scaling law of the conventional uniform B-field MHD generator (UFC-type) were significantly improved by the SFC-design of the spatial distribution of the magnetic field. The arcing processes were also examined by a high speed camera and the post-test observation of arc spot traces on electrodes. Further, the characteristic frequencies of each of the so-called micro and constricted arcs were clarified by spectral analyses. The critical current densities, which define the transient conditions of each from the diffuse-to micro arc, and from the micro-to constricted arc modes could be clearly obtained by the present spectral analysis method. We also investigated the three-dimensional behavior under strong magnetic field based on the coupled electrical and hydrodynamical equations for both of the middle scale SFC-and UFC-type generators. Finally, it is concluded from the above mentioned various aspects that the shaped 2-D magnetic field design will offer a most useful means for the realization of a compact, high efficiency and a long duration open-cycle MHD generator.
Pseudo-reconnection in MHD numerical simulation
无
2000-01-01
A class of pseudo-reconnections caused by a shifted mesh in magnetohydrodynamics (MHD) simulations is reported. In terms of this mesh system, some non-physical results may be obtained in certain circumstances, e.g. magnetic reconnection occurs without resistivity. After comparison, another kind of mesh is strongly recommended.
Collisionless magnetic reconnection under anisotropic MHD approximation
Hirabayashi, Kota; Hoshino, Masahiro
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless magneto-hydro-dynamic (MHD) simulations based on the double adiabatic approximation, which is an important step to bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observation. According to our results, a pair of slow shocks does form in the reconnection layer. The resultant shock waves, however, are quite weak compared with those in an isotropic MHD from the point of view of the plasma compression and the amount of the magnetic energy released across the shock. Once the slow shock forms, the downstream plasma are heated in highly anisotropic manner and a firehose-sense (P_{||}>P_{⊥}) pressure anisotropy arises. The maximum anisotropy is limited by the marginal firehose criterion, 1-(P_{||}-P_{⊥})/B(2) =0. In spite of the weakness of the shocks, the resultant reconnection rate is kept at the same level compared with that in the corresponding ordinary MHD simulations. It is also revealed that the sequential order of propagation of the slow shock and the rotational discontinuity, which appears when the guide field component exists, changes depending on the magnitude of the guide field. Especially, when no guide field exists, the rotational discontinuity degenerates with the contact discontinuity remaining at the position of the initial current sheet, while with the slow shock in the isotropic MHD. Our result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.
An MHD model for magnetar giant flares
Meng, Y.; Lin, J.; Zhang, Q. S. [Yunnan Observatories, Chinese Academy of Sciences, P.O. Box 110, Kunming, Yunnan 650011 (China); Zhang, L. [Department of Physics, Yunnan University, Kunming, Yunnan 650091 (China); Reeves, K. K. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Yuan, F., E-mail: mengy@ynao.ac.cn, E-mail: jlin@ynao.ac.cn [Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030 (China)
2014-04-10
Giant flares on soft gamma-ray repeaters that are thought to take place on magnetars release enormous energy in a short time interval. Their power can be explained by catastrophic instabilities occurring in the magnetic field configuration and the subsequent magnetic reconnection. By analogy with the coronal mass ejection events on the Sun, we develop a theoretical model via an analytic approach for magnetar giant flares. In this model, the rotation and/or displacement of the crust causes the field to twist and deform, leading to flux rope formation in the magnetosphere and energy accumulation in the related configuration. When the energy and helicity stored in the configuration reach a threshold, the system loses its equilibrium, the flux rope is ejected outward in a catastrophic way, and magnetic reconnection helps the catastrophe develop to a plausible eruption. By taking SGR 1806–20 as an example, we calculate the free magnetic energy released in such an eruptive process and find that it is more than 10{sup 47} erg, which is enough to power a giant flare. The released free magnetic energy is converted into radiative energy, kinetic energy, and gravitational energy of the flux rope. We calculated the light curves of the eruptive processes for the giant flares of SGR 1806–20, SGR 0526–66, and SGR 1900+14, and compared them with the observational data. The calculated light curves are in good agreement with the observed light curves of giant flares.
Yousefian, V.; Weinberg, M.H.; Haimes, R.
1980-02-01
The NASA CEC Code was the starting point for PACKAGE, whose function is to evaluate the composition of a multiphase combustion product mixture under the following chemical conditions: (1) total equilibrium with pure condensed species; (2) total equilibrium with ideal liquid solution; (3) partial equilibrium/partial finite rate chemistry; and (4) fully finite rate chemistry. The last three conditions were developed to treat the evolution of complex mixtures such as coal combustion products. The thermodynamic variable pairs considered are either pressure (P) and enthalpy, P and entropy, at P and temperature. Minimization of Gibbs free energy is used. This report gives detailed discussions of formulation and input/output information used in the code. Sample problems are given. The code development, description, and current programming constraints are discussed. (DLC)
Localization of MHD modes and consistency with q-profiles in JET
De Angelis, R., E-mail: riccardo.deangelis@enea.i [Associazione Euratom/ENEA sulla Fusione, CP 65-00044 Frascati, Rome (Italy); Baruzzo, M. [Consorzio RFX, EURATOM-ENEA Association, Corso Stati Uniti 4, 35127 Padova (Italy); Buratti, P. [Associazione Euratom/ENEA sulla Fusione, CP 65-00044 Frascati, Rome (Italy); Alper, B. [Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Barrera, L. [Laboratorio Nacional de Fusion, Asociacion EURATOM-CIEMAT, 28040 Madrid (Spain); Botrugno, A. [Associazione Euratom/ENEA sulla Fusione, CP 65-00044 Frascati, Rome (Italy); Brix, M. [Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Figini, L. [Istituto di Fisica del Plasma, Associazione EURATOM ENEA-CNR, Milano (Italy); Fonseca, A. [Associacao Euratom-IST, Centro de Fusao Nuclear, Av. Rovisco Pais, Lisbon (Portugal); Giroud, C.; Hawkes, N.; Howell, D. [Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); De La Luna, E. [Laboratorio Nacional de Fusion, Asociacion EURATOM-CIEMAT, 28040 Madrid (Spain); Orsitto, F.; Pericoli, V. [Associazione Euratom/ENEA sulla Fusione, CP 65-00044 Frascati, Rome (Italy); Rachlew, E. [Association EURATOM-VR, KTH Royal Inst. of Technology, SE-10691 Stockholm (Sweden); Tudisco, O. [Associazione Euratom/ENEA sulla Fusione, CP 65-00044 Frascati, Rome (Italy)
2010-11-11
The measurement of the safety factor q in tokamaks, which describes the winding of the helical magnetic field lines, is very important especially for the achievement of advanced scenarios. The motional Stark effect diagnostic can provide a direct measurement of the magnetic field orientation but the derivation of the q-profiles requires a simulation of the magnetic equilibrium taking into account inputs from several other diagnostics. This analysis can be affected by large errors. In order to validate the results, q-profiles are compared with the radii of MHD modes, which can be attributed to surfaces of known q.
Localization of MHD modes and consistency with q-profiles in JET
De Angelis, R.; Baruzzo, M.; Buratti, P.; Alper, B.; Barrera, L.; Botrugno, A.; Brix, M.; Figini, L.; Fonseca, A.; Giroud, C.; Hawkes, N.; Howell, D.; De La Luna, E.; Orsitto, F.; Pericoli, V.; Rachlew, E.; Tudisco, O.; JET-EFDA Contributors
2010-11-01
The measurement of the safety factor q in tokamaks, which describes the winding of the helical magnetic field lines, is very important especially for the achievement of advanced scenarios. The motional Stark effect diagnostic can provide a direct measurement of the magnetic field orientation but the derivation of the q-profiles requires a simulation of the magnetic equilibrium taking into account inputs from several other diagnostics. This analysis can be affected by large errors. In order to validate the results, q-profiles are compared with the radii of MHD modes, which can be attributed to surfaces of known q.
Summary report for ITER task - T68: MHD facility preparation for Li/V blanket option
Reed, C.B.; Haglund, R.C.; Miller, M.E. [and others
1995-08-01
A key feasibility issue for the ITER Vanadium/Lithium breeding blanket is the question of insulator coatings. Design calculations show that an electrically insulating layer is necessary to maintain an acceptably low MHD pressure drop. To enable experimental investigations of the MHD performance of candidate insulator materials and the technology for putting them in place, the room-temperature ALEX (Argonne`s Liquid Metal EXperiment) NaK facility was upgraded to a 300{degrees}C lithium system. The objective of this upgrade was to modify the existing facility to the minimum extent necessary, consistent with providing a safe, flexible, and easy to operate MHD test facility which uses lithium at ITER-relevant temperatures, Hartmann numbers, and interaction parameters. The facility was designed to produce MHD pressure drop data, test section voltage distributions, and heat transfer data for mid-scale test sections and blanket mockups. The system design description for this lithium upgrade of the ALEX facility is given in this document.
Understanding Accretion Disks through Three Dimensional Radiation MHD Simulations
Jiang, Yan-Fei
I study the structures and thermal properties of black hole accretion disks in the radiation pressure dominated regime. Angular momentum transfer in the disk is provided by the turbulence generated by the magneto-rotational instability (MRI), which is calculated self-consistently with a recently developed 3D radiation magneto-hydrodynamics (MHD) code based on Athena. This code, developed by my collaborators and myself, couples both the radiation momentum and energy source terms with the ideal MHD equations by modifying the standard Godunov method to handle the stiff radiation source terms. We solve the two momentum equations of the radiation transfer equations with a variable Eddington tensor (VET), which is calculated with a time independent short characteristic module. This code is well tested and accurate in both optically thin and optically thick regimes. It is also accurate for both radiation pressure and gas pressure dominated flows. With this code, I find that when photon viscosity becomes significant, the ratio between Maxwell stress and Reynolds stress from the MRI turbulence can increase significantly with radiation pressure. The thermal instability of the radiation pressure dominated disk is then studied with vertically stratified shearing box simulations. Unlike the previous results claiming that the radiation pressure dominated disk with MRI turbulence can reach a steady state without showing any unstable behavior, I find that the radiation pressure dominated disks always either collapse or expand until we have to stop the simulations. During the thermal runaway, the heating and cooling rates from the simulations are consistent with the general criterion of thermal instability. However, details of the thermal runaway are different from the predictions of the standard alpha disk model, as many assumptions in that model are not satisfied in the simulations. We also identify the key reasons why previous simulations do not find the instability. The thermal
Towards breaking temperature equilibrium in multi-component Eulerian schemes
Grove, John W [Los Alamos National Laboratory; Masser, Thomas [Los Alamos National Laboratory
2009-01-01
We investigate the effects ofthermal equilibrium on hydrodynamic flows and describe models for breaking the assumption ofa single temperature for a mixture of components in a cell. A computational study comparing pressure-temperature equilibrium simulations of two dimensional implosions with explicit front tracking is described as well as implementation and J-D calculations for non-equilibrium temperature methods.
New tests for a singularity of ideal MHD
Kerr, R M; Kerr, Robert M.; Brandenburg, Axel
2000-01-01
Analysis using new calculations with 3 times the resolution of the earlier linked magnetic flux tubes confirms the transition from singular to saturated growth rate reported by Grauer and Marliani \\cite{GrauerMar99} for the incompressible cases is confirmed. However, all of the secondary tests point to a transition back to stronger growth rate at a different location at late times. Similar problems in ideal hydrodynamics are discussed, pointing out that initial negative results eventually led to better initial conditions that did show evidence for a singularity of Euler. Whether singular or near-singular growth in ideal MHD is eventually shown, this study could have bearing on fast magnetic reconnection, high energy particle production and coronal heating.
3D MHD disruptions simulations of tokamaks plasmas
Paccagnella, Roberto; Strauss, Hank; Breslau, Joshua
2008-11-01
Tokamaks Vertical Displacement Events (VDEs) and disruptions simulations in toroidal geometry by means of a single fluid visco-resistive magneto-hydro-dynamic (MHD) model are presented in this paper. The plasma model, implemented in the M3D code [1], is completed with the presence of a 2D homogeneous wall with finite resistivity. This allows the study of the relatively slowly growing magneto-hydro-dynamical perturbation, the resistive wall mode (RWM), which is, in this work, the main drive of the disruptions. Amplitudes and asymmetries of the halo currents pattern at the wall are also calculated and comparisons with tokamak experimental databases and predictions for ITER are given. [1] W. Park, E.V. Belova, G.Y. Fu, X.Z. Tang, H.R. Strauss, L.E. Sugiyama, Phys. Plasmas 6 (1999) 1796.
ON VECTOR NETWORK EQUILIBRIUM PROBLEMS
Guangya CHEN
2005-01-01
In this paper we define a concept of weak equilibrium for vector network equilibrium problems.We obtain sufficient conditions of weak equilibrium points and establish relation with vector network equilibrium problems and vector variational inequalities.
Geochemical Calculations Using Spreadsheets.
Dutch, Steven Ian
1991-01-01
Spreadsheets are well suited to many geochemical calculations, especially those that are highly repetitive. Some of the kinds of problems that can be conveniently solved with spreadsheets include elemental abundance calculations, equilibrium abundances in nuclear decay chains, and isochron calculations. (Author/PR)
VisAn MHD: a toolbox in Matlab for MHD computer model data visualisation and analysis
P. Daum
2007-03-01
Full Text Available Among the many challenges facing modern space physics today is the need for a visualisation and analysis package which can examine the results from the diversity of numerical and empirical computer models as well as observational data. Magnetohydrodynamic (MHD models represent the latest numerical models of the complex Earth's space environment and have the unique ability to span the enormous distances present in the magnetosphere from several hundred kilometres to several thousand kilometres above the Earth surface. This feature enables scientist to study complex structures of processes where otherwise only point measurements from satellites or ground-based instruments are available. Only by combining these observational data and the MHD simulations it is possible to enlarge the scope of the point-to-point observations and to fill the gaps left by measurements in order to get a full 3-D representation of the processes in our geospace environment. In this paper we introduce the VisAn MHD toolbox for Matlab as a tool for the visualisation and analysis of observational data and MHD simulations. We have created an easy to use tool which is capable of highly sophisticated visualisations and data analysis of the results from a diverse set of MHD models in combination with in situ measurements from satellites and ground-based instruments. The toolbox is being released under an open-source licensing agreement to facilitate and encourage community use and contribution.
Turco, F., E-mail: turcof@fusion.gat.com; Hanson, J. M.; Navratil, G. A. [Columbia University, 116th and Broadway, New York, New York 10027 (United States); Turnbull, A. D. [General Atomics, PO Box 85608, San Diego, California 92186-5608 (United States)
2015-02-15
Experiments conducted at DIII-D investigate the role of drift kinetic damping and fast neutral beam injection (NBI)-ions in the approach to the no-wall β{sub N} limit. Modelling results show that the drift kinetic effects are significant and necessary to reproduce the measured plasma response at the ideal no-wall limit. Fast neutral-beam ions and rotation play important roles and are crucial to quantitatively match the experiment. In this paper, we report on the model validation of a series of plasmas with increasing β{sub N}, where the plasma stability is probed by active magnetohydrodynamic (MHD) spectroscopy. The response of the plasma to an externally applied field is used to probe the stable side of the resistive wall mode and obtain an indication of the proximity of the equilibrium to an instability limit. We describe the comparison between the measured plasma response and that calculated by means of the drift kinetic MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)], which includes the toroidal rotation, the electron and ion drift-kinetic resonances, and the presence of fast particles for the modelled plasmas. The inclusion of kinetic effects allows the code to reproduce the experimental results within ∼13% for both the amplitude and phase of the plasma response, which is a significant improvement with respect to the undamped MHD-only model. The presence of fast NBI-generated ions is necessary to obtain the low response at the highest β{sub N} levels (∼90% of the ideal no-wall limit). The toroidal rotation has an impact on the results, and a sensitivity study shows that a large variation in the predicted response is caused by the details of the rotation profiles at high β{sub N}.
Brignole, Esteban Alberto
2013-01-01
Traditionally, the teaching of phase equilibria emphasizes the relationships between the thermodynamic variables of each phase in equilibrium rather than its engineering applications. This book changes the focus from the use of thermodynamics relationships to compute phase equilibria to the design and control of the phase conditions that a process needs. Phase Equilibrium Engineering presents a systematic study and application of phase equilibrium tools to the development of chemical processes. The thermodynamic modeling of mixtures for process development, synthesis, simulation, design and
A Simple Ideal MHD Model of Vertical Disruption Events in Tokamaks
Fitzpatrick, Richard
2008-11-01
A simple model of axisymmetric vertical disruption events (VDEs) in tokamaks is presented in which the halo current force exerted on the vacuum vessel is calculated directly from linear, marginally stable, ideal-magnetohydrodynamical (MHD) stability analysis. The basic premise of the model is that the halo current force modifies pressure balance at the edge of the plasma, and therefore also modifies ideal-MHD plasma stability. In order to prevent the ideal vertical instability, responsible for the VDE, from growing on the very short Alfv'en time- scale, the halo current force must adjust itself such that the instability is rendered marginally stable. The model predicts halo currents which are similar in magnitude to those observed experimentally. An approximate non-axisymmetric version of the model is developed in order to calculate the toroidal peaking factor of the halo current force.
MHD Shallow Water Waves: Linear Analysis
Heng, Kevin
2009-01-01
We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincare modes and one magneto-Rossby mode) are previously known. The other two wave modes are strongly influenced by the magnetic field and rotation, and have substantially lower angular frequencies; as such, we term them "magnetostrophic modes". We obtain analytical functions for the velocity, height and magnetic field perturbations in the limit that the magnitude of the MHD analogue of Lamb's parameter is large. On a sphere, the magnetostrophic modes reside near the poles, while the other modes are equatorially confined. Magnetostrophic modes may be an ingredient in explaining the frequency drifts observed in Type I X-ray bursts from neutron stars.
Cosmic ray transport in MHD turbulence
Yan, Huirong
2007-01-01
Numerical simulations shed light onto earlier not trackable problem of magnetohydrodynamic (MHD) turbulence. They allowed to test the predictions of different models and choose the correct ones. Inevitably, this progress calls for revisions in the picture of cosmic ray (CR) transport. It also shed light on the problems with the present day numerical modeling of CR. In this paper we focus on the analytical way of describing CR propagation and scattering, which should be used in synergy with the numerical studies. In particular, we use recently established scaling laws for MHD modes to obtain the transport properties for CRs. We include nonlinear effects arising from large scale trapping, to remove the 90 degree divergence. We determine how the efficiency of the scattering and CR mean free path depend on the characteristics of ionized media, e.g. plasma $\\beta$, Coulomb collisional mean free path. Implications for particle transport in interstellar medium and solar corona are discussed. We also examine the perp...
Type I Planetary Migration with MHD Turbulence
Laughlin, G; Adams, F; Laughlin, Gregory; Steinacker, Adriane; Adams, Fred
2004-01-01
This paper examines how type I planet migration is affected by the presence of turbulent density fluctuations in the circumstellar disk. For type I migration, the planet does not clear a gap in the disk and its secular motion is driven by torques generated by the wakes it creates in the surrounding disk fluid. MHD turbulence creates additional density perturbations that gravitationally interact with the planet and can dominate the torques produced by the migration mechanism itself. This paper shows that conventional type I migration can be readily overwhelmed by turbulent perturbations and hence the usual description of type I migration should be modified in locations where the magnetorotational instability is active. In general, the migrating planet does not follow a smooth inward trned, but rather exhibits a random walk through phase space. Our main conclusion is that MHD turbulence will alter the time scales for type I planet migration and -- because of chaos -- requires the time scales to be described by ...
Magnetic Reconnection in a Compressible MHD Plasma
Hesse, Michael; Birn, Joachim; Zenitani, Seiji
2011-01-01
Using steady-state resistive MHD, magnetic reconnection is reinvestigated for conditions of high resistivity/low magnetic Reynolds number, when the thickness of the diffusion region is no longer small compared to its length. Implicit expressions for the reconnection rate and other reconnection parameters are derived based on the requirements of mass, momentum, and energy conservation. These expressions are solved via simple iterative procedures. Implications specifically for low Reynolds number/high resistivity are being discussed
MHD simulations on an unstructured mesh
Strauss, H.R. [New York Univ., NY (United States); Park, W.; Belova, E.; Fu, G.Y. [Princeton Univ., NJ (United States). Plasma Physics Lab.; Longcope, D.W. [Univ. of Montana, Missoula, MT (United States); Sugiyama, L.E. [Massachusetts Inst. of Tech., Cambridge, MA (United States)
1998-12-31
Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D.
Statistical Theory of the Ideal MHD Geodynamo
Shebalin, J. V.
2012-01-01
A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the
MHD Technology Transfer, Integration and Review Committee
1992-01-01
This fifth semi-annual status report of the MHD Technology Transfer, Integration, and Review Committee (TTIRC) summarizes activities of the TTIRC during the period April 1990 through September 1990. It includes summaries and minutes of committee meetings, progress summaries of ongoing Proof-of-Concept (POC) contracts, discussions pertaining to technical integration issues in the POC program, and planned activities for the next six months.
Design Study: Rocket Based MHD Generator
1997-01-01
This report addresses the technical feasibility and design of a rocket based MHD generator using a sub-scale LOx/RP rocket motor. The design study was constrained by assuming the generator must function within the performance and structural limits of an existing magnet and by assuming realistic limits on (1) the axial electric field, (2) the Hall parameter, (3) current density, and (4) heat flux (given the criteria of heat sink operation). The major results of the work are summarized as follows: (1) A Faraday type of generator with rectangular cross section is designed to operate with a combustor pressure of 300 psi. Based on a magnetic field strength of 1.5 Tesla, the electrical power output from this generator is estimated to be 54.2 KW with potassium seed (weight fraction 3.74%) and 92 KW with cesium seed (weight fraction 9.66%). The former corresponds to a enthalpy extraction ratio of 2.36% while that for the latter is 4.16%; (2) A conceptual design of the Faraday MHD channel is proposed, based on a maximum operating time of 10 to 15 seconds. This concept utilizes a phenolic back wall for inserting the electrodes and inter-electrode insulators. Copper electrode and aluminum oxide insulator are suggested for this channel; and (3) A testing configuration for the sub-scale rocket based MHD system is proposed. An estimate of performance of an ideal rocket based MHD accelerator is performed. With a current density constraint of 5 Amps/cm(exp 2) and a conductivity of 30 Siemens/m, the push power density can be 250, 431, and 750 MW/m(sup 3) when the induced voltage uB have values of 5, 10, and 15 KV/m, respectively.
Inductive ionospheric solver for magnetospheric MHD simulations
H. Vanhamäki
2011-01-01
Full Text Available We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances and similar output is produced (ionospheric electric field. The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km^{−1} in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981.
The Statistical Mechanics of Ideal MHD Turbulence
Shebalin, John V.
2003-01-01
Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.
Inductive ionospheric solver for magnetospheric MHD simulations
Vanhamäki, H.
2011-01-01
We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).
Nonlinear MHD dynamo operating at equipartition
Archontis, V.; Dorch, Bertil; Nordlund, Åke
2007-01-01
Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......-equipartition and a turbulent state. The generation and evolution of such strong magnetic fields is relevant for the understanding of dynamo action that occurs in stars and other astrophysical objects. Aims.We study the mode of operation of this dynamo, in the linear and non-linear saturation regimes. We also consider...... the effect of varying the magnetic and fluid Reymolds number on the non-linear behaviour of the system. Methods.We perform three-dimensional non-linear MHD simulations and visualization using a high resolution numerical scheme. Results.We find that this dynamo has a high growth rate in the linear regime...
Physics of the Solar Chromosphere: Beyond the Ideal MHD Description
Leake, James
2015-08-01
The solar chromosphere is the dynamic, physically complex, layer that lies between the visible solar surface and the magnetically dominated corona. Despite being a moderator of the amount of mass, magnetic field, and energy, that is transferred into the solar corona and the heliosphere and beyond, there are still important open questions regarding the chromosphere. Recent advancements in both observation and theoretical descriptions of the chromosphere have created new ideas about how the chromosphere controls the transfer of the above quantities from the Sun's interior into the heliosphere. Open questions still remain, such as, how is the chromosphere heated, and how do chromospheric events such as spicules, jets, reconnection, and wave propagation and dissipation contribute to the mass and energy balance in the solar atmosphere. Central to these questions are extensions to the standard magneto-hydro-dynamic (MHD) model of the Sun, such as non-local-thermodynamic-equilibrium radiation, and multi-fluid physics. In this talk, we summarize the importance of these extensions and look for the necessary developments to answer open questions about the chromosphere.
MHD stability of configurations with distorted toroidal coils
Cooper, W.A.; Ardela, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1997-06-01
We have investigated the local ideal MHD stability properties of a compact tokamak/torsatron configuration that models the proposed EPEIUS device. The {beta} limits imposed by the Mercier criterion and ballooning modes approach 1% in 50 kA peaked toroidal current and in current-free cases. A sequence at {beta}=6.75% is demonstrated to become marginally stable to local modes when the 180 kA toroidal current prescribed becomes sufficiently hollow that the maximum value of the inverse rotational transform q{sub max} exceeds 5 and the minimum value q{sub min} near the plasma edge approaches 2. The stabilisation mechanism is associated with the shape of the flux surface average of the parallel current density {sigma}>. A {sigma}> profile that increases in magnitude radially exercises a strong stabilizing influence on the energy principle. In the outer half of the plasma volume, the Mercier criterion (and to a lesser extent the ballooning eigenvalue) displays very local unstable spikes that align with rational values of 1/(qL). We interpret this as a potential for pressure-driven island formation rather than a strict stability limit. This phenomenon requires more detailed investigation using equilibrium codes that can study magnetic island structures. Global internal and external mode stability properties must also be examined, particularly for hollow current profile cases where the large toroidal plasma current concentrated near the plasma edge could destabilize external modes. (author) 1 fig., 5 refs.
MHD Simulations of the Plasma Flow in the Magnetic Nozzle
Smith, T. E. R.; Keidar, M.; Sankaran, K.; olzin, K. A.
2013-01-01
The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the
Toroidal equilibrium with low frequency wave driven currents
Ehst, D.A.
1984-12-01
In the absence of an emf the parallel current, j/sub parallel/, in a steady state tokamak will consist of a neoclassical portion plus a wave-driven contribution. Using the drift kinetic equation, the quasilinear (wave-driven) current is computed for high phase speed waves in a torus, and this is combined with the neoclassical term to obtain the general expression for the flux surface average
Study of the processes resulting from the use of alkaline seed in natural gas-fired MHD facilities
Styrikovich, M.A.; Mostinskii, I.L.
1977-01-01
Various ways of ionizing seed injection and recovery, applicable to open-cycle magnetohydrodynamic (MHD) power generation facilities, operating on sulfur-free gaseous fossil fuel, are discussed and experimentally verified. The physical and chemical changes of the seed and the heat and mass transfer processes resulting from seed application are investigated using the U-02 experimental MHD facility and laboratory test facilities. Engineering methods for calculating the processes of seed droplet vaporization, condensation and the precipitation of submicron particles of K/sub 2/CO/sub 3/ on the heat exchange surface are also included.
Evolutionary Conditions in the Dissipative MHD System Revisited
Inoue, Tsuyoshi
2007-01-01
The evolutionary conditions for the dissipative continuous magnetohydrodynamic (MHD) shocks are studied. We modify Hada's approach in the stability analysis of the MHD shock waves. The matching conditions between perturbed shock structure and asymptotic wave modes shows that all types of the MHD shocks, including the intermediate shocks, are evolutionary and perturbed solutions are uniquely defined. We also adopt our formalism to the MHD shocks in the system with resistivity without viscosity, which is often used in numerical simulation, and show that all types of shocks that are found in the system satisfy the evolutionary condition and perturbed solutions are uniquely defined. These results suggest that the intermediate shocks may appear in reality.
Jones, A.R.
1985-08-01
This System Design Description and Specification provides the basis for the design of the magnetohydrodynamic (MHD) Power Train (PT) for a nominal 200 MWe early commercial tiHD/Steam Power Plant. This document has been developed under Task 2, Conceptual Design, of Contract DE-AC22-83PC60575 and is to be used by the project as the controlling and coordinating documentation during future design efforts. Modification and revision of this specification will occur as the design matures, and tiie-Westinghouse MHD Project Manager will be the focal point for maintaining this document and issuing periodic revisions. This document is intended to delineate the power train and-power train components requirements and assumptions that properly reflect the MHD/Steam Power Plant in the PT design. The parameters discussed in this document have been established through system calculations as well as through constraints set by technology and by limitations on materials, cost, physical processes associated with MHD, and the expected operating data for the plant. The specifications listed in this document have precedence over all referenced documents. Where this specification appears to conflict with the requirements of a reference document, such conflicts should be brought to the attention of the Westinghouse MHD Project Manager for resolution.
Three-Dimensional Multiscale MHD Model of Cometary Plasma Environments
Gombosi, Tamas I.; DeZeeuw, Darren L.; Haberli, Roman M.; Powell, Kenneth G.
1996-01-01
First results of a three-dimensional multiscale MHD model of the interaction of an expanding cometary atmosphere with the magnetized solar wind are presented. The model starts with a supersonic and super-Alfvenic solar wind far upstream of the comet (25 Gm upstream of the nucleus) with arbitrary interplanetary magnetic field orientation. The solar wind is continuously mass loaded with cometary ions originating from a 10-km size nucleus. The effects of photoionization, electron impact ionization, recombination, and ion-neutral frictional drag are taken into account in the model. The governing equations are solved on an adaptively refined unstructured Cartesian grid using our new multiscale upwind scalar conservation laws-type numerical technique (MUSCL). We have named this the multiscale adaptive upwind scheme for MHD (MAUS-MHD). The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the diamagnetic cavity of the comet. The main findings are the following: (1) Mass loading decelerates the solar wind flow upstream of the weak cometary shock wave (M approximately equals 2, M(sub A) approximately equals 2), which forms at a subsolar standoff distance of about 0.35 Gm. (2) A cometary plasma cavity is formed at around 3 x 10(exp 3) km from the nucleus. Inside this cavity the plasma expands outward due to the frictional interaction between ions and neutrals. On the nightside this plasma cavity considerably narrows and a relatively fast and dense cometary plasma beam is ejected into the tail. (3) Inside the plasma cavity a teardrop-shaped inner shock is formed, which is terminated by a Mach disk on the nightside. Only the region inside the inner shock is the 'true' diamagnetic cavity. (4) The model predicts four distinct current systems in the inner coma: the density peak current, the cavity boundary current, the inner shock current, and finally the cross-tail current
Conjugate Acid-Base Pairs, Free Energy, and the Equilibrium Constant
Beach, Darrell H.
1969-01-01
Describes a method of calculating the equilibrium constant from free energy data. Values of the equilibrium constants of six Bronsted-Lowry reactions calculated by the author's method and by a conventional textbook method are compared. (LC)
Berty, J.M.; Krishnan, C.; Elliott, J.R. Jr. (Berty Reaction Engineers, Ltd. (USA))
1990-10-01
Methanol is synthesised catalytically from H{sub 2}, CO and CO{sub 2}. Equilibrium considerations dictated the use of high pressures until the advent of copper-based catalysts. But equilibrium problems still exist; single pass conversions of CO and H{sub 2} are low, typically 30-40%. A solvent methanol process (SMP) is proposed to overcome existing problems. A high-boiling inert solvent is introduced with the synthesis gas. The solvent selectively absorbs CH{sub 3}OH, thus shifting the equilibrium towards the product. The strongest solvent identified and tested is tetraethyleneglycol dimethyl ether (tetraglyme). 24 refs., 4 figs., 2 tabs.
Chemical Principles Revisited: Chemical Equilibrium.
Mickey, Charles D.
1980-01-01
Describes: (1) Law of Mass Action; (2) equilibrium constant and ideal behavior; (3) general form of the equilibrium constant; (4) forward and reverse reactions; (5) factors influencing equilibrium; (6) Le Chatelier's principle; (7) effects of temperature, changing concentration, and pressure on equilibrium; and (8) catalysts and equilibrium. (JN)
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
An advanced implicit solver for MHD
Udrea, Bogdan
A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel
Characteristics of Linear MHD Generators with One or a Few Loads
Witalis, E.A.
1966-02-15
The theoretical performance of linear series segmented MHD generators with finite size electrodes and one or a few identical external loads is investigated. The analysis is an extension of our conformal mapping investigation previously reported. The electrical characteristics are evaluated as functions of the segmentation degree, the Hall parameter and the relative position of short-circuited electrodes. Special consideration is given to the influence of staggering the electrodes, i. e. shifting the relative positions of short-circuited electrodes. General electrical terminal characteristics, i. e. the full current-voltage relation, can not be obtained by the exact analytical method, which is applicable only to so-called design load conditions or infinitely long MHD channels. However, it is shown how the general properties can be explained qualitatively and calculated approximately by describing off-design modes of operation in terms of a fictitious 'effective' number of external loads.
The energy associated with MHD waves generation in the solar wind plasma
delaTorre, A.
1995-01-01
Gyrotropic symmetry is usually assumed in measurements of electron distribution functions in the heliosphere. This prevents the calculation of a net current perpendicular to the magnetic field lines. Previous theoretical results derived by one of the authors for a collisionless plasma with isotropic electrons in a strong magnetic field have shown that the excitation of MHD modes becomes possible when the external perpendicular current is non-zero. We consider then that any anisotropic electron population can be thought of as 'external', interacting with the remaining plasma through the self-consistent electromagnetic field. From this point of view any perpendicular current may be due to the anisotropic electrons, or to an external source like a stream, or to both. As perpendicular currents cannot be derived from the measured distribution functions, we resort to Ampere's law and experimental data of magnetic field fluctuations. The transfer of energy between MHD modes and external currents is then discussed.
Comparison of MHD-induced rotation damping with NTV predictions on MAST
Hua, M.-D.; Chapman, I. T.; Field, A. R.; Hastie, R. J.; Pinches, S. D.; MAST Team
2010-03-01
Plasma rotation in tokamaks is of special interest for its potential stabilizing effect on micro- and macro-instabilities, leading to increased confinement. In MAST, the torque from neutral beam injection can spin the plasma to a core velocity ~300 km s-1 (Alfvén Mach number ~0.3). Low density plasmas often exhibit a weakly non-monotonic safety factor profile just above unity. Theory predicts that such equilibria are prone to magneto-hydro-dynamic (MHD) instabilities, which was confirmed by recent observations. The appearance of the mode is accompanied by strong damping of core rotation on a timescale much faster than the momentum confinement time. The mode's saturated structure is estimated using the CASTOR code together with soft x-ray measurements, enabling the calculation of the plasma braking by the MHD mode according to neoclassical toroidal viscosity (NTV) theory. The latter exhibits strong similarities with the torque measured experimentally.
Ring-shaped discharge structures in a closed cycle MHD disk generator
Fukuda, H.; Kabashima, S.
1987-06-01
Numerical simulations are carried out to study plasma properties in a nonequilibrium disk-type MHD generator. The analysis is based on a two-dimensional time-dependent MHD equation, and is performed in the r-z plane. From the r-z analysis, the current distributions in the boundary layer, electrode regions are obtained, as well as the channel main flow region. The two-state nature of plasma, i.e., the formation of streamers and their dynamical behavior in the channel is confirmed. The dependence of the streamer properties on the magnetic field strength and load resistance is examined. The calculations suggest the existence of an eddy current in the boundary layer for the high-loading parameter. Some enhanced eddy currents in the nozzle region and the intensive eddy current at the upper-stream edge of the cathode are obtained for some plasma parameters. 19 references.
Io's Magnetospheric Interaction: An MHD Model with Day-Night Asymmetry
Kabin, K.; Combi, M. R.; Gombosi, T. I.; DeZeeuw, D. L.; Hansen, K. C.; Powell, K. G.
2001-01-01
In this paper we present the results of all improved three-dimensional MHD model for Io's interaction with Jupiter's magnetosphere. We have included the day-night asymmetry into the spatial distribution of our mass-loading, which allowed us to reproduce several smaller features or the Galileo December 1995 data set. The calculation is performed using our newly modified description of the pick-up processes that accounts for the effects of the corotational electric field existing in the Jovian magnetosphere. This change in the formulation of the source terms for the MHD equations resulted in significant improvements in the comparison with the Galileo measurements. We briefly discuss the limitations of our model and possible future improvements.
Modeling magnetized neutron stars using resistive MHD
Palenzuela, Carlos
2013-01-01
This work presents an implementation of the resistive MHD equations for a generic algebraic Ohm's law which includes the effects of finite resistivity within full General Relativity. The implementation naturally accounts for magnetic-field-induced anisotropies and, by adopting a phenomenological current, is able to accurately describe electromagnetic fields in the star and in its magnetosphere. We illustrate the application of this approach in interesting systems with astrophysical implications; the aligned rotator solution and the collapse of a magnetized rotating neutron star to a black hole.
Local potential analysis of MHD instability
Sen, K. K.; Wilson, S. J.
1985-02-01
The use of the local potential method for studying instabilities of MHD fluids is examined. The mathematical method is similar to that developed by the authors for studying the time-dependent radiative transfer problem and the radiative stability of interstellar masers. The scheme is based on the universal evolution criterion proposed by Glansdorff and Prigogine (1964) as demonstrated by Hays (1965) for the heat equation and Schechter and Himmelblau (1965) for the Benard problem in hydrodynamics. The scheme for securing stability criteria is demonstrated for two particular cases.
MHD Equations with Regularity in One Direction
Zujin Zhang
2014-01-01
Full Text Available We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, ∂3u∈Lp0, T;LqR3, with 2/p + 3/q = γ ∈ [1,3/2, 3/γ ≤ q ≤ 1/(γ - 1, then the solution is in fact smooth. This improves previous results greatly.
MHD squeezing flow between two infinite plates
Umar Khan
2014-03-01
Full Text Available Magneto hydrodynamic (MHD squeezing flow of a viscous fluid has been discussed. Conservation laws combined with similarity transformations have been used to formulate the flow mathematically that leads to a highly nonlinear ordinary differential equation. Analytical solution to the resulting differential equation is determined by employing Variation of Parameters Method (VPM. Runge–Kutta order-4 method is also used to solve the same problem for the sake of comparison. It is found that solution using VPM reduces the computational work yet maintains a very high level of accuracy. The influence of different parameters is also discussed and demonstrated graphically.
Relativistic MHD with Adaptive Mesh Refinement
Anderson, M; Liebling, S L; Neilsen, D; Anderson, Matthew; Hirschmann, Eric; Liebling, Steven L.; Neilsen, David
2006-01-01
We solve the relativistic magnetohydrodynamics (MHD) equations using a finite difference Convex ENO method (CENO) in 3+1 dimensions within a distributed parallel adaptive mesh refinement (AMR) infrastructure. In flat space we examine a Balsara blast wave problem along with a spherical blast wave and a relativistic rotor test both with unigrid and AMR simulations. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. We also investigate the impact of hyperbolic divergence cleaning for the spherical blast wave and relativistic rotor. We include unigrid and mesh refinement parallel performance measurements for the spherical blast wave.
Evaluation of feedback in conductive MHD devices
Grinberg, G.K.
1977-01-01
A method is recommended for computing feedback and the self-energizing threshold of conducting MHD devices. Circuits of equivalent magnetizing currents are used for this purpose in addition to equivalent electrical circuits. This kind of an approach makes it possible to reflect the influence of R/sub m/ on the operation of the device. Dimensionless functions were found which determine the critical value of the Reynolds magnetic number. The computations demonstrated that the redistribution of the magnetic field in the machine's operating zone under the influence of an induced field must be considered.
Superconducting magnet system for an experimental disk MHD facility
Knoopers, H.G.; Kate, ten H.H.J.; Klundert, van de L.J.M.
1991-01-01
A predesign of a split-pair magnet for a magnetohydrodynamic (MHD) facility for testing a 10-MW open-cycle disk or a 5-MW closed-cycle disk generator is presented. The magnet system consists of a NbTi and a Nb 3Sn section, which provide a magnetic field of 9 T in the active area of the MHD channel.
The Calculus of Variations and the Ideal MHD Energy Principle
Schnack, Dalton D.
In Lecture 22, we showed that the ideal MHD force operator is self-adjoint and suggested that this allowed a formulation in which the stability of a system could be determined without solving a differential equation. Going further requires a little background in the calculus of variations. In the lecture we begin this discussion,1 and formulate the ideal MHD energy principle.
Thermodynamics "beyond" local equilibrium
Vilar, Jose; Rubi, Miguel
2002-03-01
Nonequilibrium thermodynamics has shown its applicability in a wide variety of different situations pertaining to fields such as physics, chemistry, biology, and engineering. As successful as it is, however, its current formulation considers only systems close to equilibrium, those satisfying the so-called local equilibrium hypothesis. Here we show that diffusion processes that occur far away from equilibrium can be viewed as at local equilibrium in a space that includes all the relevant variables in addition to the spatial coordinate. In this way, nonequilibrium thermodynamics can be used and the difficulties and ambiguities associated with the lack of a thermodynamic description disappear. We analyze explicitly the inertial effects in diffusion and outline how the main ideas can be applied to other situations. [J.M.G. Vilar and J.M. Rubi, Proc. Natl. Acad. Sci. USA 98, 11081-11084 (2001)].
Katalin Martinás
2007-02-01
Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.
Response reactions: equilibrium coupling.
Hoffmann, Eufrozina A; Nagypal, Istvan
2006-06-01
It is pointed out and illustrated in the present paper that if a homogeneous multiple equilibrium system containing k components and q species is composed of the reactants actually taken and their reactions contain only k + 1 species, then we have a unique representation with (q - k) stoichiometrically independent reactions (SIRs). We define these as coupling reactions. All the other possible combinations with k + 1 species are the coupled reactions that are in equilibrium when the (q - k) SIRs are in equilibrium. The response of the equilibrium state for perturbation is determined by the coupling and coupled equilibria. Depending on the circumstances and the actual thermodynamic data, the effect of coupled equilibria may overtake the effect of the coupling ones, leading to phenomena that are in apparent contradiction with Le Chatelier's principle.
Boričić Zoran
2009-01-01
Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
Operational analysis of open-cycle MHD
Lippert, T. E.; McCutchan, D. A.
1980-07-01
Open cycle magnetohydrodynamic (OCMHD) conceptual power plant designs are studied in the context of a utility system to form a better basis for understanding their design, design requirements, and market possibilities. Based on assumed or projected plant costs and performance characteristics, assumed economics and escalation factors, and one coal supply and delivery scenario, overall and regional OCMHD utility market possibilities are reviewed. Additionally, for one hypothetical utility system a generation expansion plan is developed that includes OCMHD as a baseload power generating station. The impact on generation system economics and operation of alternating selected MHD plant cost and performance characteristics is reviewed. Baseload plant availability is shown as an important plant design consideration, and a general methodology and data base is developed to assess the impact on design and cost of various reliability decisions. An overall plant availability goal is set and the required availabilities of various MHD high technology components are derived to meet the plant goal. The approach is then extended to projecting channel life goals for various plant design configurations and assumptions.
Sullivan, L. D.; Klepeis, J. E.; Coderre, W. J.; Fischer, W. H.
1980-01-01
For electrical power generation utilizing a high temperature alkali-seeded coal combustion plasma, the certainty of high electrical conductivity in the presence of coal ash and trace impurities is vitally important, especially for use in extrapolation of existing designs to higher power levels, as envisioned for commercial applications. The paper surveys the results of the workshop which provides an industry wide overview of the computational methods and analyses that are currently in use. Attention is given to uncertainty bands for plasma electrical conductivity. Also discussed are other issues such as coal, slag, seed, and conductivity. Finally, the paper gives suggested areas for further work.
宋彭生; 黄雪莉
2007-01-01
According to the basic physic-chemical principal of electrolyte solution and Pitzer Ion Interaction Approach, study on the calculation of the equilibrium of salt-water system was carried out by calculating the activity coefficient of electrolyte solution and osmotic coefficient of water. The research showed:the method of minifying free energy was effective for the calculation of the equilibrium of salt-water system, its result was accord with that of method of solubility product.% 根据电解质溶液的基本物理化学原理和近代电解质溶液理论的Pitzer离子相互作用模型，通过计算浓电解质溶液的活度系数和水的活度，研究了盐-水体系溶解平衡的计算方法。结果表明，体系Gibbs自由能最小化方法是计算盐-水体系溶解平衡的一种有效方法，其计算结果与溶度积法一致。
Cavalcanti, Rafaelly L.; Oliveira, Jackson A. [Universidade Federal do Rio Grande do Norte (UFRN), Natal, RN (Brazil). Dept. de Engenharia Quimica; Rojas, Leopoldo O.A. [Centro de Tecnologias do Gas (CTGAS), Natal, RN (Brazil)
2008-07-01
This work has the main objective of evaluating the mathematical model developed by Jaubert e Mutelet (2004) in terms of the prediction capacity for the calculation of the vapor-liquid equilibrium (VLE). This model is based on Peng-Robinson equation of state (EOS) and it considers the binary interaction parameters (Kij(T)) estimated by a contribution group method and dependent of the temperature. The model proposed by Jaubert e Mutelet (2004), named PPR78 (Predictive Peng-Robinson), was implemented in this work by using the Fortran language. An optimization approach based on the stochastic algorithm of Particle Swarm Optimization (PSO) was used in order to calculate the vapor-liquid equilibrium. Simulations were accomplished for several binary systems and the results were concordant with some experimental data of the investigated systems. However, for some systems different from those presented by Jaubert and Mutelet (2004), the model presented low prediction capacity. In spite of the great demand of computational performance, the algorithm PSO demonstrated robustness during the calculation of VLE and it assured convergence in most of the cases. (author)
Neoclassical equilibrium in gyrokinetic simulations
Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Sarazin, Y.; Grandgirard, V.; Ghendrih, Ph.
2009-06-01
This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.
Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model
Frank, Adam; Jones, T. W.; Ryu, Dongsu
1995-01-01
Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.
Li, Angsheng; Zhang, Xiaohui; Pan, Yicheng; Peng, Pan
2014-12-01
It seems a universal phenomenon of networks that the attacks on a small number of nodes by an adversary player Alice may generate a global cascading failure of the networks. It has been shown (Li et al., 2013) that classic scale-free networks (Barabási and Albert, 1999, Barabási, 2009) are insecure against attacks of as small as O(logn) many nodes. This poses a natural and fundamental question: Can we introduce a second player Bob to prevent Alice from global cascading failure of the networks? We proposed a game in networks. We say that a network has an equilibrium game if the second player Bob has a strategy to balance the cascading influence of attacks by the adversary player Alice. It was shown that networks of the preferential attachment model (Barabási and Albert, 1999) fail to have equilibrium games, that random graphs of the Erdös-Rényi model (Erdös and Rényi, 1959, Erdös and Rényi, 1960) have, for which randomness is the mechanism, and that homophyly networks (Li et al., 2013) have equilibrium games, for which homophyly and preferential attachment are the underlying mechanisms. We found that some real networks have equilibrium games, but most real networks fail to have. We anticipate that our results lead to an interesting new direction of network theory, that is, equilibrium games in networks.
Laboratory identification of MHD eruption criteria in the solar corona
Myers, Clayton E.
2015-11-01
Ideal magnetohydrodynamic (MHD) instabilities such as the kink and torus instabilities are believed to play an important role in driving ``storage-and-release'' eruptions in the solar corona. These instabilities act on long-lived, arched magnetic flux ropes that are ``line-tied'' to the solar surface. In spite of numerous observational and computational studies, the conditions under which these instabilities produce an eruption remain a subject of intense debate. In this paper, we use a line-tied, arched flux rope experiment to study storage-and-release eruptions in the laboratory. An in situ array of miniature magnetic probes is used to assess the equilibrium and stability of the laboratory flux ropes. Two major results are reported here: First, a new stability regime is identified where torus-unstable flux ropes fail to erupt. In this ``failed torus'' regime, the flux rope is torus-unstable but kink-stable. Under these conditions, a dynamic ``toroidal field tension force'' surges in magnitude, causing the flux rope to contract. This tension force, which is missing from existing eruption models, is the J × B force between self-generated poloidal currents in the flux rope and the toroidal (guide) component of the vacuum field. Secondly, a clear torus instability threshold is observed in the kink-unstable regime. This latter result, which is consistent with existing theoretical and numerical results, verifies the key role of the torus instability in driving solar eruptions. In collaboration with M. Yamada, H. Ji, J. Yoo, W. Fox, J. Jara-Almonte, A. Savcheva, and E. E. DeLuca. This research is supported by DoE Contract No. DE-AC02-09CH11466 and by the NSF/DoE Center for Magnetic Self-Organization (CMSO).
Eberl, Gérard
2016-08-01
The classical model of immunity posits that the immune system reacts to pathogens and injury and restores homeostasis. Indeed, a century of research has uncovered the means and mechanisms by which the immune system recognizes danger and regulates its own activity. However, this classical model does not fully explain complex phenomena, such as tolerance, allergy, the increased prevalence of inflammatory pathologies in industrialized nations and immunity to multiple infections. In this Essay, I propose a model of immunity that is based on equilibrium, in which the healthy immune system is always active and in a state of dynamic equilibrium between antagonistic types of response. This equilibrium is regulated both by the internal milieu and by the microbial environment. As a result, alteration of the internal milieu or microbial environment leads to immune disequilibrium, which determines tolerance, protective immunity and inflammatory pathology.
High-Order Finite Difference GLM-MHD Schemes for Cell-Centered MHD
Mignone, A; Bodo, G
2010-01-01
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting...
3D MHD Jet in a Non-Uniform Magnetic Field
Huang Hulin; Han Dong
2005-01-01
The purpose of this paper is to present a two-phase 3D magnetohydrodynamics (MHD) flow model that combines the volume of fluid (VOF) method with the technique derived from induced-magnetic-field equations for liquid metal free surface MHD-jet-flow. Analogy between the induced-magnetic-filed equation and the conventional computational fluid dynamics (CFD) equation is made, so that the equation can be conveniently accounted for by CFD. A penalty factor numerical method is introduced in order to force the local divergence-free condition of the magnetic fields and an extension of the void insulating calculation domain is applied to ensure that the induced-magnetic field at its boundaries is null. These simulation results for lithium liquid metal jets under magnetic field configurations of Magnetic Torus (Mtor) and National Spherical Torus Experiment (NSTX) outboard divertor have shown that three dimensional jet can not be annihilated by magnetic braking and its cross-section will deform in such a way that the momentum flux of the jet is conserved. 3D MHD effects from a magnetic field gradient cause return currents to interact with applied magnetic fields and produce unfavorable Lorentz forces.Under 3D applied non-uniform magnetic fields of the divertor, unfavorable Lorentz forces lead to a substantial change in flow pattern and a reduction in flow velocity, with the jet cross-section moving to one side of the jet space. These critical phenomena can not be revealed by 2D models.
Global and Kinetic MHD Simulation by the Gpic-MHD Code
Hiroshi NAITOU; Yusuke YAMADA; Kenji KAJIWARA; Wei-li LEE; Shinji TOKUDA; Masatoshi YAGI
2011-01-01
In order to implement large-scale and high-beta tokamak simulation, a new algorithm of the electromagnetic gyrokinetic PIC （particle-in-cell） code was proposed and installed on the Gpic-MHD code [Gyrokinetic PIC code for magnetohydrodynamic （MHD） simulation]. In the new algorithm, the vorticity equation and the generalized Ohm＇s law along the magnetic field are derived from the basic equations of the gyrokinetic Vlasov, Poisson, and Ampere system and are used to describe the spatio-temporal evolution of the field quantities of the electrostatic potential φ and the longitudinal component of the vector potential Az. The basic algorithm is equivalent to solving the reduced-MHD-type equations with kinetic corrections, in which MHD physics related to Alfven modes are well described. The estimation of perturbed electron pressure from particle dynamics is dominant, while the effects of other moments are negligible. Another advantage of the algorithm is that the longitudinal induced electric field, ETz = -δAz/δt, is explicitly estimated by the generalized Ohm＇s law and used in the equations of motion. Furthermore, the particle velocities along the magnetic field are used （vz-formulation） instead of generalized momentums （pz-formulation）, hence there is no problem of ＇cancellation＇, which would otherwise appear when Az is estimated from the Ampere＇s law in the pz-formulation. The successful simulation of the collisionless internal kink mode by the new Gpic-MHD with realistic values of the large-scale and high-beta tokamaks revealed the usefulness of the new algorithm.
Neuman, M.W.
1982-01-01
The conundrum of blood undersaturation with respect to bone mineralization and its supersaturation with respect to bone's homeostatic function has acquired a new equation. On the supply side, Ca/sup 2 +/ is pumped in across bone cells to provide the needed Ca/sup 2 +/ x P/sub i/ for brushite precipitation. On the demand side, blood is in equilibrium with bone fluid, which is in equilibrium with a mineral more soluble than apatite. The function of potassium in this equation is yet to be found.
A comparative study on 3-D solar wind structure observed by Ulysses and MHD simulation
FENG Xueshang; XIANG Changqing; ZHONG Dingkun; FAN Quanlin
2005-01-01
During Ulysses' first rapid pole-to-pole transit from September 1994 to June 1995, its observations showed that middle- or high-speed solar winds covered all latitudes except those between -20° and +20° near the ecliptic plane,where the velocity was 300-450 km/s. At poleward 40°,however, only fast solar winds at the speed of 700-870 km/s were observed. In addition, the transitions from low-speed wind to high-speed wind or vice versa were abrupt. In this paper, the large-scale structure of solar wind observed by Ulysses near solar minimum is simulated by using the three-dimensional numerical MHD model. The model combines TVD Lax-Friedrich scheme and MacCormack Ⅱ scheme and decomposes the calculation region into two regions: one from 1 to 22 Rs and the other from 18 Rs to 1 AU.Based on the observations of the solar photospheric magnetic field and an addition of the volumetric heating to MHD equations, the large-scale solar wind structure mentioned above is reproduced by using the three-dimensional MHD model and the numerical results are roughly consistent with Ulysses' observations. Our simulation shows that the initial magnetic field topology and the addition of volume heating may govern the bimodal structure of solar wind observed by Ulysses and also demonstrates that the three-dimensional MHD numerical model used here is efficient in modeling the large-scale solar wind structure.
Thornhill, J. W.; Giuliani, J. L.; Chong, Y. K.; Velikovich, A. L.; Dasgupta, A.; Apruzese, J. P.; Jones, B.; Ampleford, D. J.; Coverdale, C. A.; Jennings, C. A.; Waisman, E. M.; Lamppa, D. C.; McKenney, J. L.; Cuneo, M. E.; Krishnan, M.; Coleman, P. L.; Madden, R. E.; Elliott, K. W.
2012-09-01
Argon Z-pinch experiments are to be performed on the refurbished Z machine (which we will refer to as ZR here in order to distinguish between pre-refurbishment Z) at Sandia National Laboratories with a new 8 cm diameter double-annulus gas puff nozzle constructed by Alameda Applied Sciences Corporation (AASC). The gas exits the nozzle from an outer and inner annulus and a central jet. The amount of gas present in each region can be varied. Here a two-dimensional radiation MHD (2DRMHD) model, MACH2-TCRE, with tabular collisional radiative equilibrium atomic kinetics is used to theoretically investigate stability and K-shell emission properties of several measured (interferometry) initial gas distributions emanating from this new nozzle. Of particular interest is to facilitate that the distributions employed in future experiments have stability and K-shell emission properties that are at least as good as the Titan nozzle generated distribution that was successfully fielded in earlier experiments on the Z machine before it underwent refurbishment. The model incorporates a self-consistent calculation for non-local thermodynamic equilibrium kinetics and ray-trace based radiation transport. This level of detail is necessary in order to model opacity effects, non-local radiation effects, and the high temperature state of K-shell emitting Z-pinch loads. Comparisons of radiation properties and stability of measured AASC gas profiles are made with that of the distribution used in the pre-refurbished Z experiments. Based on these comparisons, an optimal K-shell emission producing initial gas distribution is determined from among the AASC nozzle measured distributions and predictions are made for K-shell yields attainable from future ZR experiments.
Analogue Kerr-like geometries in a MHD inflow
Noda, Sousuke; Takahashi, Masaaki
2016-01-01
We present a model of the analogue black hole in magnetohydrodynamic (MHD) flow. For a two dimensional axisymmetric stationary trans-magnetosonic inflow with a sink, using the dispersion relation of the MHD waves, we introduce the effective geometries for magnetoacoustic waves propagating in the MHD flow. Investigating the properties of the effective potentials for magnetoacoustic rays, we find that the effective geometries can be classified into five types which include analogue spacetimes of the Kerr black hole, ultra spinning stars with ergoregions and spinning stars without ergoregions. We address the effects of the magnetic pressure and the magnetic tension on each magnetoacoustic geometries.
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
Finite Larmor radius influence on MHD solitary waves
E. Mjølhus
2009-04-01
Full Text Available MHD solitons are studied in a model where the usual Hall-MHD model is extended to include the finite Larmor radius (FLR corrections to the pressure tensor. The resulting 4-dimensional set of differential equations is treated numerically. In this extended model, the point at infinity can be of several types. Necessary for the existence of localized solutions is that it is either a saddle-saddle, a saddle-center, or, possibly, a focus-focus. In cases of saddle-center, numerical solutions for localized travelling structures have been obtained, and compared with corresponding results from the Hall-MHD model.
Housing Price Fluctuations Across China: An Equilibrium Mechanism Perspective
ZHANG Hong; WENG Shaoqun; ZHOU Xuan
2007-01-01
The mechanisms affecting housing prices were studied using the equilibrium housing prices based on classic supply/demand theory. The fluctuations of the actual housing prices were then analyzed relative to the equilibrium prices. The equilibrium prices for each area were calculated from economic statistics and housing prices in 35 China metropolitan areas. The fluctuations of the actual prices are then manifested as functions of the equilibrium price, the mean reversion, and the autocorrelation coefficient. The results show that the equilibrium prices are determined by the basic economic conditions in China and that the equilibrium prices greatly affect the fluctuation of the actual prices, which return to the equilibrium price through self-adjustments. The data also shows that the actual prices in China have the trend of continuing to rise in the future.
Observational Tests of Recent MHD Turbulence Perspectives
Ghosh, Sanjoy
2001-06-01
This grant seeks to analyze the Heliospheric Missions data to test current theories on the angular dependence (with respect to mean magnetic field direction) of magnetohydrodynamic (MHD) turbulence in the solar wind. Solar wind turbulence may be composed of two or more dynamically independent components. Such components include magnetic pressure-balanced structures, velocity shears, quasi-2D turbulence, and slab (Alfven) waves. We use a method, developed during the first two years of this grant, for extracting the individual reduced spectra of up to three separate turbulence components from a single spacecraft time series. The method has been used on ISEE-3 data, Pioneer Venus Orbiter, Ulysses, and Voyager data samples. The correlation of fluctuations as a function of angle between flow direction and magnetic-field direction is the focus of study during the third year.
MHD Turbulence in Accretion Disk Boundary Layers
Chan, Chi-kwan
2012-01-01
The physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations...
Drag reduction in turbulent MHD pipe flows
Orlandi, P.
1996-01-01
This is a preliminary study devoted to verifying whether or not direct simulations of turbulent Magneto-Hydro-Dynamic (MHD) flows in liquid metals reproduce experimental observations of drag reduction. Two different cases have been simulated by a finite difference scheme which is second order accurate in space and time. In the first case, an external azimuthal magnetic field is imposed. In this case, the magnetic field acts on the mean axial velocity and complete laminarization of the flow at N(sub a) = 30 has been achieved. In the second case, an axial magnetic field is imposed which affects only fluctuating velocities, and thus the action is less efficient. This second case is more practical, but comparison between numerical and experimental results is only qualitative.
The Biermann Catastrophe in Numerical MHD
Graziani, Carlo; Lee, Dongwook; Lamb, Donald Q; Weide, Klaus; Fatenejad, Milad; Miller, Joshua
2014-01-01
The Biermann Battery effect is a popular mechanism for generating magnetic fields in initially unmagnetized plasmas, and is frequently invoked in cosmic magnetogenesis and studied in High-Energy Density laboratory physics experiments. Generation of magnetic fields by the Biermann effect due to mis-aligned density and temperature gradients in smooth flow _behind_ shocks is well known. We show that a magnetic field is also generated _within_ shocks as a result of the electron-ion charge separation that they induce. A straightforward implementation of the Biermann effect in MHD codes does not capture this physical process, and worse, produces unphysical magnetic fields at shocks whose value does not converge with resolution. We show that this breakdown of convergence is due to naive discretization. We show that a careful consideration of the kinetic picture of ion viscous shocks leads to a formulation of the Biermann effect in terms of the electron temperature -- which is continuous across shocks -- that gives r...
MHD power generation with fully ionized seed
Yamasaki, H.; Shioda, S.
1977-01-01
Recovery of power density in the regime of fully ionized seed has been demonstrated experimentally using an MHD disk generator with the effective Hall parameter up to 5.0 when the seed was fully ionized. The experiments were conducted with a shock-heated and potassium-seeded argon plasma under the following conditions: stagnation gas pressure = 0.92 atm, stagnation gas temperature = 2750 K, flow Mach number = 2.5, and seed fraction = 1.4 x 10/sup -5/. Measurements of electron-number density and spectroscopic observations of both potassium and argon lines confirmed that the recovery of power output was due to the reduction of ionization instability. This fact indicates that the successful operation of a disk generator utilizing nonequilibrium ionization seems to be possible and that the suppression of ionization instability can also provide higher adiabatic efficiency. Furthermore, the lower seed fraction offers technological advantages related to seed problems.
A helically distorted MHD flux rope model
Theobald, Michael L.; Montgomery, David
1990-01-01
A flux rope model is proposed which has a variable degree of helical distortion from axisymmetry. The basis for this suggestion is a series of numerical and analytical investigations of magnetohydrodynamic states which result when an axial electric current is directed down on dc magnetic field. The helically distorted states involve a flow velocity and seem to be favored because of their lower rate of energy dissipation. Emphasis is on the magnetometer and particle energy analyzer traces that might be characteristic of such flux ropes. It is shown that even a fractionally small helical distortion may considerably alter the traces in minimum-variance coordinates. In short, what may be fairly common MHD processes can render a flux rope almost unrecognizable under standard diagnostics, even if the departures from axisymmetry are not great.
Global MHD Models of the Solar Corona
Suess, S. T.; Rose, Franklin (Technical Monitor)
2001-01-01
Global magnetohydrodynamic (MHD) models of the solar corona are computationally intensive, numerically complex simulations that have produced important new results over the past few years. After a brief overview of how these models usually work, I will address three topics: (1) How these models are now routinely used to predict the morphology of the corona and analyze Earth and space-based remote observations of the Sun; (2) The direct application of these models to the analysis of physical processes in the corona and chromosphere and to the interpretation of in situ solar wind observations; and (3) The use of results from global models to validate the approximations used to make detailed studies of physical processes in the corona that are not otherwise possible using the global models themselves.
The Biermann catastrophe of numerical MHD
Graziani, C.; Tzeferacos, P.; Lee, D.; Lamb, D. Q.; Weide, K.; Fatenejad, M.; Miller, J.
2016-05-01
The Biermann Battery effect is frequently invoked in cosmic magnetogenesis and studied in High-Energy Density laboratory physics experiments. Unfortunately, direct implementation of the Biermann effect in MHD codes is known to produce unphysical magnetic fields at shocks whose value does not converge with resolution. We show that this convergence breakdown is due to naive discretization, which fails to account for the fact that discretized irrotational vector fields have spurious solenoidal components that grow without bound near a discontinuity. We show that careful consideration of the kinetics of ion viscous shocks leads to a formulation of the Biermann effect that gives rise to a convergent algorithm. We note a novel physical effect a resistive magnetic precursor in which Biermann-generated field in the shock “leaks” resistively upstream. The effect appears to be potentially observable in experiments at laser facilities.
Activation of MHD reconnection on ideal timescales
Landi, S; Del Zanna, L; Tenerani, A; Pucci, F
2016-01-01
Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number $S$, up to $10^7$. Results confirm that when the critical aspect ratio of $S^{1/3}$ is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfv\\'enic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be ro...
Resonant interactions of perturbations in MHD flows
Sagalakov, A.M.; Shtern, V.N.
1977-01-17
The nonlinear theory of hydrodynamic stability differentiates three types of interactions: deformation of the initial velocity profile by Reynolds stress pulsations, multiplication of harmonics, and the resonant interaction of harmonics with dissimilar wave numbers and frequencies. This article analyzes an approach considering the first and third of these non-linear mechanisms, producing an acceptable approximation of the averaged characteristics of a developing pulsation movement, particularly the averaged turbulent velocity profile. The approach consists in analysis of triharmonic oscillations, the parameters of which satisfy the resonant relationships. A model of a triharmonic pulsation mode is studied which is applicable to MHD flows. It is shown in particular how a magnetic field transverse to the flow plane suppresses the resonant interaction of three-dimensional perturbations. This agrees with experimental studies on two-dimensional turbulence conducted earlier. 11 references, 3 figures.
Turlur, S.
1996-09-20
In tokamaks such as Tore Supra, the plasma confinement magnetic structure can be severely affected when Magnetohydrodynamic (M.H.D.) instabilities are destabilized. Experimentally, these instabilities are detected as magnetic fluctuations with captors located against the inner wall of the vacuum vessel. Fourier analysis provides amplitude, frequency and wave numbers of magnetic modes. In case of fast or transient phenomena, the analysis of magnetic fluctuations is completed using the singular value decomposition. In this dissertation, these analysis techniques are used to study two specific examples of M.H.D. activity related to the m = 2, n = 1 mode. On Tore Supra, the onset of this mode have strong consequences on the stability of partially or fully non inductive discharges. A regular and persistent sawtooth-like regime is observed on the electronic temperature leading to a significant degradation of the central confinement. Heat exhaust and particle balance are also essential parameters to achieve stationary discharges. On Tore Supra, these are studied with the ergodic divertor which produces stochastic magnetic field lines at the plasma edge. For optimal operating conditions of the ergodic divertor, the growth of the m = 2, N = 1 mode can lead to sudden destruction of magnetic equilibrium. For both cases, understanding and characterization of mechanisms leading to the observed m = 2, n = 1 M.H.D. activity are fundamental to obtain stationary discharges. (author). 115 refs.
Turlur, S.
1996-09-20
In tokamaks such as Tore Supra, the plasma confinement magnetic structure can be severely affected when Magnetohydrodynamic (M.H.D.) instabilities are destabilized. Experimentally, these instabilities are detected as magnetic fluctuations with captors located against the inner wall of the vacuum vessel. Fourier analysis provides amplitude, frequency and wave numbers of magnetic modes. In case of fast or transient phenomena, the analysis of magnetic fluctuations is completed using the singular value decomposition. In this dissertation, these analysis techniques are used to study two specific examples of M.H.D. activity related to the m = 2, n = 1 mode. On Tore Supra, the onset of this mode have strong consequences on the stability of partially or fully non inductive discharges. A regular and persistent sawtooth-like regime is observed on the electronic temperature leading to a significant degradation of the central confinement. Heat exhaust and particle balance are also essential parameters to achieve stationary discharges. On Tore Supra, these are studied with the ergodic divertor which produces stochastic magnetic field lines at the plasma edge. For optimal operating conditions of the ergodic divertor, the growth of the m = 2, N = 1 mode can lead to sudden destruction of magnetic equilibrium. For both cases, understanding and characterization of mechanisms leading to the observed m = 2, n = 1 M.H.D. activity are fundamental to obtain stationary discharges. (author). 115 refs.
Global MHD simulations of Neptune's magnetosphere
Mejnertsen, L.; Eastwood, J. P.; Chittenden, J. P.; Masters, A.
2016-08-01
A global magnetohydrodynamic (MHD) simulation has been performed in order to investigate the outer boundaries of Neptune's magnetosphere at the time of Voyager 2's flyby in 1989 and to better understand the dynamics of magnetospheres formed by highly inclined planetary dipoles. Using the MHD code Gorgon, we have implemented a precessing dipole to mimic Neptune's tilted magnetic field and rotation axes. By using the solar wind parameters measured by Voyager 2, the simulation is verified by finding good agreement with Voyager 2 magnetometer observations. Overall, there is a large-scale reconfiguration of magnetic topology and plasma distribution. During the "pole-on" magnetospheric configuration, there only exists one tail current sheet, contained between a rarefied lobe region which extends outward from the dayside cusp, and a lobe region attached to the nightside cusp. It is found that the tail current always closes to the magnetopause current system, rather than closing in on itself, as suggested by other models. The bow shock position and shape is found to be dependent on Neptune's daily rotation, with maximum standoff being during the pole-on case. Reconnection is found on the magnetopause but is highly modulated by the interplanetary magnetic field (IMF) and time of day, turning "off" and "on" when the magnetic shear between the IMF and planetary fields is large enough. The simulation shows that the most likely location for reconnection to occur during Voyager 2's flyby was far from the spacecraft trajectory, which may explain the relative lack of associated signatures in the observations.
A Two-Fluid, MHD Coronal Model
Suess, S. T.; Wang, A.-H.; Wu, S. T.; Poletto, G.; McComas, D. J.
1999-01-01
We describe first results from a numerical two-fluid MHD model of the global structure of the solar Corona. The model is two-fluid in the sense that it accounts for the collisional energy exchange between protons and electrons. As in our single-fluid model, volumetric heat and Momentum sources are required to produce high speed wind from Corona] holes, low speed wind above streamers, and mass fluxes similar to the empirical solar wind. By specifying different proton and electron heating functions we obtain a high proton temperature in the coronal hole and a relatively low proton temperature above the streamer (in comparison with the electron temperature). This is consistent with inferences from SOHO/UltraViolet Coronagraph Spectrometer instrument (UVCS), and with the Ulysses/Solar Wind Observations Over the Poles of the Sun instrument (SWOOPS) proton and electron temperature measurements which we show from the fast latitude scan. The density in the coronal hole between 2 and 5 solar radii (2 and 5 R(sub S)) is similar to the density reported from SPARTAN 201.-01 measurements by Fisher and Guhathakurta [19941. The proton mass flux scaled to 1 AU is 2.4 x 10(exp 8)/sq cm s, which is consistent with Ulysses observations. Inside the closed field region, the density is sufficiently high so that the simulation gives equal proton and electron temperatures due to the high collision rate. In open field regions (in the coronal hole and above the streamer) the proton and electron temperatures differ by varying amounts. In the streamer the temperature and density are similar to those reported empirically by Li et al. [1998], and the plasma beta is larger than unity everywhere above approx. 1.5 R(sub S), as it is in all other MHD coronal streamer models [e.g., Steinolfson et al., 1982; also G. A. Gary and D. Alexander, Constructing the coronal magnetic field, submitted to Solar Physics, 1998].
Extension of the MURaM Radiative MHD Code for Coronal Simulations
Rempel, M.
2017-01-01
We present a new version of the MURaM radiative magnetohydrodynamics (MHD) code that allows for simulations spanning from the upper convection zone into the solar corona. We implement the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction, and an equilibrium ionization equation of state. We artificially limit the coronal Alfvén and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantify the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be obtained with values of the reduced speed of light just marginally larger than the maximum sound speed. Overall this leads to a fully explicit code that can compute the time evolution of the solar corona in response to photospheric driving using numerical time steps not much smaller than 0.1 s. Numerical simulations of the coronal response to flux emergence covering a time span of a few days are well within reach using this approach.
MHD simulations of three-dimensional resistive reconnection in a cylindrical plasma column
Striani, E.; Mignone, A.; Vaidya, B.; Bodo, G.; Ferrari, A.
2016-11-01
Magnetic reconnection is a plasma phenomenon where a topological rearrangement of magnetic field lines with opposite polarity results in dissipation of magnetic energy into heat, kinetic energy and particle acceleration. Such a phenomenon is considered as an efficient mechanism for energy release in laboratory and astrophysical plasmas. An important question is how to make the process fast enough to account for observed explosive energy releases. The classical model for steady state magnetic reconnection predicts reconnection times scaling as S1/2 (where S is the Lundquist number) and yields time-scales several order of magnitude larger than the observed ones. Earlier two-dimensional MHD simulations showed that for large Lundquist number the reconnection time becomes independent of S (`fast reconnection' regime) due to the presence of the secondary tearing instability that takes place for S ≳ 1 × 104. We report on our 3D MHD simulations of magnetic reconnection in a magnetically confined cylindrical plasma column under either a pressure balanced or a force-free equilibrium and compare the results with 2D simulations of a circular current sheet. We find that the 3D instabilities acting on these configurations result in a fragmentation of the initial current sheet in small filaments, leading to enhanced dissipation rate that becomes independent of the Lundquist number already at S ≃ 1 × 103.
Multi-MW Closed Cycle MHD Nuclear Space Power Via Nonequilibrium He/Xe Working Plasma
Litchford, Ron J.; Harada, Nobuhiro
2011-01-01
Prospects for a low specific mass multi-megawatt nuclear space power plant were examined assuming closed cycle coupling of a high-temperature fission reactor with magnetohydrodynamic (MHD) energy conversion and utilization of a nonequilibrium helium/xenon frozen inert plasma (FIP). Critical evaluation of performance attributes and specific mass characteristics was based on a comprehensive systems analysis assuming a reactor operating temperature of 1800 K for a range of subsystem mass properties. Total plant efficiency was expected to be 55.2% including plasma pre-ionization power, and the effects of compressor stage number, regenerator efficiency and radiation cooler temperature on plant efficiency were assessed. Optimal specific mass characteristics were found to be dependent on overall power plant scale with 3 kg/kWe being potentially achievable at a net electrical power output of 1-MWe. This figure drops to less than 2 kg/kWe when power output exceeds 3 MWe. Key technical issues include identification of effective methods for non-equilibrium pre-ionization and achievement of frozen inert plasma conditions within the MHD generator channel. A three-phase research and development strategy is proposed encompassing Phase-I Proof of Principle Experiments, a Phase-II Subscale Power Generation Experiment, and a Phase-III Closed-Loop Prototypical Laboratory Demonstration Test.
Kanki, Takashi; Nagata, Masayoshi; Kagei, Yasuhiro
2011-10-01
The dynamics of structures of magnetic field, current density, and plasma flow generated during multi-pulsed coaxial helicity injection in spherical torus is investigated by 3-D nonlinear MHD simulations. During the driven phase, the flux and current amplifications occur due to the merging and magnetic reconnection between the preexisting plasma in the confinement region and the ejected plasma from the gun region involving the n = 1 helical kink distortion of the central open flux column (COFC). Interestingly, the diamagnetic poloidal flow which tends toward the gun region is then observed due to the steep pressure gradients of the COFC generated by ohmic heating through an injection current winding around the inboard field lines, resulting in the formation of the strong poloidal flow shear at the interface between the COFC and the core region. This result is consistent with the flow shear observed in the HIST. During the decay phase, the configuration approaches the axisymmetric MHD equilibrium state without flow because of the dissipation of magnetic fluctuation energy to increase the closed flux surfaces, suggesting the generation of ordered magnetic field structure. The parallel current density λ concentrated in the COFC then diffuses to the core region so as to reduce the gradient in λ, relaxing in the direction of the Taylor state.
HIDENEK: An implicit particle simulation of kinetic-MHD phenomena in three-dimensional plasmas
Tanaka, Motohiko
1993-05-01
An advanced 'kinetic-MHD' simulation method and its applications to plasma physics are given in this lecture. This method is quite stable for studying strong nonlinear, kinetic processes associated with large space-scale, low-frequency electromagnetic phenomena of plasmas. A full set of the Maxwell equations, and the Newton-Lorentz equations of motion for particle ions and guiding-center electrons are adopted. In order to retain only the low-frquency waves and instabilities, implicit particle-field equations are derived. The present implicit-particle method is proved to reproduce the MHD eigenmodes such as Alfven, magnetosonic and kinetic Alfven waves in a thermally near-equilibrium plasma. In the second part of the lecture, several physics applications are shown. These include not only the growth of the instabilities of beam ions against the background plasmas and helical link of the current, but they also demonstrate nonlinear results such as pitch-angle scattering of the ions. Recent progress in the simulation of the Kelvin-Helmholtz instability is also presented with a special emphasis on the mixing of the plasma particles.
Demaison, Jean; Császár, Attila G.
2012-09-01
Based on a sample of 38 molecules, 47 accurate equilibrium CO bond lengths have been collected and analyzed. These ultimate experimental (reEX), semiexperimental (reSE), and Born-Oppenheimer (reBO) equilibrium structures are compared to reBO estimates from two lower-level techniques of electronic structure theory, MP2(FC)/cc-pVQZ and B3LYP/6-311+G(3df,2pd). A linear relationship is found between the best equilibrium bond lengths and their MP2 or B3LYP estimates. These (and similar) linear relationships permit to estimate the CO bond length with an accuracy of 0.002 Å within the full range of 1.10-1.43 Å, corresponding to single, double, and triple CO bonds, for a large number of molecules. The variation of the CO bond length is qualitatively explained using the Atoms in Molecules method. In particular, a nice correlation is found between the CO bond length and the bond critical point density and it appears that the CO bond is at the same time covalent and ionic. Conditions which permit the computation of an accurate ab initio Born-Oppenheimer equilibrium structure are discussed. In particular, the core-core and core-valence correlation is investigated and it is shown to roughly increase with the bond length.
MHD Disk Winds and Planetary Nebulae I. Existence and Applicability
Frank, A; Blackman, E G
2002-01-01
Winds from accretion disks have been proposed as the driving source for precessing jets and extreme bipolar morphologies in Planetary Nebulae (PNe) and proto-PNe (pPNe). In this paper we address the applicability of self-consistent MHD disk wind models to PNe and pPNe. We first review the basic features of magneto-centrifugal launching disk wind models adapting results from previously published non-self similar calculations of Peltier & Pudritz (1992). We then estimate the relevant conditions whichshould occur in PNe and pPNe accretion disks that form via binary interactions. Finally, examining conditions on dimensionless parameters needed for magneto-centrifugal disk wind models we show that such winds can recover the observed momentum and energy input rates for PNe and pPNe. High accretion rates are required in thelatter case (M_a approx 10^{-4} \\mdot) and we find that the observed total energy and momentum in pPNe can be recovered with disk wind models using existing disk formation scenarios
New aspects of plasma sheet dynamics - MHD and kinetic theory
H. Wiechen
Full Text Available Magnetic reconnection is a process of fundamental importance for the dynamics of the Earth's plasma sheet. In this context, the development of thin current sheets in the near-Earth plasma sheet is a topic of special interest because they could be a possible cause of microscopic fluctuations acting as collective non-idealness from a macroscopic point of view. Simulations of the near-Earth plasma sheet including boundary perturbations due to localized inflow through the northern (or southern plasma sheet boundary show developing thin current sheets in the near-Earth plasma sheet about 810 R_{E} tailwards of the Earth. This location is largely independent from the localization of the perturbation. The second part of the paper deals with the problem of the macroscopic non-ideal consequences of microscopic fluctuations. A new model is presented that allows the quantitative calculation of macroscopic non-idealness without considering details of microscopic instabilities or turbulence. This model is only based on the assumption of a strongly fluctuating, mixing dynamics on microscopic scales in phase space. The result of this approach is an expression for anomalous non-idealness formally similar to the Krook resistivity but now describing the macroscopic consequences of collective microscopic fluctuations, not of collisions.
Key words. Magnetospheric physics (plasma sheet · Space plasma physics (kinetic and MHD theory; magnetic reconnection
Local conservative regularizations of compressible MHD and neutral flows
Krishnaswami, Govind S; Thyagaraja, Anantanarayanan
2016-01-01
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper we propose a minimal, local, conservative, nonlinear, dispersive regularization of compressible flow and ideal MHD, in analogy with the KdV regularization of the 1D kinematic wave equation. This work extends and significantly generalizes earlier work on incompressible Euler and ideal MHD. It involves a micro-scale cutoff length lambda which is a function of density, unlike in the incompressible case. In MHD, it can be taken to be of order the electron collisionless skin depth c/omega_pe. Our regularization preserves the symmetries of the original systems, and with appropriate boundary conditions, leads to associated conservation laws. Energy and enstrophy are subject to a priori bounds determined by initial data in contrast to the unregularized systems. A Hamiltonian and Poisson bracket formulation is developed and applied ...
Generalized similarity method in unsteady two-dimensional MHD ...
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International Journal of Engineering, Science and Technology. Vol. 1, No. ... Controlling of crystallization processes in metallurgy and influence of magnetic field on discrete chemical systems bring. MHD and heat ...... Nomenclature. B. [T].
Laser-powered MHD generators for space application
Jalufka, N. W.
1986-10-01
Magnetohydrodynamic (MHD) energy conversion systems of the pulsed laser-supported detonation (LSD) wave, plasma MHD, and liquid-metal MHD (LMMHD) types are assessed for their potential as space-based laser-to-electrical power converters. These systems offer several advantages as energy converters relative to the present chemical, nuclear, and solar devices, including high conversion efficiency, simple design, high-temperature operation, high power density, and high reliability. Of these systems, the Brayton cycle liquid-metal MHD system appears to be the most attractive. The LMMHD technology base is well established for terrestrial applications, particularly with regard to the generator, mixer, and other system components. However, further research is required to extend this technology base to space applications and to establish the technology required to couple the laser energy into the system most efficiently. Continued research on each of the three system types is recommended.
Unsteady MHD free convective flow past a vertical porous plate ...
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2000 Mathematics subject classification: 76 W 05. Keywords: Free ... the design of MHD generators and accelerators, underground water energy storage system etc. ... In many works on plasma physics, the Hall effect is disregarded. But if the.
Resistive Tearing Instability in Electron-MHD: Application to Neutron Star Crusts
Gourgouliatos, Konstantinos N
2016-01-01
We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as $\\gamma \\propto B^{2/3} \\sigma^{-1/3}$ where $B$ is the magnetic field and $\\sigma$ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed the magnetic field forms the characteristic islands and X-type reconnection points, where ...
Modelling stellar jets with magnetospheres using as initial states analytical MHD solutions
Todorov, P; Cayatte, V; Sauty, C; Lima, J J G; Tsinganos, K
2016-01-01
In this paper we focus on the construction of stellar outflow models emerging from a polar coronal hole-type region surrounded by a magnetosphere in the equatorial regions during phases of quiescent accretion. The models are based on initial analytical solutions. We adopt a meridionally self-similar solution of the time-independent and axisymmetric MHD equations which describes effectively a jet originating from the corona of a star. We modify appropriately this solution in order to incorporate a physically consistent stellar magnetosphere. We find that the closed fieldline region may exhibit different behaviour depending on the associated boundary conditions and the distribution of the heat flux. However, the stellar jet in all final equilibrium states is very similar to the analytical one prescribed in the initial conditions. When the initial net heat flux is maintained, the magnetosphere takes the form of a dynamical helmet streamer with a quasi steady state slow magnetospheric wind. With no heat flux, a s...
Extraction of MHD Signal Based on Wavelet Transform
赵晴初; 赵彤; 李旻; 黄胜华; 徐佩霞
2002-01-01
Mirnov signals mixed with interferences are a kind of non-stationary signal. It can not obtain satisfactory effects to extract MHD signals from mirnov signals by Fourier Transform. This paper suggests that the wavelet transform can be used to treat mirnov signals. Theoretical analysis and experimental result have indicated that using the time-frequency analysis characteristics of the wavelet transform to filter mirnov signals can remove effectively interferences and extract useful MHD signals.
A "User-Friendly" Program for Vapor-Liquid Equilibrium.
Da Silva, Francisco A.; And Others
1991-01-01
Described is a computer software package suitable for teaching and research in the area of multicomponent vapor-liquid equilibrium. This program, which has a complete database, can accomplish phase-equilibrium calculations using various models and graph the results. (KR)
Thermodynamic and transport properties of gaseous tetrafluoromethane in chemical equilibrium
Hunt, J. L.; Boney, L. R.
1973-01-01
Equations and in computer code are presented for the thermodynamic and transport properties of gaseous, undissociated tetrafluoromethane (CF4) in chemical equilibrium. The computer code calculates the thermodynamic and transport properties of CF4 when given any two of five thermodynamic variables (entropy, temperature, volume, pressure, and enthalpy). Equilibrium thermodynamic and transport property data are tabulated and pressure-enthalpy diagrams are presented.
Equilibrium and pre-equilibrium emissions in proton-induced reactions on 203,205Tl
A Kaplan; A Aydin; E Tel; B Şarer
2009-02-01
In this study, the excitation functions for the reactions 203Tl(, )203Pb, 203Tl(, 3)203Pb, 203Tl(, 2)202Pb, 205Tl(, 4)202Pb, 203Tl(, 3)201Pb, 205Tl(, 5)201Pb, 203Tl(, 4)200Pb and 205Tl(, 6)200Pb have been calculated using pre-equilibrium and equilibrium reaction mechanisms. Calculated results based on hybrid model, geometry-dependent hybrid model and cascade-exciton model have been compared with the experimental data.
Mikel' son, Yu.Ya.; Yakovich, A.T.; Pavlov, S.I.
1978-01-01
Turbulent stresses are considered in an incompressible fluid due to MHD flow induced within an axisymmetric region by electromagnetic forces on the basis of the linearized equation of motion as well as on the basis of the stress tensor in terms of average velocities and turbulent viscosity. The turbulent viscosity is treated according to the Boussinesq hypothesis (constant turbulent viscosity), according to the generalized Karman hypothesis (turbulent viscosity a function of the derivatives of the velocity components with respect to the respective coordinates), or as the product of its coordinate functions. The results of numerical calculations indicate a close agreement between all these formulas for an average MHD flow and experimental data. Calculations including this additional turbulent force, appropriately related to the flow parameters, are applicable to the design of liquid-metal devices. 7 references, 3 figures.
Problems in equilibrium theory
Aliprantis, Charalambos D
1996-01-01
In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.
Bounded Computational Capacity Equilibrium
Hernandez, Penelope
2010-01-01
We study repeated games played by players with bounded computational power, where, in contrast to Abreu and Rubisntein (1988), the memory is costly. We prove a folk theorem: the limit set of equilibrium payoffs in mixed strategies, as the cost of memory goes to 0, includes the set of feasible and individually rational payoffs. This result stands in sharp contrast to Abreu and Rubisntein (1988), who proved that when memory is free, the set of equilibrium payoffs in repeated games played by players with bounded computational power is a strict subset of the set of feasible and individually rational payoffs. Our result emphasizes the role of memory cost and of mixing when players have bounded computational power.
Maget, P.; Huysmans, G. T. A.; Lütjens, H.; Ottaviani, M.; Moreau, Ph; Ségui, J.-L.
2009-06-01
Attempts to run non-inductive plasma discharges on Tore Supra sometimes fail due to the triggering of magneto-hydro-dynamic (MHD) instabilities that saturate at a large amplitude, producing degraded confinement and loss of wave driven fast electrons (the so-called MHD regime (Maget et al 2005 Nucl. Fusion 45 69-80)). In this paper we investigate the transition to this soft (in the sense of non-disruptive) MHD limit from experimental observations, and compare it with non-linear code predictions. Such a comparison suggests that different non-linear regimes, with periodic relaxations or saturation, are correctly understood. However, successful non-inductive discharges without detectable magnetic island at q = 2 cannot be reproduced if realistic transport coefficients are used in the computation. Additional physics seems mandatory for explaining these discharges, such as diamagnetic effects, that could also justify cases of abrupt transition to the MHD regime.
Golovin, Sergey V., E-mail: sergey@hydro.nsc.r [Lavrentyev Institute of Hydrodynamics SB RAS, 630090 Novosibirsk (Russian Federation); Department of Mechanics and Mathematics, Novosibirsk State University, 630090 Novosibirsk (Russian Federation)
2011-01-17
Equations of magnetohydrodynamics (MHD) in the natural curvilinear system of coordinates where trajectories and magnetic lines play a role of coordinate curves are reduced to the non-linear vector wave equation coupled with the incompressibility condition in the form of the generalized Cauchy integral. The symmetry group of obtained equation, equivalence transformation, and group classification with respect to the constitutive equation are calculated. New exact solutions with functional arbitrariness describing non-stationary incompressible flows with constant total pressure are given by explicit formulae. The corresponding magnetic surfaces have the shape of deformed nested cylinders, tori, or knotted tubes.
3D MHD VDE and disruptions simulations of tokamaks plasmas including some ITER scenarios
Paccagnella, R.; Strauss, H. R.; Breslau, J.
2009-03-01
Tokamaks vertical displacement events (VDEs) and disruptions simulations in toroidal geometry by means of a single fluid visco-resistive magneto-hydro-dynamic (MHD) model are presented in this paper. The plasma model is completed with the presence of a 2D wall with finite resistivity which allows the study of the relatively slowly growing magnetic perturbation, the resistive wall mode (RWM), which is, in this paper, the main drive of the disruption evolution. Amplitudes and asymmetries of the halo currents pattern at the wall are also calculated and comparisons with tokamak experimental databases and predictions for ITER are given.
Jahan, Shah; Sakidin, Hamzah; Nazar, Roslinda Mohd
2016-11-01
The behavior of magnetohydrodynamics (MHD) flow of viscous fluid near the stagnation point over a stretching cylinder with variable thermal conductivity is analyzed. Thermal conductivity is assumed to be linearly related with temperature. The joule heating effects due to magnetic field is also encountered here. Analytical solutions are developed for both momentum and energy equations by using the homotopy analysis method (HAM). The variations of different parameters on the velocity and temperature distributions along with the skin friction coefficient and local Nusselt number are displayed graphically. Numerical values for the skin friction coefficient are calculated and discussed
Fault analysis of mid-channel power takeoff in DCW MHD generators
Ishikawa, M.; Wu, Y. C. L.; Scott, M. H.
1982-06-01
Analysis is presented of the effect of loading faults on the mid-channel power takeoff of a diagonal-conducting-wall MHD generator in special loading schemes. Two-dimensional calculations indicate that an open-circuit condition in the upstream load circuit results in a large current density at the power takeoff anode and drives a shorting current over the interframe insulators at the cathode side. A short-circuit condition in the upstream load circuit results in a large current density at the power takeoff cathode and a shorting current over the interframe insulators at the anode side.
General Search Market Equilibrium
Albrecht, James W.; Axell, Bo
1982-01-01
In this paper we extend models of “search market equilibrium” to incorporate general equilibrium considerations. The model we treat is one with a single product market and a single labor market. Imperfectly informed individuals follow optimal strategies in searching for a suitably low price and high wage. For any distribution of price and wage offers across firms these optimal strategies generate product demand and labor supply schedules. Firms then choose prices and wages to maximize expecte...
Equilibrium statistical mechanics
Jackson, E Atlee
2000-01-01
Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t
Tourism Equilibrium Price Trends
Mohammad Mohebi
2012-01-01
Full Text Available Problem statement: A review of the tourism history shows that tourism as an industry was virtually unknown in Malaysia until the late 1960s. Since then, it has developed and grown into a major industry, making an important contribution to the country's economy. By allocating substantial funds to the promotion of tourism and the provision of the necessary infrastructure, the government has played an important role in the impressive progress of the Malaysian tourism industry. One of the important factors which can attract tourists to Malaysia is the tourism price. Has the price of tourism decreased? To answer this question, it is necessary to obtain the equilibrium prices as well as the yearly trend for Malaysia during the sample period as it will be useful for analysis of the infrastructure situation of the tourism industry in this country. The purpose of the study is to identify equilibrium tourism price trends in Malaysian tourism market. Approach: We use hotel room as representative of tourism market. Quarterly data from 1995-2009 are used and a dynamic model of simultaneous equation is employed. Results: Based on the result during the period of 1995 until 2000, the growth rate of the equilibrium price was greater than consumer price index and producer price index. Conclusion: In the Malaysian tourism market, new infrastructure during this period had not been developed to keep pace with tourist arrivals.
Kourdey, A.
2002-09-15
The determination of the sliding surface of slope (dam, slope natural..) is one of the important and complicated problems in geotechnics. The Analyze of stability by the methods of Limit Equilibrium like the method of slices are the most used methods. They are able to determine a safety factor for a geometrically defined failure surface. These methods well adapted to the homogeneous mediums, have been developed a lot but they do not integrate the basic relations of mechanics (stress-strain). The numerical methods are better adapted to mediums having more complexity (effect of water, seismicity, fracturing,..). But, they are seldom used to determine a sliding surface and a safety factor. Each family offers appreciable advantages in the analysis of slope stability. For that purpose, we have developed a method that combines the advantages of the numerical methods as well as those of Limit Equilibrium allowing obtaining a slip surface determined by the calculated constraints. This slip surface may be imposed or better optimized, thus providing a minimal safety factor. Methods of operation research are used to obtain this surface. They are search methods by level, dynamic research.. or both at the same time. We integrated these developments in an existing computer code based on the method of Finite Differences known as FLAC. The stresses are determined for a linear behavior and for nonlinear. Interfaces and graphic tools are also produced to facilitate the analysis of stability. The validity of this approach was carried out for a standard case of slope, we analyzed and compared the results with the methods of Limit Equilibrium. The parametric study shows that this approach takes account of different parameters, which influences stability. We also kept a particular place for the application on real cases presenting slopes of different nature (dams, mining slops,...). (author)
Pulse Detonation Rocket MHD Power Experiment
Litchford, Ron J.; Cook, Stephen (Technical Monitor)
2002-01-01
A pulse detonation research engine (MSFC (Marshall Space Flight Center) Model PDRE (Pulse Detonation Rocket Engine) G-2) has been developed for the purpose of examining integrated propulsion and magnetohydrodynamic power generation applications. The engine is based on a rectangular cross-section tube coupled to a converging-diverging nozzle, which is in turn attached to a segmented Faraday channel. As part of the shakedown testing activity, the pressure wave was interrogated along the length of the engine while running on hydrogen/oxygen propellants. Rapid transition to detonation wave propagation was insured through the use of a short Schelkin spiral near the head of the engine. The measured detonation wave velocities were in excess of 2500 m/s in agreement with the theoretical C-J velocity. The engine was first tested in a straight tube configuration without a nozzle, and the time resolved thrust was measured simultaneously with the head-end pressure. Similar measurements were made with the converging-diverging nozzle attached. The time correlation of the thrust and head-end pressure data was found to be excellent. The major purpose of the converging-diverging nozzle was to configure the engine for driving an MHD generator for the direct production of electrical power. Additional tests were therefore necessary in which seed (cesium-hydroxide dissolved in methanol) was directly injected into the engine as a spray. The exhaust plume was then interrogated with a microwave interferometer in an attempt to characterize the plasma conditions, and emission spectroscopy measurements were also acquired. Data reduction efforts indicate that the plasma exhaust is very highly ionized, although there is some uncertainty at this time as to the relative abundance of negative OH ions. The emission spectroscopy data provided some indication of the species in the exhaust as well as a measurement of temperature. A 24-electrode-pair segmented Faraday channel and 0.6 Tesla permanent
Pulse Detonation Rocket MHD Power Experiment
Litchford, Ron J.; Cook, Stephen (Technical Monitor)
2002-01-01
A pulse detonation research engine (MSFC (Marshall Space Flight Center) Model PDRE (Pulse Detonation Rocket Engine) G-2) has been developed for the purpose of examining integrated propulsion and magnetohydrodynamic power generation applications. The engine is based on a rectangular cross-section tube coupled to a converging-diverging nozzle, which is in turn attached to a segmented Faraday channel. As part of the shakedown testing activity, the pressure wave was interrogated along the length of the engine while running on hydrogen/oxygen propellants. Rapid transition to detonation wave propagation was insured through the use of a short Schelkin spiral near the head of the engine. The measured detonation wave velocities were in excess of 2500 m/s in agreement with the theoretical C-J velocity. The engine was first tested in a straight tube configuration without a nozzle, and the time resolved thrust was measured simultaneously with the head-end pressure. Similar measurements were made with the converging-diverging nozzle attached. The time correlation of the thrust and head-end pressure data was found to be excellent. The major purpose of the converging-diverging nozzle was to configure the engine for driving an MHD generator for the direct production of electrical power. Additional tests were therefore necessary in which seed (cesium-hydroxide dissolved in methanol) was directly injected into the engine as a spray. The exhaust plume was then interrogated with a microwave interferometer in an attempt to characterize the plasma conditions, and emission spectroscopy measurements were also acquired. Data reduction efforts indicate that the plasma exhaust is very highly ionized, although there is some uncertainty at this time as to the relative abundance of negative OH ions. The emission spectroscopy data provided some indication of the species in the exhaust as well as a measurement of temperature. A 24-electrode-pair segmented Faraday channel and 0.6 Tesla permanent
Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions
Allegrini, Paolo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo; West, Bruce J.
2005-03-01
We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.
EVIDENCE OF ACTIVE MHD INSTABILITY IN EULAG-MHD SIMULATIONS OF SOLAR CONVECTION
Lawson, Nicolas; Strugarek, Antoine; Charbonneau, Paul, E-mail: nicolas.laws@gmail.ca, E-mail: strugarek@astro.umontreal.ca, E-mail: paulchar@astro.umontreal.ca [Département de Physique, Université de Montréal, C.P. 6128 Succ. Centre-ville, Montréal, Qc H3C 3J7 (Canada)
2015-11-10
We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD “millennium simulation” of Passos and Charbonneau. This simulation sustains a large-scale magnetic cycle characterized by solar-like polarity reversals taking place on a regular multidecadal cadence, and in which zonally oriented bands of strong magnetic fields accumulate below the convective layers, in response to turbulent pumping from above in successive magnetic half-cycles. Key aspects of this simulation include low numerical dissipation and a strongly sub-adiabatic fluid layer underlying the convectively unstable layers corresponding to the modeled solar convection zone. These properties are conducive to the growth and development of two-dimensional instabilities that are otherwise suppressed by stronger dissipation. We find evidence for the action of a non-axisymmetric magnetoshear instability operating in the upper portions of the stably stratified fluid layers. We also investigate the possibility that the Tayler instability may be contributing to the destabilization of the large-scale axisymmetric magnetic component at high latitudes. On the basis of our analyses, we propose a global dynamo scenario whereby the magnetic cycle is driven primarily by turbulent dynamo action in the convecting layers, but MHD instabilities accelerate the dissipation of the magnetic field pumped down into the overshoot and stable layers, thus perhaps significantly influencing the magnetic cycle period. Support for this scenario is found in the distinct global dynamo behaviors observed in an otherwise identical EULAG-MHD simulations, using a different degree of sub-adiabaticity in the stable fluid layers underlying the convection zone.
何世文; 刘咏; 郭晟
2009-01-01
The cooling rate of aluminum alloy powders prepared by ultrasonic gas atomization process was calculated through the convection heat transfer principle.A simple and theoretical model is established,which can be expressed as |dTd/dt|=12/ρ·Cp·(Td-Tf)·kg/d2.The average cooling rates of Al-Ni-Ce-Fe-Cu alloy powders prepared by argon gas atomization and by helium gas atomization are about 104～107 K/s and 105～108 K/s,respectively.The critical cooling rate is calculated to be 3.74× 105 K/s for Al-Ni-Ce-Fe-Cu alloy amorphous powders prepared by argon gas atomization.The cooling rates of gas-atomized powder particles estimated from secondary dendrite arm spacing are in consistence to those predicted from the theoretical model.%依据对流换热原理,对超音速气体雾化非平衡态铝合金粉末的冷却速度进行了理论计算.获得了一个较简单的理论计算公式,其表达式为|dTd/dt|=12/p·Cp·(Td-Tf)·kg/d2.根据理论公式,氩气和氦气雾化制备铝合金粉的冷却速度分别为104～107和105～108K、s,其结果与前期科研者的计算结果相符,且计算公式更简化.对于氩气雾化制各Al-NiCe-Fe-Cu合金而言,获得非晶态粉末其临界冷却速度为3.74×109K/S.通过测定合金晶态粉末的二次枝晶臂间距,并利用冷却速度和枝晶臂间距之间的经验关系,验算了合金粉末的冷却速度.其结果与理论计算相吻合.
Thermodynamic Calculations for Complex Chemical Mixtures
Mcbride, B. J.
1986-01-01
General computer program, CECTRP, developed for calculation of thermodynamic properties of complex mixtures with option to calculate transport properties of these mixtures. Free-energy minimization technique used in equilibrium calculation. Rigorous equations used in transport calculations. Program calculates equilibrium compositions and corresponding thermodynamic and transport properties of mixtures. CECTRP accommodates up to 24 reactants, 20 elements, and 600 products, 400 of which are condensed. Written in FORTRAN IV for any large computer system.
Noncompact Equilibrium Points and Applications
Zahra Al-Rumaih
2012-01-01
Full Text Available We prove an equilibrium existence result for vector functions defined on noncompact domain and we give some applications in optimization and Nash equilibrium in noncooperative game.
MHD Disc Winds and Linewidth Distributions
Chajet, Laura S
2013-01-01
We study AGN emission line profiles combining an improved version of the accretion disc-wind model of Murray & Chiang with the magneto-hydrodynamic model of Emmering et al. We show how the shape, broadening and shift of the C IV line depend not only on the viewing angle to the object but also on the wind launching angle, especially for small launching angles. We have compared the dispersions in our model C IV linewidth distributions to observational upper limit on that dispersion, considering both smooth and clumpy torus models. As the torus half-opening angle (measured from the polar axis) increases above about 18? degrees, increasingly larger wind launching angles are required to match the observational constraints. Above a half-opening angle of about 47? degrees, no wind launch angle (within the maximum allowed by the MHD solutions) can match the observations. Considering a model that replaces the torus by a warped disc yields the same constraints obtained with the two other models.
Simulation of MHD collimation from differential rotation
Carey, Christopher
2005-10-01
Recent observations indicate that astrophysical outflows from active galactic nuclei are permeated with helical magnetic fields[1]. The most promising theory for the formation of the magnetic configurations in these magnetically driven jets is the coiling of an initial seed field by the differential rotation of the accretion disk surrounding the central object. We have begun simulations that are relevant to these Poynting jets using the NIMROD code[2]. To simulate dynamics on length scales that are significantly larger than the accretion disk, the non-relativistic MHD equations are evolved on a hemispherical logarithmic mesh. The accretion disk is treated as a condition on the lower boundary by applying a Keplerian velocity to the azimuthal component of the fluid velocity and a prescribed flux of mass through the boundary. The magnetic field configuration is initialized to a dipole like field. Formation of a jet outflow is observed later in time. The initial field is coiled up and collimated, driving a large current density on the axis of symmetry. Slipping of magnetic field lines due to non-ideal effects has been investigated. 1. Asada K. et. al., Pub. of the Astr. Soc. of Japan, 54, L39-L43, 2002 2. Sovinec C. et. al., J. Comp. Phys., 195, 355-386, 2004
Nonlinear MHD waves in a Prominence Foot
Ofman, Leon; Kucera, Therese; Schmieder, Brigitte
2015-01-01
We study nonlinear waves in a prominence foot using 2.5D MHD model motivated by recent high-resolution observations with Hinode/SOT in Ca~II emission of a prominence on October 10, 2012 showing highly dynamic small-scale motions in the prominence material. Observations of H$\\alpha$ intensities and of Doppler shifts show similar propagating fluctuations. However the optically thick nature of the emission lines inhibits unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity ($\\delta I/I\\sim \\delta n/n$). The waves are evident as significant density fluctuations that vary with height, and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with typical period in the range of 5-11 minutes, and wavelengths $\\sim <$2000 km. Recent Doppler shift observations show the transverse displacement of the propagating wav...
Activation of MHD reconnection on ideal timescales
Landi, S.; Papini, E.; Del Zanna, L.; Tenerani, A.; Pucci, F.
2017-01-01
Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number S, up to 107. Results confirm that when the critical aspect ratio of S 1/3 is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfvénic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be robust, as the predicted scaling is measured both in inviscid simulations and when using a Prandtl number P = 1 in the viscous regime.
Corrosion and arc erosion in MHD channels
Rosa, R.J. (Montana State Univ., Bozeman, MT (United States). Dept. of Mechanical Engineering); Pollina, R.J. (Montana State Univ., Bozeman, MT (United States). Dept. of Mechanical Engineering EG and G Energy Measurements, Inc., Las Vegas, NV (United States))
1992-08-01
The problems connected with gas side corrosion for the design of the lA4 (POC) channel hardware are explored and results of gas side wear rate tests in the Textron Mark VII facility are presented. It is shown that the proposed designs meet a 2000 hour lifetime criterion based upon these materials tests. Improvement in cathode lifetime is demonstrated with lower voltage intercathode gaps. The corrosion of these materials is discussed and it is shown how lifetimes are dependent upon gap voltage and average metal temperature. The importance of uniformity of slagging to the durability of the anode wall is demonstrated. The wear mechanism of the anodes in the MHD channel is analyzed. In addition to gas-side corrosion, the results of specific water corrosion tests of sidewall materials are discussed. All of the tests reported here were carried out to confirm the gas-side performance and the manufacturability of anode and sidewall designs and to address questions posed about the durability of tungsten-copper on the waterside. the results of water corrosion tests of the tungsten copper alloy sidewall material are presented to show that with proper control of waterside pH and, if necessary, dissolved oxygen, one can obtain reliable performance with no degradation of heat transfer with this material. The final choice of materials was determined primarily by the outcome of these tests and also by the question of the manufacturability of the prospective designs.
Extended Mixed Vector Equilibrium Problems
Mijanur Rahaman
2014-01-01
Full Text Available We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005, some existence results for both problems are proved in noncompact domain.
Mean gas opacity for circumstellar environments and equilibrium temperature degeneracy
Malygin, M G; Klahr, H; Dullemond, C P; Henning, Th
2014-01-01
In a molecular cloud dust opacity typically dominates over gas opacity, yet in the vicinities of forming stars dust is depleted, and gas is the sole provider of opacity. In the optically thin circumstellar environments the radiation temperature cannot be assumed to be equal to the gas temperature, hence the two-temperature Planck means are necessary to calculate the radiative equilibrium. By using the two-temperature mean opacity one does obtain the proper equilibrium gas temperature in a circumstellar environment, which is in a chemical equilibrium. A careful consideration of a radiative transfer problem reveals that the equilibrium temperature solution can be degenerate in an optically thin gaseous environment. We compute mean gas opacities based on the publicly available code DFSYNTHE by Kurucz and Castelli. We performed the calculations assuming local thermodynamic equilibrium and an ideal gas equation of state. The values were derived by direct integration of the high-resolution opacity spectrum. We prod...
Simulated equilibrium factor studies in radon chamber
Tiehchi Chu; Holing Liu [National Tsing Hua Univ., Hsinchu, Taiwan (China). Dept. of Nuclear Science
1996-05-01
A series of experiments have been conducted to study the influences of environmental parameters on the equilibrium factor. Most of them were carried out in a walk-in type chamber. The deposition velocity was calculated using the Jacobi model. The ranges of the environmental parameters studied in the experiments are humidity 30-90% r.h. and radon concentration 2-40 kBqm{sup -3}. The aerosol sources included electric fumigator, mosquito coil, incense, a cigarette with the particle concentration 2000-6500 cm{sup -3} and the attachment rate 10-350 h{sup -1}. The results of the experiment show that the equilibrium factor tends to decrease as the radon concentration increases. On the other hand, the equilibrium factor tends to increase as the humidity increases, and so is the increasing attachment rate. Of all the parameters mentioned above, the influence that aerosols have on the equilibrium factor is the predominant factor. The calculated deposition velocity for the unattached fraction of radon daughters tends to increase as the radon concentration increases. However, it tends to decrease as the humidity increases. (Author).
Laboratory Identification of MHD Eruption Criteria in the Solar Corona
Yamada, M.; Myers, C. E.; Ji, H.; Yoo, J.; Fox, W. R., II; Jara-Almonte, J.; Savcheva, A. S.; DeLuca, E. E.
2015-12-01
Ideal magnetohydrodynamic (MHD) instabilities such as the kink [1] and torus [2] instabilities are believed to play an important role in driving "storage-and-release" eruptions in the solar corona. These instabilities act on long-lived, arched magnetic flux ropes that are "line-tied" to the solar surface. In spite of numerous observational and computational studies, the conditions under which these instabilities produce an eruption remain a subject of intense debate. In this paper, we use a line-tied, arched flux rope experiment to study storage-and-release eruptions in the laboratory [3]. An in situ array of miniature magnetic probes is used to assess the equilibrium and stability of the laboratory flux ropes. Two major results are reported here: First, a new stability regime is identified where torus-unstable flux ropes fail to erupt. In this "failed torus" regime, the flux rope is torus-unstable but kink-stable. Under these conditions, a dynamic "toroidal field tension force" surges in magnitude and causes the flux rope to contract. This tension force, which is missing from existing eruption models, is the J×B force between self-generated poloidal currents in the flux rope and the toroidal (guide) component of the vacuum field. Secondly, a clear torus instability threshold is observed in the kink-unstable regime. This latter result, which is consistent with existing theoretical [4] and numerical [5] findings, verifies the key role of the torus instability in driving some solar eruptions. This research is supported by DoE Contract No. DE-AC02-09CH11466 and by the NSF/DoE Center for Magnetic Self-Organization (CMSO). [1] Hood & Priest, Geophys. Astrophys. Fluid Dynamics 17, 297 (1981) [2] Kliem & Török, Phys. Rev. Lett. 96, 255002 (2006) [3] Myers, Ph.D. Thesis, Princeton University (2015) [4] Olmedo & Zhang, Astrophys. J. 718, 433 (2010) [5] Török & Kliem, Astrophys. J. 630, L97 (2005)
Non-equilibrium thermodynamics
De Groot, Sybren Ruurds
1984-01-01
The study of thermodynamics is especially timely today, as its concepts are being applied to problems in biology, biochemistry, electrochemistry, and engineering. This book treats irreversible processes and phenomena - non-equilibrium thermodynamics.S. R. de Groot and P. Mazur, Professors of Theoretical Physics, present a comprehensive and insightful survey of the foundations of the field, providing the only complete discussion of the fluctuating linear theory of irreversible thermodynamics. The application covers a wide range of topics: the theory of diffusion and heat conduction, fluid dyn
Doss, E.D. [ed.] [Argonne National Lab., IL (United States); Sikes, W.C. [ed.] [Newport News Shipbuilding and Dry Dock Co., VA (United States)
1992-09-01
This report describes the work performed during Phase 1 and Phase 2 of the collaborative research program established between Argonne National Laboratory (ANL) and Newport News Shipbuilding and Dry Dock Company (NNS). Phase I of the program focused on the development of computer models for Magnetohydrodynamic (MHD) propulsion. Phase 2 focused on the experimental validation of the thruster performance models and the identification, through testing, of any phenomena which may impact the attractiveness of this propulsion system for shipboard applications. The report discusses in detail the work performed in Phase 2 of the program. In Phase 2, a two Tesla test facility was designed, built, and operated. The facility test loop, its components, and their design are presented. The test matrix and its rationale are discussed. Representative experimental results of the test program are presented, and are compared to computer model predictions. In general, the results of the tests and their comparison with the predictions indicate that thephenomena affecting the performance of MHD seawater thrusters are well understood and can be accurately predicted with the developed thruster computer models.
A non-equilibrium plasma generator
Lineberry, J.T.; Wu, Y.C.L.; Martin, J.F. [ERC, Incorporated, Tullahoma, TN (United States)
1993-12-31
This paper summarizes research ideas, results and activities on a DOE MHD SBIR entitled: {open_quote}A Light Metal Fueled Nonequilibrium Plasma Generator (NPG){close_quotes}. The NPG is a concept for a device that has the capability of producing a nonequilibrium plasma from metal combustion. The results of preliminary studies on the NPG concept are given. These studies address fundamentals of the NPG including operating concepts of the NPG concept, results of studies on the quality of the plasma that it can produce, and theoretical evaluations of the nonequilibrium ionization process in an MHD disk generator driven by an NPG. A discussion of potential applications for the NPG is given. These applications encompass pulse MHD power, commercial MHD power and disk MHD generator research.
Maia, Alex S C; Nascimento, Sheila T; Nascimento, Carolina C N; Gebremedhin, Kifle G
2016-05-01
The effects of air temperature and relative humidity on thermal equilibrium of goats in a tropical region was evaluated. Nine non-pregnant Anglo Nubian nanny goats were used in the study. An indirect calorimeter was designed and developed to measure oxygen consumption, carbon dioxide production, methane production and water vapour pressure of the air exhaled from goats. Physiological parameters: rectal temperature, skin temperature, hair-coat temperature, expired air temperature and respiratory rate and volume as well as environmental parameters: air temperature, relative humidity and mean radiant temperature were measured. The results show that respiratory and volume rates and latent heat loss did not change significantly for air temperature between 22 and 26°C. In this temperature range, metabolic heat was lost mainly by convection and long-wave radiation. For temperature greater than 30°C, the goats maintained thermal equilibrium mainly by evaporative heat loss. At the higher air temperature, the respiratory and ventilation rates as well as body temperatures were significantly elevated. It can be concluded that for Anglo Nubian goats, the upper limit of air temperature for comfort is around 26°C when the goats are protected from direct solar radiation.
A New MHD-assisted Stokes Inversion Technique
Riethmüller, T. L.; Solanki, S. K.; Barthol, P.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; van Noort, M.; Blanco Rodríguez, J.; Del Toro Iniesta, J. C.; Orozco Suárez, D.; Schmidt, W.; Martínez Pillet, V.; Knölker, M.
2017-03-01
We present a new method of Stokes inversion of spectropolarimetric data and evaluate it by taking the example of a Sunrise/IMaX observation. An archive of synthetic Stokes profiles is obtained by the spectral synthesis of state-of-the-art magnetohydrodynamics (MHD) simulations and a realistic degradation to the level of the observed data. The definition of a merit function allows the archive to be searched for the synthetic Stokes profiles that best match the observed profiles. In contrast to traditional Stokes inversion codes, which solve the Unno-Rachkovsky equations for the polarized radiative transfer numerically and fit the Stokes profiles iteratively, the new technique provides the full set of atmospheric parameters. This gives us the ability to start an MHD simulation that takes the inversion result as an initial condition. After a relaxation process of half an hour solar time we obtain physically consistent MHD data sets with a target similar to the observation. The new MHD simulation is used to repeat the method in a second iteration, which further improves the match between observation and simulation, resulting in a factor of 2.2 lower mean {χ }2 value. One advantage of the new technique is that it provides the physical parameters on a geometrical height scale. It constitutes a first step toward inversions that give results consistent with the MHD equations.
Dynamo action in dissipative, forced, rotating MHD turbulence
Shebalin, John V.
2016-06-01
Magnetohydrodynamic (MHD) turbulence is an inherent feature of large-scale, energetic astrophysical and geophysical magnetofluids. In general, these are rotating and are energized through buoyancy and shear, while viscosity and resistivity provide a means of dissipation of kinetic and magnetic energy. Studies of unforced, rotating, ideal (i.e., non-dissipative) MHD turbulence have produced interesting results, but it is important to determine how these results are affected by dissipation and forcing. Here, we extend our previous work and examine dissipative, forced, and rotating MHD turbulence. Incompressibility is assumed, and finite Fourier series represent turbulent velocity and magnetic field on a 643 grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields.
Results from a large-scale MHD propulsion experiment
Petrick, M.; Libera, J.; Bouillard, J. X.; Pierson, E. S.; Hill, D.
Magnetohydrodynamic (MHD) thrusters have long been recognized as potentially attractive candidates for ship propulsion because such systems eliminate the conventional rotating drive components. The MHD thruster is essentially an electromagnetic (EM) pump operating in seawater. An electrical current is passed directly through the seawater and interacts with an applied magnetic field; the interaction of the magnetic field and the electrode current in the seawater results in a Lorentz force acting on the water, and the reaction to this force propels the vessel forward. The concept of EM propulsion has been examined periodically during the past 35 years as an alternative method of propulsion for surface ships and submersibles. The conclusions reached in early studies were that MHD thrusters restricted to fields of 2 T (the state-of-the-art at that time) were impractical and very inefficient. With the evolution of superconducting magnet technology, later studies investigated the performance of MHD thrusters with much higher magnetic field strengths and concluded that at higher fields (greater than 6-T) practical MHD propulsion systems appear possible. The feasibility of attaining the requisite higher magnetic fields has increased markedly because of rapid advances in building high-field superconducting magnets and the recent evolution of high-temperature superconductors.
Shift-and-inverse Lanczos algorithm for ideal MHD stability analysis
Chen, J.; Nakajima, N.; Okamoto, M.
1997-11-01
CAS3D and TERPSICHORE have been designed to analyze the global ideal MHD stability of three dimensional equilibria. Their critical part is to obtain the smallest eigenvalue and its corresponding eigenvector of a large but sparse real symmetric band matrix. In CAS3D the inverse iteration have been applied to do this and the spectral shift is computed by EISPACK eigensolver. It has been shown that application of such kind of software becomes very expensive in the sense of computational time and storage when matrix order and bandwidth become very large. Here this problem is resolved by using the Lanczos algorithm which is economical in CPU time and storage and particularly suitable for very large scale problems. The version of CAS3D2MN with shift-and-inverse Lanczos algorithm is called CAS3D2MNv1. Practical calculations in CAS3D2MNv1 indicate that the shift-and-inverse Lanczos recursion needs only 15 - 20 steps to calculate the smallest eigenvalue. The computation is reliable and efficient. The storage is much smaller and CPU time is saved significantly by 50 - 100 times compared with EISPACK subroutine. Finally the ballooning mode in three dimensional MHD equilibria has been mentioned briefly. (author)
A New Axisymmetric MHD Model of the Interaction of the Solar Wind with Venus
DeZeeuw, Darren L.; Nagy, Andrew F.; Gombosi, Tamas I.; Powell, Kenneth G.; Luhmann, Janet G.
1996-01-01
A new two-dimensional axisymmetric MHD model is used to study the interaction of the solar wind with Venus under conditions where the interplanetary field is approximately aligned with the solar wind velocity. This numerical model solves the MHD transport equations for density, velocity, pressure, and magnetic field on an adaptively refined, unstructured grid system. This use of an adaptive grid allows high spatial resolution in regions of large density/velocity gradients and yet can be run on a workstation. The actual grid sizes vary from about 0.06 R(sub v) near the bowshock to 2 R(sub v) in the unperturbed solar wind. The results of the calculations are compared with observed magnetic field values obtained from the magnetometer on the Pioneer Venus Orbiter, at a time when the angle between the solar wind velocity vector and the interplanetary magnetic field (IMF) was only 7.6 deg. Good qualitative agreement between the observed and calculated field behavior is found. The overall results suggest that the induced magnetotail disappears when the IMF is radial for an extended time period and implies that it weakens when the field rotated through a near-radial orientation.
Calculated Atomic Volumes of the Actinide Metals
Skriver, H.; Andersen, O. K.; Johansson, B.
1979-01-01
The equilibrium atomic volume is calculated for the actinide metals. It is possible to account for the localization of the 5f electrons taking place in americium.......The equilibrium atomic volume is calculated for the actinide metals. It is possible to account for the localization of the 5f electrons taking place in americium....
Tearing mode stability calculations with pressure flattening
Ham, C J; Cowley, S C; Hastie, R J; Hender, T C; Liu, Y Q
2013-01-01
Calculations of tearing mode stability in tokamaks split conveniently into an external region, where marginally stable ideal MHD is applicable, and a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter. Pressure and current perturbations localized around the rational surface alter the stability of tearing modes. Equations governing the changes in the external solution and - are derived for arbitrary perturbations in axisymmetric toroidal geometry. The relationship of - with and without pressure flattening is obtained analytically for four pressure flattening functions. Resistive MHD codes do not contain the appropriate layer physics and therefore cannot predict stability directly. They can, however, be used to calculate -. Existing methods (Ham et al. 2012 Plasma Phys. Control. Fusion 54 025009) for extracting - from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface ...
Standing Slow MHD Waves in Radiatively Cooling Coronal Loops
Al-Ghafri, Khalil Salim
2015-01-01
The standing slow magneto-acoustic oscillations in cooling coronal loops are investigated. There are two damping mechanisms which are considered to generate the standing acoustic modes in coronal magnetic loops namely thermal conduction and radiation. The background temperature is assumed to change temporally due to optically thin radiation. In particular, the background plasma is assumed to be radiatively cooling. The effects of cooling on longitudinal slow MHD modes is analytically evaluated by choosing a simple form of radiative function that ensures the temperature evolution of the background plasma due to radiation coincides with the observed cooling profile of coronal loops. The assumption of low-beta plasma leads to neglect the magnetic field perturbation and eventually reduces the MHD equations to a 1D system modelling longitudinal MHD oscillations in a cooling coronal loop. The cooling is assumed to occur on a characteristic time scale much larger than the oscillation period that subsequently enables...
Machine modification for active MHD control in RFX
Sonato, P. E-mail: sonato@igi.pd.cnr.it; Chitarin, G.; Zaccaria, P.; Gnesotto, F.; Ortolani, S.; Buffa, A.; Bagatin, M.; Baker, W.R.; Dal Bello, S.; Fiorentin, P.; Grando, L.; Marchiori, G.; Marcuzzi, D.; Masiello, A.; Peruzzo, S.; Pomaro, N.; Serianni, G
2003-09-01
Recent studies on RFP and Tokamak devices call for an active control of the MHD and resistive wall modes to induce plasma mode rotation and to prevent mode phase locking. The results obtained on RFX, where slow rotation of phase locked modes has been induced, support the possibility of extending active MHD mode control through a substantial modification of the device. A new first wall with an integrated system of electric and magnetic transducers has been realised. A close fitting 3 mm thick Cu shell replaces the 65 mm Al shell. A toroidal support structure (TSS) made of stainless steel replaces the shell in supporting all the forces acting on the torus. A system of 192 saddle coils is provided to actively control the MHD modes. This system completely surrounds the toroidal surface and allows the generation of harmonic fields with m=0 and m=1 poloidal wave number and with a toroidal spectrum up to n=24.
Lattice Boltzmann Large Eddy Simulation Model of MHD
Flint, Christopher
2016-01-01
The work of Ansumali \\textit{et al.}\\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single rel...
Using Coronal Hole Maps to Constrain MHD Models
Caplan, Ronald M.; Downs, Cooper; Linker, Jon A.; Mikic, Zoran
2017-08-01
In this presentation, we explore the use of coronal hole maps (CHMs) as a constraint for thermodynamic MHD models of the solar corona. Using our EUV2CHM software suite (predsci.com/chd), we construct CHMs from SDO/AIA 193Å and STEREO-A/EUVI 195Å images for multiple Carrington rotations leading up to the August 21st, 2017 total solar eclipse. We then contruct synoptic CHMs from synthetic EUV images generated from global thermodynamic MHD simulations of the corona for each rotation. Comparisons of apparent coronal hole boundaries and estimates of the net open flux are used to benchmark and constrain our MHD model leading up to the eclipse. Specifically, the comparisons are used to find optimal parameterizations of our wave turbulence dissipation (WTD) coronal heating model.
Recent observations of MHD fluctuations in the solar wind
B. Bavassano
Full Text Available A short review of recent observations of solar wind fluctuations in the magnetohydrodynamic (MHD range of scales is presented. In recent years, the use of high time-resolution data on an extended interval of heliocentric distance has allowed significant advances in our knowledge of MHD fluctuations. We first focus on the origin and evolution of the Alfvénic-type fluctuations. The role of interplanetary sources and the influence of interactions with structures convected by the solar wind are examined. Then compressive fluctuations are investigated, with special attention being given to their nature and origin. Observations are discussed in the light of recent theories and models. Finally, predictions for MHD turbulence in polar regions of the heliosphere are highlighted.
A Parametric Study of Extended-MHD Drift Tearing
King, Jacob R
2014-01-01
The linear drift-tearing mode is analyzed for different regimes of the plasma-$\\beta$, ion-skin-depth parameter space with an unreduced, extended-MHD model. New dispersion relations are found at moderate plasma $\\beta$ and previous drift-tearing results are classified as applicable at small plasma $\\beta$. The drift stabilization of the mode in the regimes varies from non-existent/weak to complete. As the diamagnetic-drift frequency is proportional to the plasma $\\beta$, verification exercises with unreduced, extended-MHD models in the small plasma-$\\beta$ regimes are impractical. The new dispersion relations in the moderate plasma-$\\beta$ regimes are used to verify the extended-MHD implementation of the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. Given the small boundary-layer skin depth, discussion of the validity of the first-order finite-Larmour-radius model is presented.
MHD discontinuities in solar flares: continuous transitions and plasma heating
Ledentsov, L S
2015-01-01
The boundary conditions for the ideal MHD equations on a plane dis- continuity surface are investigated. It is shown that, for a given mass flux through a discontinuity, its type depends only on the relation between inclina- tion angles of a magnetic field. Moreover, the conservation laws on a surface of discontinuity allow changing a discontinuity type with gradual (continu- ous) changes in the conditions of plasma flow. Then there are the so-called transition solutions that satisfy simultaneously two types of discontinuities. We obtain all transition solutions on the basis of the complete system of boundary conditions for the MHD equations. We also found the expression describing a jump of internal energy of the plasma flowing through the dis- continuity. Firstly, this allows constructing a generalized scheme of possible continuous transitions between MHD discontinuities. Secondly, it enables the examination of the dependence of plasma heating by plasma density and configuration of the magnetic field near t...
MHD Flows in Compact Astrophysical Objects Accretion, Winds and Jets
Beskin, Vasily S
2010-01-01
Accretion flows, winds and jets of compact astrophysical objects and stars are generally described within the framework of hydrodynamical and magnetohydrodynamical (MHD) flows. Analytical analysis of the problem provides profound physical insights, which are essential for interpreting and understanding the results of numerical simulations. Providing such a physical understanding of MHD Flows in Compact Astrophysical Objects is the main goal of this book, which is an updated translation of a successful Russian graduate textbook. The book provides the first detailed introduction into the method of the Grad-Shafranov equation, describing analytically the very broad class of hydrodynamical and MHD flows. It starts with the classical examples of hydrodynamical accretion onto relativistic and nonrelativistic objects. The force-free limit of the Grad-Shafranov equation allows us to analyze in detail the physics of the magnetospheres of radio pulsars and black holes, including the Blandford-Znajek process of energy e...
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Statistical physics ""Beyond equilibrium
Ecke, Robert E [Los Alamos National Laboratory
2009-01-01
The scientific challenges of the 21st century will increasingly involve competing interactions, geometric frustration, spatial and temporal intrinsic inhomogeneity, nanoscale structures, and interactions spanning many scales. We will focus on a broad class of emerging problems that will require new tools in non-equilibrium statistical physics and that will find application in new material functionality, in predicting complex spatial dynamics, and in understanding novel states of matter. Our work will encompass materials under extreme conditions involving elastic/plastic deformation, competing interactions, intrinsic inhomogeneity, frustration in condensed matter systems, scaling phenomena in disordered materials from glasses to granular matter, quantum chemistry applied to nano-scale materials, soft-matter materials, and spatio-temporal properties of both ordinary and complex fluids.
Non-equilibrium dynamics from RPMD and CMD.
Welsch, Ralph; Song, Kai; Shi, Qiang; Althorpe, Stuart C; Miller, Thomas F
2016-11-28
We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t(4)) and O(t(1)), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t(5)) and O(t(2)), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.
ON THE PROPERTIES OF SLOW MHD SAUSAGE WAVES WITHIN SMALL-SCALE PHOTOSPHERIC MAGNETIC STRUCTURES
Freij, N.; Ruderman, M. S.; Erdélyi, R. [Solar Physics and Space Plasma Research Centre (SP2RC), School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH (United Kingdom); Dorotovič, I. [Slovak Central Observatory, P.O. Box 42, SK-94701 Hurbanovo (Slovakia); Morton, R. J. [Mathematical Modelling Lab, Northumbria University, Pandon Building, Camden Street, Newcastle upon Tyne, NE1 8ST (United Kingdom); Karlovský, V., E-mail: n.freij@sheffield.ac.uk, E-mail: ivan.dorotovic@suh.sk, E-mail: richard.morton@northumbria.ac.uk, E-mail: m.s.ruderman@sheffield.ac.uk, E-mail: astrokar@hl.cora.sk, E-mail: robertus@sheffield.ac.uk [Hlohovec Observatory and Planetarium, Sládkovičova 41, SK-92001 Hlohovec (Slovakia)
2016-01-20
The presence of magnetoacoustic waves in magnetic structures in the solar atmosphere is well-documented. Applying the technique of solar magneto-seismology (SMS) allows us to infer the background properties of these structures. Here, we aim to identify properties of the observed magnetoacoustic waves and study the background properties of magnetic structures within the lower solar atmosphere. Using the Dutch Open Telescope and Rapid Oscillations in the Solar Atmosphere instruments, we captured two series of high-resolution intensity images with short cadences of two isolated magnetic pores. Combining wavelet analysis and empirical mode decomposition (EMD), we determined characteristic periods within the cross-sectional (i.e., area) and intensity time series. Then, by applying the theory of linear magnetohydrodynamics (MHD), we identified the mode of these oscillations within the MHD framework. Several oscillations have been detected within these two magnetic pores. Their periods range from 3 to 20 minutes. Combining wavelet analysis and EMD enables us to confidently find the phase difference between the area and intensity oscillations. From these observed features, we concluded that the detected oscillations can be classified as slow sausage MHD waves. Furthermore, we determined several key properties of these oscillations such as the radial velocity perturbation, the magnetic field perturbation, and the vertical wavenumber using SMS. The estimated range of the related wavenumbers reveals that these oscillations are trapped within these magnetic structures. Our results suggest that the detected oscillations are standing harmonics, and this allows us to estimate the expansion factor of the waveguides by employing SMS. The calculated expansion factor ranges from 4 to 12.
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
On the Properties of Slow MHD Sausage Waves within Small-scale Photospheric Magnetic Structures
Freij, N.; Dorotovič, I.; Morton, R. J.; Ruderman, M. S.; Karlovský, V.; Erdélyi, R.
2016-01-01
The presence of magnetoacoustic waves in magnetic structures in the solar atmosphere is well-documented. Applying the technique of solar magneto-seismology (SMS) allows us to infer the background properties of these structures. Here, we aim to identify properties of the observed magnetoacoustic waves and study the background properties of magnetic structures within the lower solar atmosphere. Using the Dutch Open Telescope and Rapid Oscillations in the Solar Atmosphere instruments, we captured two series of high-resolution intensity images with short cadences of two isolated magnetic pores. Combining wavelet analysis and empirical mode decomposition (EMD), we determined characteristic periods within the cross-sectional (i.e., area) and intensity time series. Then, by applying the theory of linear magnetohydrodynamics (MHD), we identified the mode of these oscillations within the MHD framework. Several oscillations have been detected within these two magnetic pores. Their periods range from 3 to 20 minutes. Combining wavelet analysis and EMD enables us to confidently find the phase difference between the area and intensity oscillations. From these observed features, we concluded that the detected oscillations can be classified as slow sausage MHD waves. Furthermore, we determined several key properties of these oscillations such as the radial velocity perturbation, the magnetic field perturbation, and the vertical wavenumber using SMS. The estimated range of the related wavenumbers reveals that these oscillations are trapped within these magnetic structures. Our results suggest that the detected oscillations are standing harmonics, and this allows us to estimate the expansion factor of the waveguides by employing SMS. The calculated expansion factor ranges from 4 to 12.
HAN Dong; GUO Wen-Kang; XU Ping; LIANG Rong-Qing
2007-01-01
@@ Based on the Chapman-Enskog theory, we calculate the electrical conductivity of non-equilibrium air plasma in the two-temperature model. We consider different degrees of non-equilibrium, which is defined by the ratio of electronic temperature to heavy particles temperature. The method of computing the composition of air plasma is demonstrated. After calculating the electrical conductivity from electron temperature 1000 K to 15000K, the present result is compared with Murphy's study [Plasma Chem. Plasma Process 15 (1994) 279] for equilibrium case. All the calculation is completed at atmospheric pressure. The present results may have potential applications in numerical calculation of non-equilibrium air plasma.
Dynamics of nonlinear resonant slow MHD waves in twisted flux tubes
R. Erdélyi
2002-01-01
Full Text Available Nonlinear resonant magnetohydrodynamic (MHD waves are studied in weakly dissipative isotropic plasmas in cylindrical geometry. This geometry is suitable and is needed when one intends to study resonant MHD waves in magnetic flux tubes (e.g. for sunspots, coronal loops, solar plumes, solar wind, the magnetosphere, etc. The resonant behaviour of slow MHD waves is confined in a narrow dissipative layer. Using the method of simplified matched asymptotic expansions inside and outside of the narrow dissipative layer, we generalise the so-called connection formulae obtained in linear MHD for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These connection formulae for resonant MHD waves across the dissipative layer play a similar role as the well-known Rankine-Hugoniot relations connecting solutions at both sides of MHD shock waves. The key results are the nonlinear connection formulae found in dissipative cylindrical MHD which are an important extension of their counterparts obtained in linear ideal MHD (Sakurai et al., 1991, linear dissipative MHD (Goossens et al., 1995; Erdélyi, 1997 and in nonlinear dissipative MHD derived in slab geometry (Ruderman et al., 1997. These generalised connection formulae enable us to connect solutions obtained at both sides of the dissipative layer without solving the MHD equations in the dissipative layer possibly saving a considerable amount of CPU-time when solving the full nonlinear resonant MHD problem.
MHD stability of the MHH2 stellarator
Garabedian, P.R. [New York Univ., NY (United States). Courant Inst. of Mathematical Sciences
1998-12-31
The NSTAB code provides a computer implementation of the variational principle of magnetohydrodynamics. Excellent resolution is obtained by combining a spectral representation in the toroidal and poloidal angles with a low order, but exceptionally accurate, finite difference scheme in the radial direction. Conservation form of the magnetostatics equations is used to capture islands and current sheets effectively on crude grids. This method enables one to discuss global stability by analyzing bifurcated solutions of the equilibrium problem. The author applies it to investigate the physics of the MHH2 stellarator, whose magnetic structure has a remarkable property of quasi-axial symmetry.
Magnetohydrodynamic (MHD) modelling of solar active phenomena via numerical methods
Wu, S. T.
1988-01-01
Numerical ideal MHD models for the study of solar active phenomena are summarized. Particular attention is given to the following physical phenomena: (1) local heating of a coronal loop in an isothermal and stratified atmosphere, and (2) the coronal dynamic responses due to magnetic field movement. The results suggest that local heating of a magnetic loop will lead to the enhancement of the density of the neighboring loops through MHD wave compression. It is noted that field lines can be pinched off and may form a self-contained magnetized plasma blob that may move outward into interplanetary space.
Advances in Simulation of Wave Interactions with Extended MHD Phenomena
Batchelor, Donald B [ORNL; D' Azevedo, Eduardo [ORNL; Bateman, Glenn [ORNL; Bernholdt, David E [ORNL; Bonoli, P. [Massachusetts Institute of Technology (MIT); Bramley, Randall B [ORNL; Breslau, Joshua [ORNL; Elwasif, Wael R [ORNL; Foley, S. [Indiana University; Jaeger, Erwin Frederick [ORNL; Jardin, S. C. [Princeton Plasma Physics Laboratory (PPPL); Klasky, Scott A [ORNL; Kruger, Scott E [ORNL; Ku, Long-Poe [ORNL; McCune, Douglas [Princeton Plasma Physics Laboratory (PPPL); Ramos, J. [Massachusetts Institute of Technology (MIT); Schissel, David P [ORNL; Schnack, Dalton D [ORNL
2009-01-01
The Integrated Plasma Simulator (IPS) provides a framework within which some of the most advanced, massively-parallel fusion modeling codes can be interoperated to provide a detailed picture of the multi-physics processes involved in fusion experiments. The presentation will cover four topics: (1) recent improvements to the IPS, (2) application of the IPS for very high resolution simulations of ITER scenarios, (3) studies of resistive and ideal MHD stability in tokamak discharges using IPS facilities, and (4) the application of RF power in the electron cyclotron range of frequencies to control slowly growing MHD modes in tokamaks and initial evaluations of optimized location for RF power deposition.
Advances in Simulation of Wave Interaction with Extended MHD Phenomena
Batchelor, Donald B [ORNL; Abla, Gheni [ORNL; D' Azevedo, Ed F [ORNL; Bateman, Glenn [Lehigh University, Bethlehem, PA; Bernholdt, David E [ORNL; Berry, Lee A [ORNL; Bonoli, P. [Massachusetts Institute of Technology (MIT); Bramley, R [Indiana University; Breslau, Joshua [ORNL; Chance, M. [Princeton Plasma Physics Laboratory (PPPL); Chen, J. [Princeton Plasma Physics Laboratory (PPPL); Choi, M. [General Atomics; Elwasif, Wael R [ORNL; Foley, S. [Indiana University; Fu, GuoYong [Princeton Plasma Physics Laboratory (PPPL); Harvey, R. W. [CompX, Del Mar, CA; Jaeger, Erwin Frederick [ORNL; Jardin, S. C. [Princeton Plasma Physics Laboratory (PPPL); Jenkins, T [University of Wisconsin; Keyes, David E [Columbia University; Klasky, Scott A [ORNL; Kruger, Scott [Tech-X Corporation; Ku, Long-Poe [Princeton Plasma Physics Laboratory (PPPL); Lynch, Vickie E [ORNL; McCune, Douglas [Princeton Plasma Physics Laboratory (PPPL); Ramos, J. [Massachusetts Institute of Technology (MIT); Schissel, D. [General Atomics; Schnack, [University of Wisconsin; Wright, J. [Massachusetts Institute of Technology (MIT)
2009-01-01
The Integrated Plasma Simulator (IPS) provides a framework within which some of the most advanced, massively-parallel fusion modeling codes can be interoperated to provide a detailed picture of the multi-physics processes involved in fusion experiments. The presentation will cover four topics: 1) recent improvements to the IPS, 2) application of the IPS for very high resolution simulations of ITER scenarios, 3) studies of resistive and ideal MHD stability in tokamk discharges using IPS facilities, and 4) the application of RF power in the electron cyclotron range of frequencies to control slowly growing MHD modes in tokamaks and initial evaluations of optimized location for RF power deposition.
Advances in simulation of wave interactions with extended MHD phenomena
Batchelor, D; D' Azevedo, E; Bernholdt, D E; Berry, L; Elwasif, W; Jaeger, E [Oak Ridge National Laboratory (United States); Abla, G; Choi, M [General Atomics (United States); Bateman, G [Lehigh University (United States); Bonoli, P [Plasma Science and Fusion Center, Massachusetts Institute of Technology (United States); Bramley, R; Foley, S [Indiana University (United States); Breslau, J; Chance, M; Chen, J; Fu, G; Jardin, S [Princeton Plasma Physics Laboratory (United States); Harvey, R [CompX International (United States); Jenkins, T [University of Wisconsin (United States); Keyes, D, E-mail: batchelordb@ornl.go [Columbia University (United States)
2009-07-01
The Integrated Plasma Simulator (IPS) provides a framework within which some of the most advanced, massively-parallel fusion modeling codes can be interoperated to provide a detailed picture of the multi-physics processes involved in fusion experiments. The presentation will cover four topics: 1) recent improvements to the IPS, 2) application of the IPS for very high resolution simulations of ITER scenarios, 3) studies of resistive and ideal MHD stability in tokamk discharges using IPS facilities, and 4) the application of RF power in the electron cyclotron range of frequencies to control slowly growing MHD modes in tokamaks and initial evaluations of optimized location for RF power deposition.
MHD Waves and Coronal Seismology: an overview of recent results
De Moortel, Ineke
2012-01-01
Recent observations have revealed that MHD waves and oscillations are ubiquitous in the solar atmosphere, with a wide range of periods. We give a brief review of some aspects of MHD waves and coronal seismology which have recently been the focus of intense debate or are newly emerging. In particular, we focus on four topics: (i) the current controversy surrounding propagating intensity perturbations along coronal loops, (ii) the interpretation of propagating transverse loop oscillations, (iii) the ongoing search for coronal (torsional) Alfven waves and (iv) the rapidly developing topic of quasi-periodic pulsations (QPP) in solar flares.
Superconducting magnet system for an experimental disk MHD facility
Knoopers, H.G.; Kate, ten, H.H.J.; Klundert, van de, L.J.M.
1991-01-01
A predesign of a split-pair magnet for a magnetohydrodynamic (MHD) facility for testing a 10-MW open-cycle disk or a 5-MW closed-cycle disk generator is presented. The magnet system consists of a NbTi and a Nb 3Sn section, which provide a magnetic field of 9 T in the active area of the MHD channel. The optimization process, which is based on minimum conductor costs is discussed, and the proposed conductor design is described. Basic solutions for the construction of the magnet, the cryostat an...
Relativistic MHD and excision: formulation and initial tests
Neilsen, David; Hirschmann, Eric W; Millward, R Steven [Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602 (United States)
2006-08-21
A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids and elliptic and hyperbolic divergence cleaning.
Relativistic MHD and black hole excision: Formulation and initial tests
Neilsen, D; Millward, R S; Hirschmann, Eric W; Neilsen, David
2006-01-01
A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids, and elliptic and hyperbolic divergence cleaning.
Extended MHD Effects in High Energy Density Experiments
Seyler, Charles
2016-10-01
The MHD model is the workhorse for computational modeling of HEDP experiments. Plasma models are inheritably limited in scope, but MHD is expected to be a very good model for studying plasmas at the high densities attained in HEDP experiments. There are, however, important ways in which MHD fails to adequately describe the results, most notably due to the omission of the Hall term in the Ohm's law (a form of extended MHD or XMHD). This talk will discuss these failings by directly comparing simulations of MHD and XMHD for particularly relevant cases. The methodology is to simulate HEDP experiments using a Hall-MHD (HMHD) code based on a highly accurate and robust Discontinuous Galerkin method, and by comparison of HMHD to MHD draw conclusions about the impact of the Hall term. We focus on simulating two experimental pulsed power machines under various scenarios. We examine the MagLIF experiment on the Z-machine at Sandia National Laboratories and liner experiments on the COBRA machine at Cornell. For the MagLIF experiment we find that power flow in the feed leads to low density plasma ablation into the region surrounding the liner. The inflow of this plasma compresses axial magnetic flux onto the liner. In MHD this axial flux tends to resistively decay, whereas in HMHD a force-free current layer sustains the axial flux on the liner leading to a larger ratio of axial to azimuthal flux. During the liner compression the magneto-Rayleigh-Taylor instability leads to helical perturbations due to minimization of field line bending. Simulations of a cylindrical liner using the COBRA machine parameters can under certain conditions exhibit amplification of an axial field due to a force-free low-density current layer separated by some distance from the liner. This results in a configuration in which there is predominately axial field on the liner inside the current layer and azimuthal field outside the layer. We are currently attempting to experimentally verify the simulation
The superconducting MHD-propelled ship YAMATO-1
Sasakawa, Yohei; Takezawa, Setsuo; Sugawara, Yoshinori; Kyotani, Yoshihiro
1995-04-01
In 1985 the Ship & Ocean Foundation (SOF) created a committee under the chairmanship of Mr. Yohei Sasakawa, Former President of the Ship & Ocean Foundation, and began researches into superconducting magnetohydrodynamic (MHD) ship propulsion. In 1989 SOF set to construction of a experimental ship on the basis of theoretical and experimental researches pursued until then. The experimental ship named YAMATO-1 became the world's first superconducting MHD-propelled ship on her trial runs in June 1992. This paper describes the outline of the YAMATO-1 and sea trial test results.
Minimizing the Free Energy: A Computer Method for Teaching Chemical Equilibrium Concepts.
Heald, Emerson F.
1978-01-01
Presents a computer method for teaching chemical equilibrium concepts using material balance conditions and the minimization of the free energy. Method for the calculation of chemical equilibrium, the computer program used to solve equilibrium problems and applications of the method are also included. (HM)
Calculations of Non-equilibrium Effects in Nano-conductors
Christensen, Rasmus Bjerregaard
This thesis is concerned with the interplay between electrical current and vibrational and plasmonic excitations. The development of nano-scale devices for electronics relies on the ability to identify individual atoms and molecules as well as their geometry and electronic structure. In this thesis...... of detecting defects in the hydrogen passivisation by IETS. Lastly a preliminary study of the heating due to the electrical current is described, investigating the effect of the deterministic current-induced forces, treated within the framework of the semi-classical generalized Langevin equation......(SGLE). For a pristine zigzag ribbon the deterministic current-induced forces is seen to give rise to runaway modes. For an armchair ribbon with partly dehydrogenated edges the deterministic current-induced forces is seen to break the symmetry and increase the excess heating...
General equilibrium without utility functions
Balasko, Yves; Tvede, Mich
2010-01-01
How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to re......How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known...... and the diffeomorphism of the equilibrium manifold with a Euclidean space; (2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; (3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; (4) for small trade vectors, the uniqueness, regularity...
Equilibrium models and variational inequalities
Konnov, Igor
2007-01-01
The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control. This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.- Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field- Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models- Covers the basics of theory and solution methods both for the complementarity and variational inequality probl...
On the Local Equilibrium Principle
Hessling, H
2001-01-01
A physical system should be in a local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This seems to be a natural characterization of local equilibrium, however the problem is to give a precise meaning to the qualitative phrase ``infinitesimally localized measurements''. A solution is suggested in form of a {\\em Local Equilibrium Condition} (LEC) which can be applied to non-interacting quanta. The Unruh temperature of massless quanta is derived by applying LEC to an arbitrary point inside the Rindler Wedge. Massless quanta outside a hot sphere are analyzed. A stationary spherically symmetric local equilibrium does only exist according to LEC if the temperature is globally constant. Using LEC a non-trivial stationary local equilibrium is found for rotating massless quanta between two concentric cylinders of different temperatures. This shows that quanta may behave like a fluid with a B\\'enard instability.
Dynamical Non-Equilibrium Molecular Dynamics
Giovanni Ciccotti
2013-12-01
Full Text Available In this review, we discuss the Dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD, which extends stationary NEMD to time-dependent situations, be they responses or relaxations. Based on the original Onsager regression hypothesis, implemented in the nineteen-seventies by Ciccotti, Jacucci and MacDonald, the approach permits one to separate the problem of dynamical evolution from the problem of sampling the initial condition. D-NEMD provides the theoretical framework to compute time-dependent macroscopic dynamical behaviors by averaging on a large sample of non-equilibrium trajectories starting from an ensemble of initial conditions generated from a suitable (equilibrium or non-equilibrium distribution at time zero. We also discuss how to generate a large class of initial distributions. The same approach applies also to the calculation of the rate constants of activated processes. The range of problems treatable by this method is illustrated by discussing applications to a few key hydrodynamic processes (the “classical” flow under shear, the formation of convective cells and the relaxation of an interface between two immiscible liquids.
Exploring Equilibrium Chemistry for Hot Exoplanets
Blumenthal, Sarah; Harrington, Joseph; Mandell, Avi; Hébrard, Eric; Venot, Olivia; Cubillos, Patricio; Challener, Ryan
2015-11-01
It has been established that equilibrium chemistry is usually achieved deep in the atmosphere of hot Jovians where timescales are short (Line and Young 2013). Thus, equilibrium chemistry has been used as a starting point (setting initial conditions) for evaluating disequilibrium processes. We explore parameters of setting these initial conditions including departures from solar metallicity, the number of species allowed in a system, the types of species allowed in a system, and different thermodynamic libraries in an attempt to create a standard for evaluating equilibrium chemistry. NASA's open source code Chemical Equilibrium and Applications (CEA) is used to calculate model planet abundances by varying the metallicity, in the pressure regime of 0.1 to 1 bar. These results are compared to a variety of exoplanets (Teq between 600 and 2100K) qualitatively by color maps of the dayside with different temperature redistributions. Additionally, CEA (with an updated thermodynamic library) is validated with the thermochemical model presented in Venot et al. (2012) for HD 209458b and HD 189733b. This same analysis has then been extended to the cooler planet HD 97658b. Spectra are generated from both models’ abundances using the open source code transit (https://github.com/exosports/transit) using the opacities of 15 molecules. We make the updated CEA thermodyanamic library and supporting Python scripts to do the CEA analyses available open source. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G.
Exploring Chemical Equilibrium in Hot Jovians
Blumenthal, Sarah; Harrington, Joseph; Mandell, Avi; Hébrard, Eric; Venot, Olivia; Cubillos, Patricio; Blecic, Jasmina; Challener, Ryan
2016-01-01
It has been established that equilibrium chemistry is usually achieved deep in the atmosphere of hot Jovians where timescales are short (Line and Yung 2013). Thus, equilibrium chemistry has been used as a starting point (setting initial conditions) for evaluating disequilibrium processes. We explore parameters of setting these initial conditions including departures from solar metallicity, the number of species allowed in a system, the types of species allowed in a system, and different thermodynamic libraries in an attempt to create a standard for evaluating equilibrium chemistry. NASA's open source code Chemical Equilibrium and Applications (CEA) is used to calculate model planet abundances by varying the metallicity, in the pressure regime 0.1 to 1 bar. These results are compared to a variety of exoplanets(Teq between 600 and 2100K) qualitatively by color maps of the dayside with different temperature redistributions. Additionally, CEA (with an up-dated thermodynamic library) is compared with the thermochemical model presented in Venotet al. (2012) for HD 209458b and HD 189733b. This same analysis is then applied to the cooler planet HD 97658b. Spectra are generated and we compare both models' outputs using the open source codetransit (https://github.com/exosports/transit) using the opacities of 15 molecules. We make the updated CEA thermodyanamic library and supporting Python scripts to do the CEA analyses available open source. Thiswork was supported by NASA Planetary Atmospheres grant NNX12AI69G.
2D-simulation of stationary MHD flows in the ducts of rectangular cross-section
Khalzov, Ivan; Ilgisonis, Victor
2005-10-01
The numerical code for a calculation of 2D stationary MHD flows of incompressible conducting viscous fluids (liquid metals) in straight and circular ducts of rectangular cross-section is developed. The flows are driven by the electrical current perpendicular both to the duct axis and to the external magnetic field. The code generalizes the well-known iterative Gauss-Seidel method for the case of systems of elliptic equations. The algorithm developed allows us to carry out the calculations of stationary flows in a wide range of Hartmann (Ha=110^3) and Reynolds (Re=110^6) numbers. The numerical results are presented for the experimental device, which is under construction in Russia.
Lyons, B. C.; Jardin, S. C.; Ramos, J. J.
2012-08-01
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f) in the conventional banana regime for both ions and electrons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h). We work in a 4D phase space in which ψ defines a flux surface, θ is the poloidal angle, v is the magnitude of the velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ. The Rosenbluth potentials, Φ and Ψ, which define the integral part of the collision operator, are expanded in Legendre series in cosχ, where χ is the pitch angle, Fourier series in cosθ, and finite elements in v. At each ψ, we solve a block tridiagonal system for hi (independent of fe), then solve another block tridiagonal system for he (dependent on fi). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia et al., J. Comput. Phys. 37, 183-204 (1980)] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D -C1 [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]).
Lyons, B. C. [Program in Plasma Physics, Princeton University, Princeton, New Jersey 08543-0451 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543-0451 (United States); Ramos, J. J. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 (United States)
2012-08-15
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f) in the conventional banana regime for both ions and electrons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h). We work in a 4D phase space in which {psi} defines a flux surface, {theta} is the poloidal angle, v is the magnitude of the velocity referenced to the mean flow velocity, and {lambda} is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and {lambda}. The Rosenbluth potentials, {Phi} and {Psi}, which define the integral part of the collision operator, are expanded in Legendre series in cos{chi}, where {chi} is the pitch angle, Fourier series in cos{theta}, and finite elements in v. At each {psi}, we solve a block tridiagonal system for h{sub i} (independent of f{sub e}), then solve another block tridiagonal system for h{sub e} (dependent on f{sub i}). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia et al., J. Comput. Phys. 37, 183-204 (1980)] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C{sup 1}[S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]).
B.C. Lyons, S.C. Jardin, and J.J. Ramos
2012-06-28
A new code, the Neoclassical Ion-Electron Solver (NIES), has been written to solve for stationary, axisymmetric distribution functions (f ) in the conventional banana regime for both ions and elec trons using a set of drift-kinetic equations (DKEs) with linearized Fokker-Planck-Landau collision operators. Solvability conditions on the DKEs determine the relevant non-adiabatic pieces of f (called h ). We work in a 4D phase space in which Ψ defines a flux surface, θ is the poloidal angle, v is the total velocity referenced to the mean flow velocity, and λ is the dimensionless magnetic moment parameter. We expand h in finite elements in both v and λ . The Rosenbluth potentials, φ and ψ, which define the integral part of the collision operator, are expanded in Legendre series in cos χ , where χ is the pitch angle, Fourier series in cos θ , and finite elements in v . At each ψ , we solve a block tridiagonal system for hi (independent of fe ), then solve another block tridiagonal system for he (dependent on fi ). We demonstrate that such a formulation can be accurately and efficiently solved. NIES is coupled to the MHD equilibrium code JSOLVER [J. DeLucia, et al., J. Comput. Phys. 37 , pp 183-204 (1980).] allowing us to work with realistic magnetic geometries. The bootstrap current is calculated as a simple moment of the distribution function. Results are benchmarked against the Sauter analytic formulas and can be used as a kinetic closure for an MHD code (e.g., M3D-C1 [S.C. Jardin, et al ., Computational Science & Discovery, 4 (2012).]).
Wexler, David B.; Hollweg, Joseph V.; Jensen, Elizabeth; Lionello, Roberto; Macneice, Peter J.; Coster, Anthea J.
2017-08-01
Study of coronal MHD wave energetics relies upon accurate representation of plasma particle number densities (ne) and magnetic field strengths. In the lower corona, these parameters are obtained indirectly, and typically presented as empirical equations as a function of heliocentric radial distance (solar offset, SO). The development of coronal global models using synoptic solar surface magnetogram inputs has provided refined characterization of the coronal plasma organization and magnetic field. We present a cross-analysis between a MHD thermodynamic simulation and Faraday rotation (FR) observations over SO 1.63-1.89 solar radii (Rs) near solar minimum. MESSENGER spacecraft radio signals with a line of sight (LOS) passing through the lower corona were recorded in dual polarization using the Green Bank Telescope in November 2009. Polarization position angle changes were obtained from Stokes parameters. The magnetic field vector (B) and ne along the LOS were obtained from a MHD thermodynamic simulation provided by the Community Coordinated Modeling Center. The modeled FR was computed as the integrated product of ne and LOS-aligned B component. The observations over the given SO range yielded an FR change of 7 radians. The simulation reproduced this change when the modeled ne was scaled up by 2.8x, close to values obtained using the Allen-Baumbach equation. No scaling of B from the model was necessary. A refined fit to the observations was obtained when the observationally based total electron content (TEC) curves were introduced. Changes in LOS TEC were determined from radio frequency shifts as the signal passed to successively lower electron concentrations during egress. A good fit to the observations was achieved with an offset of 7e21 m-2 added. Back-calculating ne along the LOS from the TEC curves, we found that the equivalent ne scaling compared to the model output was higher by a factor of 3. The combination of solar surface magnetogram-based MHD coronal
V. A. Sergeev
2008-08-01
Full Text Available We performed global MHD simulations to investigate the magnetotail response to the solar wind directional changes (V_{z}-variations. These changes, although small, cause significant variations of the neutral sheet shape and location even in the near and middle tail regions. They display a complicated temporal response, in which ~60 to 80% of the final shift of the neutral sheet in Z direction occurs within first 10–15 min (less for faster solar wind, whereas a much longer time (exceeding half hour is required to reach a new equilibrium. The asymptotic equilibrium shape of the simulated neutral sheet is consistent with predictions of Tsyganenko-Fairfield (2004 empirical model. To visualize a physical origin of the north-south tail motion we compared the values of the total pressure in the northern and southern tail lobes and found a considerable difference (10–15% for only 6° change of the solar wind direction used in the simulation. That difference builds up during the passage of the solar wind directional discontinuity and is responsible for the vertical shift of the neutral sheet, although some pressure difference remains in the near tail even near the new equilibrium. Surprisingly, at a given tailward distance, the response was found to be first initiated in the tail center (the "leader effect", rather than near the flanks, which can be explained by the wave propagation in the tail, and which may have interesting implications for the substorm triggering studies. The present results have serious implications for the data-based modeling, as they place constraints on the accuracy of tail magnetic configurations to be derived for specific events using data of multi-spacecraft missions, e.g. such as THEMIS.
Phillips, Rob
2015-03-01
It has been said that the cell is the test tube of the twenty-first century. If so, the theoretical tools needed to quantitatively and predictively describe what goes on in such test tubes lag sorely behind the stunning experimental advances in biology seen in the decades since the molecular biology revolution began. Perhaps surprisingly, one of the theoretical tools that has been used with great success on problems ranging from how cells communicate with their environment and each other to the nature of the organization of proteins and lipids within the cell membrane is statistical mechanics. A knee-jerk reaction to the use of statistical mechanics in the description of cellular processes is that living organisms are so far from equilibrium that one has no business even thinking about it. But such reactions are probably too hasty given that there are many regimes in which, because of a separation of timescales, for example, such an approach can be a useful first step. In this article, we explore the power of statistical mechanical thinking in the biological setting, with special emphasis on cell signaling and regulation. We show how such models are used to make predictions and describe some recent experiments designed to test them. We also consider the limits of such models based on the relative timescales of the processes of interest.
Non-equilibrium properties of hadronic mixtures
Prakasch, Madappa (State Univ. of New York, Stony Brook, NY (United States). Physics Dept.); Prakasch, Manju (State Univ. of New York, Stony Brook, NY (United States). Physics Dept.); Venugopalan, R. (State Univ. of New York, Stony Brook, NY (United States). Physics Dept.); Welke, G. (Michigan State Univ., East Lansing, MI (United States). National Superconducting Cyclotron Lab.)
1993-05-01
The equilibration of hot hadronic matter is studied in the framework of relativistic kinetic theory. Various non-equilibrium properties of a mixture comprised of pions, kaons and nucleons are calculated in the dilute limit for small deviations from local thermal equilibrium. Interactions between these constituents are specified through the empirical phase shifts. The properties calculated include the relaxation/collision times, momentum and energy persistence ratios in elastic collisions, and transport properties such as the viscosity, the thermal conductivity, and the diffusion and thermal diffusion coefficients. The Chapman-Enskog formalism is extended to extract relaxation times associated with shear and heat flows, and drag and diffusion flows in a mixture. The equilibrium number concentration of the constituents is chosen to mimic those expected in the mid-rapidity interval of CERN and RHIC experiments. In this case, kaons and nucleons are found to equilibrate significantly more slowly than pions. These results shed new light on the influence of collective flow effects on the transverse momentum distributions of kaons and nucleons versus those of pions in ultra-relativistic nuclear collisions. (orig.)
Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: I. Turbulence Statistics
Klein, R I; Li, P S; McKee, C F; Fisher, R
2008-04-10
Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256{sup 3} and 512{sup 3} simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li et al. (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. Changes in the density PDF, total magnetic energy, and ionization fraction are determined as a function of the AD Reynolds number. The power spectra for the neutral gas properties of a strongly magnetized medium with a low AD Reynolds number are similar to those for a weakly magnetized medium; in particular, the power spectrum of the neutral velocity is close to that for Burgers turbulence.
Realistic Modeling of Multi-Scale MHD Dynamics of the Solar Atmosphere
Kitiashvili, Irina; Mansour, Nagi N.; Wray, Alan; Couvidat, Sebastian; Yoon, Seokkwan; Kosovichev, Alexander
2014-01-01
Realistic 3D radiative MHD simulations open new perspectives for understanding the turbulent dynamics of the solar surface, its coupling to the atmosphere, and the physical mechanisms of generation and transport of non-thermal energy. Traditionally, plasma eruptions and wave phenomena in the solar atmosphere are modeled by prescribing artificial driving mechanisms using magnetic or gas pressure forces that might arise from magnetic field emergence or reconnection instabilities. In contrast, our 'ab initio' simulations provide a realistic description of solar dynamics naturally driven by solar energy flow. By simulating the upper convection zone and the solar atmosphere, we can investigate in detail the physical processes of turbulent magnetoconvection, generation and amplification of magnetic fields, excitation of MHD waves, and plasma eruptions. We present recent simulation results of the multi-scale dynamics of quiet-Sun regions, and energetic effects in the atmosphere and compare with observations. For the comparisons we calculate synthetic spectro-polarimetric data to model observational data of SDO, Hinode, and New Solar Telescope.
Zhang, Haocheng; Li, Hui; Taylor, Gregory B.
2017-08-01
In addition to multiwavelength variability, blazar polarization signatures are highly variable. Optical polarimetry has shown two distinct features: first, in both quiescent and flaring states, blazar polarization degree generally stays around 10% to 30%; second, after major polarization variations, such as polarization angle swings, the polarization degree quickly restores to its initial state. We have performed integrated relativistic magnetohydrodynamic (MHD) + radiation and polarization simulations of the blazar emission region. Our approach evolves the magnetic fields and flows using the first principles, so we can calculate the spatial and temporal dependent polarization signatures and compare them with observations.Our results show that the above two observational trends indicate the blazar flaring region should be strongly magnetized with the magnetic energy density higher than the plasma rest mass energy density. In such an environment, the 3D kink instability may trigger magnetic reconnection to accelerate particles and give rise to flares. In view of future high-energy polarimetry, this integrated MHD+polarization simulation technique will deliver new constraints on jet’s physical conditions and particle acceleration mechanisms.
A new MHD-assisted Stokes inversion technique
Riethmüller, T L; Barthol, P; Gandorfer, A; Gizon, L; Hirzberger, J; van Noort, M; Rodríguez, J Blanco; Iniesta, J C Del Toro; Suárez, D Orozco; Schmidt, W; Pillet, V Martínez; Knölker, M
2016-01-01
We present a new method of Stokes inversion of spectropolarimetric data and evaluate it by taking the example of a SUNRISE/IMaX observation. An archive of synthetic Stokes profiles is obtained by the spectral synthesis of state-of-the-art magnetohydrodynamics (MHD) simulations and a realistic degradation to the level of the observed data. The definition of a merit function allows the archive to be searched for the synthetic Stokes profiles that match the observed profiles best. In contrast to traditional Stokes inversion codes, which solve the Unno-Rachkovsky equations for the polarized radiative transfer numerically and fit the Stokes profiles iteratively, the new technique provides the full set of atmospheric parameters. This gives us the ability to start an MHD simulation that takes the inversion result as initial condition. After a relaxation process of half an hour solar time we obtain physically consistent MHD data sets with a target similar to the observation. The new MHD simulation is used to repeat t...