Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Neoclassical MHD equations for tokamaks
International Nuclear Information System (INIS)
Callen, J.D.; Shaing, K.C.
1986-03-01
The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Directory of Open Access Journals (Sweden)
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses 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 magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
MHD stability properties of a system of reduced toroidal MHD equations
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1993-01-01
A system of reduced toroidal magneto-hydrodynamic (MHD) equations is derived from a general scalar representation of the complete MHD system, using an ordering in terms of the inverse aspect ratio ε of a toroidal plasma. It is shown that the energy principle for the reduced equations is identical with the usual energy principle of the complete MHD system, to the appropriate order in ε. Thus, the reduced equations have the same ideal MHD stability limits as the full MHD equations. (authors). 6 refs
3-D resistive MHD calculations for tokamak plasmas: beyond the simple reduced set of equations
International Nuclear Information System (INIS)
Carreras, B.A.; Garcia, L.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.; Masden, B.F.
1983-01-01
Numerical studies of the resistive stability of tokamak plasmas in cylindrical geometry have been performed using: (1) the full set of resistive Magnetohydrodynamic (MHD) equations and (2) an extended version of the reduced set of resistive MHD equations including diamagnetic and electron temperature effects. In particular, the nonlinear interaction of tearing modes of many helicities has been investigated. The numerical results confirm many of the features uncovered previously using the simple reduced equations. (author)
Equations of state for self-excited MHD generator studies
Energy Technology Data Exchange (ETDEWEB)
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.
Construction of a Roe linearization for the ideal MHD equations
International Nuclear Information System (INIS)
Cargo, P.; Gallice, G.; Raviart, P.A.
1996-01-01
In [3], Munz has constructed a Roe linearization for the equations of gas dynamics in Lagrangian coordinates. We extend this construction to the case of the ideal magnetohydrodynamics equations again in Lagrangian coordinates. As a consequence we obtain a Roe linearization for the MHD equations in Eulerian coordinates. (author)
MAIA, Eigenvalues for MHD Equation of Tokamak Plasma Stability Problems
International Nuclear Information System (INIS)
Tanaka, Y.; Azumi, M.; Kurita, G.; Tsunematsu, T.; Takeda, T.
1986-01-01
1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real
Eigenvalues of the simplified ideal MHD ballooning equation
International Nuclear Information System (INIS)
Paris, R.B.; Auby, N.; Dagazian, R.Y.
1986-01-01
The investigation of the spectrum of the simplified differential equation describing the variation of the amplitude of the ideal MHD ballooning instability along magnetic field lines constitutes a multiparameter Schroedinger eigenvalue problem. An exact eigenvalue relation for the discrete part of the spectrum is obtained in terms of the oblate spheroidal functions. The dependence of the eigenvalues lambda on the two free parameters γ 2 and μ 2 of the equation is discussed, together with certain analytical approximations in the limits of small and large γ 2 . A brief review of the principal properties of the spheroidal functions is given in an appendix
Transfer equations for spectral densities of inhomogeneous MHD turbulence
International Nuclear Information System (INIS)
Tu, C.-Y.; Marsch, E.
1990-01-01
On the basis of the dynamic equations governing the evolution of magnetohydrodynamic fluctuations expressed in terms of Elsaesser variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented describing the evolutions of the energy spectrum e ± and of the residual energy spectra e R and e S of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e ± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for e R the triple correlations do not correspond to an 'energy' conserving process, but also represent a nonlinear source term for e R . If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations. (author)
MHD model including small-scale perturbations in a plasma with temperature variations
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Mikhailovskii, A.B.
1996-01-01
The possibility is studied of using a hydrodynamic model to describe a magnetized plasma with density and temperature variations on scales that are arbitrary with respect to the ion Larmor radius. It is shown that the inertial component of the transverse ion thermal flux should be taken into account. This component is found from the collisionless kinetic equation. It can also be obtained from the equations of the Grad type. A set of two-dimensional hydrodynamic equations for ions is obtained with this component taken into account. These equations are used to derive model hydrodynamic expressions for the density and temperature variations. It is shown that, for large-scale perturbations (when the wavelengths are longer than the ion Larmor radius), the expressions derived coincide with the corresponding kinetic expressions and, for perturbations on sub-Larmor scales (when the wavelengths are shorter than the Larmor radius), they agree qualitatively. Hydrodynamic dispersion relations are derived for several types of drift waves with arbitrary wavenumbers. The range of applicability of the MHD model is determined from a comparison of these dispersion relations with the kinetic ones. It is noted that, on the basis of results obtained, drift effects can be included in numerical MHD codes for studying plasma instabilities in high-temperature regimes in tokamaks
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
International Nuclear Information System (INIS)
Webb, G. M.; Brio, M.; Zank, G. P.
1996-01-01
A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation
Energy Technology Data Exchange (ETDEWEB)
Fierros Palacios, Angel [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico)
2001-02-01
In this work the complete set of differential field equations which describes the dynamic state of a continuos conducting media which flow in presence of a perturbed magnetic field is obtained. Then, the thermic equation of state, the wave equation and the conservation law of energy for the Alfven MHD waves are obtained. [Spanish] Es este trabajo se obtiene el conjunto completo de ecuaciones diferenciales de campo que describen el estado dinamico de un medio continuo conductor que se mueve en presencia de un campo magnetico externo perturbado. Asi, se obtiene la ecuacion termica de estado, la ecuacion de onda y la ley de la conservacion de la energia para las ondas de Alfven de la MHD.
Nonlinear MHD-equations: symmetries, solutions and conservation laws
International Nuclear Information System (INIS)
Samokhin, A.V.
1985-01-01
To investigate stability and nonlinear effects in a high-temperature plasma the system of two scalar nonlinear equations is considered. The algebra of classical symmetries of this system and a certain natural part of its conservation laws are described. It is shown that first, with symmetries one can derive invariant (self-similar) solutions, second, acting with symmetry on the known solution the latter can be included into parametric family
On the regularity criterion of weak solutions for the 3D MHD equations
Gala, Sadek; Ragusa, Maria Alessandra
2017-12-01
The paper deals with the 3D incompressible MHD equations and aims at improving a regularity criterion in terms of the horizontal gradient of velocity and magnetic field. It is proved that the weak solution ( u, b) becomes regular provided that ( \
Variational Integration for Ideal MHD with Built-in Advection Equations
Energy Technology Data Exchange (ETDEWEB)
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.
Three-scale expansion of the solution of MHD and Reynolds equations for tokamak
International Nuclear Information System (INIS)
Maslov, V.P.; Omel'yanov, G.A.
1994-01-01
An asymptotic solution of the magnetohydrodynamic equations is constructed. The three scales asymptotic solution describes the non-linear evolution of small, rapidly varying perturbations of equilibrium. It is shown, that an anisotropic coherent structure appears in the linear nonstability situation, and the structures evolution directs to energy interaction between high-frequency and low-frequency waves. The closed system of MHD Reynolds equations for anisotropic structure is derived
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Edery, D.
1983-11-01
The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper
International Nuclear Information System (INIS)
Furuya, Atsushi; Yagi, Masatoshi; Itoh, Sanae-I.
2003-01-01
The linear neoclassical tearing mode is investigated using the four-field reduced neoclassical MHD equations, in which the fluctuating ion parallel flow and ion neoclassical viscosity are taken into account. The dependences of the neoclassical tearing mode on collisionality, diamagnetic drift and q profile are investigated. These results are compared with the results from the conventional three-field model. It is shown that the linear neoclassical tearing mode is stabilized by the ion neoclassical viscosity in the banana regime even if Δ' > 0. (author)
Four-dimensional integral equations for the MHD diffraction waves in plasma
International Nuclear Information System (INIS)
Alexandrova, A.A.; Khizhnyak, N.A.
2000-01-01
The superficial analysis of the boundary-value nonstationary problem for Alfven wave has shown the principal possibility of using the method of evolutionary integral equations of non-stationary macroscopic electrodynamical in a case of MHD description of waves in plasma. With the importance of strict mathematical solutions obtained for simple model problems that is the diffraction of one separately taken Alfven wave is that it can be the basis for construction of the approximate solutions of more complex boundary-value problems
International Nuclear Information System (INIS)
Guzik, J.A.; Swenson, F.J.
1997-01-01
We compare the thermodynamic and helioseismic properties of solar models evolved using three different equation of state (EOS) treatments: the Mihalas, Daeppen ampersand Hummer EOS tables (MHD); the latest Rogers, Swenson, ampersand Iglesias EOS tables (OPAL), and a new analytical EOS (SIREFF) developed by Swenson et al. All of the models include diffusive settling of helium and heavier elements. The models use updated OPAL opacity tables based on the 1993 Grevesse ampersand Noels solar element mixture, incorporating 21 elements instead of the 14 elements used for earlier tables. The properties of solar models that are evolved with the SIREFF EOS agree closely with those of models evolved using the OPAL or MHD tables. However, unlike the MHD or OPAL EOS tables, the SIREFF in-line EOS can readily account for variations in overall Z abundance and the element mixture resulting from nuclear processing and diffusive element settling. Accounting for Z abundance variations in the EOS has a small, but non-negligible, effect on model properties (e.g., pressure or squared sound speed), as much as 0.2% at the solar center and in the convection zone. The OPAL and SIREFF equations of state include electron exchange, which produces models requiring a slightly higher initial helium abundance, and increases the convection zone depth compared to models using the MHD EOS. However, the updated OPAL opacities are as much as 5% lower near the convection zone base, resulting in a small decrease in convection zone depth. The calculated low-degree nonadiabatic frequencies for all of the models agree with the observed frequencies to within a few microhertz (0.1%). The SIREFF analytical calibrations are intended to work over a wide range of interior conditions found in stellar models of mass greater than 0.25M circle-dot and evolutionary states from pre-main-sequence through the asymptotic giant branch (AGB). It is significant that the SIREFF EOS produces solar models that both measure up
Proceedings of the workshop on nonlinear MHD and extended MHD
International Nuclear Information System (INIS)
1998-01-01
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
Proceedings of the workshop on nonlinear MHD and extended MHD
Energy Technology Data Exchange (ETDEWEB)
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.
A spatial discretization of the MHD equations based on the finite volume - spectral method
International Nuclear Information System (INIS)
Miyoshi, Takahiro
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
Zhang, Jianwen; Zhao, Xiaokui
2015-01-01
In general, the resistivity is inversely proportional to the electrical conductivity, and is usually taken to be zero when the conducting fluid is of extremely high conductivity (e.g., ideal conductors). In this paper, we first establish the global well-posedness of strong solution to an initial-boundary value problem of the one-dimensional compressible, viscous, heat-conductive, non-resistive MHD equations with general heat-conductivity coefficient and large data. Then, the non-resistive lim...
International Nuclear Information System (INIS)
Hoelzl, M; Merkel, P; Lackner, K; Strumberger, E; Huijsmans, G T A; Aleynikova, K; Liu, F; Atanasiu, C; Nardon, E; Fil, A; McAdams, R; Chapman, I
2014-01-01
The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described
Heat transfer including radiation and slag particles evolution in MHD channel-I
International Nuclear Information System (INIS)
Im, K.H.; Ahluwalia, R.K.
1980-01-01
Accurate estimates of convective and radiative heat transfer in the magnetohydrodynamic channel are provided. Calculations performed for a base load-size channel indicate that heat transfer by gas radiation almost equals that by convection for smooth walls, and amounts to 70% as much as the convective heat transfer for rough walls. Carbon dioxide, water vapor, and potassium atoms are the principal participating gases. The evolution of slag particles by homogeneous nucleation and condensation is also investigated. The particle-size spectrum so computed is later utilized to analyze the radiation enhancement by slag particles in the MHD diffuser. The impact of the slag particle spectrum on the selection of a workable and design of an efficient seed collection system is discussed
Reduced, three-dimensional, nonlinear equations for high-β plasmas including toroidal effects
International Nuclear Information System (INIS)
Schmalz, R.
1980-11-01
The resistive MHD equations for toroidal plasma configurations are reduced by expanding to the second order in epsilon, the inverse aspect ratio, allowing for high β = μsub(o)p/B 2 of order epsilon. The result is a closed system of nonlinear, three-dimensional equations where the fast magnetohydrodynamic time scale is eliminated. In particular, the equation for the toroidal velocity remains decoupled. (orig.)
Solution of neutron slowing down equation including multiple inelastic scattering
International Nuclear Information System (INIS)
El-Wakil, S.A.; Saad, A.E.
1977-01-01
The present work is devoted the presentation of an analytical method for the calculation of elastically and inelastically slowed down neutrons in an infinite non absorbing homogeneous medium. On the basis of the Central limit theory (CLT) and the integral transform technique the slowing down equation including inelastic scattering in terms of the Green function of elastic scattering is solved. The Green function is decomposed according to the number of collisions. A formula for the flux at any lethargy O (u) after any number of collisions is derived. An equation for the asymptotic flux is also obtained
MHD SIMULATIONS OF CORONAL SUPRA-ARCADE DOWNFLOWS INCLUDING ANISOTROPIC THERMAL CONDUCTION
International Nuclear Information System (INIS)
Zurbriggen, E.; Costa, A.; Schneiter, M.; Cécere, M.; Esquivel, A.
2016-01-01
Coronal supra-arcade downflows (SADs) are observed as dark trails descending toward hot turbulent-fan-shaped regions. Due to the large temperature values and gradients in these fan regions, the thermal conduction (TC) should be very efficient. While several models have been proposed to explain the triggering and the evolution of SADs, none of these scenarios address a systematic consideration of TC. Thus, we accomplish this task numerically simulating the evolution of SADs within this framework. That is, SADs are conceived as voided (subdense) cavities formed by nonlinear waves triggered by downflowing bursty localized reconnection events in a perturbed hot fan. We generate a properly turbulent fan, obtained by a stirring force that permits control of the energy and vorticity input in the medium where SADs develop. We include anisotropic TC and consider plasma properties consistent with observations. Our aim is to study whether it is possible to prevent SADs from vanishing by thermal diffusion. We find that this will be the case, depending on the turbulence parameters, in particular if the magnetic field lines are able to envelope the voided cavities, thermally isolating them from the hot environment. Velocity shear perturbations that are able to generate instabilities of the Kelvin–Helmholtz type help to produce magnetic islands, extending the lifetime of SADs.
MHD SIMULATIONS OF CORONAL SUPRA-ARCADE DOWNFLOWS INCLUDING ANISOTROPIC THERMAL CONDUCTION
Energy Technology Data Exchange (ETDEWEB)
Zurbriggen, E.; Costa, A.; Schneiter, M.; Cécere, M. [Instituto de Investigaciones en Astronomía Teórica y Experimental (IATE), Córdoba (Argentina); Esquivel, A., E-mail: ezurbriggen@unc.edu.ar, E-mail: acosta@unc.edu.ar [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (Mexico)
2016-11-20
Coronal supra-arcade downflows (SADs) are observed as dark trails descending toward hot turbulent-fan-shaped regions. Due to the large temperature values and gradients in these fan regions, the thermal conduction (TC) should be very efficient. While several models have been proposed to explain the triggering and the evolution of SADs, none of these scenarios address a systematic consideration of TC. Thus, we accomplish this task numerically simulating the evolution of SADs within this framework. That is, SADs are conceived as voided (subdense) cavities formed by nonlinear waves triggered by downflowing bursty localized reconnection events in a perturbed hot fan. We generate a properly turbulent fan, obtained by a stirring force that permits control of the energy and vorticity input in the medium where SADs develop. We include anisotropic TC and consider plasma properties consistent with observations. Our aim is to study whether it is possible to prevent SADs from vanishing by thermal diffusion. We find that this will be the case, depending on the turbulence parameters, in particular if the magnetic field lines are able to envelope the voided cavities, thermally isolating them from the hot environment. Velocity shear perturbations that are able to generate instabilities of the Kelvin–Helmholtz type help to produce magnetic islands, extending the lifetime of SADs.
International Nuclear Information System (INIS)
McCarthy, K.A.; Abdou, M.A.
1991-01-01
A computationally fast and efficient method for analyzing MHD flow at high Hartmann number and interaction parameter is presented and used to analyze a multiple duct geometry. This type of geometry is of practical interest in fusion applications. Because the Hartmann number and interaction parameter are generally large in fusion applications, the inertial and viscous terms in the Navier-Stokes equation can often be neglected in the core flow region, making this equation linear. In addition, because the magnetic fields in a fusion reactor vary slowly and the magnetic Reynolds number is small, the induced magnetic field can be neglected. The resulting equations representing core flow have certain characteristics which make it possible to reduce them to two dimensional without losing the three dimensional characteristics. The method which has been developed is an 'iterative' method. A velocity profile is assumed, then Ohm's law and the current conservation equation are combined and used to solve for the potential distribution in a plane in the fluid, and in a surface in the duct wall. The potential variation along magnetic field lines is checked, and if necessary, the velocities are adjusted. This procedure is repeated until the potentials along field lines vary to within a specified error. The analysis of the multiple duct geometry shows the importance of global effects. The results of two basic cases are presented. In the first, the average velocity in each duct is the same, but the wall conductance ratios of the walls perpendicular to the magnetic field vary from duct to duct. The total pressure drop in the electrically connected ducts was greater than or equal to the total pressure drop in the same ducts electrically isolated. In addition, the velocity profile in the ducts can be significantly affected by the presence of neighboring ducts. (orig./AH)
Neoclassical MHD descriptions of tokamak plasmas
International Nuclear Information System (INIS)
Callen, J.D.; Kim, Y.B.; Sundaram, A.K.
1988-01-01
Considerable progress has been made in extending neoclassical MHD theory and in exploring the linear instabilities, nonlinear behavior and turbulence models it implies for tokamak plasmas. The areas highlighted in this paper include: extension of the neoclassical MHD equations to include temperature-gradient and heat flow effects; the free energy and entropy evolution implied by this more complete description; a proper ballooning mode formalism analysis of the linear instabilities; a new rippling mode type instability; numerical simulation of the linear instabilities which exhibit a smooth transition from resistive ballooning modes at high collisionality to neoclassical MHD modes at low collisionality; numerical simulation of the nonlinear growth of a single helicity tearing mode; and a Direct-Interaction-Approximation model of neoclassical MHD turbulence and the anomalous transport it induces which substantially improves upon previous mixing length model estimates. 34 refs., 2 figs
Bifurcation theory for toroidal MHD instabilities
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1992-01-01
Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found
International Nuclear Information System (INIS)
Nagata, A.; Ashida, H.; Okamoto, M.; Hirano, K.
1981-03-01
Two dimentional fluid simulation code ''TOPICS'' is developed for the STP-2, the shock heated screw pinch at Nagoya. It involves the effects of impurity ions and neutral atoms. In order to estimate the radiation losses, the impurity continuity equations with ionizations and recombinations are solved simultaneously with the plasma fluid equations. The results are compared with the coronal equilibrium model. It is found that the coronal equilibrium model underestimates the radiation losses from shock heated pinch plasmas in its initial dynamic phase. The present calculations including impurities and neutrals show the importance of the radiation losses from the plasma of the STP-2. Introducing the anomalous resistivity caused by the ion acoustic instability, the observed magnetic field penetration is explained fairly well. (author)
Explosive instabilities of reaction-diffusion equations including pinch effects
International Nuclear Information System (INIS)
Wilhelmsson, H.
1992-01-01
Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch and source processes certain 'bell-shaped' distributions may grow explosively in time with preserved shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or. more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma. (au) (18 refs.)
International Nuclear Information System (INIS)
Brassier, Stephane
1998-01-01
The Magnetohydrodynamic (MHD) equations represent the coupling between fluid dynamics equations and Maxwell's equations. We consider here a new MHD model with two temperatures. A Roe scheme is first constructed in the one dimensional case, for a multi-species model and a general equation of state. The multidimensional case is treated thanks to the Powell approach. The notion of Roe-Powell matrix, generalization of the notion of Roe matrix for multidimensional MHD, allows us to develop an original scheme on a curvilinear grid. We focus on a second part on the modelling of a Plasma Opening Switch (POS). A front-tracking method is first set up, in order to correctly handle the deformation of the front between the vacuum and the plasma. Besides, by taking into account a general Ohm's law, we have to deal with the Hall effect, which leads to nonlinear transport equations with discontinuous coefficients. Several numerical schemes are proposed and tested on a variety of test cases. This work has allowed us to construct an industrial MHD code, intended to handle complex flows and in particular to correctly simulate the behaviour of the POS. (author) [fr
Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations
DEFF Research Database (Denmark)
Kallesøe, Bjarne Skovmose
2007-01-01
This paper extends Hodges-Dowell's partial differential equations of blade motion, by including the effects from gravity, pitch action and varying rotor speed. New equations describing the pitch action and rotor speeds are also derived. The physical interpretation of the individual terms...... in the equations is discussed. The partial differential equations of motion are approximated by ordinary differential equations of motion using an assumed mode method. The ordinary differential equations are used to simulate a sudden pitch change of a rotating blade. This work is a part of a project on pitch blade...
Extension of Gibbs-Duhem equation including influences of external fields
Guangze, Han; Jianjia, Meng
2018-03-01
Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.
A kinetic-MHD model for low frequency phenomena
International Nuclear Information System (INIS)
Cheng, C.Z.
1991-07-01
A hybrid kinetic-MHD model for describing low-frequency phenomena in high beta anisotropic plasmas that consist of two components: a low energy core component and an energetic component with low density. The kinetic-MHD model treats the low energy core component by magnetohydrodynamic (MHD) description, the energetic component by kinetic approach such as the gyrokinetic equation, and the coupling between the dynamics of these two components through plasma pressure in the momentum equation. The kinetic-MHD model optimizes both the physics contents and the theoretical efforts in studying low frequency MHD waves and transport phenomena in general magnetic field geometries, and can be easily modified to include the core plasma kinetic effects if necessary. It is applicable to any magnetized collisionless plasma system where the parallel electric field effects are negligibly small. In the linearized limit two coupled eigenmode equations for describing the coupling between the transverse Alfven type and the compressional Alfven type waves are derived. The eigenmode equations are identical to those derived from the full gyrokinetic equation in the low frequency limit and were previously analyzed both analytically nd numerically to obtain the eigenmode structure of the drift mirror instability which explains successfully the multi-satellite observation of antisymmetric field-aligned structure of the compressional magnetic field of Pc 5 waves in the magnetospheric ring current plasma. Finally, a quadratic form is derived to demonstrate the stability of the low-frequency transverse and compressional Alfven type instabilities in terms of the pressure anisotropy parameter τ and the magnetic field curvature-pressure gradient parameter. A procedure for determining the stability of a marginally stable MHD wave due to wave-particle resonances is also presented
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...
MHD stability analyses of a tokamak plasma by time-dependent codes
International Nuclear Information System (INIS)
Kurita, Gen-ichi
1982-07-01
The MHD properties of a tokamak plasma are investigated by using time evolutional codes. As for the ideal MHD modes we have analyzed the external modes including the positional instability. Linear and nonlinear ideal MHD codes have been developed. Effects of the toroidicity and conducting shell on the external kink mode are studied minutely by the linear code. A new rezoning algorithm is devised and it is successfully applied to express numerically the axisymmetric plasma perturbation in a cylindrical geometry. As for the resistive MHD modes we have developed nonlinear codes on the basis of the reduced set of the resistive MHD equations. By using the codes we have studied the major disruption processes and properties of the low n resistive modes. We have found that the effects of toroidicity and finite poloidal beta are very important. Considering the above conclusion we propose a new scenario of the initiation of the major disruption. (author)
International Nuclear Information System (INIS)
Salat, A.
1981-12-01
The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f(ω 1 t,ω 2 t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω 1 , ω 2 a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained. The equation considered is a model for the magneto-hydrodynamic 'continuum' in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently irrational magnetic surfaces. (orig.)
Directory of Open Access Journals (Sweden)
Boričić Zoran
2005-01-01
Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.
International Nuclear Information System (INIS)
Petit, J.P.
1995-01-01
Jean-Pierre PETIT, one of the best MHD specialists, is telling this technology story and he is insisting on its military consequences. Civil MHD is only one iceberg emerged part, including a lot of leader technologies, interesting he defense. 3 notes
International Nuclear Information System (INIS)
1991-10-01
The current MHD program being implemented is a result of a consensus established in public meetings held by the Department of Energy in 1984. Essential elements of the current program include: (1) develop technical and environmental data for the integrated MHD topping cycle system through POC testing (1,000 hours); (2) develop technical and environmental data for the integrated MHD bottoming cycle sub system through POC testing (4,000 hours); (3) design, construct, and operate a seed regeneration POC facility (SRPF) capable of processing spent seed materials from the MHD bottoming cycle; (4) prepare conceptual designs for a site specific MHD retrofit plant; and (5) continue system studies and supporting research necessary for system testing. The current MHD program continues to be directed toward coal fired power plant applications, both stand-alone and retrofit. Development of a plant should enhance the attractiveness of MHD for applications other than electrical power. MHD may find application in electrical energy intensive industries and in the defense sector
Characteristics of laminar MHD fluid hammer in pipe
International Nuclear Information System (INIS)
Huang, Z.Y.; Liu, Y.J.
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.
The CHEASE code for toroidal MHD equilibria
Energy Technology Data Exchange (ETDEWEB)
Luetjens, H. [Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique; Bondeson, A. [Chalmers Univ. of Technology, Goeteborg (Sweden). Inst. for Electromagnetic Field Theory and Plasma Physics; Sauter, O. [ITER-San Diego, La Jolla, CA (United States)
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function {Psi}. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs.
The CHEASE code for toroidal MHD equilibria
International Nuclear Information System (INIS)
Luetjens, H.
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function Ψ. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs
International Nuclear Information System (INIS)
Alvi, Kashif
2002-01-01
First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds
Shumilin, A. V.; Kabanov, V. V.; Dediu, V. I.
2018-03-01
We derive kinetic equations for polaron hopping in organic materials that explicitly take into account the double occupation possibility and pair intersite correlations. The equations include simplified phenomenological spin dynamics and provide a self-consistent framework for the description of the bipolaron mechanism of the organic magnetoresistance. At low applied voltages, the equations can be reduced to those for an effective resistor network that generalizes the Miller-Abrahams network and includes the effect of spin relaxation on the system resistivity. Our theory discloses the close relationship between the organic magnetoresistance and the intersite correlations. Moreover, in the absence of correlations, as in an ordered system with zero Hubbard energy, the magnetoresistance vanishes.
Critical Dynamics : The Expansion of the Master Equation Including a Critical Point
Dekker, H.
1980-01-01
In this thesis it is shown how to solve the master equation for a Markov process including a critical point by means of successive approximations in terms of a small parameter. A critical point occurs if, by adjusting an externally controlled quantity, the system shows a transition from normal
Development of Reference Equations of State for Refrigerant Mixtures Including Hydrocarbons
Miyamoto, Hiroyuki; Watanabe, Koichi
In recent years, most accurate equations of state for alternative refrigerants and their mixtures can easily be used via convenient software package, e.g., REFPROP. In the present paper, we described the current state-of-the-art equations of state for refrigerant mixtures including hydrocarbons as components. Throughout our discussion, the limitation of the available experimental data and the necessity of the improvement against the arbitrary fitting of recent modeling were confirmed. The enough number of reliable experimental data, especially for properties in the higher pressures and temperatures and for derived properties, should be accumulated in the near future for the development of the physically-sound theoretical background. The present review argued about the possibility of the progress for the future thermodynamic property modeling throughout the detailed discussion regarding the several types of the equations of state as well as the recent innovative measurement technique.
International Nuclear Information System (INIS)
Falgarone, Edith; Rieutord, Michel; Richard, Denis; Zahn, Jean-Paul; Dauchot, Olivier; Daviaud, Francois; Dubrulle, Berengere; Laval, Jean-Philippe; Noullez, Alain; Bourgoin, Mickael; Odier, Philippe; Pinton, Jean-Francois; Leveque, Emmanuel; Chainais, Pierre; Abry, Patrice; Mordant, Nicolas; Michel, Olivier; Marie, Louis; Chiffaudel, Arnaud; Daviaud, Francois; Petrelis, Francois; Fauve, Stephan; Nore, C.; Brachet, M.-E.; Politano, H.; Pouquet, A.; Leorat, Jacques; Grapin, Roland; Brun, Sacha; Delour, Jean; Arneodo, Alain; Muzy, Jean-Francois; Magnaudet, Jacques; Braza, Marianna; Boree, Jacques; Maurel, S.; Ben, L.; Moreau, J.; Bazile, R.; Charnay, G.; Lewandowski, Roger; Laveder, Dimitri; Bouchet, Freddy; Sommeria, Joel; Le Gal, P.; Eloy, C.; Le Dizes, S.; Schneider, Kai; Farge, Marie; Bottausci, Frederic; Petitjeans, Philippe; Maurel, Agnes; Carlier, Johan; Anselmet, Fabien
2001-05-01
This publication gathers extended summaries of presentations proposed during two days on astrophysics and magnetohydrodynamics (MHD). The first session addressed astrophysics and MHD: The cold interstellar medium, a low ionized turbulent plasma; Turbulent convection in stars; Turbulence in differential rotation; Protoplanetary disks and washing machines; gravitational instability and large structures; MHD turbulence in the sodium von Karman flow; Numerical study of the dynamo effect in the Taylor-Green eddy geometry; Solar turbulent convection under the influence of rotation and of the magnetic field. The second session addressed the description of turbulence: Should we give up cascade models to describe the spatial complexity of the velocity field in a developed turbulence?; What do we learn with RDT about the turbulence at the vicinity of a plane surface?; Qualitative explanation of intermittency; Reduced model of Navier-Stokes equations: quickly extinguished energy cascade; Some mathematical properties of turbulent closure models. The third session addressed turbulence and coherent structures: Alfven wave filamentation and formation of coherent structures in dispersive MHD; Statistical mechanics for quasi-geo-strophic turbulence: applications to Jupiter's coherent structures; Elliptic instabilities; Physics and modelling of turbulent detached unsteady flows in aerodynamics and fluid-structure interaction; Intermittency and coherent structures in a washing machine: a wavelet analysis of joint pressure/velocity measurements; CVS filtering of 3D turbulent mixing layer using orthogonal wavelets. The last session addressed experimental methods: Lagrangian velocity measurements; Energy dissipation and instabilities within a locally stretched vortex; Study by laser imagery of the generation and breakage of a compressed eddy flow; Study of coherent structures of turbulent boundary layer at high Reynolds number
Numerical computation of MHD equilibria
International Nuclear Information System (INIS)
Atanasiu, C.V.
1982-10-01
A numerical code for a two-dimensional MHD equilibrium computation has been carried out. The code solves the Grad-Shafranov equation in its integral form, for both formulations: the free-boundary problem and the fixed boundary one. Examples of the application of the code to tokamak design are given. (author)
Calculation code NIRVANA for free boundary MHD equilibrium
International Nuclear Information System (INIS)
Ninomiya, Hiromasa; Suzuki, Yasuo; Kameari, Akihisa
1975-03-01
The calculation method and code of solving the free boundary problem for MHD equilibrium has been developed. Usage of the code ''NIRVANA'' is described. The toroidal plasma current density determined as a function of the flux function PSI is substituted by a group of the ring currents, whereby the equation of MHD equilibrium is transformed into an integral equation. Either of the two iterative methods is chosen to solve the integral equation, depending on the assumptions made of the plasma surface points. Calculation of the magnetic field configurations is possible when the plasma surface coincides self-consistently with the magnetic flux including the separatrix points. The code is usable in calculation of the circular or non-circular shell-less Tokamak equilibrium. (auth.)
Experimental rigs for MHD studies
International Nuclear Information System (INIS)
Venkataramani, N.; Jayakumar, R.; Iyer, D.R.; Dixit, N.S.
1976-01-01
An MHD experimental rig is a miniature MHD installation consisting of basic equipments necessary for specific investigations. Some of the experimental rigs used in the investigations being carried out at the Bhabha Atomic Research Centre, Bombay (India) are dealt with. The experiments included diagnostics and evaluation of materials in seeded combustion plasmas and argon plasmas. The design specifications, schematics and some of the results of the investigations are also mentioned. (author)
Magnetohydrodynamic (MHD) power generation
International Nuclear Information System (INIS)
Chandra, Avinash
1980-01-01
The concept of MHD power generation, principles of operation of the MHD generator, its design, types, MHD generator cycles, technological problems to be overcome, the current state of the art in USA and USSR are described. Progress of India's experimental 5 Mw water-gas fired open cycle MHD power generator project is reported in brief. (M.G.B.)
O'Connell, R.; Forest, C. B.; Plard, F.; Kendrick, R.; Lovell, T.; Thomas, M.; Bonazza, R.; Jensen, T.; Politzer, P.; Gerritsen, W.; McDowell, M.
1997-11-01
A MHD experiment is being constructed which will have the possibility of showing dynamo action: the self--generation of currents from fluid motion. The design allows sufficient experimental flexibility and diagnostic access to study a variety of issues central to dynamo theory, including mean--field electrodynamics and saturation (backreaction physics). Initially, helical flows required for dynamo action will be driven by propellers embedded in liquid sodium. The flow fields will first be measured using laser doppler velocimetry in a water experiment with an identical fluid Reynolds number. The magnetic field evolution will then be predicted using a MHD code, replacing the water with sodium; if growing magnetic fields are found, the experiment will be repeated with sodium.
Two-dimensional simulation of the MHD stability, (1)
International Nuclear Information System (INIS)
Kurita, Gen-ichi; Amano, Tsuneo.
1976-03-01
The two-dimensional computer code has been prepared to study MHD stability of an axisymmetric toroidal plasma with and without the surrounding vacuum region. It also includes the effect of magnetic surfaces with non-circular cross sections. The linearized equations of motion are solved as an initial value problem. The results by computer simulation are compared with those by the theory for the cylindrical plasma; they are in good agreement. (auth.)
An innovative method for ideal and resistive MHD stability analysis of tokamaks
International Nuclear Information System (INIS)
Tokuda, S.
2001-01-01
An advanced asymptotic matching method of ideal and resistive MHD stability analysis in tokamaks is reported. A solution method for the two dimensional Newcomb equation, a dispersion relation for an unstable ideal MHD mode in tokamaks and a new scheme for solving resistive MHD inner layer equations as an initial value problem are reported. (author)
An innovative method for ideal and resistive MHD stability analysis of tokamaks
International Nuclear Information System (INIS)
Tokuda, S.
2001-01-01
An advanced asymptotic matching method of ideal and resistive MHD stability analysis in tokamak is reported. The report explains a solution method of two-dimensional Newcomb equation, dispersion relation for an unstable ideal MHD mode in tokamak, and a new scheme for solving resistive MHD inner layer equations as an initial-value problem. (author)
MHD intermediate shock discontinuities: Pt. 1
International Nuclear Information System (INIS)
Kennel, C.F.; Blandford, R.D.; Coppi, P.
1989-01-01
Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic. (author)
Implementation of a 3-D nonlinear MHD [magnetohydrodynamics] calculation on the Intel hypercube
International Nuclear Information System (INIS)
Lynch, V.E.; Carreras, B.A.; Drake, J.B.; Hicks, H.R.; Lawkins, W.F.
1987-01-01
The optimization of numerical schemes and increasing computer capabilities in the last ten years have improved the efficiency of 3-D nonlinear resistive MHD calculations by about two to three orders of magnitude. However, we are still very limited in performing these types of calculations. Hypercubes have a large number of processors with only local memory and bidirectional links among neighbors. The Intel Hypercube at Oak Ridge has 64 processors with 0.5 megabytes of memory per processor. The multiplicity of processors opens new possibilities for the treatment of such computations. The constraint on time and resources favored the approach of using the existing RSF code which solves as an initial value problem the reduced set of MHD equations for a periodic cylindrical geometry. This code includes minimal physics and geometry, but contains the basic three dimensionality and nonlinear structure of the equations. The code solves the reduced set of MHD equations by Fourier expansion in two angular coordinates and finite differences in the radial one. Due to the continuing interest in these calculations and the likelihood that future supercomputers will take greater advantage of parallelism, the present study was initiated by the ORNL Exploratory Studies Committee and funded entirely by Laboratory Discretionary Funds. The objectives of the study were: to ascertain the suitability of MHD calculation for parallel computation, to design and implement a parallel algorithm to perform the computations, and to evaluate the hypercube, and in particular, ORNL's Intel iPSC, for use in MHD computations
Kim, Sun Jung; Yoo, Il Young
2016-03-01
The purpose of this study was to explain the health promotion behavior of Chinese international students in Korea using a structural equation model including acculturation factors. A survey using self-administered questionnaires was employed. Data were collected from 272 Chinese students who have resided in Korea for longer than 6 months. The data were analyzed using structural equation modeling. The p value of final model is .31. The fitness parameters of the final model such as goodness of fit index, adjusted goodness of fit index, normed fit index, non-normed fit index, and comparative fit index were more than .95. Root mean square of residual and root mean square error of approximation also met the criteria. Self-esteem, perceived health status, acculturative stress and acculturation level had direct effects on health promotion behavior of the participants and the model explained 30.0% of variance. The Chinese students in Korea with higher self-esteem, perceived health status, acculturation level, and lower acculturative stress reported higher health promotion behavior. The findings can be applied to develop health promotion strategies for this population. Copyright © 2016. Published by Elsevier B.V.
International Nuclear Information System (INIS)
Woesler, Richard
2007-01-01
The computations of the present text with non-relativistic quantum teleportation equations and special relativity are totally speculative, physically correct computations can be done using quantum field theory, which remain to be done in future. Proposals for what might be called statistical time loop experiments with, e.g., photon polarization states are described when assuming the simplified non-relativistic quantum teleportation equations and special relativity. However, a closed time loop would usually not occur due to phase incompatibilities of the quantum states. Histories with such phase incompatibilities are called inconsistent ones in the present text, and it is assumed that only consistent histories would occur. This is called an exclusion principle for inconsistent histories, and it would yield that probabilities for certain measurement results change. Extended multiple parallel experiments are proposed to use this statistically for transmission of classical information over distances, and regarding time. Experiments might be testable in near future. However, first a deeper analysis, including quantum field theory, remains to be done in future
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Conservation properties and potential systems of vorticity-type equations
International Nuclear Information System (INIS)
Cheviakov, Alexei F.
2014-01-01
Partial differential equations of the form divN=0, N t +curl M=0 involving two vector functions in R 3 depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R 4 (t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented
Energy Technology Data Exchange (ETDEWEB)
Dewar, R L; Mills, R; Hole, M J, E-mail: robert.dewar@anu.edu.a [Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)
2009-05-01
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics. To resolve the continuation problem we regularize the Newcomb equation, solve it in terms of Legendre functions of imaginary argument, and define the small weak solutions of the Newcomb equation as generalized functions in the manner of Lighthill, i.e. via a limiting sequence of analytic functions that connect smoothly across the singularity.
Dewar, R. L.; Mills, R.; Hole, M. J.
2009-05-01
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics. To resolve the continuation problem we regularize the Newcomb equation, solve it in terms of Legendre functions of imaginary argument, and define the small weak solutions of the Newcomb equation as generalized functions in the manner of Lighthill, i.e. via a limiting sequence of analytic functions that connect smoothly across the singularity.
International Nuclear Information System (INIS)
Dewar, R L; Mills, R; Hole, M J
2009-01-01
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics. To resolve the continuation problem we regularize the Newcomb equation, solve it in terms of Legendre functions of imaginary argument, and define the small weak solutions of the Newcomb equation as generalized functions in the manner of Lighthill, i.e. via a limiting sequence of analytic functions that connect smoothly across the singularity.
An online interactive geometric database including exact solutions of Einstein's field equations
International Nuclear Information System (INIS)
Ishak, Mustapha; Lake, Kayll
2002-01-01
We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models in astrophysics to abstract space-time classification schemes. The database is built using a modular and object-oriented design and uses several Java technologies (e.g. Applets, Servlets, JDBC). These are platform-independent and well adapted for applications developed for the World Wide Web. GRDB is accompanied by a virtual calculator (GRTensorJ), a graphical user interface to the computer algebra system GRTensorII, used to perform online coordinate, tetrad or basis calculations. The highly interactive nature of GRDB allows systematic internal self-checking and minimization of the required internal records. This new database is now available online at http://grdb.org
Generalized MHD for numerical stability analysis of high-performance plasmas in tokamaks
International Nuclear Information System (INIS)
Mikhailovskii, A.B.
1998-01-01
A set of generalized magnetohydrodynamic (MHD) equations is formulated to accommodate the effects associated with high ion and electron temperatures in high-performance plasmas in tokamaks. The effects of neoclassical bootstrap current, neoclassical ion viscosity, the ion finite Larmor radius effect and electron and ion drift effects are taken into account in two-fluid MHD equations together with gyroviscosity, parallel viscosity, electron parallel inertia and collisionless ion heat flux. The ion velocity is identified as the plasma velocity, while the electron velocity is expressed in terms of the plasma velocity and electric current. Ion and electron momentum equations are combined to give the plasma momentum equation. The perpendicular (with respect to the equilibrium magnetic field) ion momentum equation is used as perpendicular Ohm's law and the parallel electron momentum equation - as parallel Ohm's law. Perpendicular Ohm's law allows for the Hall and ion drift effects. Parallel Ohm's law includes the electron drift effect, collisionless skin effect and bootstrap current. In addition, both perpendicular and parallel Ohm's laws contain the resistivity. Due to the quasineutrality condition, the ions and electrons are characterized by the same number density which is described by the ion continuity equation. On the other hand, the ion and electron temperatures are allowed to be different. The ion temperature is described by the ion energy equation allowing for the oblique heat flux, in addition to the perpendicular ion heat flux. The electron temperature is determined by the condition of high parallel electron heat conductivity. The ion and electron parallel viscosities are represented in a form valid for all the collisionality regimes (Pfirsch-Schluter, plateau, and banana). An optimized form of the generalized MHD equations is then represented in terms of the toroidal coordinate system used in the JET equilibrium and stability codes. The derived equations
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
International Nuclear Information System (INIS)
He, Qingyun; Chen, Hongli; Feng, Jingchao
2015-01-01
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.
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
Energy Technology Data Exchange (ETDEWEB)
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.
A solution of the Schrodinger equation with two-body correlations included
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1984-01-01
A procedure for introducing the two-body correlations in the solution of the Schrodinger equation is described. The N-body Schrodinger equation for nucleons subject to two-(or many)-body N-N interaction has never been solved with accuracy except for few-body systems. Indeed it is difficult to take the two-body correlations generated by the interaction into account in the wave function
MHD equilibrium with toroidal rotation
International Nuclear Information System (INIS)
Li, J.
1987-03-01
The present work attempts to formulate the equilibrium of axisymmetric plasma with purely toroidal flow within ideal MHD theory. In general, the inertial term Rho(v.Del)v caused by plasma flow is so complicated that the equilibrium equation is completely different from the Grad-Shafranov equation. However, in the case of purely toroidal flow the equilibrium equation can be simplified so that it resembles the Grad-Shafranov equation. Generally one arbitrary two-variable functions and two arbitrary single variable functions, instead of only four single-variable functions, are allowed in the new equilibrium equations. Also, the boundary conditions of the rotating (with purely toroidal fluid flow, static - without any fluid flow) equilibrium are the same as those of the static equilibrium. So numerically one can calculate the rotating equilibrium as a static equilibrium. (author)
Route analysis for MHD equilibria
International Nuclear Information System (INIS)
Kikuchi, Fumio; Aizawa, Tatsuhiko
1982-01-01
In Tokamak facilities which are promising in nuclear fusion reactor development, the plasma in the core is often described by MHD approximation. Specifically, since an axisymmetric torus is approximately assumed as the first wall (shell) shape in actual Tokamak facilities, the Grad-Shafranov equation to be satisfied by an axisymmetric equilibrium solution for ideal MHD fluid must be solved, and the characteristics of its solution must be clarified. This paper shows the outline of the numerical calculation which employs both the incremental method taking the particular incremental nodal point values as the control parameters and the interaction method in accordance with Newton method at the same time, the analysis objective being a non-linear eigenvalue problem dealing the boundary of plasma region with surrounding vacuum region as the free boundary. Next, the detailed route analysis of the equilibrium solution is performed, utilizing the above numerical calculation technique, to clarify the effect of shell shape on the behaviour of the equilibrium solution. As the shape of the shell, a rectangular section torus, which have a notch depression at a part of the shell inner boundary, is considered. In the paper, the fundamental MHD equation and its approximate solution by the finite element method, the behaviour of plasma equilibrium solution in a shell having a notch, and the effect of notch shapes on plasma behaviour are described. This analysis verifies the effectiveness of the calculation method. (Wakatsuki, Y.)
Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.
2018-06-01
The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.
On nonlinear MHD-stability of toroidal magnetized plasma
International Nuclear Information System (INIS)
Ilgisonis, V.I.; Pastukhov, V.P.
1994-01-01
The variational approach to analyze the nonlinear MHD stability of ideal plasma in toroidal magnetic field is proposed. The potential energy functional to be used is expressed in terms of complete set of independent Lagrangian invariants, that allows to take strictly into account all the restrictions inherent in the varied functions due to MHD dynamic equations. (author). 3 refs
Directory of Open Access Journals (Sweden)
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.
MHD pilot industrial applications
International Nuclear Information System (INIS)
Freeman, M.; Riviere-Wekstein, G.
1994-01-01
MHD industrial applications (and their historical developments) are sketched in the fields of nuclear fission, nuclear fusion and marine vehicles propelling. Nuclear fission projects resulted in promising prototypes between 1972 and 1980, especially for liquid-metal MHD generators. All of them have been stopped by the scientific policies of the governments. Nuclear fusion projects used mainly the equilibrium plasma of tokamak type reactors; some military projects used pulsed plasma to perform pulsed MHD generators. Marine vehicle propelling is the most advanced field. By june 1992, the japanese sea-going boat 'Yamato 1' was sailing with two MHD propellers. A few months later, the building of 'Yamato 2' has begun
Investigations on high speed MHD liquid flow
International Nuclear Information System (INIS)
Yamasaki, Takasuke; Kamiyama, Shin-ichi.
1982-01-01
Lately, the pressure drop problem of MHD two-phase flow in a duct has been investigated theoretically and experimentally in conjunction with the problems of liquid metal MHD two-phase flow power-generating cycle or of liquid metal boiling two-phase flow in the blanket of a nuclear fusion reactor. Though many research results have been reported so far for MHD single-phase flow, the hydrodynamic studies on high speed two-phase flow are reported only rarely, specifically the study dealing with the generation of cavitation is not found. In the present investigation, the basic equation was derived, analyzing the high speed MHD liquid flow in a diverging duct as the one-dimensional flow of homogeneous two-phase fluid of small void ratio. Furthermore, the theoretical solution for the effect of magnetic field on cavitation-generating conditions was tried. The pressure distribution in MHD flow in a duct largely varies with load factor, and even if the void ratio is small, the pressure distribution in two-phase flow is considerably different from that in single-phase flow. Even if the MHD two-phase flow in a duct is subsonic flow at the throat, the critical conditions may be achieved sometimes in a diverging duct. It was shown that cavitation is more likely to occur as magnetic field becomes more intense if it is generated downstream of the throat. This explains the experimental results qualitatively. (Wakatsuki, Y.)
Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.
2013-08-01
By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.
MHD Integrated Topping Cycle Project
Energy Technology Data Exchange (ETDEWEB)
1992-01-01
The overall objective of the project is to design and construct prototypical hardware for an integrated MHD topping cycle, and conduct long duration proof-of-concept tests of integrated system at the US DOE Component Development and Integration Facility in Butte, Montana. The results of the long duration tests will augment the existing engineering design data base on MHD power train reliability, availability, maintainability, and performance, and will serve as a basis for scaling up the topping cycle design to the next level of development, an early commercial scale power plant retrofit. The components of the MHD power train to be designed, fabricated, and tested include: A slagging coal combustor with a rated capacity of 50 MW thermal input, capable of operation with an Eastern (Illinois {number sign}6) or Western (Montana Rosebud) coal, a segmented supersonic nozzle, a supersonic MHD channel capable of generating at least 1.5 MW of electrical power, a segmented supersonic diffuser section to interface the channel with existing facility quench and exhaust systems, a complete set of current control circuits for local diagonal current control along the channel, and a set of current consolidation circuits to interface the channel with the existing facility inverter.
Fukuhara, Keisuke; Morita, Nagayoshi
New FDTD algorithm is proposed for analyzing ultrasonic pulse propagation in the human body, the problem being connected with ESWL (Extracorporeal Shock Wave Lithotripsy). In this method, we do not use plane wave approximation but employ directly the original equations taking account of Lagrangian to derive new FDTD algorithms. This method is applied to an experimental setup and its numerical model that resemble actual treatment situation to compare sound pressure distributions obtained numerically with those obtained experimentally. It is shown that the present method gives clearly better results than the earlier method, in the viewpoint of numerical reappearance of strongly nonlinear waveform.
Design of MHD generator systems
International Nuclear Information System (INIS)
Buende, R.; Raeder, J.
1975-01-01
By assessment of the influence of the combustion efficiency on the electric output of the MHD generator, it can be shown that the construction and efficiency of the generator strongly depend on these parameters. The solutions of this system of equations are discussed. Following a derivation of criteria and boundary conditions of the design and a determination of the specific construction costs of individual system components, it is shown how the single design parameters influence the operational characteristics of such a system, especially the output, efficiency and energy production costs. (GG/LH) [de
Supernova equations of state including full nuclear ensemble with in-medium effects
Furusawa, Shun; Sumiyoshi, Kohsuke; Yamada, Shoichi; Suzuki, Hideyuki
2017-01-01
We construct new equations of state for baryons at sub-nuclear densities for the use in core-collapse supernova simulations. The abundance of various nuclei is obtained together with thermodynamic quantities. The formulation is an extension of the previous model, in which we adopted the relativistic mean field theory with the TM1 parameter set for nucleons, the quantum approach for d, t, h and α as well as the liquid drop model for the other nuclei under the nuclear statistical equilibrium. We reformulate the model of the light nuclei other than d, t, h and α based on the quasi-particle description. Furthermore, we modify the model so that the temperature dependences of surface and shell energies of heavy nuclei could be taken into account. The pasta phases for heavy nuclei and the Pauli- and self-energy shifts for d, t, h and α are taken into account in the same way as in the previous model. We find that nuclear composition is considerably affected by the modifications in this work, whereas thermodynamical quantities are not changed much. In particular, the washout of shell effect has a great impact on the mass distribution above T ∼ 1 MeV. This improvement may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.
MHD deceleration of fusion reaction products
International Nuclear Information System (INIS)
Chow, S.; Bohachevsky, I.O.
1979-04-01
The feasibility of magnetohydrodynamic (MHD) deceleration of fuel pellet debris ions exiting from an inertial confinement fusion (ICF) reactor cavity is investigated using one-dimensional flow equations. For engineering reasons, induction-type devices are emphasized; their performance characteristics are similar to those of electrode-type decelerators. Results of the analysis presented in this report indicate that MHD decelerators can be designed within conventional magnet technology to not only decelerate the high-energy fusion pellet debris ions but also to produce some net electric power in the process
Gravitational instability in isotropic MHD plasma waves
Cherkos, Alemayehu Mengesha
2018-04-01
The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.
Di Nucci, Carmine
2018-05-01
This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.
International Nuclear Information System (INIS)
Souley, Mountaka; Ghoreychi, Mehdi; Armand, Gilles
2010-01-01
viscoplastic model which aims to improve the viscoplastic strain prediction in the EDZ (Excavated Damaged Zone) is proposed by introducing damage variable in Lemaitre's model. The mains characteristics of the model are: (a) the short-term behaviour is based on a generalized Hoek-Brown model; (b) the long-term behaviour is based on the modified Lemaitre's model, the changes of viscoplastic strain rates due to damage (in pre peak phase) and failure (post-peak and residual phases) are taken into account by varying the creep activation energy and the strain-hardening as a function of the current damage rate. In addition, in order to prevent the overestimation of volumetric strain the associated flow rule initially assumed is revisited for the short term behaviour. The proposed model is implemented in FLAC3D C . In order to verify both constitutive equations and their implementations, several simulations of classical laboratory tests (uniaxial/triaxial, mono/multi stage creep and relaxation) are performed. As practical applications, the proposed model has been used to predict the behaviour of two galleries of the laboratory (at -490 m level): parallel and perpendicular to the major horizontal stress. Comparison between predicted results and the in situ measurements are then presented and discussed Finally the model limitations as well as possible improvements are discussed in this paper. (authors)
International Nuclear Information System (INIS)
Takeda, Tatsuoki
1985-01-01
In this article analyses of the MHD stabilities which govern the global behavior of a fusion plasma are described from the viewpoint of the numerical computation. First, we describe the high accuracy calculation of the MHD equilibrium and then the analysis of the linear MHD instability. The former is the basis of the stability analysis and the latter is closely related to the limiting beta value which is a very important theoretical issue of the tokamak research. To attain a stable tokamak plasma with good confinement property it is necessary to control or suppress disruptive instabilities. We, next, describe the nonlinear MHD instabilities which relate with the disruption phenomena. Lastly, we describe vectorization of the MHD codes. The above MHD codes for fusion plasma analyses are relatively simple though very time-consuming and parts of the codes which need a lot of CPU time concentrate on a small portion of the codes, moreover, the codes are usually used by the developers of the codes themselves, which make it comparatively easy to attain a high performance ratio on the vector processor. (author)
Applications of Lie-group methods to the equations of magnetohydrodynamics
International Nuclear Information System (INIS)
Mandrekas, J.
1987-01-01
The invariance properties of various sets of magnetohydrodynamic (MHD) equations are studied using techniques from the theory of differential forms. Equations considered include the ideal MHD equations in different geometries and with different magnetic field configurations, the MHD equations in the presence of gravitational forces due to self-attraction or external fields, and the MHD equations including finite thermal conductivity and magnetic viscosity. The knowledge of the group structure of these equations is then used to introduce similarity variables to these equations. For each choice of similarity variables, the original set of partial differential equations is transformed into a set of ordinary differential equations and the most general form of the initial conditions is determined. Three cases are studied in detail and the corresponding sets of ordinary differential equations are solved numerically: the problem of a blast wave in an inhomogeneous atmosphere, the problem of a piston moving according to a power law in time, and the problem of a piston moving according to an exponential law in time
The Stellar IMF from Isothermal MHD Turbulence
Haugbølle, Troels; Padoan, Paolo; Nordlund, Åke
2018-02-01
We address the turbulent fragmentation scenario for the origin of the stellar initial mass function (IMF), using a large set of numerical simulations of randomly driven supersonic MHD turbulence. The turbulent fragmentation model successfully predicts the main features of the observed stellar IMF assuming an isothermal equation of state without any stellar feedback. As a test of the model, we focus on the case of a magnetized isothermal gas, neglecting stellar feedback, while pursuing a large dynamic range in both space and timescales covering the full spectrum of stellar masses from brown dwarfs to massive stars. Our simulations represent a generic 4 pc region within a typical Galactic molecular cloud, with a mass of 3000 M ⊙ and an rms velocity 10 times the isothermal sound speed and 5 times the average Alfvén velocity, in agreement with observations. We achieve a maximum resolution of 50 au and a maximum duration of star formation of 4.0 Myr, forming up to a thousand sink particles whose mass distribution closely matches the observed stellar IMF. A large set of medium-size simulations is used to test the sink particle algorithm, while larger simulations are used to test the numerical convergence of the IMF and the dependence of the IMF turnover on physical parameters predicted by the turbulent fragmentation model. We find a clear trend toward numerical convergence and strong support for the model predictions, including the initial time evolution of the IMF. We conclude that the physics of isothermal MHD turbulence is sufficient to explain the origin of the IMF.
Dynamics of nonlinear resonant slow MHD waves in twisted flux tubes
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Thorson, W.R.; Bandarage, G.
1988-01-01
We formulate a close-coupling theory of slow ion-atom collisions based on molecular (adiabatic) electronic states, and including the electronic continuum. The continuum is represented by packet states spanning it locally and constructed explicitly from exact continuum states. Particular attention is given to two fundamental questions: (1) Unbound electrons can escape from the local region spanned by the packet states. We derive close-coupled integral equations correctly including the escape effects; the ''propagator'' generated by these integral equations does not conserve probability within the close-coupled basis. Previous molecular-state formulations including the continuum give no account of escape effects. (2) Nonadiabatic couplings of adiabatic continuum states with the same energy are singular, reflecting the fact that an adiabatic description of continuum behavior is not valid outside a local region. We treat these singularities explicitly and show that an accurate representation of nonadiabatic couplings within the local region spanned by a set of packet states is well behaved. Hence an adiabatic basis-set description can be used to describe close coupling to the continuum in a local ''interaction region,'' provided the effects of escape are included. In principle, the formulation developed here can be extended to a large class of model problems involving many-electron systems and including models for Penning ionization and collisional detachment processes
Nonlinear dynamics of single-helicity neoclassical MHD tearing instabilities
International Nuclear Information System (INIS)
Spong, D.A.; Shaing, K.C.; Carreras, B.A.; Callen, J.D.; Garcia, L.
1988-10-01
Neoclassical magnetohydrodynamic (MHD) effects can significantly alter the nonlinear evolution of resistive tearing instabilities. This is studied numerically by using a flux-surface-averaged set of evolution equations that includes the lowest-order neoclassical MHD effects. The new terms in the equations are fluctuating bootstrap current, neoclassical modification of the resistivity, and neoclassical damping of the vorticity. Single-helicity tearing modes are studied in a cylindrical model over a range of neoclassical viscosities (μ/sub e//ν/sup e/) and values of the Δ' parameter of tearing mode theory. Increasing the neoclassical viscosity leads to increased growth rate and saturated island width as predicted analytically. The larger island width is caused by the fluctuating bootstrap current contribution in Ohm's law. The Δ' parameter no longer solely determines the island width, and finite-width saturated islands may be obtained even when Δ' is negative. The importance of the bootstrap current (/approximately/∂/rho///partial derivative/psi/) in the nonlinear dynamics leads us to examine the sensitivity of the results with respect to different models for the density evolution. 11 refs., 8 figs
The MHD intermediate shock interaction with an intermediate wave: Are intermediate shocks physical?
International Nuclear Information System (INIS)
Wu, C.C.
1988-01-01
Contrary to the usual belief that MHD intermediate shocks are extraneous, the authors have recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. In this paper, he clarifies the differences between the conventional view and the results by studying the interaction of an MHD intermediate shock with an intermediate wave. The study reaffirms his results. In addition, the study shows that there exists a larger class of shocklike solutions in the time-dependent dissiaptive MHD equations than are given by the MHD Rankine-Hugoniot relations. it also suggests a mechanism for forming rotational discontinuities through the interaction of an intermediate shock with an intermediate wave. The results are of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models
Principal characteristics of SFC type MHD generator
International Nuclear Information System (INIS)
Kayukawa, Naoyuki; Oikawa, Shun-ichi; Aoki, Yoshiaki; Seidou, Tadashi; Okinaka, Noriyuki
1988-01-01
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. (author)
Safety and reliability in superconducting MHD magnets
International Nuclear Information System (INIS)
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
MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate
International Nuclear Information System (INIS)
Bhattacharyya, Krishnendu; Mukhopadhyay, Swati; Layek, G. C.
2011-01-01
An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate. (fundamental areas of phenomenology(including applications))
Petrick, Michael; Pierson, Edward S.; Schreiner, Felix
1980-01-01
According to the present invention, coal combustion gas is the primary working fluid and copper or a copper alloy is the electrodynamic fluid in the MHD generator, thereby eliminating the heat exchangers between the combustor and the liquid-metal MHD working fluids, allowing the use of a conventional coalfired steam bottoming plant, and making the plant simpler, more efficient and cheaper. In operation, the gas and liquid are combined in a mixer and the resulting two-phase mixture enters the MHD generator. The MHD generator acts as a turbine and electric generator in one unit wherein the gas expands, drives the liquid across the magnetic field and thus generates electrical power. The gas and liquid are separated, and the available energy in the gas is recovered before the gas is exhausted to the atmosphere. Where the combustion gas contains sulfur, oxygen is bubbled through a side loop to remove sulfur therefrom as a concentrated stream of sulfur dioxide. The combustor is operated substoichiometrically to control the oxide level in the copper.
International Nuclear Information System (INIS)
Edenstrasser, J.W.
1995-01-01
A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics
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 power station with coal gasification
International Nuclear Information System (INIS)
Brzozowski, W.S.; Dul, J.; Pudlik, W.
1976-01-01
A description is given of the proposed operating method of a MHD-power station including a complete coal gasification into lean gas with a simultaneous partial gas production for the use of outside consumers. A comparison with coal gasification methods actually being used and full capabilities of power stations heated with coal-derived gas shows distinct advantages resulting from applying the method of coal gasification with waste heat from MHD generators working within the boundaries of the thermal-electric power station. (author)
Formation, structure, and stability of MHD intermediate shocks
International Nuclear Information System (INIS)
Wu, C.C.
1990-01-01
Contrary to the usual belief that MHD intermediate shocks are extraneous, the author has recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear wave steepening from continuous waves. In this paper, the formation, structure and stability of intermediate shocks in dissipative MHD are considered in detail. The differences between the conventional theory and his are pointed out and clarified. He shows that all four types of intermediate shocks can be formed from smooth waves. He also shows that there are free parameters in the structure of the intermediate shocks, and that these parameters are related to the shock stability. In addition, he shows that a rotational discontinuity can not exist with finite width, indicate how this is related to the existence of time-dependent intermediate shocks, and show why the conventional theory is not a good approximation to dissipative MHD solutions whenever there is rotation in magnetic field
Technical support for open-cycle MHD program
Energy Technology Data Exchange (ETDEWEB)
None
1978-05-01
The support program for open-cycle MHD at Argonne National Lab is developing the analytical tools needed to investigate the performance of the major components in the combined-cycle MHD/steam power system. The analytical effort is centered on the primary components of the system that are unique to MHD and also on the integration of these analytical representations into a model of the entire power producing system. The present project activities include modeling of the combustor, MHD channel, slag separator, and the high-temperature air preheater. In addition, these models are combined into a complete system model, which is at present capable of carrying out optimizations of the entire system on either thermodynamic efficiency or with less confidence, cost of electrical power. Also, in support of the open-cycle program, considerable effort has gone into the formulation of a CDIF Test Plan and a National MHD Test Program.
Exact solutions for MHD flow of couple stress fluid with heat transfer
Directory of Open Access Journals (Sweden)
Najeeb Alam Khan
2016-01-01
Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.
MHD equilibrium and stability in heliotron plasmas
Energy Technology Data Exchange (ETDEWEB)
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)
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.
Algorithm and exploratory study of the Hall MHD Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Gardiner, Thomas Anthony
2010-01-01
This report is concerned with the influence of the Hall term on the nonlinear evolution of the Rayleigh-Taylor (RT) instability. This begins with a review of the magnetohydrodynamic (MHD) equations including the Hall term and the wave modes which are present in the system on time scales short enough that the plasma can be approximated as being stationary. In this limit one obtains what are known as the electron MHD (EMHD) equations which support two characteristic wave modes known as the whistler and Hall drift modes. Each of these modes is considered in some detail in order to draw attention to their key features. This analysis also serves to provide a background for testing the numerical algorithms used in this work. The numerical methods are briefly described and the EMHD solver is then tested for the evolution of whistler and Hall drift modes. These methods are then applied to study the nonlinear evolution of the MHD RT instability with and without the Hall term for two different configurations. The influence of the Hall term on the mixing and bubble growth rate are analyzed.
Pamadi, Bandu N.; Toniolo, Matthew D.; Tartabini, Paul V.; Roithmayr, Carlos M.; Albertson, Cindy W.; Karlgaard, Christopher D.
2016-01-01
The objective of this report is to develop and implement a physics based method for analysis and simulation of multi-body dynamics including launch vehicle stage separation. The constraint force equation (CFE) methodology discussed in this report provides such a framework for modeling constraint forces and moments acting at joints when the vehicles are still connected. Several stand-alone test cases involving various types of joints were developed to validate the CFE methodology. The results were compared with ADAMS(Registered Trademark) and Autolev, two different industry standard benchmark codes for multi-body dynamic analysis and simulations. However, these two codes are not designed for aerospace flight trajectory simulations. After this validation exercise, the CFE algorithm was implemented in Program to Optimize Simulated Trajectories II (POST2) to provide a capability to simulate end-to-end trajectories of launch vehicles including stage separation. The POST2/CFE methodology was applied to the STS-1 Space Shuttle solid rocket booster (SRB) separation and Hyper-X Research Vehicle (HXRV) separation from the Pegasus booster as a further test and validation for its application to launch vehicle stage separation problems. Finally, to demonstrate end-to-end simulation capability, POST2/CFE was applied to the ascent, orbit insertion, and booster return of a reusable two-stage-to-orbit (TSTO) vehicle concept. With these validation exercises, POST2/CFE software can be used for performing conceptual level end-to-end simulations, including launch vehicle stage separation, for problems similar to those discussed in this report.
Fully developed MHD turbulence near critical magnetic Reynolds number
International Nuclear Information System (INIS)
Leorat, J.; Pouquet, A.; Frisch, U.
1981-01-01
Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers Rsup(M) where magnetic fields can be self-excited by a dynamo mechanism. Such flows have kinetic Reynolds numbers Rsup(V) of the order of 10 7 and are therefore highly turbulent. The behaviour of MHD turbulence with high Rsup(V) and low magnetic Prandtl numbers is investigated, using the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity the study is restricted to homogeneous and isotropic turbulence, but includes helicity. A critical magnetic Reynolds number Rsub(c)sup(M) of the order of a few tens (non-helical case) is obtained above which magnetic energy is present. Rsub(c)sup(M) is practically independent of Rsup(V) (in the range 40 to 10 6 ) and can be considerably decreased by the presence of helicity. No attempt is made to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding Rsub(c)sup(M) such as decreased turbulent heat transport. (author)
Radiation heat transfer within an open-cycle MHD generator channel
Delil, A. A. M.
1983-05-01
Radiation heat transfer in an MHD generator was modeled using the Sparrow and Cess model for radiation in an emitting, absorbing and scattering medium. The resulting general equations can be considerably reduced by introducing simplifying approximations for the channel and MHD gas properties. The simplifications lead to an engineering model, which is very useful for one-dimensional channel flow approximation. The model can estimate thermo-optical MHD gas properties, which can be substituted in the energy equation. The model considers the contribution of solid particles in the MHD gas to radiation heat transfer, considerable in coal-fired closed cycle MHD generators. The modeling is applicable also for other types of flow at elevated temperatures, where radiation heat transfer is an important quantity.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
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 Alfven 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
Thermosolutal MHD flow and radiative heat transfer with viscous ...
African Journals Online (AJOL)
This paper investigates double diffusive convection MHD flow past a vertical porous plate in a chemically active fluid with radiative heat transfer in the presence of viscous work and heat source. The resulting nonlinear dimensionless equations are solved by asymptotic analysis technique giving approximate analytic ...
Standing Slow MHD Waves in Radiatively Cooling Coronal Loops ...
Indian Academy of Sciences (India)
The standing slow magneto-acoustic oscillations in cooling coronal loops ... turbation and, eventually, reduces the MHD equations to a 1D system modelling ..... where the function Q is expanded in power series with respect to ǫ, i.e.,. Q = Q0 + ...
International Nuclear Information System (INIS)
Kelleher, W.P.
1987-01-01
In the assessment of Magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement for toroidal axisymmetric geometry, the Grad-Shafranov equation must be solved, either analytically or numerically. Existing numerical tools have been developed primarily for mainframe usage and can prove cumbersome for screening assessments and parametric evaluations. The objective of this thesis was to develop a personal computer (PC)-based calculational tool for assessing MHD/PFC problems in a highly interactive mode, well suited for scoping studies. The approach adopted involves a two-step process: first the MHD equilibrium is calculated and then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment. The PC-based system developed consists of two programs: (1) PCEQ, which solve the MHD equilibrium problem and (2) PFDE-SIGN, which is employed to arrive at a PFC arrangement. PCEQ provides an output file including, but not limited to, the following: poloidal beta, total beta, safety factors, q, on axis and on edge. PCEQ plots the following contours and/or profiles: flux, pressure and toroidal current density, safety factor, and ratio of plasma toroidal field to vacuum field
Present state of the theory of a MHD-dynamo
Energy Technology Data Exchange (ETDEWEB)
Soward, A M; Roberts, P H
1976-01-01
A review is given of the state of the theory of a MHD-dynamo, that is, the theory of self-excited magnetic fields in homogeneous moving liquids. A description is given of two basic approaches-the turbulent dynamos of Steinbeck, Krause and Redler and the high-conductivity dynamo of Braginski, and a look is also taken at the relation between these dynamos. Finally a look is taken at the results of recent studies of the total problem of a MHD-dynamo, that is, at the results of recent attempts to solve the electro- and hydrodynamic equations and to obtain self-excited fields. 6 figs., 122 ref. (SJR)
MHD channel performance for potential early commercial MHD power plants
International Nuclear Information System (INIS)
Swallom, D.W.
1981-01-01
The commercial viability of full and part load early commercial MHD power plants is examined. The load conditions comprise a mass flow of 472 kg/sec in the channel, Rosebud coal, 34% by volume oxygen in the oxidizer preheated to 922 K, and a one percent by mass seeding with K. The full load condition is discussed in terms of a combined cycle plant with optimized electrical output by the MHD channel. Various electrical load parameters, pressure ratios, and magnetic field profiles are considered for a baseload MHD generator, with a finding that a decelerating flow rate yields slightly higher electrical output than a constant flow rate. Nominal and part load conditions are explored, with a reduced gas mass flow rate and an enriched oxygen content. An enthalpy extraction of 24.6% and an isentropic efficiency of 74.2% is predicted for nominal operation of a 526 MWe MHD generator, with higher efficiencies for part load operation
Criteria for Scaled Laboratory Simulations of Astrophysical MHD Phenomena
International Nuclear Information System (INIS)
Ryutov, D. D.; Drake, R. P.; Remington, B. A.
2000-01-01
We demonstrate that two systems described by the equations of the ideal magnetohydrodynamics (MHD) evolve similarly, if the initial conditions are geometrically similar and certain scaling relations hold. The thermodynamic properties of the gas must be such that the internal energy density is proportional to the pressure. The presence of the shocks is allowed. We discuss the applicability conditions of the ideal MHD and demonstrate that they are satisfied with a large margin both in a number of astrophysical objects, and in properly designed simulation experiments with high-power lasers. This allows one to perform laboratory experiments whose results can be used for quantitative interpretation of various effects of astrophysical MHD. (c) 2000 The American Astronomical Society
MHD instability studies in ISX-B
International Nuclear Information System (INIS)
Pare, V.K.; Dunlap, J.L.; Navarro, A.P.; Burris, R.D.
1979-01-01
MHD instabilities in Ohmically and beam heated ISX-B plasmas have been studied using collimated x-ray and Mirnov loop diagnostics. The diagnostic systems will be described and the instability signals will be illustrated for a variety of discharges. The latter will include those observed in connection with low and high β operation, density clamping, pellet injection, and deliberate introduction of toroidal field ripple
MHD simulations on an unstructured mesh
International Nuclear Information System (INIS)
Strauss, H.R.; Park, W.
1996-01-01
We describe work on a full MHD code using an unstructured mesh. MH3D++ is an extension of the PPPL MH3D resistive full MHD code. MH3D++ replaces the structured mesh and finite difference / fourier discretization of MH3D with an unstructured mesh and finite element / fourier discretization. Low level routines which perform differential operations, solution of PDEs such as Poisson's equation, and graphics, are encapsulated in C++ objects to isolate the finite element operations from the higher level code. The high level code is the same, whether it is run in structured or unstructured mesh versions. This allows the unstructured mesh version to be benchmarked against the structured mesh version. As a preliminary example, disruptions in DIIID reverse shear equilibria are studied numerically with the MH3D++ code. Numerical equilibria were first produced starting with an EQDSK file containing equilibrium data of a DIII-D L-mode negative central shear discharge. Using these equilibria, the linearized equations are time advanced to get the toroidal mode number n = 1 linear growth rate and eigenmode, which is resistively unstable. The equilibrium and linear mode are used to initialize 3D nonlinear runs. An example shows poloidal slices of 3D pressure surfaces: initially, on the left, and at an intermediate time, on the right
A civil engineering approach to ideal MHD
International Nuclear Information System (INIS)
Jensen, V.O.
1992-01-01
It is well known that a magnetic field can be conceived as a medium where an isotropic compressive stress, B 2 /2μ 0 , is superimposed on a tensile stress, B 2 /μ 0 , parallel to the lines of force. When a stationary ideal MHD plasma is present in the magnetic field, the particle pressure adds to the magnetic stresses to form a combined stress tensor. Calculations of plasma equilibria based on this concept are very similar to calculations in civil engineering of static structures based on compressive, tensile, and shear stresses. Therefore the very simple physical pictures known from civil engineering when used in plasma physics provide simple physical understanding and facilitate the physical interpretation of the results. In an earlier paper the concept was used to derive and discuss the equilibrium equations for θ-, Z-, and screw pinches and the Grad-Shafranov shift in a tokamak plasma with circular cross sections of the flux surfaces. Here the concept is used to discuss the virial theorem and to obtain a simple physical interpretation of this theorem. We also reconsider the Grad-Shafranov shift in a tokamak plasma and show that a situation where all flux surfaces have circular cross sections cannot be an exact solution to the ideal MHD equations. (author) 3 refs., 3 figs
Resistive MHD Stability Analysis in Near Real-time
Glasser, Alexander; Kolemen, Egemen
2017-10-01
We discuss the feasibility of a near real-time calculation of the tokamak Δ' matrix, which summarizes MHD stability to resistive modes, such as tearing and interchange modes. As the operational phase of ITER approaches, solutions for active feedback tokamak stability control are needed. It has been previously demonstrated that an ideal MHD stability analysis is achievable on a sub- O (1 s) timescale, as is required to control phenomena comparable with the MHD-evolution timescale of ITER. In the present work, we broaden this result to incorporate the effects of resistive MHD modes. Such modes satisfy ideal MHD equations in regions outside narrow resistive layers that form at singular surfaces. We demonstrate that the use of asymptotic expansions at the singular surfaces, as well as the application of state transition matrices, enable a fast, parallelized solution to the singular outer layer boundary value problem, and thereby rapidly compute Δ'. Sponsored by US DOE under DE-SC0015878 and DE-FC02-04ER54698.
MHD turbulent dynamo in astrophysics: Theory and numerical simulation
Chou, Hongsong
2001-10-01
This thesis treats the physics of dynamo effects through theoretical modeling of magnetohydrodynamic (MHD) systems and direct numerical simulations of MHD turbulence. After a brief introduction to astrophysical dynamo research in Chapter 1, the following issues in developing dynamic models of dynamo theory are addressed: In Chapter 2, nonlinearity that arises from the back reaction of magnetic field on velocity field is considered in a new model for the dynamo α-effect. The dependence of α-coefficient on magnetic Reynolds number, kinetic Reynolds number, magnetic Prandtl number and statistical properties of MHD turbulence is studied. In Chapter 3, the time-dependence of magnetic helicity dynamics and its influence on dynamo effects are studied with a theoretical model and 3D direct numerical simulations. The applicability of and the connection between different dynamo models are also discussed. In Chapter 4, processes of magnetic field amplification by turbulence are numerically simulated with a 3D Fourier spectral method. The initial seed magnetic field can be a large-scale field, a small-scale magnetic impulse, and a combination of these two. Other issues, such as dynamo processes due to helical Alfvénic waves and the implication and validity of the Zeldovich relation, are also addressed in Appendix B and Chapters 4 & 5, respectively. Main conclusions and future work are presented in Chapter 5. Applications of these studies are intended for astrophysical magnetic field generation through turbulent dynamo processes, especially when nonlinearity plays central role. In studying the physics of MHD turbulent dynamo processes, the following tools are developed: (1)A double Fourier transform in both space and time for the linearized MHD equations (Chapter 2 and Appendices A & B). (2)A Fourier spectral numerical method for direct simulation of 3D incompressible MHD equations (Appendix C).
Magnetic levitation and MHD propulsion
Energy Technology Data Exchange (ETDEWEB)
Tixador, P [CNRS/CRTBT-LEG, 38 - Grenoble (France)
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 our 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. (orig.).
Magnetic levitation and MHD propulsion
International Nuclear Information System (INIS)
Tixador, P.
1994-01-01
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 our 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. (orig.)
HIDENEK: an implicit particle simulation of kinetic-MHD phenomena in three-dimensional plasmas
International Nuclear Information System (INIS)
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 suitable 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-frequency 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 kink 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 plasma particles. (author)
1990-10-01
The current magnetohydrodynamic MHD program being implemented is a result of a consensus established in public meetings held by the Department of Energy in 1984. The public meetings were followed by the formulation of a June 1984 Coal-Fired MHD Preliminary Transition and Program Plan. This plan focused on demonstrating the proof-of-concept (POC) of coal-fired MHD electric power plants by the early 1990s. MHD test data indicate that while there are no fundamental technical barriers impeding the development of MHD power plants, technical risk remains. To reduce the technical risk three key subsystems (topping cycle, bottoming cycle, and seed regeneration) are being assembled and tested separately. The program does not require fabrication of a complete superconducting magnet, but rather the development and testing of superconductor cables. The topping cycle system test objectives can be achieved using a conventional iron core magnet system already in place at a DOE facility. Systems engineering-derived requirements and analytical modeling to support scale-up and component design guide the program. In response to environmental, economic, engineering, and utility acceptance requirements, design choices and operating modes are tested and refined to provide technical specifications for meeting commercial criteria. These engineering activities are supported by comprehensive and continuing systems analyses to establish realistic technical requirements and cost data. Essential elements of the current program are to: develop technical and environmental data for the integrated MHD topping cycle and bottoming cycle systems through POC testing (1000 and 4000 hours, respectively); design, construct, and operate a POC seed regeneration system capable of processing spent seed materials from the MHD bottoming cycle; prepare conceptual designs for a site specific MHD retrofit plant; and continue supporting research necessary for system testing.
GRADSPMHD: A parallel MHD code based on the SPH formalism
Vanaverbeke, S.; Keppens, R.; Poedts, S.
2014-03-01
We present GRADSPMHD, a completely Lagrangian parallel magnetohydrodynamics code based on the SPH formalism. The implementation of the equations of SPMHD in the “GRAD-h” formalism assembles known results, including the derivation of the discretized MHD equations from a variational principle, the inclusion of time-dependent artificial viscosity, resistivity and conductivity terms, as well as the inclusion of a mixed hyperbolic/parabolic correction scheme for satisfying the ∇ṡB→ constraint on the magnetic field. The code uses a tree-based formalism for neighbor finding and can optionally use the tree code for computing the self-gravity of the plasma. The structure of the code closely follows the framework of our parallel GRADSPH FORTRAN 90 code which we added previously to the CPC program library. We demonstrate the capabilities of GRADSPMHD by running 1, 2, and 3 dimensional standard benchmark tests and we find good agreement with previous work done by other researchers. The code is also applied to the problem of simulating the magnetorotational instability in 2.5D shearing box tests as well as in global simulations of magnetized accretion disks. We find good agreement with available results on this subject in the literature. Finally, we discuss the performance of the code on a parallel supercomputer with distributed memory architecture. Catalogue identifier: AERP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 620503 No. of bytes in distributed program, including test data, etc.: 19837671 Distribution format: tar.gz Programming language: FORTRAN 90/MPI. Computer: HPC cluster. Operating system: Unix. Has the code been vectorized or parallelized?: Yes, parallelized using MPI. RAM: ˜30 MB for a
Averaged description of 3D MHD equilibrium
International Nuclear Information System (INIS)
Medvedev, S.Yu.; Drozdov, V.V.; Ivanov, A.A.; Martynov, A.A.; Pashekhonov, Yu.Yu.; Mikhailov, M.I.
2001-01-01
A general approach by S.A.Galkin et al. in 1991 to 2D description of MHD equilibrium and stability in 3D systems was proposed. The method requires a background 3D equilibrium with nested flux surfaces to generate the metric of a Riemannian space in which the background equilibrium is described by the 2D equation of Grad-Shafranov type. The equation can be solved then varying plasma profiles and shape to get approximate 3D equilibria. In the framework of the method both planar axis conventional stellarators and configurations with spatial magnetic axis can be studied. In the present report the formulation and numerical realization of the equilibrium problem for stellarators with planar axis is reviewed. The input background equilibria with nested flux surfaces are taken from vacuum magnetic field approximately described by analytic scalar potential
Investigations on application of multigrid method to MHD equilibrium analysis
International Nuclear Information System (INIS)
Ikuno, Soichiro
2000-01-01
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)
Divergence-free MHD Simulations with the HERACLES Code
Directory of Open Access Journals (Sweden)
Vides J.
2013-12-01
Full Text Available Numerical simulations of the magnetohydrodynamics (MHD equations have played a significant role in plasma research over the years. The need of obtaining physical and stable solutions to these equations has led to the development of several schemes, all requiring to satisfy and preserve the divergence constraint of the magnetic field numerically. In this paper, we aim to show the importance of maintaining this constraint numerically. We investigate in particular the hyperbolic divergence cleaning technique applied to the ideal MHD equations on a collocated grid and compare it to the constrained transport technique that uses a staggered grid to maintain the property. The methods are implemented in the software HERACLES and several numerical tests are presented, where the robustness and accuracy of the different schemes can be directly compared.
1981-01-01
The reference conceptual design of the magnetohydrodynamic (MHD) Engineering Test Facility (ETF), a prototype 200 MWe coal-fired electric generating plant designed to demonstrate the commercial feasibility of open cycle MHD, is summarized. Main elements of the design, systems, and plant facilities are illustrated. System design descriptions are included for closed cycle cooling water, industrial gas systems, fuel oil, boiler flue gas, coal management, seed management, slag management, plant industrial waste, fire service water, oxidant supply, MHD power ventilating
Global and kinetic MHD simulation by the Gpic-MHD code
International Nuclear Information System (INIS)
Naitou, Hiroshi; Yamada, Yusuke; Kajiwara, Kenji; Lee, Wei-li; Tokuda, Shinji; Yagi, Masatoshi
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 vortex 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 A z . Particle information is mainly used to estimate second order moments in the generalized ohm's law. Because the lower order moments of the charge density and the longitudinal current density are not used explicitly to determine φ and A z , the numerical noise induced by the discreteness of particle quantities reduces drastically. Another advantage of the algorithm is that the longitudinal induced electric field, E Tz =-∂A z /∂t, is explicitly estimated by the generalized ohm's law and used in the equations of motion. The particle velocities along the magnetic field are used (v z -formulation) instead of generalized momentums (p z -formulation), hence there is no problem of 'cancellation', which appear when estimating A z from the Ampere's law in the p z -formulation. The successful simulation of the collisionless internal kink mode by new Gpic-MHD with the realistic values of the large-scale and high-beta, revealed the usefulness of the new algorithm. (author)
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).
Integration of Extended MHD and Kinetic Effects in Global Magnetosphere Models
Germaschewski, K.; Wang, L.; Maynard, K. R. M.; Raeder, J.; Bhattacharjee, A.
2015-12-01
Computational models of Earth's geospace environment are an important tool to investigate the science of the coupled solar-wind -- magnetosphere -- ionosphere system, complementing satellite and ground observations with a global perspective. They are also crucial in understanding and predicting space weather, in particular under extreme conditions. Traditionally, global models have employed the one-fluid MHD approximation, which captures large-scale dynamics quite well. However, in Earth's nearly collisionless plasma environment it breaks down on small scales, where ion and electron dynamics and kinetic effects become important, and greatly change the reconnection dynamics. A number of approaches have recently been taken to advance global modeling, e.g., including multiple ion species, adding Hall physics in a Generalized Ohm's Law, embedding local PIC simulations into a larger fluid domain and also some work on simulating the entire system with hybrid or fully kinetic models, the latter however being to computationally expensive to be run at realistic parameters. We will present an alternate approach, ie., a multi-fluid moment model that is derived rigorously from the Vlasov-Maxwell system. The advantage is that the computational cost remains managable, as we are still solving fluid equations. While the evolution equation for each moment is exact, it depends on the next higher-order moment, so that truncating the hiearchy and closing the system to capture the essential kinetic physics is crucial. We implement 5-moment (density, momentum, scalar pressure) and 10-moment (includes pressure tensor) versions of the model, and use local approximations for the heat flux to close the system. We test these closures by local simulations where we can compare directly to PIC / hybrid codes, and employ them in global simulations using the next-generation OpenGGCM to contrast them to MHD / Hall-MHD results and compare with observations.
Synoptic, Global Mhd Model For The Solar Corona
Cohen, Ofer; Sokolov, I. V.; Roussev, I. I.; Gombosi, T. I.
2007-05-01
The common techniques for mimic the solar corona heating and the solar wind acceleration in global MHD models are as follow. 1) Additional terms in the momentum and energy equations derived from the WKB approximation for the Alfv’en wave turbulence; 2) some empirical heat source in the energy equation; 3) a non-uniform distribution of the polytropic index, γ, used in the energy equation. In our model, we choose the latter approach. However, in order to get a more realistic distribution of γ, we use the empirical Wang-Sheeley-Arge (WSA) model to constrain the MHD solution. The WSA model provides the distribution of the asymptotic solar wind speed from the potential field approximation; therefore it also provides the distribution of the kinetic energy. Assuming that far from the Sun the total energy is dominated by the energy of the bulk motion and assuming the conservation of the Bernoulli integral, we can trace the total energy along a magnetic field line to the solar surface. On the surface the gravity is known and the kinetic energy is negligible. Therefore, we can get the surface distribution of γ as a function of the final speed originating from this point. By interpolation γ to spherically uniform value on the source surface, we use this spatial distribution of γ in the energy equation to obtain a self-consistent, steady state MHD solution for the solar corona. We present the model result for different Carrington Rotations.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
Kruger, S.E.
1999-01-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
International Nuclear Information System (INIS)
Shkarofsky, I.P.
1997-01-01
The relativistic Fokker-Planck collision term in Braams and Karney [Phys. Fluids B 1, 1355 (1989)] is expanded using Cartesian tensors (equivalent to associated Legendre spherical harmonics) retaining all non-linear terms and an arbitrary zeroth order distribution background. Expressions are given for collision terms between all harmonics and the background distribution in terms of the j and y functions in Braams and Karney. The results reduce to Braams and Karney for the first order harmonic term with a Maxwellian background and to those given by Shkarofsky [Can. J. Phys. 41, 1753 (1963)] in the non-relativistic limit. Expressions for the energy and momentum transfer associated with relativistic Coulomb collisions are given. The fast two dimensional Fokker-Planck solver in Shoucri and Shkarofsky [Comput. Phys. Commun. 82, 287 (1994)] has been extended to include the second order harmonic term. copyright 1997 American Institute of Physics
Linear ideal MHD stability calculations for ITER
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Hogan, J.T.
1988-01-01
A survey of MHD stability limits has been made to address issues arising from the MHD--poloidal field design task of the US ITER project. This is a summary report on the results obtained to date. The study evaluates the dependence of ballooning, Mercier and low-n ideal linear MHD stability on key system parameters to estimate overall MHD constraints for ITER. 17 refs., 27 figs
Modeling a Predictive Energy Equation Specific for Maintenance Hemodialysis.
Byham-Gray, Laura D; Parrott, J Scott; Peters, Emily N; Fogerite, Susan Gould; Hand, Rosa K; Ahrens, Sean; Marcus, Andrea Fleisch; Fiutem, Justin J
2017-03-01
Hypermetabolism is theorized in patients diagnosed with chronic kidney disease who are receiving maintenance hemodialysis (MHD). We aimed to distinguish key disease-specific determinants of resting energy expenditure to create a predictive energy equation that more precisely establishes energy needs with the intent of preventing protein-energy wasting. For this 3-year multisite cross-sectional study (N = 116), eligible participants were diagnosed with chronic kidney disease and were receiving MHD for at least 3 months. Predictors for the model included weight, sex, age, C-reactive protein (CRP), glycosylated hemoglobin, and serum creatinine. The outcome variable was measured resting energy expenditure (mREE). Regression modeling was used to generate predictive formulas and Bland-Altman analyses to evaluate accuracy. The majority were male (60.3%), black (81.0%), and non-Hispanic (76.7%), and 23% were ≥65 years old. After screening for multicollinearity, the best predictive model of mREE ( R 2 = 0.67) included weight, age, sex, and CRP. Two alternative models with acceptable predictability ( R 2 = 0.66) were derived with glycosylated hemoglobin or serum creatinine. Based on Bland-Altman analyses, the maintenance hemodialysis equation that included CRP had the best precision, with the highest proportion of participants' predicted energy expenditure classified as accurate (61.2%) and with the lowest number of individuals with underestimation or overestimation. This study confirms disease-specific factors as key determinants of mREE in patients on MHD and provides a preliminary predictive energy equation. Further prospective research is necessary to test the reliability and validity of this equation across diverse populations of patients who are receiving MHD.
Model for ICRF fast wave current drive in self-consistent MHD equilibria
International Nuclear Information System (INIS)
Bonoli, P.T.; Englade, R.C.; Porkolab, M.; Fenstermacher, M.E.
1993-01-01
Recently, a model for fast wave current drive in the ion cyclotron radio frequency (ICRF) range was incorporated into the current drive and MHD equilibrium code ACCOME. The ACCOME model combines a free boundary solution of the Grad Shafranov equation with the calculation of driven currents due to neutral beam injection, lower hybrid (LH) waves, bootstrap effects, and ICRF fast waves. The equilibrium and current drive packages iterate between each other to obtain an MHD equilibrium which is consistent with the profiles of driven current density. The ICRF current drive package combines a toroidal full-wave code (FISIC) with a parameterization of the current drive efficiency obtained from an adjoint solution of the Fokker Planck equation. The electron absorption calculation in the full-wave code properly accounts for the combined effects of electron Landau damping (ELD) and transit time magnetic pumping (TTMP), assuming a Maxwellian (or bi-Maxwellian) electron distribution function. Furthermore, the current drive efficiency includes the effects of particle trapping, momentum conserving corrections to the background Fokker Planck collision operator, and toroidally induced variations in the parallel wavenumbers of the injected ICRF waves. This model has been used to carry out detailed studies of advanced physics scenarios in the proposed Tokamak Physics Experiment (TPX). Results are shown, for example, which demonstrate the possibility of achieving stable equilibria at high beta and high bootstrap current fraction in TPX. Model results are also shown for the proposed ITER device
Numerical study for determining PF coil system parameters in MHD equilibrium of KT-2 tokamak plasma
International Nuclear Information System (INIS)
Ryu, J.; Hong, S.H.; Lee, K.W.; Hong, B.G.; In, S.R.; Kim, S.K.
1995-01-01
The KT-2 is a large-aspect-ratio medium-sized divertor tokamak in the conceptual design phase and planned to be operational in 1998 at the Korea Atomic Energy Research Institute (KAERI). Plasma equilibrium in tokamak can be acquired by controlling the current of poloidal field (PF) coils in appropriate geometries and positions. In this study, the authors have performed numerical calculations to achieve the various equilibrium conditions fitting given plasma shapes and satisfying PF current limitations. Usually an ideal magnetohydrodynamic (MHD) equation is used to obtain the equilibrium solution of tokamak plasma, and it is practical to take advantage of a numerical method in solving the MHD equation because it has nonlinear source terms. Two equilibrium codes have been applied to find a double-null configuration of free-boundary tokamak plasma in KT-2: one is of the authors' own developing and the other is a free-boundary tokamak equilibrium code (FBT) that has been used mainly for the verification of developed code's results. PF coil system parameters including their positions and currents are determined for the optimization of input power required when the specifications of KT-2 tokamak are met. Then, several sets of equilibrium conditions during the tokamak operation are found to observe the changes of poloidal field currents with the passing of operation time step, and the basic stability problems related with the magnetic field structure is also considered
Problems in nonlinear resistive MHD
International Nuclear Information System (INIS)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.
1998-01-01
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
Goya - an MHD equilibrium code for toroidal plasmas
International Nuclear Information System (INIS)
Scheffel, J.
1984-09-01
A description of the GOYA free-boundary equilibrium code is given. The non-linear Grad-Shafranov equation of ideal MHD is solved in a toroidal geometry for plasmas with purely poloidal magnetic fields. The code is based on a field line-tracing procedure, making storage of a large amount of information on a grid unnecessary. Usage of the code is demonstrated by computations of equi/libria for the EXTRAP-T1 device. (Author)
A nonlinear resistive MHD-code in cylindrical geometry
International Nuclear Information System (INIS)
Jakoby, A.
1987-11-01
A computer code has been developed which solves the full compressible resistive magnetohydrodynamic (MHD) equations in cylindrical geometry. The variables are expanded in Fourier series in the poloidal and axial directions while finite differences are used in the radial direction. The time advance is accomplished by using a semi-implicit predictor-corrector-scheme. Applications to the ideal m=1 ideal kink saturation in the nonlinear regime and the subsequent decay of the singular current layer due to resistivity are presented. (orig.)
International Nuclear Information System (INIS)
Moawad, S. M.; Ibrahim, D. A.
2016-01-01
The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.
Measured MHD equilibrium in Alcator C
International Nuclear Information System (INIS)
Pribyl, P.A.
1986-03-01
A method of processing data from a set of partial Rogowski loops is developed to study the MHD equilibrium in Alcator C. Time dependent poloidal fields in the vicinity of the plasma are calculated from measured currents, with field penetration effects being accounted for. Fields from eddy currents induced by the plasma in the tokamak structure are estimated as well. Each of the set of twelve B/sub θ/ measurements can then be separated into a component from the plasma current and a component from currents external to the pickup loops. Harmonic solutions to Maxwell's equations in toroidal coordinates are fit to these measurements in order to infer the fields everywhere in the vacuum region surrounding the plasma. Using this diagnostic, plasma current, position, shape, and the Shafranov term Λ = β/sub p/ + l/sub i//2 - 1 may be computed, and systematic studies of these plasma parameters are undertaken for Alcator C plasmas
Nonlinear MHD analysis for LHD plasmas
International Nuclear Information System (INIS)
Ichiguchi, K.; Nakajima, N.; Wakatani, M.; Carreras, B.A.
2003-01-01
The nonlinear behavior of the interchange modes with multi-helicity in the Large Helical Device is analyzed based on the reduced MHD equations. In the equilibrium at sufficiently low beta value, the saturation of a single mode and the following excitation of other single mode whose resonant surface is close to that of the saturated mode are slowly repeated. This sequence leads to the local deformation of the pressure profile. Increasing the beta value with the pressure profile fixed, a bursting phenomenon due to the overlap of multiple modes is observed in the kinetic energy, which results in the global reduction of the pressure profile. Increasing the beta value using the pressure profile saturated at the lower beta value suppresses the bursting behavior. This result indicates the possibility that the pressure profile is self-organized so that the LHD plasma should attain the high beta regime through a stable path. (author)
Two dimensional MHD flows between porous boundaries
International Nuclear Information System (INIS)
Gratton, F.T.
1994-01-01
Similarity solutions of dissipative MHD equations representing conducting fluids injected through porous walls and flowing out in both directions from the center of the channel, are studied as a function of four non dimensional parameters, Reynolds number R e , magnetic Reynolds number R m , Alfvenic Mach number, M A , and pressure gradient coefficient, C. The effluence is restrained by an external magnetic field normal to the walls. When R m m >>1, the solution may model a collision of plasmas of astrophysical interest. In this case the magnetic field lines help to drive the outflow acting jointly with the pressure gradient. The law for C as a function of the other parameters is given for several asymptotic limits. (author). 3 refs, 6 figs
MHD simulations of molybdenum X-pinches
International Nuclear Information System (INIS)
Ivanenkov, G.V.; Stepnevski, V.
2002-01-01
One investigates into compression of molybdenum X-pinches applying numerical MHD-models with parabolic and conical initial geometry. The second model describing plasma axial motion in greater detail offers a real geometry of a discharge and is applicable to loads characterized by higher masses in contrast to the first one. Both models enabled to describe all basic phases of compression including origination of a minidiode, occurrence of a narrow neck, microexplosion of a hot point and origination of shock waves followed by sausage instability [ru
International Nuclear Information System (INIS)
Aiba, N.; Tokuda, S.; Oyama, N.; Ozeki, T.; Furukawa, M.
2009-01-01
Effects of a sheared toroidal rotation are investigated numerically on the stability of the MHD modes in the tokamak edge pedestal, which relate to the type-I edge-localized mode. A linear MHD stability code MINERVA is newly developed for solving the Frieman-Rotenberg equation that is the linear ideal MHD equation with flow. Numerical stability analyses with this code reveal that the sheared toroidal rotation destabilizes edge localized MHD modes for rotation frequencies which are experimentally achievable, though the ballooning mode stability changes little by rotation. This rotation effect on the edge MHD stability becomes stronger as the toroidal mode number of the unstable MHD mode increases when the stability analysis was performed for MHD modes with toroidal mode numbers smaller than 40. The toroidal mode number of the unstable MHD mode depends on the stabilization of the current-driven mode and the ballooning mode by increasing the safety factor. This dependence of the toroidal mode number of the unstable mode on the safety factor is considered to be the reason that the destabilization by toroidal rotation is stronger for smaller edge safety factors.
Sub-grid-scale effects on short-wave instability in magnetized hall-MHD plasma
International Nuclear Information System (INIS)
Miura, H.; Nakajima, N.
2010-11-01
Aiming to clarify effects of short-wave modes on nonlinear evolution/saturation of the ballooning instability in the Large Helical Device, fully three-dimensional simulations of the single-fluid MHD and the Hall MHD equations are carried out. A moderate parallel heat conductivity plays an important role both in the two kinds of simulations. In the single-fluid MHD simulations, the parallel heat conduction effectively suppresses short-wave ballooning modes but it turns out that the suppression is insufficient in comparison to an experimental result. In the Hall MHD simulations, the parallel heat conduction triggers a rapid growth of the parallel flow and enhance nonlinear couplings. A comparison between single-fluid and the Hall MHD simulations reveals that the Hall MHD model does not necessarily improve the saturated pressure profile, and that we may need a further extension of the model. We also find by a comparison between two Hall MHD simulations with different numerical resolutions that sub-grid-scales of the Hall term should be modeled to mimic an inverse energy transfer in the wave number space. (author)
MHD simulation of Columbia HBT
International Nuclear Information System (INIS)
Li, X.L.
1987-01-01
The plasma of Columbia High Beta Tokamak (HBT) is studied numerically by using the two dimensional resistive MHD model. The main object of this work is to understand the high beta formation process of HBT plasma and to compare the simulation with the experiments. 21 refs., 48 figs., 2 tabs
Stabilities of MHD rotational discontinuities
International Nuclear Information System (INIS)
Wang, S.
1984-11-01
In this paper, the stabilities of MHD rotational discontinuities are analyzed. The results show that the rotational discontinuities in an incompressible magnetofluid are not always stable with respect to infinitesimal perturbation. The instability condition in a special case is obtained. (author)
MHD stability of tandem mirrors
International Nuclear Information System (INIS)
Poulsen, P.; Molvik, A.; Shearer, J.
1982-01-01
The TMX-Upgrade experiment was described, and the manner in which various plasma parameters could be affected was discussed. The initial analysis of the MHD stability of the tandem mirror was also discussed, with emphasis on the negative tandem configuration
Nonlinear evolution of MHD instabilities
International Nuclear Information System (INIS)
Bateman, G.; Hicks, H.R.; Wooten, J.W.; Dory, R.A.
1975-01-01
A 3-D nonlinear MHD computer code was used to study the time evolution of internal instabilities. Velocity vortex cells are observed to persist into the nonlinear evolution. Pressure and density profiles convect around these cells for a weak localized instability, or convect into the wall for a strong instability. (U.S.)
International Nuclear Information System (INIS)
Scheffel, J.
1984-03-01
The linear Grad-Shafranov equation for a toroidal, axisymmetric plasma is solved analytically. Exact solutions are given in terms of confluent hyper-geometric functions. As an alternative, simple and accurate WKBJ solutions are presented. With parabolic pressure profiles, both hollow and peaked toroidal current density profiles are obtained. As an example the equilibrium of a z-pinch with a square-shaped cross section is derived.(author)
Elkington, S. R.; Alam, S. S.; Chan, A. A.; Albert, J.; Jaynes, A. N.; Baker, D. N.; Wiltberger, M. J.
2017-12-01
Global simulations of radiation belt dynamics are often undertaken using either a transport formalism (e.g. Fokker-Plank), or via test particle simulations in model electric and magnetic fields. While transport formalisms offer computational efficiency and the ability to deal with a wide range of wave-particle interactions, they typically rely on simplified background fields, and often are limited to empirically-specified stochastic (diffusive) wave-particle interactions. On the other hand, test particle simulations may be carried out in global MHD simulations that include realistic physical effects such as magnetopause shadowing, convection, and substorm injections, but lack the ability to handle physics outside the MHD approximation in the realm of higher frequency (kHz) wave populations.In this work we introduce a comprehensive simulation framework combining global MHD/test particle techniques to provide realistic background fields and radial transport processes, with a Stochastic Differential Equation (SDE) method for addressing high frequency wave-particle interactions. We examine the March 17, 2013 storm-time acceleration period, an NSF-GEM focus challenge event, and use the framework to examine the relative importance of physical effects such as magnetopause shadowing, diffusive and advective transport processes, and wave-particle interactions through the various phases of the storm.
Outline of fast analyzer for MHD equilibrium 'FAME'
International Nuclear Information System (INIS)
Sakata, Shinya; Haginoya, Hirofumi; Tsuruoka, Takuya; Aoyagi, Tetsuo; Saito, Naoyuki; Harada, Hiroo; Tani, Keiji; Watanabe, Hideto.
1994-03-01
The FAME (Fast Analyzer for Magnetohydrodynamic (MHD) Equilibrium) system has been developed in order to provide more than 100 MHD equilibria in time series which are enough for the non-stationary analysis of the experimental data of JT-60 within about 20 minutes shot interval. The FAME is an MIMD type small scale parallel computer with 20 microprocessors which are connected by a multi-stage switching system. The maximum theoretical speed is 250 MFLOPS. For the software system of FAME, MHD equilibrium analysis code SELENE and its input data production code FBI are tuned up taking the parallel processing into consideration. Consequently, the computational performance of the FAME system becomes more than 7 times faster than the existing general purpose computer FACOM M780-10s. This report summarizes the outline of the FAME system including hardware, soft-ware and peripheral equipments. (author)
Upwind differencing scheme for the equations of ideal magnetohydrodynamics
International Nuclear Information System (INIS)
Brio, M.; Wu, C.C.
1988-01-01
Recently, upwind differencing schemes have become very popular for solving hyperbolic partial differential equations, especially when discontinuities exist in the solutions. Among many upwind schemes successfully applied to the problems in gas dynamics, Roe's method stands out for its relative simplicity and clarity of the underlying physical model. In this paper, an upwind differencing scheme of Roe-type for the MHD equations is constructed. In each computational cell, the problem is first linearized around some averaged state which preserves the flux differences. Then the solution is advanced in time by computing the wave contributions to the flux at the cell interfaces. One crucial task of the linearization procedure is the construction of a Roe matrix. For the special case γ = 2, a Roe matrix in the form of a mean value Jacobian is found, and for the general case, a simple averaging procedure is introduced. All other necessary ingredients of the construction, which include eigenvalues, and a complete set of right eigenvectors of the Roe matrix and decomposition coefficients are presented. As a numerical example, we chose a coplanar MHD Riemann problem. The problem is solved by the newly constructed second-order upwind scheme as well as by the Lax-Friedrichs, the Lax-Wendroff, and the flux-corrected transport schemes. The results demonstrate several advantages of the upwind scheme. In this paper, we also show that the MHD equations are nonconvex. This is a contrast to the general belief that the fast and slow waves are like sound waves in the Euler equations. As a consequence, the wave structure becomes more complicated; for example, compound waves consisting of a shock and attached to it a rarefaction wave of the same family can exist in MHD. copyright 1988 Academic Press, Inc
Incompressible LFR MHD. A fluid model for stability analysis of a fusion plasma
International Nuclear Information System (INIS)
Scheffel, J.; Faghihi, M.
1986-10-01
A fluid model including FLR effects, named Incompressible Finite Larmor Radius MagnetoHydroDynamics, is presented and derived in this paper. It is an extension of ordinary, incompressible MHD to include the Larmor radius effects due to ion gyroviscosity, Hall current and electron diamagnetism. It is intended to use the model for stability analysis, on the Alfven wave time scale, of a fusion plasma and it is consequently based on transport coefficients in the collisionless limit. It will be demonstrated that for a fairly dense and cool plasma, such as for the EXTRAP z-pinch, all three Larmor radius effects may become important, that for a JET-type plasma no FLR effect is pronounced, and that in a reactor plasma the Hall and electron diamagnetism term may play a role. For scaling lengths signigicantly smaller than the plasma radius the effect of the FLR terms becomes enhanced. To study the importance of the choice of equations of state for the model the m=1 and k 2 r 2 towards infinity instability in cylindrical geometry is given special attention for zero Larmor radius. The full stability criterion of the double adiabatic model, including pressure anisotropy, is presented for what we believe to be the first time. It is found that when perpendicular p > parallel p stability can be reached for very high plasma perpendicular β-values. We demonstrate that no less complicated energy conserving fluid model, which takes into account pressure anisotropy, other than the double adiabativ model can be obtained. Since pressure anisotropy generally only weakly affects stability, we can assume isotropy in the Incompressible FLR MHD model. Also, the energy equation is replaced by the incompressibility condition, making FLR terms appearing in the energy equation irrelevant. (authors)
Glasser, Alexander; Kolemen, Egemen; Glasser, A. H.
2018-03-01
Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1 s . Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.
Technical support for open-cycle MHD program. Progress report, July--December 1978
Energy Technology Data Exchange (ETDEWEB)
Doss, E D [ed.
1979-06-01
The support program for open-cycle MHD at Argonne National Laboratory is developing the analytical tools needed to investigate the performance of the major components in the combined cycle MHD/steam power system. The analytical effort is centered on the primary components of the system that are unique to MHD and also on the integration of these analytical representations into a model of the entire power producing system. The present project activities include modeling of the combustor, MHD channel, slag separator, and high-temperature air heater. In addition, these models are combined into a complete system model, which is at present capable of carrying out optimizations of the entire system relative to either thermodynamic efficiency or cost of electrical power. Also, in support of other aspects of the open-cycle program, test plans are developed and facility and program reviews are provided upon request in support of the needs and requirements of the DOE/MHD Division.
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
Stability analysis of resistive MHD modes via a new numerical matching technique
International Nuclear Information System (INIS)
Furukawa, M.; Tokuda, S.; Zheng, L.-J.
2009-01-01
Full text: Asymptotic matching technique is one of the principal methods for calculating linear stability of resistive magnetohydrodynamics (MHD) modes such as tearing modes. In applying the asymptotic method, the plasma region is divided into two regions: a thin inner layer around the mode-resonant surface and ideal MHD regions except for the layer. If we try to solve this asymptotic matching problem numerically, we meet practical difficulties. Firstly, the inertia-less ideal MHD equation or the Newcomb equation has a regular singular point at the mode-resonant surface, leading to the so-called big and small solutions. Since the big solution is not square-integrable, it needs sophisticated treatment. Even if such a treatment is applied, the matching data or the ratio of small solution to the big one, has been revealed to be sensitive to local MHD equilibrium accuracy and grid structure at the mode-resonant surface by numerical experiments. Secondly, one of the independent solutions in the inner layer, which should be matched onto the ideal MHD solution, is not square-integrable. The response formalism has been adopted to resolve this problem. In the present paper, we propose a new method for computing the linear stability of resistive MHD modes via matching technique, where the plasma region is divided into ideal MHD regions and an inner region with finite width. The matching technique using an inner region with finite width was recently developed for ideal MHD modes in cylindrical geometry, and good performance was shown. Our method extends this idea to resistive MHD modes. In the inner region, the low-beta reduced MHD equations are solved, and the solution is matched onto the solution of the Newcomb equation by using boundary conditions such that the parallel electric field vanishes properly as approaching the computational boundaries. If we use the inner region with finite width, the practical difficulties raised above can be avoided from the beginning. Figure
L. Braga, F.
2013-10-01
The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic (MHD) equilibrium with reversed current density (RCD) profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.
A Fast MHD Code for Gravitationally Stratified Media using ...
Indian Academy of Sciences (India)
namic (MHD) algorithms are important for numerical modelling of highly .... include OpenMP-style pragma-based programming, e.g., developed by PGI, HMPP, .... Thus, the formula (10) returns the one-dimensional index for a field point. A.
Resonant MHD modes with toroidal coupling
International Nuclear Information System (INIS)
Connor, J.W.; Hastie, R.J.; Taylor, J.B.
1990-07-01
This is part 2 of a study of resonant perturbations, such as resistive tearing and ballooning modes, in a torus. These are described by marginal ideal mhd equations in the regions between resonant surfaces; matching across these surfaces provides the dispersion relation. In part 1 we described how all the necessary information from the ideal mhd calculations could be represented by a so-called E-matrix. We also described the calculation of this E-matrix for tearing modes (even parity in perturbed magnetic field) in a large aspect ratio torus. There the toroidal modes comprise coupled cylinder tearing modes and the E-matrix is a generalization of the familiar Δ' quantity in a cylinder. In the present paper we discuss resistive ballooning, or twisting-modes, which have odd-parity in perturbed magnetic field. We show that, unlike the tearing modes, these odd-parity modes are instrinsically toroidal and are not directly related to the odd-parity modes in a cylinder. This is evident from the analysis of the high-n limit in ballooning-space, where a transition from a stable Δ' to an unstable Δ' occurs for the twisting mode when the ballooning effect exceeds the interchange effect, which can occur even at large aspect ratio (as in a tokamak). Analysis of the high-n limit in coordinate space, rather than ballooning space, clarifies this singular behaviour and indicates how one may define twisting-mode Δ'. It also yields a prescription for treating low-n twisting modes and a method for calculating an E-matrix for resistive ballooning modes in a large aspect ratio tokamak. The elements of this matrix are given in terms of cylindrical tearing mode solutions
Several hundred megawatt MHD units
International Nuclear Information System (INIS)
Pishchikov, S.; Pinkhasik, D.; Sidorov, V.
1978-01-01
The features are described of the future MHD unit U-25 tested at the Institute of High Temperatures of the Academy of Sciences of the USSR. The attainable thermal load of the combustion chamber is 290x10 6 kJ/m 3 .h. Three types of channel were tested, i.e., the Faraday channel divided into sections with modular insulating walls, the diagonal channel without metal body, and an improved Faraday channel with an output of 20 MW. The described MHD generator is equipped with an inverter which transforms direct current into alternating current, continuously adjusts the load from no-load operation to short-circuit connection and maintains the desired electrical voltage independently of the changes in loading. A new technique of connecting and disconnecting the oxygen equipment was developed which considerably reduces the time of start-up and shut-down. Natural gas is used for heating the air heaters. All equipment used in the operation of the MHD generator is remote controlled by computer or manually. (J.B.)
Several hundred megawatt MHD units
Energy Technology Data Exchange (ETDEWEB)
Pishchikov, S; Pinkhasik, D; Sidorov, V
1978-07-01
The features are described of the future MHD unit U-25 tested at the Institute of High Temperatures of the Academy of Sciences of the USSR. The attainable thermal load of the combustion chamber is 290x10/sup 6/ kJ/m/sup 3/.h. Three types of channel were tested, i.e., the Faraday channel divided into sections with modular insulating walls, the diagonal channel without metal body, and an improved Faraday channel with an output of 20 MW. The described MHD generator is equipped with an inverter which transforms direct current into alternating current, continuously adjusts the load from no-load operation to short-circuit connection and maintains the desired electrical voltage independently of the changes in loading. A new technique of connecting and disconnecting the oxygen equipment was developed which considerably reduces the time of start-up and shut-down. Natural gas is used for heating the air heaters. All equipment used in the operation of the MHD generator is remote controlled by computer or manually.
Alpha-Driven MHD and MHD-Induced Alpha Loss in TFTR DT Experiments
Chang, Zuoyang
1996-11-01
Theoretical calculation and numerical simulation indicate that there can be interesting interactions between alpha particles and MHD activity which can adversely affect the performance of a tokamak reactor (e.g., ITER). These interactions include alpha-driven MHD, like the toroidicity-induced-Alfven-eigenmode (TAE) and MHD induced alpha particle losses or redistribution. Both phenomena have been observed in recent TFTR DT experiments. Weak alpha-driven TAE activity was observed in a NBI-heated DT experiment characterized by high q0 ( >= 2) and low core magnetic shear. The TAE mode appears at ~30-100 ms after the neutral beam turning off approximately as predicted by theory. The mode has an amplitude measured by magnetic coils at the edge tildeB_p ~1 mG, frequency ~150-190 kHz and toroidal mode number ~2-3. It lasts only ~ 30-70 ms and has been seen only in DT discharges with fusion power level about 1.5-2.0 MW. Numerical calculation using NOVA-K code shows that this type of plasma has a big TAE gap. The calculated TAE frequency and mode number are close to the observation. (2) KBM-induced alpha particle loss^1. In some high-β, high fusion power DT experiments, enhanced alpha particle losses were observed to be correlated to the high frequency MHD modes with f ~100-200 kHz (the TAE frequency would be two-times higher) and n ~5-10. These modes are localized around the peak plasma pressure gradient and have ballooning characteristics. Alpha loss increases by 30-100% during the modes. Particle orbit simulations show the added loss results from wave-particle resonance. Linear instability analysis indicates that the plasma is unstable to the kinetic MHD ballooning modes (KBM) driven primarily by strong local pressure gradients. ----------------- ^1Z. Chang, et al, Phys. Rev. Lett. 76 (1996) 1071. In collaberation with R. Nazikian, G.-Y. Fu, S. Batha, R. Budny, L. Chen, D. Darrow, E. Fredrickson, R. Majeski, D. Mansfield, K. McGuire, G. Rewoldt, G. Taylor, R. White, K
Advanced energy utilization MHD power generation
International Nuclear Information System (INIS)
2008-01-01
The 'Technical Committee on Advanced Energy Utilization MHD Power Generation' was started to establish advanced energy utilization technologies in Japan, and has been working for three years from June 2004 to May 2007. This committee investigated closed cycle MHD, open cycle MHD, and liquid metal MHD power generation as high-efficiency power generation systems on the earth. Then, aero-space application and deep space exploration technologies were investigated as applications of MHD technology. The spin-off from research and development on MHD power generation such as acceleration and deceleration of supersonic flows was expected to solve unstart phenomena in scramjet engine and also to solve abnormal heating of aircrafts by shock wave. In addition, this committee investigated researches on fuel cells, on secondary batteries, on connection of wind power system to power grid, and on direct energy conversion system from nuclear fusion reactor for future. The present technical report described results of investigations by the committee. (author)
International Nuclear Information System (INIS)
Yvars, M.
1979-10-01
The materials considered for the insulating walls of a M.H.D. converter are Al 2 O 3 , and the calcium or strontium zirconates. For the conducting walls electricity conducting oxides are being considered such as ZrO 2 or CrO 3 La essentially. The principle of M.H.D. systems is recalled, the materials considered are described as is their behaviour in the corrosive atmospheres of M.H.D. streams [fr
Energy Technology Data Exchange (ETDEWEB)
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.
Effects of MHD slow shocks propagating along magnetic flux tubes in a dipole magnetic field
Directory of Open Access Journals (Sweden)
N. V. Erkaev
2002-01-01
Full Text Available Variations of the plasma pressure in a magnetic flux tube can produce MHD waves evolving into shocks. In the case of a low plasma beta, plasma pressure pulses in the magnetic flux tube generate MHD slow shocks propagating along the tube. For converging magnetic field lines, such as in a dipole magnetic field, the cross section of the magnetic flux tube decreases enormously with increasing magnetic field strength. In such a case, the propagation of MHD waves along magnetic flux tubes is rather different from that in the case of uniform magnetic fields. In this paper, the propagation of MHD slow shocks is studied numerically using the ideal MHD equations in an approximation suitable for a thin magnetic flux tube with a low plasma beta. The results obtained in the numerical study show that the jumps in the plasma parameters at the MHD slow shock increase greatly while the shock is propagating in the narrowing magnetic flux tube. The results are applied to the case of the interaction between Jupiter and its satellite Io, the latter being considered as a source of plasma pressure pulses.
A method based on a separation of variables in magnetohydrodynamics (MHD)
International Nuclear Information System (INIS)
Cessenat, M.; Genta, P.
1996-01-01
We use a method based on a separation of variables for solving a system of first order partial differential equations, in a very simple modelling of MHD. The method consists in introducing three unknown variables φ1, φ2, φ3 in addition of the time variable τ and then searching a solution which is separated with respect to φ1 and τ only. This is allowed by a very simple relation, called a 'metric separation equation', which governs the type of solutions with respect to time. The families of solutions for the system of equations thus obtained, correspond to a radial evolution of the fluid. Solving the MHD equations is then reduced to find the transverse component H Σ of the magnetic field on the unit sphere Σ by solving a non linear partial differential equation on Σ. Thus we generalize ideas due to Courant-Friedrichs and to Sedov on dimensional analysis and self-similar solutions. (authors)
Energy Technology Data Exchange (ETDEWEB)
NONE
1982-03-01
'Research on MHD generation system' was implemented by its expert committee in the electric joint study group, with the results of fiscal 1981 reported. This year, technological reexamination was conducted for a 2,000 MWt commercial MHD generation plant, with evaluation carried out on the cost performance including the construction and operation cost. In addition, for the purpose of intermediate R and D towards the practicability, examination was also conducted on a system structure, concrete specifications of component element, cost of R and D including operation expenses for example, concerning an 100 MWt class experimental plant and a 500 MWt class plant. In the investigation of the overseas trend, information was summarized in detail on the experimental devices, combustors, generation channels, electrode materials, electrode phenomena, theoretical analyses, seeds, slag, component equipment, instrumental technologies, conceptual designs of generation plant, commercial plant, etc., in Soviet Union, China, Holland, India and EPRI, on the basis of the materials from the 19th MHD symposium held in UTSI and from the coal MHD specialist conference held in Sydney. (NEDO)
Ideal MHD stability analysis of KSTAR target AT mode
International Nuclear Information System (INIS)
Yi, S.M.; Kim, J.H.; You, K.I.; Kim, J.Y.
2009-01-01
Full text: A main research objective of KSTAR (Korea Superconducting Tokamak Advanced Research) device is to demonstrate the steady-state operation capability of high-performance AT (Advanced Tokamak) mode. To meet this goal, it is critical for KSTAR to have a good MHD stability boundary, particularly against the high-beta ideal instabilities such as the external kink and the ballooning modes. To support this MHD stability KSTAR has been designed to have a strong plasma shape and a close interval between plasma and passive- plate wall. During the conceptual design phase of KSTAR, a preliminary study was performed to estimate the high beta MHD stability limit of KSTAR target AT mode using PEST and VACUUM codes and it was shown that the target AT mode can be stable up to β N ∼ 5 with a well-defined plasma pressure and current profiles. Recently, a new calculation has been performed to estimate the ideal stability limit in various KSTAR operating conditions using DCON code, and it has been observed that there is some difference between the new and old calculation results, particularly in the dependence of the maximum β N value on the toroidal mode number. Here, we thus present a more detailed analysis of the ideal MHD stability limit of KSTAR target AT mode using various codes, which include GATO as well as PEST and DCON, in the comparison of calculation results among the three codes. (author)
Measuring the equations of state in a relaxed magnetohydrodynamic plasma
Kaur, M.; Barbano, L. J.; Suen-Lewis, E. M.; Shrock, J. E.; Light, A. D.; Brown, M. R.; Schaffner, D. A.
2018-01-01
We report measurements of the equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.
Pulsed power sources based on MHD generators (A state-of-art review)
International Nuclear Information System (INIS)
Das, A.K.; Venkatramani, N.; Rohatgi, V.K.
1986-01-01
pulsed Power sources are finding increased applications in powering plasma experiments, CTF devices, investigations of structure of earth's crust or self-contained compact power supplies for military applications. This report reviews the development of magnetohydrodynamic (MHD) power systems for pulsed power applications. The major critical components, which are analysed in detail, include the combustor, high energy fuel development, high field magnet, high power density channel and power conditioning unit. The report concludes that the MHD research has now reached a stage, where it is possible to design and achieve requisite performance from short duration high power compact MHD generators. (author)
International Nuclear Information System (INIS)
Bates, J.L.; Marchant, D.D.
1979-10-01
The objectives of this program are to develop, test, characterize, and evaluate materials for open-cycle, coal-fired MHD power generators. The specific immediate goals emphasize electrode and insulator materials, including: (1) testing and evaluation of the enhanced effects of alkali seed on materials in a dc electric field; (2) development and testing of improved electrodes and insulators with controlled microstructures, compositions and properties; and (3) characterization and evaluation of materials relating to both the US MHD Program and the US-USSR Cooperative Program for MHD power generators. Progress is reported
Ion temperature increase during MHD events on the TST-2 spherical tokamak
International Nuclear Information System (INIS)
Ejiri, A.; Shiraiwa, S.; Takase, Y.; Yamada, T.; Nagashima, Y.; Kasahara, H.; Iijima, D.; Kobori, Y.; Nishi, T.; Taniguchi, T.; Aramasu, M.; Ohara, S.; Ushigome, M.; Yamagishi, K.
2003-01-01
Various types of MHD events including internal reconnection events are studied on the TST-2 spherical tokamak. In weak MHD events no positive current spike was observed, but in strong MHD events with positive current spikes, a rapid and significant impurity ion temperature increase was observed. The decrease in the poloidal magnetic energy is the most probable energy source for ion heating. The plasma current shows a stepwise change. The magnitude of this step correlates with the temperature increase and is found to be a good indicator of the strength of each event. (author)
MHD/gas turbine systems designed for low cooling water requirements
International Nuclear Information System (INIS)
Annen, K.D.; Eustis, R.H.
1983-01-01
The MHD/gas turbine combined-cycle system has been designed specifically for applications where the availability of cooling water is very limited. The base case systems which were studied consist of a coal-fired MHD plant with an air turbine bottoming plant and require no cooling water. In addition to the base case systems, systems were considered which included the addition of a vapor cycle bottoming plant to improve the thermal efficiency. These systems require a small amount of cooling water. The results show that the MHD/gas turbine systems have very good thermal and economic performances. The base case I MHD/gas turbine system (782 MW /SUB e/ ) requires no cooling water, has a heat rate which is 13% higher, and a cost of electricity which is only 7% higher than a comparable MHD/steam system (878 MW /SUB e/ ) having a cooling tower heat load of 720 MW. The case I vapor cycle bottomed systems have thermal and economic performances which approach and even exceed those of the MHD/steam system, while having substantially lower cooling water requirements. Performances of a second-generation MHD/gas turbine system and an oxygen-enriched, early commercial system are also evaluated. An analysis of nitric oxide emissions shows compliance with emission standards
A simplified MHD model of capillary Z-Pinch compared with experiments
Energy Technology Data Exchange (ETDEWEB)
Shapolov, A.A.; Kiss, M.; Kukhlevsky, S.V. [Institute of Physics, University of Pecs (Hungary)
2016-11-15
The most accurate models of the capillary Z-pinches used for excitation of soft X-ray lasers and photolithography XUV sources currently are based on the magnetohydrodynamics theory (MHD). The output of MHD-based models greatly depends on details in the mathematical description, such as initial and boundary conditions, approximations of plasma parameters, etc. Small experimental groups who develop soft X-ray/XUV sources often use the simplest Z-pinch models for analysis of their experimental results, despite of these models are inconsistent with the MHD equations. In the present study, keeping only the essential terms in the MHD equations, we obtained a simplified MHD model of cylindrically symmetric capillary Z-pinch. The model gives accurate results compared to experiments with argon plasmas, and provides simple analysis of temporal evolution of main plasma parameters. The results clarify the influence of viscosity, heat flux and approximations of plasma conductivity on the dynamics of capillary Z-pinch plasmas. The model can be useful for researchers, especially experimentalists, who develop the soft X-ray/XUV sources. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Axisymmetric MHD stable sloshing ion distributions
International Nuclear Information System (INIS)
Berk, H.L.; Dominguez, N.; Roslyakov, G.V.
1986-07-01
The MHD stability of a sloshing ion distribution is investigated in a symmetric mirror cell. Fokker-Planck calculations show that stable configurations are possible for ion injection energies that are at least 150 times greater than the electron temperture. Special axial magnetic field profiles are suggested to optimize the favorable MHD properties
International Nuclear Information System (INIS)
Lorin, E; Bandrauk, A D; Lytova, M; Memarian, A
2015-01-01
This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser–molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [1, 2], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [3–9]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects. (paper)
Intermittency in MHD turbulence and coronal nanoflares modelling
Directory of Open Access Journals (Sweden)
P. Veltri
2005-01-01
Full Text Available High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD. The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis.
Impact of Heat and Mass Transfer on MHD Oscillatory Flow of Jeffery ...
African Journals Online (AJOL)
The objective of this paper is to study Dufour, Soret and thermal conductivity on unsteady heat and mass transfer of magneto hydrodynamic (MHD) oscillatory flow of Jeffery fluid through a porous medium in a channel. The partial differential equations governing the flow have been solved numerically using semi-implicit ...
MHD free convection flow past an oscillating plate in the presence of ...
African Journals Online (AJOL)
The study of unsteady magnetohydrodynamic heat and mass transfer in MHD flow past an infinite vertical oscillating plate through porous medium, taking account of the presence of free convection and mass transfer. The energy and chemical species equations are solved in closed form by Laplace-transform technique and ...
Ideal MHD properties for proposed noncircular tokamaks
International Nuclear Information System (INIS)
Helton, F.J.; Greene, J.M.
1986-01-01
We obtain Double Dee, TFXC-C, Big Dee, and JET equlibria which are optimized with respect to both shape and current profile for stability to ideal MHD modes. With a wall reasonably far from the plasma surface we find that the external kink constrains q 1 to be above two, where q 1 is the plasma surface value of the safety factor, and the ballooning mode limits the value of β. Then a relevant stable β value for the Double Dee reactor design is over 7%. Such a Double Dee equilibrium is not in a separated second stability region and thus does not have a problem with accessibility. A relevant stable β value for the TFCX-C reactor design is over 6%. Equivalent relevant stable β values for the Big Dee (17%) and JET (7%) are included for calibration purposes. We compare these relevant stable β values with the β's determined by two recent scaling laws
Magnetic stresses in ideal MHD plasmas
DEFF Research Database (Denmark)
Jensen, V.O.
1995-01-01
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...... 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...... and the Shafranov shift. The method had pedagogical merits as it simplifies the calculations, improves the physical understanding and facilitates an assessment of the approximations made in the calculations....
EVIDENCE OF ACTIVE MHD INSTABILITY IN EULAG-MHD SIMULATIONS OF SOLAR CONVECTION
Energy Technology Data Exchange (ETDEWEB)
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.
Performance and flow characteristics of MHD seawater thruster
Energy Technology Data Exchange (ETDEWEB)
Doss, E.D.
1990-01-01
The main goal of the research is to investigate the effects of strong magnetic fields on the electrical and flow fields inside MHD thrusters. The results of this study is important in the assessment of the feasibility of MHD seawater propulsion for the Navy. To accomplish this goal a three-dimensional fluid flow computer model has been developed and applied to study the concept of MHD seawater propulsion. The effects of strong magnetic fields on the current and electric fields inside the MHD thruster and their interaction with the flow fields, particularly those in the boundary layers, have been investigated. The results of the three-dimensional computations indicate that the velocity profiles are flatter over the sidewalls of the thruster walls in comparison to the velocity profiles over the electrode walls. These nonuniformities in the flow fields give rise to nonuniform distribution of the skin friction along the walls of the thrusters, where higher values are predicted over the sidewalls relative to those over the electrode walls. Also, a parametric study has been performed using the three-dimensional MHD flow model to analyze the performance of continuous electrode seawater thrusters under different operating parameters. The effects of these parameters on the fluid flow characteristics, and on the thruster efficiency have been investigated. Those parameters include the magnetic field (10--20 T), thruster diameter, surface roughness, flow velocity, and the electric load factor. The results show also that the thruster performance improves with the strength of the magnetic field and thruster diameter, and the efficiency decreases with the flow velocity and surface roughness.
Electric potential behaviour in segmented Faraday-type MHD generators
International Nuclear Information System (INIS)
James, M.I.; Mittal, M.L.; Gupta, G.P.; Rohatgi, V.K.
1985-01-01
The potential distribution in the transverse cross-section of a segmented Faraday-type MHD generator is studied. The governing elliptic equation, derived with allowance for the finite electrode segmentation effect and nonuniformity of the gas in the channel, is solved numerically using the Alternating Direction Implicit method in the finite difference scheme, instead of the successive over-relaxation method. The computed potential distribution and the potential drops are found to compare well with experimental results. The potential drops at the electrodes are found to increase with increasing current density. (author)
MHD simulation of a beat frequency heated plasma
International Nuclear Information System (INIS)
Milroy, R.D.; Capjack, C.E.; James, C.R.; McMullin, J.N.
1976-01-01
The heating of a plasma in a solenoid, with a beat frequency harmonic which is excited at a frequency near to that of a Langmuir mode in a plasma, is examined. It is shown that at high temperatures the heating rate is very insensitive to changes in plasma density. The amount of energy that can be coupled to a plasma in a solenoid with this heating scheme is investigated by using a one-dimensional computer code which incorporates an exact solution of the relevant MHD equations. The absorption of energy from a high powered laser is shown to be significantly enhanced with this process. (author)
MHD description of plasma: handbook of plasma physics
International Nuclear Information System (INIS)
Kulsrud, R.M.
1980-10-01
The basic sets of MHD equations for the description of a plasma in various limits are derived and their usefulness and limits of validity are discussed. These limits are: the one fluid collisional plasma, the two fluid collisional plasma, the Chew-Goldberger Low formulation of the guiding center limit of a collisionless plasma and the double-adiabatic limit. Conservation relations are derived from these sets and the mathematics of the concept of flux freezing is given. An example is given illustrating the differences between guiding center theory and double adiabatic theory
A toroidal plasma MHD equilibrium code 'EQUCIR version 1'
International Nuclear Information System (INIS)
Ninomiya, Hiromasa; Shinya, Kichiro; Kameari, Akihisa.
1980-10-01
A new free-boundary toroidal MHD equilibrium code ''EQUCIR version 1'' has been developed. The central problems approached by this code is as follows: 1) The magnetic flux distribution of a plasma at equilibrium is determined in the given external field. 2) A set of circuit equations between the plasma and the external conductors are constructed. These circuit equations and the Grad-Shafranov equation are solved self-consistently and the time evolutions of plasma equilibria and currents in external conductors are determined at the same time. 3) The currents in the external conductors are determined so that the plasma cross-section and plasma parameters are to be maintained with desired ones. It is shown that this code is very useful for study of the tokamak plasma equilibria, for design of the poloidal coil system and for investigation of experimental results. (author)
MHD (Magnetohydrodynamics) recovery and regeneration
Energy Technology Data Exchange (ETDEWEB)
McIlroy, R. A. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Probert, P. B. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Lahoda, E. J. [Westinghouse Electric Corp., Pittsburgh, PA (United States); Swift, W. M. [Argonne National Lab. (ANL), Argonne, IL (United States); Jackson, D. M. [Univ. of Tennessee Space Inst. (UTSI), Tullahoma, TN (United States); Prasad, J. [Univ. of Tennessee Space Inst. (UTSI), Tullahoma, TN (United States); Martin, J. [Hudson Engineering (United States); Rogers, C. [Hudson Engineering (United States); Ho, K. K. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Senary, M. K. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Lee, S. [Univ. of Akron, OH (United States)
1988-10-01
A two-phase program investigating MHD seed regeneration is described. In Phase I, bench scale experiments were carried out to demonstrate the technical feasibility of a proposed Seed Regeneration Process. The Phase I data has been used for the preliminary design of a Proof-of-Concept (POC) plant which will be built and tested in Phase II. The Phase I data will also be used to estimate the costs of a 300 Mw(t) demonstration plant for comparison with other processes. The Seed Regeneration Process consists of two major subprocesses; a Westinghouse Dry Reduction process and a modified Tampella (sulfur) Recovery process. The Westinghouse process reduces the recovered spent seed (i.e., potassium sulfate) to potassium polysulfide in a rotary kiln. The reduction product is dissolved in water to form green liquor, clarified to remove residual coal ash, and sent to the Tampella sulfur release system. The sulfur is released using carbon dioxide from flue gas in a two stage reaction. The sulfur is converted to elemental sulfur as a marketable by product. The potassium is crystallized from the green liquor and dried to the anhydrous form for return to the MHD unit.
Alpha particle effects on MHD ballooning
International Nuclear Information System (INIS)
1991-01-01
During the period, as the first step towards the goal of detail understanding of the effects of alpha particle on MHD Ballooning Modes, a new numerical approach to investigate the stability of low-frequency fluctuations in high temperature tokamaks was developed by solving the gyrokinetic equations for the ion and electron directly as an initial value problem. The advantage of this approach is the inclusion of many important kinetic features of the problem without approximations and computationally more economical than particle-pushing simulation. The ion-temperature-gradient-mode was investigated to benchmark this new simulation technique. Previous results in literature were recovered. Both the adiabatic electron model and the full drift-kinetic electron model are studied. Numerical result shows that the full drift-kinetic electron model is more unstable. The development of subcycling technique to handle the fast electron bounce time is particularly significant to apply this new approach to the alpha particle problem since alpha particle bounce frequency is also significantly higher than the mode frequency. This new numerical technique will be the basis of future study of the microstability in high temperature tokamaks with alpha particles (or any energetic species). 15 refs., 13 figs
Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field
Moawad, S. M.; Moawad
2013-10-01
The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.
Rigo, H. S.; Bercaw, R. W.; Burkhart, J. A.; Mroz, T. S.; Bents, D. J.; Hatch, A. M.
1981-01-01
A description and the design requirements for the 200 MWe (nominal) net output MHD Engineering Test Facility (ETF) Conceptual Design, are presented. Performance requirements for the plant are identified and process conditions are indicated at interface stations between the major systems comprising the plant. Also included are the description, functions, interfaces and requirements for each of these major systems. The lastest information (1980-1981) from the MHD technology program are integrated with elements of a conventional steam electric power generating plant.
Flow aerodynamics modeling of an MHD swirl combustor - calculations and experimental verification
International Nuclear Information System (INIS)
Gupta, A.K.; Beer, J.M.; Louis, J.F.; Busnaina, A.A.; Lilley, D.G.
1981-01-01
This paper describes a computer code for calculating the flow dynamics of constant density flow in the second stage trumpet shaped nozzle section of a two stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite difference computer code has been developed to allow the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for efficient solution of the equations. Tue produces as output the flow field map of the non-dimensional stream function, axial and swirl velocity. 19 refs
Generation of compressible modes in MHD turbulence
Energy Technology Data Exchange (ETDEWEB)
Cho, Jungyeon [Chungnam National Univ., Daejeon (Korea); Lazarian, A. [Univ. of Wisconsin, Madison, WI (United States)
2005-05-01
Astrophysical turbulence is magnetohydrodynamic (MHD) in nature. We discuss fundamental properties of MHD turbulence and in particular the generation of compressible MHD waves by Alfvenic turbulence and show that this process is inefficient. This allows us to study the evolution of different types of MHD perturbations separately. We describe how to separate MHD fluctuations into three distinct families: Alfven, slow, and fast modes. We find that the degree of suppression of slow and fast modes production by Alfvenic turbulence depends on the strength of the mean field. We review the scaling relations of the modes in strong MHD turbulence. We show that Alfven modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfven modes. However, fast modes exhibit isotropy and a scaling similar to that of acoustic turbulence both in high and low {beta} plasmas. We show that our findings entail important consequences for star formation theories, cosmic ray propagation, dust dynamics, and gamma ray bursts. We anticipate many more applications of the new insight to MHD turbulence and expect more revisions of the existing paradigms of astrophysical processes as the field matures. (orig.)
Development of a predictive energy equation for maintenance hemodialysis patients: a pilot study.
Byham-Gray, Laura; Parrott, J Scott; Ho, Wai Yin; Sundell, Mary B; Ikizler, T Alp
2014-01-01
The study objectives were to explore the predictors of measured resting energy expenditure (mREE) among a sample of maintenance hemodialysis (MHD) patients, to generate a predictive energy equation (MHDE), and to compare such models to another commonly used predictive energy equation in nutritional care, the Mifflin-St. Jeor equation (MSJE). The study was a retrospective, cross-sectional cohort design conducted at the Vanderbilt University Medical Center. Study subjects were adult MHD patients (N = 67). Data collected from several clinical trials were analyzed using Pearson's correlation and multivariate linear regression procedures. Demographic, anthropometric, clinical, and laboratory data were examined as potential predictors of mREE. Limits of agreement between the MHDE and the MSJE were evaluated using Bland-Altman plots. The a priori α was set at P lean body mass [LBM]) of mREE included (R(2) = 0.489) FFM, ALB, age, and CRP. Two additional models (MHDE-CRP and MHDE-CR) with acceptable predictability (R(2) = 0.460 and R(2) = 0.451) were derived to improve the clinical utility of the developed energy equation (MHDE-LBM). Using Bland-Altman plots, the MHDE over- and underpredicted mREE less often than the MSJE. Predictive models (MHDE) including selective demographic, clinical, and anthropometric data explained less than 50% variance of mREE but had better precision in determining energy requirements for MHD patients when compared with MSJE. Further research is necessary to improve predictive models of mREE in the MHD population and to test its validity and clinical application. Copyright © 2014 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.
Using packaged software for solving two differential equation problems that arise in plasma physics
International Nuclear Information System (INIS)
Gaffney, P.W.
1980-01-01
Experience in using packaged numerical software for solving two related problems that arise in Plasma physics is described. These problems are (i) the solution of the reduced resistive MHD equations and (ii) the solution of the Grad-Shafranov equation
United States Superconducting MHD Magnet Technology Development Program
International Nuclear Information System (INIS)
Dawson, A.M.; Marston, P.G.; Thome, R.J.; Iwasa, Y.; Tarrh, J.M.
1981-01-01
A three-faceted program supported by the U.S. Dep of Energy is described. These facets include basic technology development, technology transfer and construction by industry of magnets for the national MHD program. The program includes the maintenance of a large component test facility; investigation of superconductor stability and structural behavior; measurements of materials' properties at low temperatures; structural design optimization; analytical code development; cryogenic systems and power supply design. The technology transfer program is designed to bring results of technology development and design and construction effort to the entire superconducting magnet community. The magnet procurement program is responsible for developing conceptual designs of magnets needed for the national MHD program, for issuing requests for quotation, selecting vendors and supervising design, construction, installation and test of these systems. 9 refs
Decay of MHD-scale Kelvin-Helmholtz vortices mediated by parasitic electron dynamics
International Nuclear Information System (INIS)
Nakamura, T.K.M.; Hayashi, D.; Fujimoto, M.; Shinohara, I.
2004-01-01
We have simulated nonlinear development of MHD-scale Kelvin-Helmholtz (KH) vortices by a two-dimensional two-fluid system including finite electron inertial effects. In the presence of moderate density jump across a shear layer, in striking contrast to MHD results, MHD KH vortices are found to decay by the time one eddy turnover is completed. The decay is mediated by smaller vortices that appear within the parent vortex and stays effective even when the shear layer width is made larger. It is shown that the smaller vortices are basically of MHD nature while the seeding for these is achieved by the electron inertial effect. Application of the results to the magnetotail boundary layer is discussed
Study on closed cycle MHD generation systems; Closed cycle MHD hatsuden system no kento
Energy Technology Data Exchange (ETDEWEB)
NONE
1988-03-01
The closed cycle noble gas MHD generation systems are surveyed and studied. The concept of closed cycle noble gas MHD generation is confirmed to extract high enthalpy, and now going into the engineering demonstration stage from the basic research stage. These systems have various characteristics. The highest working temperature is around 1,700 degrees C, which is close to that associated with the existing techniques. Use of helium or argon gas as the working fluid makes the system relatively free of various problems, e.g., corrosion. It can attain a much higher efficiency than the combined cycle involving gas turbine. It suffers less heat loss in the passages, is suitable for small- to medium-capacity power generation systems, and copes with varying load. The compact power generation passages decrease required size of the superconducting magnet. The technical problems to be solved include optimization of power generation conditions, demonstration of durability of the power generation passages, injection/recovery of the seed material, treatment of the working gas to remove molecular impurities, and development of heat exchangers serviceable at high temperature produced by direct combustion of coal. The conceptual designs of the triple combined system are completed. (NEDO)
Report on studies on closed cycle MHD power generation; Closed cycle MHD hatsuden kento hokokusho
Energy Technology Data Exchange (ETDEWEB)
NONE
1991-04-01
Summarized herein are results of the studies on closed cycle MHD (CCMHD) power generation by the study committee. The studied system is based on the MHD gas turbine combined Brayton cycle of about 500,000 kW in output power, firing natural gas as the fuel, and the conceptual design works therefor are completed. The major findings are: the overall plant efficiency: 54.2% at the power transmission side, plot area required per unit power output: 0.04 m{sup 2}/KW, unit construction cost: 251,000 yen/KW, and unit power generation cost: 10.2 yen/KWh. This system will be more operable than the gas turbine combined cycle with steam system, because start-up time, output change rate, optimum load and so on are constrained not on the power generator side but on the gas turbine side. The expected environmental effects include the exhaust gas NOX concentration being equivalent with that associated with the conventional power generator of 2-stage combustion system, quantity of combustion gases to be treated being approximately 40% of that associated with the gas turbine combined cycle, and reduced CO2 gas emissions, resulting from enhanced power generation efficiency. It is expected that the CCMHD system can exhibit higher efficiency than the high-temperature gas turbine combined cycle system. (NEDO)
On MHD waves, fire-hose and mirror instabilities in anisotropic plasmas
Directory of Open Access Journals (Sweden)
L.-N. Hau
2007-09-01
Full Text Available Temperature or pressure anisotropies are characteristic of space plasmas, standard magnetohydrodynamic (MHD model for describing large-scale plasma phenomena however usually assumes isotropic pressure. In this paper we examine the characteristics of MHD waves, fire-hose and mirror instabilities in anisotropic homogeneous magnetized plasmas. The model equations are a set of gyrotropic MHD equations closed by the generalized Chew-Goldberger-Low (CGL laws with two polytropic exponents representing various thermodynamic conditions. Both ions and electrons are allowed to have separate plasma beta, pressure anisotropy and energy equations. The properties of linear MHD waves and instability criteria are examined and numerical examples for the nonlinear evolutions of slow waves, fire-hose and mirror instabilities are shown. One significant result is that slow waves may develop not only mirror instability but also a new type of compressible fire-hose instability. Their corresponding nonlinear structures thus may exhibit anticorrelated density and magnetic field perturbations, a property used for identifying slow and mirror mode structures in the space plasma environment. The conditions for nonlinear saturation of both fire-hose and mirror instabilities are examined.
Liquid metal MHD generator systems
International Nuclear Information System (INIS)
Satyamurthy, P.; Dixit, N.S.; Venkataramani, N.; Rohatgi, V.K.
1985-01-01
Liquid Metal MHD (LMMHD) Generator Systems are becoming increasingly important in space and terrestrial applications due to their compactness and versatility. This report gives the current status and economic viability of LMMHD generators coupled to solar collectors, fast breeder reactors, low grade heat sources and conventional high grade heat sources. The various thermodynamic cycles in the temperatures range of 100degC-2000degC have been examined. The report also discusses the present understanding of various loss mechanisms inherent in LMMHD systems and the techniques for overcoming these losses. A small mercury-air LMMHD experimental facility being set up in Plasma Physics Division along with proposals for future development of this new technology is also presented in this report. (author)
MHD waves, reconnection, and plasma transport at the dayside magnetopause
International Nuclear Information System (INIS)
Johnson, J.R.; Cheng, C.Z.
1996-01-01
The magnetic field of the Earth creates a huge cavity in the solar wind known as the magnetosphere. The transition region between the solar wind plasma and magnetosphere plasma is of substantial interest because many magnetospheric processes are governed by the transport of particles, momentum and energy across that boundary. At this boundary, the magnetopause, there is an abrupt decrease in plasma bulk flow, density and pressure, and large increase in temperature and magnetic field. Throughout this region the plasmas is large. Large amplitude compressional waves are nearly always found in the region just outside of the magnetopause. These waves are either intrinsic solar wind fluctuations or they may be global mirror modes which are generated in a localized region of large pressure anisotropy just outside the magnetopause. The substantial background gradients observed at the magnetopause strongly couple the compressional waves with kinetic Alfven waves near the Alfven resonance location, leading to substantial particle transport. Moreover, for a sheared background magnetic field, as is found at times of southward interplanetary magnetic field, the mode converted kinetic Alfven waves can propagate to the location where k parallel = 0 and generate islands in phase space. We present a solution of the kinetic-MHD wave equations for the magnetic field structure based on a realistic steady state profile which includes: a sheared magnetic field; magnetic curvature; and gradients in the background density, pressure and magnetic field. We incorporate wave-particle resonance interactions for electrons and ions to obtain the dissipation. The background magnetic Keld curvature and gradient give rise to drifts which alter the resonance condition for the various particle species (ω - k circ V d - k parallel v parallel ) and reduces the Landau damping of the kinetic Alfven wave, allowing it to propagate to the k parallel = 0 location
MHD PbLi experiments in MaPLE loop at UCLA
International Nuclear Information System (INIS)
Courtessole, C.; Smolentsev, S.; Sketchley, T.; Abdou, M.
2016-01-01
Highlights: • The paper overviews the MaPLE facility at UCLA: one-of-a-few PbLi MHD loop in the world. • We present the progress achieved in development and testing of high-temperature PbLi flow diagnostics. • The most important MHD experiments carried out since the first loop operation in 2011 are summarized. - Abstract: Experiments on magnetohydrodynamic (MHD) flows are critical to understanding complex flow phenomena in ducts of liquid metal blankets, in particular those that utilize eutectic alloy lead–lithium as breeder/coolant, such as self-cooled, dual-coolant and helium-cooled lead–lithium blanket concepts. The primary goal of MHD experiments at UCLA using the liquid metal flow facility called MaPLE (Magnetohydrodynamic PbLi Experiment) is to address important MHD effects, heat transfer and flow materials interactions in blanket-relevant conditions. The paper overviews the one-of-a-kind MaPLE loop at UCLA and presents recent experimental activities, including the development and testing of high-temperature PbLi flow diagnostics and experiments that have been performed since the first loop operation in 2011. We also discuss MaPLE upgrades, which need to be done to substantially expand the experimental capabilities towards a new class of MHD flow phenomena that includes buoyancy effects.
MHD PbLi experiments in MaPLE loop at UCLA
Energy Technology Data Exchange (ETDEWEB)
Courtessole, C., E-mail: cyril@fusion.ucla.edu; Smolentsev, S.; Sketchley, T.; Abdou, M.
2016-11-01
Highlights: • The paper overviews the MaPLE facility at UCLA: one-of-a-few PbLi MHD loop in the world. • We present the progress achieved in development and testing of high-temperature PbLi flow diagnostics. • The most important MHD experiments carried out since the first loop operation in 2011 are summarized. - Abstract: Experiments on magnetohydrodynamic (MHD) flows are critical to understanding complex flow phenomena in ducts of liquid metal blankets, in particular those that utilize eutectic alloy lead–lithium as breeder/coolant, such as self-cooled, dual-coolant and helium-cooled lead–lithium blanket concepts. The primary goal of MHD experiments at UCLA using the liquid metal flow facility called MaPLE (Magnetohydrodynamic PbLi Experiment) is to address important MHD effects, heat transfer and flow materials interactions in blanket-relevant conditions. The paper overviews the one-of-a-kind MaPLE loop at UCLA and presents recent experimental activities, including the development and testing of high-temperature PbLi flow diagnostics and experiments that have been performed since the first loop operation in 2011. We also discuss MaPLE upgrades, which need to be done to substantially expand the experimental capabilities towards a new class of MHD flow phenomena that includes buoyancy effects.
3D simulation studies of tokamak plasmas using MHD and extended-MHD models
International Nuclear Information System (INIS)
Park, W.; Chang, Z.; Fredrickson, E.; Fu, G.Y.
1996-01-01
The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-β disruption studies in reversed shear plasmas using the MHD level MH3D code, ω *i stabilization and nonlinear island saturation of TAE mode using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D ++ code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree which agree well with experimental data
Major disruptions, inverse cascades, and the Strauss equations
International Nuclear Information System (INIS)
Montgomery, D.
1982-01-01
Current-carrying plasmas in a strong dc magnetic field are subject to violent disruptions above certain thresholds. At present difficult to verify, explanations are typically sought in terms of tearing modes. An alternative explanation is in terms of inverse magnetic helicity cascades, generated from a variety of possible sources of small-scale MHD turbulence. Strongly anisotropic MHD plasmas may be described by the Strauss equations. Indications of turbulent inverse cascade behavior for the Strauss equations are sought, in parallel with earlier examples from MHD and fluid mechanics
MHD instabilities in heliotron/torsatron
International Nuclear Information System (INIS)
Wakatani, Masahiro; Nakamura, Yuji; Ichiguchi, Katsuji
1992-01-01
Recent theoretical results on MHD instabilities in heliotron/torsatron are reviewed. By comparing the results with experimental data in Heliotron E, Heliotron DR and ATF, it is pointed out that resistive interchange modes are the most crucial instabilities, since the magnetic hill occupies a substantial region of the plasma column. Development of three-dimensional MHD equilibrium codes has made significant progress. By applying the local stability criteria shown by D 1 (ideal MHD mode) and D R (resistive MHD mode) to the equilibria given by the three-dimensional codes such as BETA and VMEC, stability thresholds for the low n ideal modes or the low n resistive modes may be estimated with resonable accuracy, where n is a toroidal mode number. (orig.)
International Nuclear Information System (INIS)
Furusawa, S; Togashi, H; Nagakura, H; Sumiyoshi, K; Yamada, S; Suzuki, H; Takano, M
2017-01-01
We have constructed a nuclear equation of state (EOS) that includes a full nuclear ensemble for use in core-collapse supernova simulations. It is based on the EOS for uniform nuclear matter that two of the authors derived recently, applying a variational method to realistic two- and three-body nuclear forces. We have extended the liquid drop model of heavy nuclei, utilizing the mass formula that accounts for the dependences of bulk, surface, Coulomb and shell energies on density and/or temperature. As for light nuclei, we employ a quantum-theoretical mass evaluation, which incorporates the Pauli- and self-energy shifts. In addition to realistic nuclear forces, the inclusion of in-medium effects on the full ensemble of nuclei makes the new EOS one of the most realistic EOSs, which covers a wide range of density, temperature and proton fraction that supernova simulations normally encounter. We make comparisons with the FYSS EOS, which is based on the same formulation for the nuclear ensemble but adopts the relativistic mean field theory with the TM1 parameter set for uniform nuclear matter. The new EOS is softer than the FYSS EOS around and above nuclear saturation densities. We find that neutron-rich nuclei with small mass numbers are more abundant in the new EOS than in the FYSS EOS because of the larger saturation densities and smaller symmetry energy of nuclei in the former. We apply the two EOSs to 1D supernova simulations and find that the new EOS gives lower electron fractions and higher temperatures in the collapse phase owing to the smaller symmetry energy. As a result, the inner core has smaller masses for the new EOS. It is more compact, on the other hand, due to the softness of the new EOS and bounces at higher densities. It turns out that the shock wave generated by core bounce is a bit stronger initially in the simulation with the new EOS. The ensuing outward propagations of the shock wave in the outer core are very similar in the two simulations, which
International Nuclear Information System (INIS)
Dunn, P.F.
1978-01-01
The basic features of the two-phase liquid-metal MHD energy conversion under development at Argonne National Laboratory are presented. The results of system studies on the Rankine-cycle and the open-cycle coal-fired cycle options are discussed. The liquid-metal MHD experimental facilities are described in addition to the system's major components, the generator, mixer and nozzle-separator-diffuser
MHD stability analysis of helical system plasmas
International Nuclear Information System (INIS)
Nakamura, Yuji
2000-01-01
Several topics of the MHD stability studies in helical system plasmas are reviewed with respect to the linear and ideal modes mainly. Difference of the method of the MHD stability analysis in helical system plasmas from that in tokamak plasmas is emphasized. Lack of the cyclic (symmetric) coordinate makes an analysis more difficult. Recent topic about TAE modes in a helical system is also described briefly. (author)
Scaling, Intermittency and Decay of MHD Turbulence
International Nuclear Information System (INIS)
Lazarian, A.; Cho, Jungyeon
2005-01-01
We discuss a few recent developments that are important for understanding of MHD turbulence. First, MHD turbulence is not so messy as it is usually believed. In fact, the notion of strong non-linear coupling of compressible and incompressible motions along MHD cascade is not tenable. Alfven, slow and fast modes of MHD turbulence follow their own cascades and exhibit degrees of anisotropy consistent with theoretical expectations. Second, the fast decay of turbulence is not related to the compressibility of fluid. Rates of decay of compressible and incompressible motions are very similar. Third, viscosity by neutrals does not suppress MHD turbulence in a partially ionized gas. Instead, MHD turbulence develops magnetic cascade at scales below the scale at which neutrals damp ordinary hydrodynamic motions. Forth, density statistics does not exhibit the universality that the velocity and magnetic field do. For instance, at small Mach numbers the density is anisotropic, but it gets isotropic at high Mach numbers. Fifth, the intermittency of magnetic field and velocity are different. Both depend on whether the measurements are done in a local system of reference oriented along the local magnetic field or in the global system of reference related to the mean magnetic field
Diagnostics for a coal-fired MHD retrofit of an existing power station
Energy Technology Data Exchange (ETDEWEB)
Cook, R L; Shepard, W S [Mississippi State Univ. (USA). Diagnostic Instrumentation and Analysis Lab.
1990-01-01
MHD flows represent one of the most severe environments encountered by gasdynamic diagnostics. Special state-of-the-art techniques and instrumentation systems are required to monitor and collect data for the MHD components, and these diagnostic systems must operate under very severe environmental and magnetic field conditions. The Diagnostic Instrumentation and Analysis Laboratory (DIAL) at Mississippi State University has developed, and is continuing to develop, advanced optical diagnostic techniques and instrumentation systems to provide nonintrusive, remote real-time measurements and to operate successfully in the industrial-like environment of a large-scale MHD retrofit power station. Such diagnostic instrumentation can provide the information to completely evaluate the performance of individual components, as well as, the entire power plant. It is essential to determine as much detail as possible about the various component operations in an MHD retrofit system so that a commercial plant design can be optimized quickly. This paper discusses the instrumentation systems which DIAL proposed for an MHD retrofit of an existing power station. Instruments which have been making measurements on the U.S. MHD test facilities for several years are presented, along with instruments which will be available within two years. Parameters to be measured along with location and frequency are discussed in detail. These parameters include electron density, electrical conductivity, K-atom density, gas temperature, gas velocity, temperature and velocity profiles, gas composition, and particle size, number, density and distrib00000
Multi-scale-nonlinear interactions among macro-MHD mode, micro-turbulence, and zonal flow
International Nuclear Information System (INIS)
Ishizawa, Akihiro; Nakajima, Noriyoshi
2007-01-01
This is the first numerical simulation demonstrating that macro-magnetohydrodynamic (macro-MHD) mode is exited as a result of multi-scale interaction in a quasi-steady equilibrium formed by a balance between zonal flow and micro-turbulence via reduced-two-fluid simulation. Only after obtaining the equilibrium which includes zonal flow and the turbulence caused by kinetic ballooning mode is this simulation of macro-MHD mode, double tearing mode, accomplished. In the quasi-steady equilibrium a macro-fluctuation which has the same helicity as that of double tearing mode is a part of the turbulence until it grows as a macro-MHD mode finally. When the macro-MHD grows it effectively utilize free energy of equilibrium current density gradient because of positive feedback loop between suppression of zonal flow and growth of the macro-fluctuation causing magnetic reconnection. Thus once the macro-MHD grows from the quasi-equilibrium, it does not go back. This simulation is more comparable with experimental observation of growing macro-fluctuation than traditional MHD simulation of linear instabilities in a static equilibrium. (author)
International Nuclear Information System (INIS)
Olschewski, J.; Stein, E.; Wagner, W.; Wetjen, D.
1981-01-01
This paper is a first step in the development of thermodynamically consistent material equations for inelastic materials, such as polycrystalline rock salt. In this context it is of particular importance to reduce the number and the structure of the internal variables, in order to allow for a fit with available experimental data. As an example this is demonstrated in detail in the case of the so-called dislocation model. As physical non-linearities and in addition also geometrical non-linearities lead to an inhomogeneous deformation - and stress state even in the case of simple samples, boundary value problems have to be studied, in order to test the material equations. For this purpose the finite element method has been used. (orig./HP) [de
MHD stability, operational limits and disruptions
International Nuclear Information System (INIS)
1999-01-01
The present physics understandings of magnetohydrodynamic (MHD) stability of tokamak plasmas, the threshold conditions for onset of MHD instability, and the resulting operational limits on attainable plasma pressure (beta limit) and density (density limit), and the consequences of plasma disruption and disruption related effects are reviewed and assessed in the context of their application to a future DT burning reactor prototype tokamak experiment such as ITER. The principal considerations covered within the MHD stability and beta limit assessments are (i) magnetostatic equilibrium, ideal MHD stability and the resulting ideal MHD beta limit; (ii) sawtooth oscillations and the coupling of sawtooth activity to other types of MHD instability; (iii) neoclassical island resistive tearing modes and the corresponding limits on beta and energy confinement; (iv) wall stabilization of ideal MHD instabilities and resistive wall instabilities; (v) mode locking effects of non-axisymmetric error fields; (vi) edge localized MHD instabilities (ELMs, etc.); and (vii) MHD instabilities and beta/pressure gradient limits in plasmas with actively modified current and magnetic shear profiles. The principal considerations covered within the density limit assessments are (i) empirical density limits; (ii) edge power balance/radiative density limits in ohmic and L-mode plasmas; and (iii) edge parameter related density limits in H-mode plasmas. The principal considerations covered in the disruption assessments are (i) disruption causes, frequency and MHD instability onset; (ii) disruption thermal and current quench characteristics; (iii) vertical instabilities (VDEs), both before and after disruption, and plasma and in-vessel halo currents; (iv) after disruption runaway electron formation, confinement and loss; (v) fast plasma shutdown (rapid externally initiated dissipation of plasma thermal and magnetic energies); (vi) means for disruption avoidance and disruption effect mitigation; and
Analytic MHD Theory for Earth's Bow Shock at Low Mach Numbers
Grabbe, Crockett L.; Cairns, Iver H.
1995-01-01
A previous MHD theory for the density jump at the Earth's bow shock, which assumed the Alfven M(A) and sonic M(s) Mach numbers are both much greater than 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M(A) and M(s), and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M(A) and M(s) in the solar wind when the angle theta between the normal to the bow shock and magnetic field is not close to 0 deg or 180 deg (the solutions are symmetric about 90 deg). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when theta is close to 90 deg. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For theta approx. = 90 deg another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth's bow shock, except in the rare circumstance that M(A) is less than or = 2. MHD and gasdynamic simulations have produced empirical models in which the shock's standoff distance a(s) is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between a(s) and X obtained from MHD simulations, a(s) values predicted using the MHD solutions for X are compared with the predictions of phenomenological models commonly used for modeling observational data, and with the predictions of a
HPC parallel programming model for gyrokinetic MHD simulation
International Nuclear Information System (INIS)
Naitou, Hiroshi; Yamada, Yusuke; Tokuda, Shinji; Ishii, Yasutomo; Yagi, Masatoshi
2011-01-01
The 3-dimensional gyrokinetic PIC (particle-in-cell) code for MHD simulation, Gpic-MHD, was installed on SR16000 (“Plasma Simulator”), which is a scalar cluster system consisting of 8,192 logical cores. The Gpic-MHD code advances particle and field quantities in time. In order to distribute calculations over large number of logical cores, the total simulation domain in cylindrical geometry was broken up into N DD-r × N DD-z (number of radial decomposition times number of axial decomposition) small domains including approximately the same number of particles. The axial direction was uniformly decomposed, while the radial direction was non-uniformly decomposed. N RP replicas (copies) of each decomposed domain were used (“particle decomposition”). The hybrid parallelization model of multi-threads and multi-processes was employed: threads were parallelized by the auto-parallelization and N DD-r × N DD-z × N RP processes were parallelized by MPI (message-passing interface). The parallelization performance of Gpic-MHD was investigated for the medium size system of N r × N θ × N z = 1025 × 128 × 128 mesh with 4.196 or 8.192 billion particles. The highest speed for the fixed number of logical cores was obtained for two threads, the maximum number of N DD-z , and optimum combination of N DD-r and N RP . The observed optimum speeds demonstrated good scaling up to 8,192 logical cores. (author)
MHD magnet technology development program summary, September 1982
Energy Technology Data Exchange (ETDEWEB)
1983-11-01
The program of MHD magnet technology development conducted for the US Department of Energy by the Massachusetts Institute of Technology during the past five years is summarized. The general strategy is explained, the various parts of the program are described and the results are discussed. Subjects covered include component analysis, research and development aimed at improving the technology base, preparation of reference designs for commercial-scale magnets with associated design evaluations, manufacturability studies and cost estimations, the detail design and procurement of MHD test facility magnets involving transfer of technology to industry, investigations of accessory subsystem characteristics and magnet-flow-train interfacing considerations and the establishment of tentative recommendations for design standards, quality assurance procedures and safety procedures. A systematic approach (framework) developed to aid in the selection of the most suitable commercial-scale magnet designs is presented and the program status as of September 1982 is reported. Recommendations are made for future work needed to complete the design evaluation and selection process and to provide a sound technological base for the detail design and construction of commercial-scale MHD magnets. 85 references.
Magnus: A New Resistive MHD Code with Heat Flow Terms
Navarro, Anamaría; Lora-Clavijo, F. D.; González, Guillermo A.
2017-07-01
We present a new magnetohydrodynamic (MHD) code for the simulation of wave propagation in the solar atmosphere, under the effects of electrical resistivity—but not dominant—and heat transference in a uniform 3D grid. The code is based on the finite-volume method combined with the HLLE and HLLC approximate Riemann solvers, which use different slope limiters like MINMOD, MC, and WENO5. In order to control the growth of the divergence of the magnetic field, due to numerical errors, we apply the Flux Constrained Transport method, which is described in detail to understand how the resistive terms are included in the algorithm. In our results, it is verified that this method preserves the divergence of the magnetic fields within the machine round-off error (˜ 1× {10}-12). For the validation of the accuracy and efficiency of the schemes implemented in the code, we present some numerical tests in 1D and 2D for the ideal MHD. Later, we show one test for the resistivity in a magnetic reconnection process and one for the thermal conduction, where the temperature is advected by the magnetic field lines. Moreover, we display two numerical problems associated with the MHD wave propagation. The first one corresponds to a 3D evolution of a vertical velocity pulse at the photosphere-transition-corona region, while the second one consists of a 2D simulation of a transverse velocity pulse in a coronal loop.
MHD magnet technology development program summary, September 1982
International Nuclear Information System (INIS)
1983-11-01
The program of MHD magnet technology development conducted for the US Department of Energy by the Massachusetts Institute of Technology during the past five years is summarized. The general strategy is explained, the various parts of the program are described and the results are discussed. Subjects covered include component analysis, research and development aimed at improving the technology base, preparation of reference designs for commercial-scale magnets with associated design evaluations, manufacturability studies and cost estimations, the detail design and procurement of MHD test facility magnets involving transfer of technology to industry, investigations of accessory subsystem characteristics and magnet-flow-train interfacing considerations and the establishment of tentative recommendations for design standards, quality assurance procedures and safety procedures. A systematic approach (framework) developed to aid in the selection of the most suitable commercial-scale magnet designs is presented and the program status as of September 1982 is reported. Recommendations are made for future work needed to complete the design evaluation and selection process and to provide a sound technological base for the detail design and construction of commercial-scale MHD magnets. 85 references
Directory of Open Access Journals (Sweden)
Nor Athirah Mohd Zin
Full Text Available In this article, the influence of thermal radiation on unsteady magnetohydrodynamics (MHD free convection flow of rotating Jeffrey nanofluid passing through a porous medium is studied. The silver nanoparticles (AgNPs are dispersed in the Kerosene Oil (KO which is chosen as conventional base fluid. Appropriate dimensionless variables are used and the system of equations is transformed into dimensionless form. The resulting problem is solved using the Laplace transform technique. The impact of pertinent parameters including volume fraction Ï, material parameters of Jeffrey fluid Î»1, Î», rotation parameter r, Hartmann number Ha, permeability parameter K, Grashof number Gr, Prandtl number Pr, radiation parameter Rd and dimensionless time t on velocity and temperature profiles are presented graphically with comprehensive discussions. It is observed that, the rotation parameter, due to the Coriolis force, tends to decrease the primary velocity but reverse effect is observed in the secondary velocity. It is also observed that, the Lorentz force retards the fluid flow for both primary and secondary velocities. The expressions for skin friction and Nusselt number are also evaluated for different values of emerging parameters. A comparative study with the existing published work is provided in order to verify the present results. An excellent agreement is found. Keywords: Jeffrey nanofluid, AgNPs, MHD and Porosity, Rotating flow, Laplace transform technique
MHD diffuser model test program
Energy Technology Data Exchange (ETDEWEB)
Idzorek, J J
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment.
MHD diffuser model test program
International Nuclear Information System (INIS)
Idzorek, J.J.
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment
MHD waveguides in space plasma
International Nuclear Information System (INIS)
Mazur, N. G.; Fedorov, E. N.; Pilipenko, V. A.
2010-01-01
The waveguide properties of two characteristic formations in the Earth's magnetotail-the plasma sheet and the current (neutral) sheet-are considered. The question of how the domains of existence of different types of MHD waveguide modes (fast and slow, body and surface) in the (k, ω) plane and their dispersion properties depend on the waveguide parameters is studied. Investigation of the dispersion relation in a number of particular (limiting) cases makes it possible to obtain a fairly complete qualitative pattern of all the branches of the dispersion curve. Accounting for the finite size of perturbations across the wave propagation direction reveals new additional effects such as a change in the critical waveguide frequencies, the excitation of longitudinal current at the boundaries of the sheets, and a change in the symmetry of the fundamental mode. Knowledge of the waveguide properties of the plasma and current sheets can explain the occurrence of preferred frequencies in the low-frequency fluctuation spectra in the magnetotail. In satellite observations, the type of waveguide mode can be determined from the spectral properties, as well as from the phase relationships between plasma oscillations and magnetic field oscillations that are presented in this paper.
Energy Technology Data Exchange (ETDEWEB)
Cessenat, M.; Genta, P.
1996-12-31
We use a method based on a separation of variables for solving a system of first order partial differential equations, in a very simple modelling of MHD. The method consists in introducing three unknown variables {phi}1, {phi}2, {phi}3 in addition of the time variable {tau} and then searching a solution which is separated with respect to {phi}1 and {tau} only. This is allowed by a very simple relation, called a `metric separation equation`, which governs the type of solutions with respect to time. The families of solutions for the system of equations thus obtained, correspond to a radial evolution of the fluid. Solving the MHD equations is then reduced to find the transverse component H{sub {Sigma}} of the magnetic field on the unit sphere {Sigma} by solving a non linear partial differential equation on {Sigma}. Thus we generalize ideas due to Courant-Friedrichs and to Sedov on dimensional analysis and self-similar solutions. (authors).
Khan, Imad; Ullah, Shafquat; Malik, M. Y.; Hussain, Arif
2018-06-01
The current analysis concentrates on the numerical solution of MHD Carreau fluid flow over a stretching cylinder under the influences of homogeneous-heterogeneous reactions. Modelled non-linear partial differential equations are converted into ordinary differential equations by using suitable transformations. The resulting system of equations is solved with the aid of shooting algorithm supported by fifth order Runge-Kutta integration scheme. The impact of non-dimensional governing parameters on the velocity, temperature, skin friction coefficient and local Nusselt number are comprehensively delineated with the help of graphs and tables.
MHD Boundary Layer Flow of Dilatant Fluid in a Divergent Channel with Suction or Blowing
International Nuclear Information System (INIS)
Bhattacharyya, Krishnendu; Layek, G. C.
2011-01-01
An analysis is carried out to study a steady magnetohydrodynamic (MHD) boundary layer flow of an electrically conducting incompressible power-law non-Newtonian fluid through a divergent channel. The channel walls are porous and subjected to either suction or blowing of equal magnitude of the same kind of fluid on both walls. The fluid is permeated by a magnetic field produced by electric current along the line of intersection of the channel walls. The governing partial differential equation is transformed into a self-similar nonlinear ordinary differential equation using similarity transformations. The possibility of boundary layer flow in a divergent channel is analyzed with the power-law fluid model. The analysis reveals that the boundary layer flow (without separation) is possible for the case of the dilatant fluid model subjected to suitable suction velocity applied through its porous walls, even in the absence of a magnetic field. Further, it is found that the boundary layer flow is possible even in the presence of blowing for a suitable value of the magnetic parameter. It is found that the velocity increases with increasing values of the power-law index for the case of dilatant fluid. The effects of suction/blowing and magnetic field on the velocity are shown graphically and discussed physically. (fundamental areas of phenomenology(including applications))
Analysis of Linear MHD Power Generators
Energy Technology Data Exchange (ETDEWEB)
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.
MHD Modeling of Conductors at Ultra-High Current Density
International Nuclear Information System (INIS)
ROSENTHAL, STEPHEN E.; DESJARLAIS, MICHAEL P.; SPIELMAN, RICK B.; STYGAR, WILLIAM A.; ASAY, JAMES R.; DOUGLAS, M.R.; HALL, C.A.; FRESE, M.H.; MORSE, R.L.; REISMAN, D.B.
2000-01-01
In conjunction with ongoing high-current experiments on Sandia National Laboratories' Z accelerator, the authors have revisited a problem first described in detail by Heinz Knoepfel. Unlike the 1-Tesla MITLs of pulsed power accelerators used to produce intense particle beams, Z's disc transmission line (downstream of the current addition) is in a 100--1,200 Tesla regime, so its conductors cannot be modeled simply as static infinite conductivity boundaries. Using the MHD code MACH2 they have been investigating the conductor hydrodynamics, characterizing the joule heating, magnetic field diffusion, and material deformation, pressure, and velocity over a range of current densities, current rise-times, and conductor materials. Three purposes of this work are (1) to quantify power flow losses owing to ultra-high magnetic fields, (2) to model the response of VISAR diagnostic samples in various configurations on Z, and (3) to incorporate the most appropriate equation of state and conductivity models into the MHD computations. Certain features are strongly dependent on the details of the conductivity model
MHD Modeling of Conductors at Ultra-High Current Density
International Nuclear Information System (INIS)
Rosenthal, S.E.; Asay, J.R.; Desjarlais, M.P.; Douglas, M.R.; Frese, M.H.; Hall, C.A.; Morse, R.L.; Reisman, D.; Spielman, R.B.; Stygar, W.A.
1999-01-01
In conjunction with ongoing high-current experiments on Sandia National Laboratories' Z accelerator we have revisited a problem first described in detail by Heinz Knoepfel. MITLs of previous pulsed power accelerators have been in the 1-Tesla regime. Z's disc transmission line (downstream of the current addition) is in a 100-1200 Tesla regime, so its conductors cannot be modeled simply as static infinite conductivity boundaries. Using the MHD code MACH2 we have been investigating conductor hydrodynamics, characterizing the joule heating, magnetic field diffusion, and material deformation, pressure, and velocity over a range of current densities, current rise-times, and conductor materials. Three purposes of this work are ( 1) to quantify power flow losses owing to ultra-high magnetic fields, (2) to model the response of VISAR diagnostic samples in various configurations on Z, and (3) to incorporate the most appropriate equation of state and conductivity models into our MHD computations. Certain features are strongly dependent on the details of the conductivity model. Comparison with measurements on Z will be discussed
Nonequilibrium fluctuations in micro-MHD effects on electrodeposition
International Nuclear Information System (INIS)
Aogaki, Ryoichi; Morimoto, Ryoichi; Asanuma, Miki
2010-01-01
In copper electrodeposition under a magnetic field parallel to electrode surface, different roles of two kinds of nonequilibrium fluctuations for micro-magnetohydrodynamic (MHD) effects are discussed; symmetrical fluctuations are accompanied by the suppression of three dimensional (3D) nucleation by micro-MHD flows (the 1st micro-MHD effect), whereas asymmetrical fluctuations controlling 2D nucleation yield secondary nodules by larger micro-MHD flows (the 2nd micro-MHD effect). Though the 3D nucleation with symmetrical fluctuations is always suppressed by the micro-MHD flows, due to the change in the rate-determining step from electron transfer to mass transfer, the 2D nucleation with asymmetrical fluctuations newly turns unstable, generating larger micro-MHD flows. As a result, round semi-spherical deposits, i.e., secondary nodules are yielded. Using computer simulation, the mechanism of the 2nd micro-MHD effect is validated.
Towards Integrated Pulse Detonation Propulsion and MHD Power
Litchford, Ron J.; Thompson, Bryan R.; Lineberry, John T.
1999-01-01
The interest in pulse detonation engines (PDE) arises primarily from the advantages that accrue from the significant combustion pressure rise that is developed in the detonation process. Conventional rocket engines, for example, must obtain all of their compression from the turbopumps, while the PDE provides additional compression in the combustor. Thus PDE's are expected to achieve higher I(sub sp) than conventional rocket engines and to require smaller turbopumps. The increase in I(sub sp) and the decrease in turbopump capacity must be traded off against each other. Additional advantages include the ability to vary thrust level by adjusting the firing rate rather than throttling the flow through injector elements. The common conclusion derived from these aggregated performance attributes is that PDEs should result in engines which are smaller, lower in cost, and lighter in weight than conventional engines. Unfortunately, the analysis of PDEs is highly complex due to their unsteady operation and non-ideal processes. Although the feasibility of the basic PDE concept has been proven in several experimental and theoretical efforts, the implied performance improvements have yet to be convincingly demonstrated. Also, there are certain developmental issues affecting the practical application of pulse detonation propulsion systems which are yet to be fully resolved. Practical detonation combustion engines, for example, require a repetitive cycle of charge induction, mixing, initiation/propagation of the detonation wave, and expulsion/scavenging of the combustion product gases. Clearly, the performance and power density of such a device depends upon the maximum rate at which this cycle can be successfully implemented. In addition, the electrical energy required for direct detonation initiation can be significant, and a means for direct electrical power production is needed to achieve self-sustained engine operation. This work addresses the technological issues associated
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Method of operating a MHD power plant
International Nuclear Information System (INIS)
Wysk, S.R.
1982-01-01
A fossil fuel is burned substoichiometrically in the combustor of a mhd power plant to produce a high temperature, fuelrich product gas. The product gas is passed through a mhd channel to generate electricity. A reducing agent, preferably natural gas or hydrocarbon, is injected into the fuelrich product gas leaving the mhd generator; and the resulting mixture is held at a temperature in the range of 950 to 1500 0 C for about 1 second to permit the reducing agent to decompose a portion of the nitrogen oxides formed in the combustor. The fuel-rich product gas then passes thru an afterburner wherein combustion is completed and any excess reducing agent is consumed
Numerical study of MHD supersonic flow control
Ryakhovskiy, A. I.; Schmidt, A. A.
2017-11-01
Supersonic MHD flow around a blunted body with a constant external magnetic field has been simulated for a number of geometries as well as a range of the flow parameters. Solvers based on Balbas-Tadmor MHD schemes and HLLC-Roe Godunov-type method have been developed within the OpenFOAM framework. The stability of the solution varies depending on the intensity of magnetic interaction The obtained solutions show the potential of MHD flow control and provide insights into for the development of the flow control system. The analysis of the results proves the applicability of numerical schemes, that are being used in the solvers. A number of ways to improve both the mathematical model of the process and the developed solvers are proposed.
Experiments and models of MHD jets and their relevance to astrophysics and solar physics
Bellan, Paul M.
2018-05-01
Magnetohydrodynamic (MHD)-driven jets involve poloidal and toroidal magnetic fields, finite pressure gradients, and unbalanced forces. The mechanism driving these jets is first discussed qualitatively by decomposing the magnetic force into a curvature and a gradient component. The mechanism is then considered quantitatively by consideration of all terms in the three components of the MHD equation of motion and in addition, the implications of Ampere's law, Faraday's law, the ideal Ohm's law, and the equation of continuity. The analysis shows that jets are self-collimating with the tip of the jet moving more slowly than the main column of the jet so there is a continuous stagnation near the tip in the jet frame. Experiments supporting these conclusions are discussed and it is shown how this mechanism relates to jets in astrophysical and solar corona contexts.
Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD
Gao, Song
2013-05-01
The Richtmyer-Meshkov instability occurs when density-stratified interfaces are impulsively accelerated, typically by a shock wave. We present a numerical method to simulate the Richtmyer-Meshkov instability in cylindrical geometry. The ideal MHD equations are linearized about a time-dependent base state to yield linear partial differential equations governing the perturbed quantities. Convergence tests demonstrate that second order accuracy is achieved for smooth flows, and the order of accuracy is between first and second order for flows with discontinuities. Numerical results are presented for cases of interfaces with positive Atwood number and purely azimuthal perturbations. In hydrodynamics, the Richtmyer-Meshkov instability growth of perturbations is followed by a Rayleigh-Taylor growth phase. In MHD, numerical results indicate that the perturbations can be suppressed for sufficiently large perturbation wavenumbers and magnetic fields.
Investigations of MHD activity in ASDEX discharges
International Nuclear Information System (INIS)
Stambaugh, R.; Gernhardt, J.; Klueber, O.; Wagner, F.
1984-06-01
This report makes a strong attempt to relate some specific observations of MHD activity in ADEX discharges to observations made on the Doublet III and PDX tokamaks and to theoretical work on high β MHD modes at GA and PPPL. Three topics are discussed. The first topic is the detailed analysis of the time history of MHD activity in a β discharge. The β limit discharge in ASDEX is identified as a discharge in which, during constant neutral beam power, β reaches a maximum and then decreases, often to a lower steady level if the heating pulse is long enough. During the L phase of this discharge, the MHD activity observed in the B coils is both a continuous and bursting coupled m >= 1 mode of the 'fishbone' type. When β is rising in the H phase, this mode disappears; only ELMs are present. At βsub(max), a different mode appears, the m=2, n=1 tearing mode, which grows rapidly as β decreases. The second topic is the very new observation of the fishbone-like mode in a discharge heated by combined neutral beam and ion cyclotron heating power. The mode characteristics are modulated by sawtooth oscillations in a manner consistent with the importance of q(0) in the stability of this mode. The third topic is the search for ELM precursors in discharges designed to have no other competing and complicating MHD activity. In these cases nonaxisymmetric precursors to the Hsub(α) spike were observed. Hence, it appears that an MHD mode, rather than an energy balance problem, must be the origin of the ELM. (orig./GG)
The Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media
DEFF Research Database (Denmark)
Ghsemi, E; Soleimani, S; Barari, Amin
2012-01-01
The steady two-dimensional laminar forced magneto-hydrodynamic (MHD) Hiemenz flow against a flat plate with variable wall temperature in a porous medium is analyzed. The transformed nonlinear boundary-layer equations are solved analytically by homotopy analysis method (HAM). Results for the veloc...
Compact torus theory: MHD equilibrium and stability
International Nuclear Information System (INIS)
Barnes, D.C.; Seyler, C.E.; Anderson, D.V.
1979-01-01
Field reversed theta pinches have demonstrated the production and confinement of compact toroidal configurations with surprisingly good MHD stability. In these observations, the plasma is either lost by diffusion or by the loss of the applied field or is disrupted by an n = 2 (where n is the toroidal mode number) rotating instability only after 30 to 100 MHD times, when the configuration begins to rotate rigidly above a critical speed. These experiments have led one to investigate the equilibrium, stability, and rotation of a very elongated, toroidally axisymmetric configuration with no toroidal field. Many of the above observations are explained by recent results of these investigations which are summarized
Free-boundary perturbed MHD equilibria
International Nuclear Information System (INIS)
Nührenberg, C
2012-01-01
The concept of perturbed ideal MHD equilibria [Boozer A H and Nuhrenberg C 2006 Phys. Plasmas 13 102501] is employed to study the influence of external error-fields and of small plasma-pressure changes on toroidal plasma equilibria. In tokamak and stellarator free-boundary calculations, benchmarks were successful of the perturbed-equilibrium version of the CAS3D stability code [Nührenberg C et al. 2009 Phys. Rev. Lett. 102 235001] with the ideal MHD equilibrium code NEMEC [Hirshman S P et al. 1986 Comput. Phys. Commun. 43 143].
MHD equilibrium of heliotron J plasmas
International Nuclear Information System (INIS)
Suzuki, Yasuhiro; Nakamura, Yuji; Kondo, Katsumi; Nakajima, Noriyoshi; Hayashi, Takaya
2004-01-01
MHD equilibria of Heliotron J plasma are investigated by using HINT code. By assuming some profiles of the current density, effects of the net toroidal currents on the magnetohydrodynamics (MHD) equilibrium are investigated. If the rotational transform can be controlled by the currents, the generation of good flux surfaces is expected. In order to study equilibria with self-consistent bootstrap current, the boozer coordinates are constructed by converged HINT equilibrium as a preliminary study. Obtained spectra are compared with ones of VMEC code and both results are consistent. (author)
PHYSICAL PERFORMANCE AND BODY COMPOSITION IN MAINTENANCE HEMODIALYSIS (MHD PATIENTS
Directory of Open Access Journals (Sweden)
M Zhang
2012-06-01
Conclusions: These findings indicate that adult MHD pts had a higher % body fat. Measures of physical performance were markedly reduced in MHD pts as compared to Normals. Physical performance in MHD, measured especially by 6-MW, correlated negatively with some measures of body composition, particularly with LBMI.
Closed cycle MHD specialist meeting. Progress report, 1971--1972
International Nuclear Information System (INIS)
Rietjens, L.H.
1972-04-01
Abstracts of the conference papers on closed cycle MHD research are presented. The general areas of discussion are the following: results on closed cycle experiments; plasma properties, and instabilities and stabilization in nonequilibrium plasmas; loss mechanisms, current distributions, electrode effects, boundary layers, and gas dynamic effects; and design concepts of large MHD generators, and nuclear MHD power plants. (GRA)
NOVA: a nonvariational code for solving MHD stability of axisymmetric toroidal plasmas
International Nuclear Information System (INIS)
Cheng, C.Z.; Chance, M.S.
1986-04-01
A nonvariational approach for determining the ideal MHD stability of axisymmetric toroidal confinement systems is presented. The code (NOVA) employs cubic B-spline finite elements and Fourier expansion in a general flux coordinate (psi, theta, zeta) system. Better accuracy and faster convergence were obtained in comparison with the variational PEST and ERATO codes. The nonvariational approach can be extended to problems having non-Hermitian eigenmode equations where variational energy principles cannot be obtained
Semi-implicit method for three-dimensional compressible MHD simulation
International Nuclear Information System (INIS)
Harned, D.S.; Kerner, W.
1984-03-01
A semi-implicit method for solving the full compressible MHD equations in three dimensions is presented. The method is unconditionally stable with respect to the fast compressional modes. The time step is instead limited by the slower shear Alfven motion. The computing time required for one time step is essentially the same as for explicit methods. Linear stability limits are derived and verified by three-dimensional tests on linear waves in slab geometry. (orig.)
Finite-element semi-discretization of linearized compressible and resistive MHD
International Nuclear Information System (INIS)
Kerner, W.; Jakoby, A.; Lerbinger, K.
1985-08-01
The full resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as an initial-value problem. The semi-discretization using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance yields very accurate results even for small values of the resistivity. In the application different phenomena such as waves, resistive instabilities and overstable modes are addressed. (orig.)
Reduced equations for finite beta tearing modes in tokamaks
International Nuclear Information System (INIS)
Izzo, R.; Monticello, D.A.; DeLucia, J.; Park, W.; Ryu, C.M.
1985-01-01
The equations of resistive magnetohydrodynamics (MHD) are recast in a form that is useful for studying the evolution of those toroidal systems where the fast magnetosonic wave plays no important role. The equations are exact and have del x B = 0 satisfied explicitly. From this set of equations it is a simple matter to derive the equations of reduced MHD to any order in the inverse aspect ratio epsilon of the torus and for βapprox.epsilon or smaller. This is demonstrated by deriving a reduced set of MHD equations that are correct to fifth order in epsilon. These equations contain the exact equilibrium relation and, as such, can be used to find three-dimensional stellarator equilibria. In addition, if a subsidiary ordering in eta, the resistivity, is made, the equations of Glasser, Greene, and Johnson [Phys. Fluids 8, 875 (1967); 19, 567 (1967)] are recovered. This set of reduced equations has been coded by extending the initial value code hIlo [Phys. Fluids 26, 3066 (1983)]. Results obtained for both ideal and resistive linear stability from the reduced equations are compared with those obtained by solving the full set of MHD equations in a cylinder. Good agreement is shown for both zero and finite-beta calculations. Comparisons are also made with analytic theory illuminating the present limitations of the latter
Reduced equations for finite beta tearing modes in tokamaks
International Nuclear Information System (INIS)
Izzo, R.; Monticello, D.A.; DeLucia, J.; Park, W.; Ryu, C.M.
1984-10-01
The equations of resistive magnetohydrodynamics (MHD) are recast in a form that is useful for studying the evolution of those toroidal systems where the fast magnetosonic wave plays no important role. The equations are exact and have nabla vector.B vector = O satisfied explicitly. From this set of equations it is a simple matter to derive the equations of reduced MHD to any order in the inverse aspect ratio epsilon of the torus, and for β approx. epsilon or smaller. We demonstrate this by deriving a reduced set of MHD equations that are correct to 5th order in epsilon. These equations contain the exact equilibrium relation and as such can be used to find 3-D stellarator equilibria. In addition, if a subsidiary ordering in eta, the resistivity, is made, the equations of Glasser, Greene, and Johnson are recovered. This set of reduced equations has been coded by extending the initial value code, HILO. Results obtained, for both ideal and resistive linear stability, from the reduced equations are compared with those obtained by solving the full set of MHD equations in a cylinder. The agreement is shown to be excellent for both zero and finite beta calculations. Comparisons are also made with analytic theory illuminating the present limitations of the latter
Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations
International Nuclear Information System (INIS)
Morros Tosas, J.
1989-05-01
The nonlinear saturation of a plasma magnetohydrodynamic instabilities is studied, by means of a bifurcation theory. The work includes: an accurate mathematical method to study the MHD equations, in which the physical content is clear; and the study of the nonlinear solutions of the branch bifurcations, applied to different unstable plasma models. A scalar function representation is proposed for the MHD equations. This representation is characterized by a reference steady magnetic field and by a velocity field, which allow to write the equations for the scalar functions. An approximation method, leading to the obtention of the reduced equations applied in the instability study, is given. The cylindrical or toroidal plasmas are studied by using the nonlinear solutions bifurcation. Concerning the cylindrical plasma, the representation leads to a reduced system which enables the analytical calculations: two different steady bifurcation solutions are obtained. In the case of the toroidal plasma, an appropriate reduced equations system, is obtained. A qualitative approach of the Kink-type steady solution bifurcation, in a toroidal geometry, is performed [fr
MHD stability analysis using higher order spline functions
Energy Technology Data Exchange (ETDEWEB)
Ida, Akihiro [Department of Energy Engineering and Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi (Japan); Todoroki, Jiro; Sanuki, Heiji
1999-04-01
The eigenvalue problem of the linearized magnetohydrodynamic (MHD) equation is formulated by using higher order spline functions as the base functions of Ritz-Galerkin approximation. When the displacement vector normal to the magnetic surface (in the magnetic surface) is interpolated by B-spline functions of degree p{sub 1} (degree p{sub 2}), which is continuously c{sub 1}-th (c{sub 2}-th) differentiable on neighboring finite elements, the sufficient conditions for the good approximation is given by p{sub 1}{>=}p{sub 2}+1, c{sub 1}{<=}c{sub 2}+1, (c{sub 1}{>=}1, p{sub 2}{>=}c{sub 2}{>=}0). The influence of the numerical integration upon the convergence of calculated eigenvalues is discussed. (author)
MHD-Vlasov simulation of the toroidal Alfven eigenmode
International Nuclear Information System (INIS)
Todo, Y.; Sato, T.; Watanabe, K.; Watanabe, T.H.; Horiuchi, R.
1994-11-01
A new simulation method has been developed to investigate the excitation and saturation processes of toroidal Alfven eigenmodes (TAE modes). The background plasma is described by a full-MHD fluid model, while the kinetic evolution of energetic alpha particles is followed by the drift kinetic equation. The magnetic fluctuation of n = 2 mode develops and saturates at the level of 1.8x10 -3 of the equilibrium field when the initial beta of alpha particles is 2% at the magnetic axis. After saturation, the TAE mode amplitude shows an oscillatory behavior with a frequency corresponding to the bounce frequency of the alpha particles trapped by the TEA mode. The decrease of the power transfer rate from the alpha particles to the TAE mode, which is due to the trapped particle effect of a finite-amplitude wave, causes the saturation. From the linear growth rate the saturation level can be estimated. (author)
MHD equilibrium of toroidal fusion plasma with stationary flows
International Nuclear Information System (INIS)
Galkowski, A.
1994-01-01
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
Generation of sheet currents by high frequency fast MHD waves
Energy Technology Data Exchange (ETDEWEB)
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.
MHD pressure drop in ducts with imperfectly insulating coatings
International Nuclear Information System (INIS)
Malang, S.; Buehler, L.
1994-08-01
Liquid metal cooled blankets in fusion tokamak's are feasible only with electrically insulating coatings at the coolant channel walls. The requirements of such coatings are investigated and a simple analytical model is developed to determine the influence of imperfections in the coatings on the magneto-hydrodynamic pressure drop. This model is compared with the results of a 3D-MHD code based on the core flow approach. Both methods are in good agreement as long as the imperfections do not increase the pressure drop by more than 20%. The analytical model over-estimates the pressure drop for values larger than 20%. The importance of self-healing of coatings in case of cracking or flaking is quantified and an equation for the equilibrium conditions between the generation of imperfection and the healing of such spots is provided
International Nuclear Information System (INIS)
Kobayashi, Junichi
1979-01-01
The study on the transient flow characteristics in MHD ducts under orthogonal magnetic field is divided into handling two problems: the problem of changing pressure gradient in a uniform orthogonal magnetic field and the problem in which the orthogonal magnetic field itself changes with time. The former has been investigated by many persons, but the latter has not been investigated so often as the former because of its difficulty of handling. In addition, if it is intended to grasp properly the transient flow characteristics in actual MHD ducts, it will be also important that the effects of the electric conductivity of side walls and aspect ratio are clarified. In other words, this paper deals with the problem in which a uniform orthogonal magnetic field is suddenly applied in such manner as Heaviside's step function to or removed from the conductive fluids flowing in sufficiently long rectangular MHD ducts. First, the MHD fundamental equations are described, then they are normalized to give boundary conditions and initial conditions. Next, the transient flow and the derived magnetic field characteristics are numerically analyzed by the difference calculus, and thus the effects of conductor, insulated wall, aspect ratio, Hartmann number, magnetic Prandtl number and others on the above characteristics are clarified. (Wakatsuki, Y.)
INCORPORATING AMBIPOLAR AND OHMIC DIFFUSION IN THE AMR MHD CODE RAMSES
International Nuclear Information System (INIS)
Masson, J.; Mulet-Marquis, C.; Chabrier, G.; Teyssier, R.; Hennebelle, P.
2012-01-01
We have implemented non-ideal magnetohydrodynamics (MHD) effects in the adaptive mesh refinement code RAMSES, namely, ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test, and the Alfvén wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, allowing us to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics.
Energy Technology Data Exchange (ETDEWEB)
1978-01-01
The purpose of this document is to develop an environmental, health and safety (EH and S) assessment and begin a site - specific assessment of these and socio - economic impacts for the magnetohydrodynamics program of the United States Department of Energy. This assessment includes detailed scientific and technical information on the specific EH and S issues mentioned in the MHD Environmental Development Plan. A review of current literature on impact-related subjects is also included. This document addresses the coal-fired, open-cycle MHD technology and reviews and assesses potential EH and S impacts resulting from operation of commercially-installed technology.
3D simulation studies of tokamak plasmas using MHD and extended-MHD models
International Nuclear Information System (INIS)
Park, W.; Chang, Z.; Fredrickson, E.; Fu, G.Y.; Pomphrey, N.; Sugiyama, L.E.
1997-01-01
The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-β disruption studies in reversed shear plasmas using the MHD level MH3D code, ω *i stabilization and nonlinear island rotation studies using the two-fluid level MH3D-T code, studies of nonlinear saturation of TAE modes using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D ++ code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree well with experimental data
Directory of Open Access Journals (Sweden)
C. Nabert
2017-05-01
Full Text Available 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.
Evaluation of MHD materials for use in high-temperature fuel cells
Energy Technology Data Exchange (ETDEWEB)
Guidotti, R.
1978-06-15
The MHD and high-temperature fuel cell literature was surveyed for data pertaining to materials properties in order to identify materials used in MHD power generation which also might be suitable for component use in high-temperature fuel cells. Classes of MHD-electrode materials evaluated include carbides, nitrides, silicides, borides, composites, and oxides. Y/sub 2/O/sub 3/-stabilized ZrO/sub 2/ used as a reference point to evaluate materials for use in the solid-oxide fuel cell. Physical and chemical properties such as electrical resistivity, coefficient of thermal expansion, and thermodynamic stability toward oxidation were used to screen candidate materials. A number of the non-oxide ceramic MHD-electrode materials appear promising for use in the solid-electrolyte and molten-carbonate fuel cell as anodes or anode constituents. The MHD-insulator materials appear suitable candidates for electrolyte-support tiles in the molten-carbonate fuel cells. The merits and possible problem areas for these applications are discussed and additional needed areas of research are delineated.
Variational formalism for kinetic-MHD instabilities in tokamaks
International Nuclear Information System (INIS)
Edery, D.; Garbet, X.; Roubin, J.P.; Samain, A.
1991-07-01
A variational formalism that includes in a consistent way the tokamak plasma fluid response to an electromagnetic field as well as the particle-field resonant interaction effects is presented. The integrability of the unperturbed motion of the particles is used to establish a general functional similar to the classical Lagrangian for the electromagnetic field, which is extremum with respect to the field potentials. This functional is the sum of fluid terms closely related to the classical MHD energy and of resonant terms describing the kinetic effects. The formalism is used to study a critical issue in tokamak confinement, namely the sawteeth stabilization by energetic particles
MHD stability of vertically asymmetric tokamak equilibria
International Nuclear Information System (INIS)
Dalhed, H.E.; Grimm, R.C.; Johnson, J.L.
1981-03-01
The ideal MHD stability properties of a special class of vertically asymmetric tokamak equilibria are examined. The calculations confirm that no major new physical effects are introduced and the modifications can be understood by conventional arguments. The results indicate that significant departures from up-down symmetry can be tolerated before the reduction in β becomes important for reactor operation
On the stability of dissipative MHD equilibria
International Nuclear Information System (INIS)
Teichmann, J.
1979-04-01
The global stability of stationary equilibria of dissipative MHD is studied uisng the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian system with the full dissipative operators are given. The case of the two-fluid isentropic flow is discussed. (orig.)
MHD Ballooning Instability in the Plasma Sheet
International Nuclear Information System (INIS)
Cheng, C.Z.; Zaharia, S.
2003-01-01
Based on the ideal-MHD model the stability of ballooning modes is investigated by employing realistic 3D magnetospheric equilibria, in particular for the substorm growth phase. Previous MHD ballooning stability calculations making use of approximations on the plasma compressibility can give rise to erroneous conclusions. Our results show that without making approximations on the plasma compressibility the MHD ballooning modes are unstable for the entire plasma sheet where beta (sub)eq is greater than or equal to 1, and the most unstable modes are located in the strong cross-tail current sheet region in the near-Earth plasma sheet, which maps to the initial brightening location of the breakup arc in the ionosphere. However, the MHD beq threshold is too low in comparison with observations by AMPTE/CCE at X = -(8 - 9)R(sub)E, which show that a low-frequency instability is excited only when beq increases over 50. The difficulty is mitigated by considering the kinetic effects of ion gyrorad ii and trapped electron dynamics, which can greatly increase the stabilizing effects of field line tension and thus enhance the beta(sub)eq threshold [Cheng and Lui, 1998]. The consequence is to reduce the equatorial region of the unstable ballooning modes to the strong cross-tail current sheet region where the free energy associated with the plasma pressure gradient and magnetic field curvature is maximum
Stability of a two-volume MRxMHD model in slab geometry
Tuen, Li Huey
Ideal MHD models are known to be inadequate to describe various physical attributes of a toroidal field with non-continuous symmetry, such as magnetic islands and stochastic regions. Motivated by this omission, a new variational principle MRXMHD was developed; rather than include an infinity of magnetic flux surfaces, MRxMHD has a finite number of flux surfaces, and thus supports partial plasma relaxation. The model comprises of relaxed plasma regions which are separated by nested ideal MHD interfaces (flux surfaces), and can be encased in a perfectly conducting wall. In each region the pressure is constant, but can jump across interfaces. The field and field pitch, or rotational transform, can also jump across the interfaces. Unlike ideal MHD, MRxMHD plasmas can support toroidally non-axisymmetric confined magnetic fields, magnetic islands and stochastic regions. In toroidally non-axisymmetric plasma, the existence of interfaces in MRxMHD is contingent on the irrationality of the rotational transform of flux surfaces. That is, the KAM theorem shows that invariant tori (flux surfaces) continue to exist for sufficiently small perturbations to an integrable system (which describes flux surfaces), provided that the rotational transform is sufficiently irrational. Building upon the MRxMHD stability model, we study the effects of irrationality of the rotational transform at interfaces in MRxMHD on plasma stability. We present an MRxMHD equilibrium model to investigate the effects of magnetic field pitch within the plasma and across the aforementioned flux surfaces within a chosen geometry. In this model, it is found that the 2D system stability conditions are dependent on the interface and resonant surface magnetic field pitch at minimised energy states, and the stability of a system as a function of magnetic field pitch destabilises at particular values of magnetic field pitch. We benchmark the treatment of a two-volume system, along with the calculations for
Energy Technology Data Exchange (ETDEWEB)
NONE
1982-03-01
'Research on MHD generation system' was implemented by its expert committee in the electric joint study group, with the results of fiscal 1981 reported. This year, technological reexamination was conducted for a 2,000 MWt commercial MHD generation plant, with evaluation carried out on the cost performance including the construction and operation cost. In addition, for the purpose of intermediate R and D towards the practicability, examination was also conducted on a system structure, concrete specifications of component element, cost of R and D including operation expenses for example, concerning an 100 MWt class experimental plant and a 500 MWt class plant. In the investigation of the overseas trend, information was summarized in detail on the experimental devices, combustors, generation channels, electrode materials, electrode phenomena, theoretical analyses, seeds, slag, component equipment, instrumental technologies, conceptual designs of generation plant, commercial plant, etc., in Soviet Union, China, Holland, India and EPRI, on the basis of the materials from the 19th MHD symposium held in UTSI and from the coal MHD specialist conference held in Sydney. (NEDO)
Structure of reconnection boundary layers in incompressible MHD
International Nuclear Information System (INIS)
Sonnerup, B.U.Oe.; Wang, D.J.
1987-01-01
The incompressible MHD equations with nonvanishing viscosity and resistivity are simplified by use of the boundary layer approximation to describe the flow and magnetic field in the exit flow regions of magnetic field reconnection configurations when the reconnection rate is small. The conditions are derived under which self-similar solutions exist of the resulting boundary layer equations. For the case of zero viscosity and resistivity, the equations describing such self-similar layers are then solved in terms of quadratures, and the resulting flow and field configurations are described. Symmetric solutions, relevant, for example, to reconnection in the geomagnetic tail, as well as asymmetric solutions, relevant to reconnection at the earth's magnetopause, are found to exist. The nature of the external solutions to which the boundary layer solutions should be matched is discussed briefly, but the actual matching, which is to occur at Alfven-wave characteristic curves in the boundary layer solutions, is not carried out. Finally, it is argued that the solutions obtained may also be used to describe the structure of the intense vortex layers observed to occur at magnetic separatrices in computer simulations and in certain analytical models of the reconnection process
Conceptual design study of potential early commercial MHD powerplant. Report of task 2 results
Hals, F. A.
1981-03-01
The conceptual design of one of the potential early commercial MHD power plants was studied. The plant employs oxygen enrichment of the combustion air and preheating of this oxygen enriched air to an intermediate temperature of 1200 F attainable with a tubular type recuperative heat exchanger. Conceptual designs of plant componets and equipment with performance, operational characteristics, and costs are reported. Plant economics and overall performance including full and part load operation are reviewed. The projected performance and estimated cost of this early MHD plant are compared to conventional power plants, although it does not offer the same high efficiency and low costs as the mature MHD power plant. Environmental aspects and the methods incorporated in plant design for emission control of sulfur and nitrogen are reviewed.
Buttery, Richard
2011-08-01
This annual workshop on MHD Stability Control has been held since 1996 with a focus on understanding and developing control of MHD instabilities for future fusion reactors. The workshop generally covers a wide range of stability topics: from disruptions, to tearing modes, error fields, ELMs, resistive wall modes (RWMs) and ideal MHD. It spans many device types, particularly tokamaks, stellarators and reversed field pinches, to pull out commonalities in the physics and improve understanding. In 2010 the workshop was held on 15-17 November at the University of Wisconsin in Madison and was combined with the annual US-Japan MHD Workshop. The theme was `3D Magnetic Field Effects in MHD Control', with a focus on multidisciplinary sessions exploring issues of plasma response to 3D fields, the manifestation of such fields in the plasma, and how they influence stability. This has been a topic of renewed interest, with utilisation of 3D fields for ELM control now planned in ITER, and a focus on the application of such fields for error field correction, disruption avoidance, and RWM control. Key issues included the physics of the interaction, types of coils and harmonic spectra needed to control instabilities, and subsidiary effects such as braking (or rotating) the plasma. More generally, a wider range of issues were discussed including RWM physics, tearing mode physics, disruption mitigation, ballooning stability, the snowflake divertor concept, and the line tied pinch! A novel innovation to the meeting was a panel discussion session, this year on Neoclassical Toroidal Viscosity, which ran well; more will be tried next year. In this special section of Plasma Physics and Controlled Fusion we present several of the invited and contributed papers from the 2010 workshop, which have been subject to the normal refereeing procedures of the journal. These papers give a sense of the exceptional quality of the presentations at this workshop, all of which may be found at http://fusion.gat.com/conferences/mhd
Critical spaces for quasilinear parabolic evolution equations and applications
Prüss, Jan; Simonett, Gieri; Wilke, Mathias
2018-02-01
We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.
Two dimensional analysis of MHD generator by means of equivalent circuit
International Nuclear Information System (INIS)
Yoshida, Masaharu; Umoto, Juro
1975-01-01
The authors report on the method analyzing generally the MHD generator by means of the equivalent circuit including the negative resistance. At first, they divide the duct space into many space elements, and for each space element they derive the fundamental equivalent four-terminal circuit which satisfies the two-dimensional Ohm's law. Next, they make an attempt to apply the equivalent circuits to the typical MHD generators such as diagonal, Faraday and Hall generators considering the boundary layer in the duct and the wall leakage current. Using their analysis, the current density, Joul's heat, generated and output electrical powers, electrical efficiency etc. in the generator can be fairly easily calculated. (auth.)
Directory of Open Access Journals (Sweden)
M. Kiyasatfar
2011-01-01
Full Text Available In the present study, simulation of steady state, incompressible and fully developed laminar flow has been conducted in a magneto hydrodynamic (MHD pump. The governing equations are solved numerically by finite-difference method. The effect of the magnetic flux density and current on the flow and temperature distributions in a MHD pump is investigated. The obtained results showed that controlling the flow and the temperature is possible through the controlling of the applied current and the magnetic flux. Furthermore, the effects of the magnetic flux density and current on entropy generation in MHD pump are considered. Our presented numerical results are in good agreement with the experimental data showed in literature.
MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux
International Nuclear Information System (INIS)
Ishak, Anuar; Nazar, Roslinda; Pop, Ioan
2009-01-01
The steady magnetohydrodynamic (MHD) mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing fow
Quantum chaos theory and the spectrum of ideal-MHD instabilities in toroidal plasmas
International Nuclear Information System (INIS)
Dewar, Robert L.; Carolin, Nuehrenberg; Tatsuno, Tomoya
2004-01-01
In a fully 3-D system such as a stellarator, the toroidal mode number n ceases to be a good quantum number - all ns within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD (magnetohydrodynamic) instabilities ceases to exist unless MHD is modified (regularized) by introducing a short-perpendicular-wavelength cutoff. Attempts to use ray tracing to estimate the regularized MHD spectrum fail due to the occurrence of chaotic ray trajectories. In quantum chaos theory, strong chaos in the semiclassical limit leads to eigenvalue statistics the same as those of a suitable ensemble of random matrices. For instance, the probability distribution function for the separation between neighboring eigenvalues is as derived from random matrix theory and goes to zero at zero separation. This contrasts with the Poissonian distribution found in separable systems, showing that a signature of quantum chaos is level repulsion. In order to determine whether eigenvalues of the regularized MHD problem obey the same statistics as those of the Schroedinger equation in both the separable 1-D case and the chaotic 3-D cases, we have assembled data sets of ideal MHD eigenvalues for a Suydam-unstable cylindrical (1-D) equilibrium using Mathematica and a Mercier-unstable (3-D) equilibrium using the CAS3D code. In the 1-D case, we find that the unregularized Suydam-approximation spectrum has an anomalous peak at zero eigenvalue separation. On the other hand, regularization by restricting the domain of κsub(perpendicular) recovers the expected Poissonian distribution. In the 3-D case we find strong evidence of level repulsion within mode families, but mixing mode families produces Poissonian statistics. (author)
Energy Technology Data Exchange (ETDEWEB)
NONE
1991-03-01
The pressurized coal partial combustion (PCPC) furnace is surveyed/studied for its incorporation in MHD generation. The technical development of the atmospheric CPC has been basically completed, and the concept is demonstrated using a test system of commercial size. Many techniques developed for the atmospheric CPC are applicable to the PCPC system. These include structures of the CPC furnace walls, and slag handling and simulation techniques. Combination of PFBC with PCPC or IGCC can bring about many merits, e.g., enhanced efficiency and abated NOx emissions for the combined cycle power generation. These topping cycles, therefore, should be developed in the early stage. MHD power generation is one of the concepts that can enhance efficiency. In particular, the techniques for closed cycle MHD generation have notably advanced recently. The PCPC techniques are useful for coal combustors for MHD generation. Full-scale development works for the direct coal combustion gas turbine systems have been just started for the IGCC systems of the next generation, and the PCPC-related techniques are expected to serve as the central techniques for these turbine systems. (NEDO)
Directory of Open Access Journals (Sweden)
M. Rajashekar
2012-01-01
Full Text Available The combined effects of couple stress and surface roughness on the MHD squeeze-film lubrication between a sphere and a porous plane surface are analyzed, based upon the thin-film magnetohydrodynamic (MHD theory. Using Stoke’s theory to account for the couple stresses due to the microstructure additives and the Christensen’s stochastic method developed for hydrodynamic lubrication of rough surfaces derives the stochastic MHD Reynolds-type equation. The expressions for the mean MHD squeeze-film pressure, mean load-carrying capacity, and mean squeeze-film time are obtained. The results indicate that the couple stress fluid in the film region enhances the mean MHD squeeze-film pressure, load-carrying capacity, and squeeze-film time. The effect of roughness parameter is to increase (decrease the load-carrying capacity and lengthen the response time for azimuthal (radial roughness patterns as compared to the smooth case. Also, the effect of porous parameter is to decrease the load-carrying capacity and increase the squeeze-film time as compared to the solid case.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Some Fluid Dynamic Effects in Large-Scale MHD Generators
Energy Technology Data Exchange (ETDEWEB)
Hunt, J. C.R. [University of Warwick, Coventry (United Kingdom)
1966-10-15
At the present time we are unable to carry out a complete analysis of the fluid dynamics and electrodynamics of an MHD generator. However, various aspects of the behaviour of an MHD generator may be examined by the use of simplified models, for example: (1) one-dimensional gas dynamics (Louis et al. 1964); (2) the current distribution can be found if the velocity is assumed constant across the duct (Witalis, 1965); (3) the skin friction and heat transfer to the walls can be calculated by boundary layer analysis if the flow is assumed to be laminar (Kerrebrock, 1961), and (4) a complete description of the velocity and current distribution across the duct can be given if the flow is assumed to be uniform, laminar, incompressible and not varying in the flow direction (Hunt and Stewartson, 1965). Taken together, these and other models will enable us to describe most of the effects in an MHD generator. In this paper another simplification is considered in which the electromagnetic forces are assumed to be much larger than the inertial forces. The ratio of these two forces is measured by the parameter, S = aB{sup 2}{sub 0}d/pU, where o is the conductivity, B{sub 0} the magnetic field, d the width of the duct, p the density and U the mean velocity. Thus S >> 1. We also assume that the magnetic Reynolds number is very much less than one. In the largest experimental generators now being built S {approx} 2 . Thus, though the results of this model are not immediately applicable, they should indicate the effects of increasing the magnetic field strength and the size of MHD generators. When S >> 1, one can can consider the duct to be divided into 2 regions: (1) a core region where electromagnetic forces are balanced by the pressure gradient and where inertial as well as viscous forces are negligible, and (2) boundary layers on the walls where again inertial forces are negligible but where the viscous, electromagnetic and pressure forces are of the same order. We show how it is
International Nuclear Information System (INIS)
Pletzer, A.; Bondeson, A.; Dewar, R.L.
1993-11-01
The quest to determine accurately the stability of tearing and resistive interchange modes in two-dimensional toroidal geometry led to the development of the PEST-3 code, which is based on solving the singular, zero-frequency ideal MHD equation in the plasma bulk and determining the outer data Δ', Γ' and A' needed to match the outer region solutions to those arising in the inner layers. No assumption regarding the aspect ratio, the number of rational surfaces or the pressure are made a priori. This approach is numerically less demanding than solving the full set of resistive equations, and has the major advantage of non-MHD theories of the non-ideal layers. Good convergence is ensured by the variational Galerkin scheme used to compute the outer matching data. To validate the code, we focus on the growth rate calculations of resistive kink modes which are reproduced in good agreement with those obtained by the full resistive MHD code MARS. (author) 11 figs., 27 refs
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping
2018-02-01
We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.
International Nuclear Information System (INIS)
McCarville, T.J.; Berwald, D.H.; Wong, C.P.C.
1984-09-01
Magnetohydrodynamic (MHD) effects which result from the use of liquid metal coolants in magnetic fusion reactors include the modification of flow profiles (including the suppression of turbulence) and increases in the primary loop pressure drop and the hydrostatic pressure at the first wall of the blanket. In the reference fission-suppressed tandem mirror fusion breeder design concept, flow profile modification is a relatively minor concern, but the MHD pressure drop in flowing the liquid lithium coolant through an annular packed bed of beryllium/thorium pebbles is directly related to the required first wall structure thickness. As such, it is a major concern which directly impacts fissile breeding efficiency. Consequently, an improved model for the packed bed pressure drop has been developed. By considering spacial averages of electric fields, currents, and fluid flow velocities the general equations have been reduced to simple expressions for the pressure drop. The averaging approach results in expressions for the pressure drop involving a constant which reflects details of the flow around the pebbles. Such details are difficult to assess analytically, and the constant may eventually have to be evaluated by experiment. However, an energy approach has been used in this study to bound the possible values of the constant, and thus the pressure drop. In anticipation that an experimental facility might be established to evaluate the undetermined constant as well as to address other uncertainties, a survey of existing facilities is presented
One-dimensional MHD simulations of MTF systems with compact toroid targets and spherical liners
Khalzov, Ivan; Zindler, Ryan; Barsky, Sandra; Delage, Michael; Laberge, Michel
2017-10-01
One-dimensional (1D) MHD code is developed in General Fusion (GF) for coupled plasma-liner simulations in magnetized target fusion (MTF) systems. The main goal of these simulations is to search for optimal parameters of MTF reactor, in which spherical liquid metal liner compresses compact toroid plasma. The code uses Lagrangian description for both liner and plasma. The liner is represented as a set of spherical shells with fixed masses while plasma is discretized as a set of nested tori with circular cross sections and fixed number of particles between them. All physical fields are 1D functions of either spherical (liner) or small toroidal (plasma) radius. Motion of liner and plasma shells is calculated self-consistently based on applied forces and equations of state. Magnetic field is determined by 1D profiles of poloidal and toroidal fluxes - they are advected with shells and diffuse according to local resistivity, this also accounts for flux leakage into the liner. Different plasma transport models are implemented, this allows for comparison with ongoing GF experiments. Fusion power calculation is included into the code. We performed a series of parameter scans in order to establish the underlying dependencies of the MTF system and find the optimal reactor design point.
Improvements of characteristics of open cycle Faraday type MHD power generator
International Nuclear Information System (INIS)
Yoshida, Masaharu; Umoto, Juro; Aoki, Sigeo
1982-01-01
MHD power generators are classified into two types: Faraday type and diagonal type (including Hall type). It is considered also in Faraday type generators that the characteristics can be improved further by selecting the aspect ratio appropriately, and employing cap electrodes which approach diagonal conducting side-wall type from parallel plate electrodes. First, the three-dimensional analysis using a new equivalent circuit is introduced, in which finite electrode division and working gas boundary layer are considered using the generalized Ohm's law, Maxwell's electromagnetic equations and others. The above described improvement of characteristics is investigated numerically fully applying this analyzing method. If the wall temperature is low, the increase in the aspect ratio of a generating duct cross-section considerably improves the characteristics because plasma non-uniformity decreases. If the cap electrodes having an optimum side-wall length are used, the output increases considerably because the load current is given and received through the side-wall electrodes. Efficiency is a little lower than the case using parallel plate electrodes. Therefore, if the aspect ratio is taken sufficiently large, and the cap electrodes with optimum side-wall electrode length are used, the generator characteristics are greatly improved since the above mentioned effects are multiplied. (Wakatsuki, Y.)
Energy principles for linear dissipative systems with application to resistive MHD stability
International Nuclear Information System (INIS)
Pletzer, A.
1997-04-01
A formalism for the construction of energy principles for dissipative systems is presented. It is shown that dissipative systems satisfy a conservation law for the bilinear Hamiltonian provided the Lagrangian is time invariant. The energy on the other hand, differs from the Hamiltonian by being quadratic and by having a negative definite time derivative (positive power dissipation). The energy is a Lyapunov functional whose definiteness yields necessary and sufficient stability criteria. The stability problem of resistive magnetohydrodynamic (MHD) is addressed: the energy principle for ideal MHD is generalized and the stability criterion by Tasso is shown to be necessary in addition to sufficient for real growth rates. An energy principle is found for the inner layer equations that yields the resistive stability criterion D R <0 in the incompressible limit, whereas the tearing mode criterion Δ'<0 is shown to result from the conservation law of the bilinear concomitant in the resistive layer. (author) 1 fig., 25 refs
The effect of compressive viscosity and thermal conduction on the longitudinal MHD waves
Bahari, K.; Shahhosaini, N.
2018-05-01
longitudinal Magnetohydrodynamic (MHD) oscillations have been studied in a slowly cooling coronal loop, in the presence of thermal conduction and compressive viscosity, in the linear MHD approximation. WKB method has been used to solve the governing equations. In the leading order approximation the dispersion relation has been obtained, and using the first order approximation the time dependent amplitude has been determined. Cooling causes the oscillations to amplify and damping mechanisms are more efficient in hot loops. In cool loops the oscillation amplitude increases with time but in hot loops the oscillation amplitude decreases with time. Our conclusion is that in hot loops the efficiency of the compressive viscosity in damping longitudinal waves is comparable to that of the thermal conduction.
Nonlinear 2D convection and enhanced cross-field plasma transport near the MHD instability threshold
International Nuclear Information System (INIS)
Pastukhov, V.P.; Chudin, N.V.
2003-01-01
Results of theoretical study and computer simulations of nonlinear 2D convection induced by a convective MHD instability near its threshold in FRC-like non-paraxial magnetic confinement system are presented. An appropriate closed set of weakly nonideal reduced MHD equations is derived to describe the self-consistent plasma dynamics. It is shown that the convection forms nonlinear large scale stochastic vortices (convective cells), which tend to restore and to maintain the marginally stable pressure pro e and result in an essentially nonlocal enhanced heat transport. A large amount of data on the structure of the nascent convective flows is obtained and analyzed. The computer simulations of long time plasma evolutions demonstrate such features of the resulting anomalous transport as pro e consistency, L-H transition, external transport barrier, pinch of impurities, etc. (author)
International Nuclear Information System (INIS)
Kim, Hee Reyoung; Park, Jon Ho; Kim, Jong Man; Nam, Ho Yoon; Choi, Jong Hyun
2001-01-01
Magnetic field has many effects on the hydraulic pressure drop of fluids with high electrical conductivity. The theoretical solution about MHD pressure drop is sought for the uniform current density model with simplified physical geometry. Using the MHD equation in the rectangular duct of the sodium liquid flow under a transverse magnetic field, the electrical potential is sought in terms of the duct geometry and the electrical parameters of the liquid metal and duct material. By the product of the induced current inside the liquid metal and transverse magnetic field, the pressure gradients is found as a function of the duct size and the electrical conductivity of the liquid metal. The theoretically predicted pressure drop is compared with experimental results on the change of flow velocity and magnetic flux density
Research report on a study in MHD power generators - end effects
International Nuclear Information System (INIS)
Mittal, M.L.
In MHD devices, there are significant losses due to end effects, boundary layers and instabilities. The present investigations concern the estimation of losses due to end effects. The basic equations and boundary conditions for the analysis of end effects are derived. Using a sinusoidal and exponential termination, at the entrance region of a rectangular MHD channel with continuous electrodes, the end effect phenomenon is analysed. The normal current density on the electrode walls, is examined and the effects of the Hall currents on end losses is discussed. The end effects with diverging electrode walls are also investigated. The normal current distribution on the electrodes and the efficiency are calculated for two different velocity profiles - one with viscosity and the other with source velocity. (K.M.)
Newtonian CAFE: a new ideal MHD code to study the solar atmosphere
González-Avilés, J. J.; Cruz-Osorio, A.; Lora-Clavijo, F. D.; Guzmán, F. S.
2015-12-01
We present a new code designed to solve the equations of classical ideal magnetohydrodynamics (MHD) in three dimensions, submitted to a constant gravitational field. The purpose of the code centres on the analysis of solar phenomena within the photosphere-corona region. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As solar tests we present the transverse oscillations of Alfvénic pulses in coronal loops using a 2.5D model, and as 3D tests we present the propagation of impulsively generated MHD-gravity waves and vortices in the solar atmosphere. The code is based on high-resolution shock-capturing methods, uses the Harten-Lax-van Leer-Einfeldt (HLLE) flux formula combined with Minmod, MC, and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the Flux Constrained Transport method.
Gasdynamic performance in relation to the power extraction of an MHD generator
International Nuclear Information System (INIS)
Massee, P.
1983-01-01
A study of the gasdynamical processes in MHD generators has been made both theoretically and experimentally. A core flow and boundary layer model has been developed. In order to obtain a fast computer code which can be used for engineering purposes the quasi-one-dimensional approximation is used. It is shown in this thesis that the boundary layers have to be calculated from integral equations describing momentum, kinetic energy and stagnation enthalpy respectively, when the MHD effects in the boundary layers are properly taken into account. Calculations with the developed core flow and boundary layer model have shown that the electrical power output is limited by the design of the existing facility and have indicated possibilities to circumvent this limitation. (Auth.)
Nonlinear MHD dynamo operating at equipartition
DEFF Research Database (Denmark)
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......, and that it can saturate at a level significantly higher than intermittent turbulent dynamos, namely at energy equipartition, for high values of the magnetic and fluid Reynolds numbers. The equipartition solution however does not remain time-independent during the simulation but exhibits a much more intricate...
Neoclassical MHD equilibria with ohmic current
International Nuclear Information System (INIS)
Tokuda, Shinji; Takeda, Tatsuoki; Okamoto, Masao.
1989-01-01
MHD equilibria of tokamak plasmas with neoclassical current effects (neoclassical conductivity and bootstrap current) were calculated self-consistently. Neoclassical effects on JFT-2M tokamak plasmas, sustained by ohmic currents, were studied. Bootstrap currents flow little for L-mode type equilibria because of low attainable values of poloidal beta, β J . H-mode type equilibria give bootstrap currents of 30% ohmic currents for β J attained by JFT-2M and 100% for β J ≥ 1.5, both of which are sufficient to change the current profiles and the resultant MHD equilibria. Neoclassical conductivity which has roughly half value of the classical Spitzer conductivity brings peaked ohmic current profiles to yield low safety factor at the magnetic axis. Neoclassical conductivity reduces the value of effective Z(Z eff ) which is necessary to give the observed one-turn voltage but it needs impurities accumulating at the center when such peaked current profiles are not observed. (author)
Regular shock refraction in planar ideal MHD
International Nuclear Information System (INIS)
Delmont, P; Keppens, R
2010-01-01
We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest, in planar ideal (magneto)hydrodynamics. In the hydrodynamical case, 3 signals arise and the interface becomes Richtmyer-Meshkov unstable due to vorticity deposition on the shocked contact. In the magnetohydrodynamical case, on the other hand, when the normal component of the magnetic field does not vanish, 5 signals will arise. The interface then typically remains stable, since the Rankine-Hugoniot jump conditions in ideal MHD do not allow for vorticity deposition on a contact discontinuity. We present an exact Riemann solver based solution strategy to describe the initial self similar refraction phase. Using grid-adaptive MHD simulations, we show that after reflection from the top wall, the interface remains stable.
Evolution of the MHD sheet pinch
International Nuclear Information System (INIS)
Matthaeus, W.H.; Montgomery, D.
1979-01-01
A magnetohydrodynamic (MHD) problem of recurrent interest for both astrophysical and laboratory plasmas is the evolution of the unstable sheet pinch, a current sheet across which a dc magnetic field reverses sign. The evolution of such a sheet pinch is followed with a spectral-method, incompressible, two-dimensional, MHD turbulence code. Spectral diagnostics are employed, as are contour plots of vector potential (magnetic field lines), electric current density, and velocity stream function (velocity streamlines). The nonlinear effect which seems most important is seen to be current filamentation: the concentration of the current density onto sets of small measure near a mgnetic X point. A great deal of turbulence is apparent in the current distribution, which, for high Reynolds numbers, requires large spatial grids (greater than or equal to (64) 2 ). 11 figures, 1 table
Impulsive relaxation process in MHD driven reconnection
International Nuclear Information System (INIS)
Kitabata, H.; Hayashi, T.; Sato, T.
1997-01-01
Compressible magnetohydrodynamic (MHD) simulation is carried out in order to investigate energy relaxation process of the driven magnetic reconnection in an open finite system through a long time calculation. It is found that a very impulsive energy release occurs in an intermittent fashion through magnetic reconnection for a continuous magnetic flux injection on the boundary. We focus our attention on the detailed process in the impulsive phase, which is the reconnection rate is remarkably enhanced up. (author)
MHD simulations on an unstructured mesh
International Nuclear Information System (INIS)
Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Sugiyama, L.E.
1998-01-01
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
Hopes for commercial use of MHD
International Nuclear Information System (INIS)
1968-01-01
Magnetohydrodynamics (MHD) is the study of the motion of fluids and gases in magnetic fields. After 25 years of theoretical and experimental work, it seems commercially promising for a new type of power station, where heat would be converted directly into electricity by generators without moving parts. Nuclear reactors would be well suited as the heat sources. At an Agency symposium in Warsaw in July it was felt that international cooperation is essential to develop the technique for industrial use. (author)
Status report on the Indian MHD programme
International Nuclear Information System (INIS)
Ambasankaran, C.
1978-03-01
MHD programme in India, which has been started recently as a collaborative effort by the Bhabha Atomic Research Centre and Bharat Heavy Electricals Ltd., with the technical consultation provided by the High Temperature Institute, Moscow, is described. The basic considerations which led to the launching of this project and the details of the experimental plant for R and D work are spelt out. (K.B.)
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Elms: MHD Instabilities at the transport barrier
Energy Technology Data Exchange (ETDEWEB)
Huysmans, G.T.A
2005-07-01
Significant progress has been made in recent years both on the experimental characterisation of ELMs (edge localized modes) and the theory and modelling of ELMs. The observed maximum pressure gradient is in good agreement with the calculated ideal MHD stability limits due to peeling-ballooning modes. The dependence on plasma current and plasma shape are also reproduced by the ideal MHD model. It will be a challenge to verify experimentally the influence of the extensions to the ideal MHD theory such as the possibly incomplete diamagnetic stabilisation, the influence of shear flow, finite resistivity or the stabilizing influence of the separatrix on peeling modes. The observations of the filamentary structures find their explanation in the theory and simulations of the early non-linear phase of the evolution of ballooning modes. One of the remaining open questions is what determines the size of the ELM and its duration. This is related to the loss mechanism of energy and density. Some heuristic descriptions of possible mechanisms have been proposed in literature but none of the models so far makes quantitative predictions on the ELM size. Also the numerical simulations are not yet advanced to the point where the full ELM crash can be modelled. The theory and simulations of the ELMs are necessary to decide between the possible parameters, such as the collisionality or the parallel transport time, that are proposed for the extrapolation of ELM sizes to ITER.
Elms: MHD Instabilities at the transport barrier
International Nuclear Information System (INIS)
Huysmans, G.T.A.
2005-01-01
Significant progress has been made in recent years both on the experimental characterisation of ELMs (edge localized modes) and the theory and modelling of ELMs. The observed maximum pressure gradient is in good agreement with the calculated ideal MHD stability limits due to peeling-ballooning modes. The dependence on plasma current and plasma shape are also reproduced by the ideal MHD model. It will be a challenge to verify experimentally the influence of the extensions to the ideal MHD theory such as the possibly incomplete diamagnetic stabilisation, the influence of shear flow, finite resistivity or the stabilizing influence of the separatrix on peeling modes. The observations of the filamentary structures find their explanation in the theory and simulations of the early non-linear phase of the evolution of ballooning modes. One of the remaining open questions is what determines the size of the ELM and its duration. This is related to the loss mechanism of energy and density. Some heuristic descriptions of possible mechanisms have been proposed in literature but none of the models so far makes quantitative predictions on the ELM size. Also the numerical simulations are not yet advanced to the point where the full ELM crash can be modelled. The theory and simulations of the ELMs are necessary to decide between the possible parameters, such as the collisionality or the parallel transport time, that are proposed for the extrapolation of ELM sizes to ITER
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.
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.
Energetic particle effects on global MHD modes
International Nuclear Information System (INIS)
Cheng, C.Z.
1990-01-01
The effects of energetic particles on MHD type modes are studied by analytical theories and the nonvariational kinetic-MHD stability code (NOVA-K). In particular we address the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant ''fishbone'' internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral-beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n=1 internal kink mode in the hot particle beat space exists even in the absence of core ion finite Larmor radius effect (finite ω *i ). On the other hand, the trapped alpha particles are found to resonantly excite instability of the n=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 23 refs., 5 figs
Magnetohydrodynamic (MHD) simulation of solar prominence formation
International Nuclear Information System (INIS)
Bao, J.
1987-01-01
Formation of Kippenhahn-Schluter type solar prominences by chromospheric mass injection is studied via numerical simulation. The numerical model is based on a two-dimensional, time-dependent magnetohydrodynamic (MHD) theory. In addition, an analysis of gravitational thermal MHD instabilities related to condensation is performed by using the small-perturbation method. The conclusions are: (1) Both quiescent and active-region prominences can be formed by chromospheric mass injection, provided certain optimum conditions are satisfied. (2) Quiescent prominences cannot be formed without condensation, though enough mass is supplied from chromosphere. The mass of a quiescent prominence is composed of both the mass injected from the chromosphere and the mass condensed from the corona. On the other hand, condensation is not important to active region prominence formation. (3) In addition to channeling and supporting effects, the magnetic field plays another important role, i.e. containing the prominence material. (4) In the model cases, prominences are supported by the Lorentz force, the gas-pressure gradient and the mass-injection momentum. (5) Due to gravity, more MHD condensation instability modes appear in addition to the basic condensation mode
SCMS-1, Superconducting Magnet System for an MHD generator
International Nuclear Information System (INIS)
Zenkevich, V.B.; Kirenin, I.A.; Tovma, V.A.
1977-01-01
The research and development effort connected with the building of the superconducting magnet systems for MHD generators at the Institute for High Temperatures of the U.S.S.R. Academy of Sciences included the designing, fabrication and testing of the superconducting magnet system for an MHD generator (SCMS-1), producing a magnetic field up to 4 Tesla in a warm bore tube 300 mm in diameter and 1000 mm long (the nonuniformity of the magnetic field in the warm bore did not exceed +-5%. The superconducting magnet system is described. The design selected consisted of a dipole, saddle-form coil, wound around a tube. The cooling of the coils is of the external type with helium access to each layer of the winding. For winding of the superconducting magnet system a 49-strand cable was used consisting of 42 composition conductors, having a diameter of 0.3 mm each, containing six superconducting strands with a niobium-titanium alloy base (the superconducting strands were 70 microns in diameter), and seven copper conductors of the same diameter as the composite conductors. The cable is made monolithic with high purity indium and insulated with lavsan fiber. The cable diameter with insulation is 3.5 mm
Sunspot Modeling: From Simplified Models to Radiative MHD Simulations
Directory of Open Access Journals (Sweden)
Rolf Schlichenmaier
2011-09-01
Full Text Available We review our current understanding of sunspots from the scales of their fine structure to their large scale (global structure including the processes of their formation and decay. Recently, sunspot models have undergone a dramatic change. In the past, several aspects of sunspot structure have been addressed by static MHD models with parametrized energy transport. Models of sunspot fine structure have been relying heavily on strong assumptions about flow and field geometry (e.g., flux-tubes, "gaps", convective rolls, which were motivated in part by the observed filamentary structure of penumbrae or the necessity of explaining the substantial energy transport required to maintain the penumbral brightness. However, none of these models could self-consistently explain all aspects of penumbral structure (energy transport, filamentation, Evershed flow. In recent years, 3D radiative MHD simulations have been advanced dramatically to the point at which models of complete sunspots with sufficient resolution to capture sunspot fine structure are feasible. Here overturning convection is the central element responsible for energy transport, filamentation leading to fine-structure and the driving of strong outflows. On the larger scale these models are also in the progress of addressing the subsurface structure of sunspots as well as sunspot formation. With this shift in modeling capabilities and the recent advances in high resolution observations, the future research will be guided by comparing observation and theory.
Kinetic analysis of MHD ballooning modes in tokamaks
International Nuclear Information System (INIS)
Tang, W.M.; Rewoldt, G.; Cheng, C.Z.; Chance, M.S.
1984-10-01
A comprehensive analysis of the stability properties of the appropriate kinetically generalized form of MHD ballooning modes together with the usual trapped-particle drift modes is presented. The calculations are fully electromagnetic and include the complete dynamics associated with compressional ion acoustic waves. Trapped-particle effects along with all forms of collisionless dissipation are taken into account without approximations. The influence of collisions is estimated with a model Krook operator. Results from the application of this analysis to realistic tokamak operating conditions indicate that unstable short-wavelength modes with significant growth rates can extend from β = 0 to value above the upper ideal-MHD-critical-beta associated with the so-called second stability regime. Since the strength of the relevant modes appears to vary gradually with β, these results support a soft beta limit picture involving a continuous (rather than abrupt or hard) modification of anomalous transport already present in low-β-tokamaks. However, at higher beta the increasing dominance of the electromagnetic component of the perturbations indicated by these calculations could also imply significantly different transport scaling properties
MHD biconvective flow of Powell Eyring nanofluid over stretched surface
Naseem, Faiza; Shafiq, Anum; Zhao, Lifeng; Naseem, Anum
2017-06-01
The present work is focused on behavioral characteristics of gyrotactic microorganisms to describe their role in heat and mass transfer in the presence of magnetohydrodynamic (MHD) forces in Powell-Eyring nanofluids. Implications concerning stretching sheet with respect to velocity, temperature, nanoparticle concentration and motile microorganism density were explored to highlight influential parameters. Aim of utilizing microorganisms was primarily to stabilize the nanoparticle suspension due to bioconvection generated by the combined effects of buoyancy forces and magnetic field. Influence of Newtonian heating was also analyzed by taking into account thermophoretic mechanism and Brownian motion effects to insinuate series solutions mediated by homotopy analysis method (HAM). Mathematical model captured the boundary layer regime that explicitly involved contemporary non linear partial differential equations converted into the ordinary differential equations. To depict nanofluid flow characteristics, pertinent parameters namely bioconvection Lewis number Lb, traditional Lewis number Le, bioconvection Péclet number Pe, buoyancy ratio parameter Nr, bioconvection Rayleigh number Rb, thermophoresis parameter Nt, Hartmann number M, Grashof number Gr, and Eckert number Ec were computed and analyzed. Results revealed evidence of hydromagnetic bioconvection for microorganism which was represented by graphs and tables. Our findings further show a significant effect of Newtonian heating over a stretching plate by examining the coefficient values of skin friction, local Nusselt number and the local density number. Comparison was made between Newtonian fluid and Powell-Eyring fluid on velocity field and temperature field. Results are compared of with contemporary studies and our findings are found in excellent agreement with these studies.
Ballester, J. L.; Carbonell, M.; Soler, R.; Terradas, J.
2018-01-01
Context. During heating or cooling processes in prominences, the plasma microscopic parameters are modified due to the change of temperature and ionization degree. Furthermore, if waves are excited on this non-stationary plasma, the changing physical conditions of the plasma also affect wave dynamics. Aims: Our aim is to study how temporal variation of temperature and microscopic plasma parameters modify the behaviour of magnetohydrodynamic (MHD) waves excited in a prominence-like hydrogen plasma. Methods: Assuming optically thin radiation, a constant external heating, the full expression of specific internal energy, and a suitable energy equation, we have derived the profiles for the temporal variation of the background temperature. We have computed the variation of the ionization degree using a Saha equation, and have linearized the single-fluid MHD equations to study the temporal behaviour of MHD waves. Results: For all the MHD waves considered, the period and damping time become time dependent. In the case of Alfvén waves, the cut-off wavenumbers also become time dependent and the attenuation rate is completely different in a cooling or heating process. In the case of slow waves, while it is difficult to distinguish the slow wave properties in a cooling partially ionized plasma from those in an almost fully ionized plasma, the period and damping time of these waves in both plasmas are completely different when the plasma is heated. The temporal behaviour of the Alfvén and fast wave is very similar in the cooling case, but in the heating case, an important difference appears that is related with the time damping. Conclusions: Our results point out important differences in the behaviour of MHD waves when the plasma is heated or cooled, and show that a correct interpretation of the observed prominence oscillations is very important in order to put accurate constraints on the physical situation of the prominence plasma under study, that is, to perform prominence
MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects
Institute of Scientific and Technical Information of China (English)
M Ramzan; M Farooq; T Hayat; A Alsaedi; J Cao
2015-01-01
Combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained. Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.
MHD power generation for the synthetic-fuels industry
International Nuclear Information System (INIS)
Jones, M.S. Jr.
1982-01-01
The integration of open cycle MHD with various processes for the recovery of hydrocarbons for heavy oil deposits, oil sands, and oil shales are examined along with its use in producing medium Btu gas, synthetic natural gas and solvent refined coal. The major features of the MHD cycle which are of interest are: (a) the ability to produce hydrogen through the shift reaction by introducing H 2 O into the substoichiometric combustion product flow exiting the MHD diffuser, (b) the use of high temperature waste heat in the MHD exhaust, and (c) the ability of the seed in the MHD flow to remove sulfur from the combustion products. Therefore the use of the MHD cycle allows coal to be used in an environmentally acceptable manner in place of hydrocarbons which are now used to produce process heat and hydrogen. The appropriate plant sizes are in the range of 25 to 50 MWe and the required MHD generator enthalpy extraction efficiencies are low. Sale of electricity produced, over and above that used in the process, can provide a revenue stream which can improve the economics of the hydrocarbon processing. This, coupled with the replacement of coal for hydrocarbons in certain phases of the process, should improve the overall economics, while not requiring a high level of performance by the MHD components. Therefore, this area should be an early target of opportunity for the commercialization of MHD
MHD power plants - a reality of the 80's
International Nuclear Information System (INIS)
Pishchikov, S.
1981-01-01
A 300 MW MHD generator and a conventional turbogenerator of the same capacity will be used for the first MHD power block assembly projected in the USSR. The power plant's own consumption will not exceed 12% and the availability will be approximately 50%. Compared with a conventional power generating unit of a capacity of 500 MW the projected unit will provide fuel savings of at least 23%. The project is based on almost seven years long experience with the U-25 experimental MHD facility. Similar to the U-25, the MHD power plant projected will be fired with natural gas. (B.S.)
MHD power plants - a reality of the 80's
Energy Technology Data Exchange (ETDEWEB)
Pishchikov, S
1981-02-01
A 300 MW MHD generator and a conventional turbogenerator of the same capacity will be used for the first MHD power block assembly projected in the USSR. The power plant's own consumption will not exceed 12% and the availability will be approximately 50%. Compared with a conventional power generating unit of a capacity of 500 MW the projected unit will provide fuel savings of at least 23%. The project is based on almost seven years long experience with the U-25 experimental MHD facility. Similar to the U-25, the MHD power plant projected will be fired with natural gas.
Contribution to the resolution of magnetohydrodynamic and magnetostatic equations
International Nuclear Information System (INIS)
Boulbe, C.
2007-10-01
Interaction between a plasma and a magnetic field appears and has an important role in various domains such as thermonuclear fusion by magnetic confinement or astrophysical plasmas for example. In evolution, these interactions are described by the equations of magnetohydrodynamics (MHD). At equilibrium, the MHD equations result in the magnetostatic equations involving the magnetic field and the kinetic pressure of the plasma. The magnetostatic equations form a system of 3-dimensional non linear partial differential equations involving a magnetic field and a kinetic plasma pressure. When the pressure is supposed negligible, the magnetic field is known as Beltrami field. In a first time, we propose to solve numerically the Beltrami field problem using a fixed point iterative algorithm associated with finite element methods. This iterative strategy is extended in a second time to the computation of magnetostatic configurations with pressure. In the sequel, we interest in the approximation of ideal MHD equations. This system forms a nonlinear hyperbolic conservation law. We propose to use a finite volume approach, in which fluxes are calculated by a Roe's method on a tetrahedral mesh. Fluxes of the magnetic field are modified in order to satisfy the constraint of divergence free imposed on it. The proposed methods have been implemented in two new 3-dimensional codes called TETRAFFF for equilibrium, and TETRAMHD for MHD. The obtained numerical results confirm the high performance of these methods. (author)
MHD aspects of coronal transients
International Nuclear Information System (INIS)
Anzer, U.
1979-10-01
If one defines coronal transients as events which occur in the solar corona on rapid time scales (< approx. several hours) then one would have to include a large variety of solar phenomena: flares, sprays, erupting prominences, X-ray transients, white light transients, etc. Here we shall focus our attention on the latter two phenomena. (orig.) 891 WL/orig. 892 RDG
Regularity criteria for the 3D magneto-micropolar fluid equations via ...
Indian Academy of Sciences (India)
3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier–Stokes and MHD equations. Keywords. Magneto-micropolar fluid equations; regularity criteria; direction of velocity. 2010 Mathematics Subject Classification. 35Q35, 76W05 ...
An new MHD/kinetic model for exploring energetic particle production in macro-scale systems
Drake, J. F.; Swisdak, M.; Dahlin, J. T.
2017-12-01
A novel MHD/kinetic model is being developed to explore magneticreconnection and particle energization in macro-scale systems such asthe solar corona and the outer heliosphere. The model blends the MHDdescription with a macro-particle description. The rationale for thismodel is based on the recent discovery that energetic particleproduction during magnetic reconnection is controlled by Fermireflection and Betatron acceleration and not parallel electricfields. Since the former mechanisms are not dependent on kineticscales such as the Debye length and the electron and ion inertialscales, a model that sheds these scales is sufficient for describingparticle acceleration in macro-systems. Our MHD/kinetic model includesmacroparticles laid out on an MHD grid that are evolved with the MHDfields. Crucially, the feedback of the energetic component on the MHDfluid is included in the dynamics. Thus, energy of the total system,the MHD fluid plus the energetic component, is conserved. The systemhas no kinetic scales and therefore can be implemented to modelenergetic particle production in macro-systems with none of theconstraints associated with a PIC model. Tests of the new model insimple geometries will be presented and potential applications will bediscussed.
Energy Technology Data Exchange (ETDEWEB)
1992-01-01
The overall objective of the project is to design and construct prototypical hardware for an integrated MHD topping cycle, and conduct long duration proof-of-concept tests of integrated system at the US DOE Component Development and Integration Facility in Butte, Montana. The results of the long duration tests will augment the existing engineering design data base on MHD power train reliability, availability, maintainability, and performance, and will serve as a basis for scaling up the topping cycle design to the next level of development, an early commercial scale power plant retrofit. The components of the MHD power train to be designed, fabricated, and tested include: A slagging coal combustor with a rated capacity of 50 MW thermal input, capable of operation with an Eastern (Illinois {number_sign}6) or Western (Montana Rosebud) coal, a segmented supersonic nozzle, a supersonic MHD channel capable of generating at least 1.5 MW of electrical power, a segmented supersonic diffuser section to interface the channel with existing facility quench and exhaust systems, a complete set of current control circuits for local diagonal current control along the channel, and a set of current consolidation circuits to interface the channel with the existing facility inverter.
Towards a Scalable Fully-Implicit Fully-coupled Resistive MHD Formulation with Stabilized FE Methods
Energy Technology Data Exchange (ETDEWEB)
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.
Jackson, B. V.; Yu, H. S.; Hick, P. P.; Buffington, A.; Odstrcil, D.; Kim, T. K.; Pogorelov, N. V.; Tokumaru, M.; Bisi, M. M.; Kim, J.; Yun, J.
2017-12-01
The University of California, San Diego has developed an iterative remote-sensing time-dependent three-dimensional (3-D) reconstruction technique which provides volumetric maps of density, velocity, and magnetic field. We have applied this technique in near real time for over 15 years with a kinematic model approximation to fit data from ground-based interplanetary scintillation (IPS) observations. Our modeling concept extends volumetric data from an inner boundary placed above the Alfvén surface out to the inner heliosphere. We now use this technique to drive 3-D MHD models at their inner boundary and generate output 3-D data files that are fit to remotely-sensed observations (in this case IPS observations), and iterated. These analyses are also iteratively fit to in-situ spacecraft measurements near Earth. To facilitate this process, we have developed a traceback from input 3-D MHD volumes to yield an updated boundary in density, temperature, and velocity, which also includes magnetic-field components. Here we will show examples of this analysis using the ENLIL 3D-MHD and the University of Alabama Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS) heliospheric codes. These examples help refine poorly-known 3-D MHD variables (i.e., density, temperature), and parameters (gamma) by fitting heliospheric remotely-sensed data between the region near the solar surface and in-situ measurements near Earth.
MHD instabilities in astrophysical plasmas: very different from MHD instabilities in tokamaks!
Goedbloed, J. P.
2018-01-01
The extensive studies of MHD instabilities in thermonuclear magnetic confinement experiments, in particular of the tokamak as the most promising candidate for a future energy producing machine, have led to an 'intuitive' description based on the energy principle that is very misleading for
Directory of Open Access Journals (Sweden)
M. Jayachandra Babu
2017-12-01
Full Text Available The knowledge of heat and mass transfer of MHD flows over different geometries is very important for heat exchangers design, transpiration, fiber coating, etc. With this initiation, a mathematical model is proposed to investigate the two-dimensional flow, heat and mass transfer of magnetohydrodynamic flow over three different geometries (vertical cone, vertical wedge, and a vertical plate. Cattaneo-Christov heat flux with external magnetic field, thermophoresis and Brownian movement effect are introduced in the model. Runge-Kutta and Newtonâs methods are employed to solve the altered governing nonlinear equations. The influences of the parameters of concern on the common profiles (velocity, temperature, and concentration are conversed (in three cases. By viewing the same parameters, skin friction coefficient, heat and mass transfer rates are discussed with the assistance of tables. It is discovered that the momentum and thermal boundary layers are non-uniform for the MHD flow over three geometries (vertical cone, wedge, and a plate. Thermal and solutal Grashof numbers regulate the temperature and concentration fields. The heat and mass transfer rates of the flow over a cone are highly influenced by the thermal relaxation parameter. Keywords: MHD, Cattaneo-Christov heat flux, Thermal relaxation, Thermophoresis, Brownian motion
On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes
Energy Technology Data Exchange (ETDEWEB)
Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo; Aloy, Miguel-Ángel [Departamento de Astronomía y Astrofísica, Universidad de Valencia, C/Dr. Moliner 50, E-46100 Burjassot (Spain); Müller, Ewald, E-mail: tomasz.rembiasz@uv.es [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)
2017-06-01
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.
Laser-Plasma Modeling Using PERSEUS Extended-MHD Simulation Code for HED Plasmas
Hamlin, Nathaniel; Seyler, Charles
2017-10-01
We discuss the use of the PERSEUS extended-MHD simulation code for high-energy-density (HED) plasmas in modeling the influence of Hall and electron inertial physics on laser-plasma interactions. By formulating the extended-MHD equations as a relaxation system in which the current is semi-implicitly time-advanced using the Generalized Ohm's Law, PERSEUS enables modeling of extended-MHD phenomena (Hall and electron inertial physics) without the need to resolve the smallest electron time scales, which would otherwise be computationally prohibitive in HED plasma simulations. We first consider a laser-produced plasma plume pinched by an applied magnetic field parallel to the laser axis in axisymmetric cylindrical geometry, forming a conical shock structure and a jet above the flow convergence. The Hall term produces low-density outer plasma, a helical field structure, flow rotation, and field-aligned current, rendering the shock structure dispersive. We then model a laser-foil interaction by explicitly driving the oscillating laser fields, and examine the essential physics governing the interaction. This work is supported by the National Nuclear Security Administration stewardship sciences academic program under Department of Energy cooperative agreements DE-FOA-0001153 and DE-NA0001836.
Nonlinear MHD Waves in a Prominence Foot
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
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-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.
MHD dynamo action in space plasmas
International Nuclear Information System (INIS)
Faelthammar, C.G.
1984-05-01
Electric currents are now recognized to play a major role in the physical process of the Earths magnetosphere as well as in distant astrophysical plasmas. In driving these currents MHD dynamos as well as generators of a thermoelectric nature are important. The primary source of power for the Earths magnetospheric process is the solar wind, which supplies a voltage of the order of 200 kV across the magnetosphere. The direction of the large-scale solar wind electric field varies of many different time scales. The power input to the magnetosphere is closely correlated with the direction of the large-scale solar wind electric field in such a fashion as to mimick the response of a half-wave rectifier with a down-to-dusk conduction direction. Behind this apparently simple response there are complex plasma physical processes that are still very incompletely understood. They are intimately related to auroras, magnetic storms, radiation belts and changes in magnetospheric plasma populations. Similar dynamo actions should occur at other planets having magnetospheres. Recent observations seem to indicate that part of the power input to the Earths magnetosphere comes through MHD dynamo action of a forced plasma flow inside the flanks of the magnetopause and may play a role in other parts of the magnetosphere, too. An example of a cosmical MHD connected to a solid load is the corotating plasma of Jupiters inner magnetosphere, sweeping past the plants inner satelites. In particular the electric currents thereby driven to and from the satellite Io have attracted considerable interest.(author)
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
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.
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Characteristics of Plasma Probes in an MHD Working Fluid
Energy Technology Data Exchange (ETDEWEB)
Whitman, A. M.; Hsuan, Yeh [Towne School of Civil and Mechanical Engineering, University of Pennsylvania (United States)
1966-10-15
In this paper an attempt is made to formulate a theory of electrostatic probes in a high-pressure plasma in which an external electrical field may be imposed. Such a situation exists in high-pressure arc discharges and in MHD channels. First, it is shown that an adequate theory must include the ionization and recombination phenomena which were ignored in almost all previous theories. Secondly, due to the preferred direction induced by the presence of the electric field, the probe problem is no longer a symmetrical one. The analysis is based on the assumption that the three-body recombination and ionization is the dominant process. In a typical MHD working fluid, say an argon gas seeded with caesium at 2000 Degree-Sign K and one atmosphere of pressure, the penetration length I of ions and electrons, i.e. the distance that an ion or electron diffuses before recombination, is of the order of 10{sup -3} cm. (It is to be noted that ambipolar diffusion prevents the electrons from travelling much faster than the ions. ) We thus have a situation where Script-Small-L /L << 1, d/ Script-Small-L << 1, {lambda}/L <<1, and {lambda}/d >> 1, where L is the characteristic dimension of the probe {lambda} is the mean free path and d the Debye length. Because of the last condition, i. e, d << {lambda}, the space charge region is contained wholly in a ''free-falling'' zone in the immediate neighbourhood of the probe. Since, also, (d/ Script-Small-L ) << 1, the region outside of the ''free-falling'' zone is in a state of ''quasi-neutrality'', i.e. the number densities of electrons and ions are approximately equal. In this latter region, the mechanisms of diffusion and recombination are both important. The two regions must of course be matched at their connecting boundaries. Furthermore, the external boundary of the ''quasi-neutrality'' region must be matched to the discharge field. Using the approximations of the classical boundary layer theory, analytic solutions are obtained in
MHD oxidant intermediate temperature ceramic heater study
Carlson, A. W.; Chait, I. L.; Saari, D. P.; Marksberry, C. L.
1981-09-01
The use of three types of directly fired ceramic heaters for preheating oxygen enriched air to an intermediate temperature of 1144K was investigated. The three types of ceramic heaters are: (1) a fixed bed, periodic flow ceramic brick regenerative heater; (2) a ceramic pebble regenerative heater. The heater design, performance and operating characteristics under conditions in which the particulate matter is not solidified are evaluated. A comparison and overall evaluation of the three types of ceramic heaters and temperature range determination at which the particulate matter in the MHD exhaust gas is estimated to be a dry powder are presented.
MHD power conversion employing liquid metals
International Nuclear Information System (INIS)
Houben, J.W.M.A.; Massee, P.
1969-02-01
The work performed in the field of MHD generation of electricity by means of liquid metals is described. It is shown that the study of two-phase flows is essential in this topic of research; two-phase flows are therefore described. Two types of generators which can be utilized with liquid metals have been studied. The results of this study are described. A short survey of the prospects of other liquid metal systems which emerge from a study of the literature is given. Finally, conclusions are drawn concerning possibilities for further investigation
MHD equilibrium identification on ASDEX-Upgrade
International Nuclear Information System (INIS)
McCarthy, P.J.; Schneider, W.; Lakner, K.; Zehrfeld, H.P.; Buechl, K.; Gernhardt, J.; Gruber, O.; Kallenbach, A.; Lieder, G.; Wunderlich, R.
1992-01-01
A central activity accompanying the ASDEX-Upgrade experiment is the analysis of MHD equilibria. There are two different numerical methods available, both using magnetic measurements which reflect equilibrium states of the plasma. The first method proceeds via a function parameterization (FP) technique, which uses in-vessel magnetic measurements to calculate up to 66 equilibrium parameters. The second method applies an interpretative equilibrium code (DIVA) for a best fit to a different set of magnetic measurements. Cross-checks with the measured particle influxes from the inner heat shield and the divertor region and with visible camera images of the scrape-off layer are made. (author) 3 refs., 3 figs
International Nuclear Information System (INIS)
Huysmans, G.
1998-03-01
One of the aims of the JET, the Joint European Torus, project is to optimise the maximum fusion performance as measured by the neutron rate. At present, two different scenarios are developed at JET to achieve the high performance the so-called Hot-Ion H-mode scenario and the more recent development of the Optimised Shear scenario. Both scenarios have reached similar values of the neutron rate in Deuterium plasmas, up to 5 10 17 neutrons/second. Both scenarios are characterised by a transport barrier, i.e., a region in the plasma where the confinement is improved. The Hot-Ion H-mode has a transport barrier at the plasma boundary just inside the separatrix, an Optimised Shear plasma exhibits a transport barrier at about mid radius. Associated with the improved confinement of the transport barriers are locally large pressure gradients. It is these pressure gradients which, either directly or indirectly, can drive MHD instabilities. The instabilities limit the maximum performance. In the optimised shear scenario a global MHD instability leads to a disruptive end of the discharge. In the Hot-Ion H-mode plasmas, so-called Outer Modes can occur which are localised at the plasma boundary and lead to a saturation of the plasma performance. In this paper, two examples of the MHD instabilities are discussed and identified by comparing the experimentally observed modes with theoretical calculations from the ideal MHD code MISHKA-1. Also, the MHD stability boundaries of the two scenarios are presented. Section 3 contains a discussion of the mode observed just before the disruption
Directory of Open Access Journals (Sweden)
S. Mamatha Upadhya
2018-06-01
Full Text Available A Comprehensive study on laminar, magnetohydrodynamic (MHD boundary layer flow of nanofluid (water + Silver, water + Graphene embedded with conducting micrometer sized dust particles over a stretching cylinder with the incorporation of Cattaneo-Christov heat flux model is conducted. Appropriate similarity variables are employed to the flow governing equations and the resulting ordinary differential equations are solved by employing Runge-Kutta-Fehlberg method. The results for varied controlling parameters for both dusty nano fluid and dust phase are shown through graphs, table and discussed in detail. Authentication of the obtained results is provided by comparing with published results. Results indicate that Graphene + water dusty nanofluid shows better heat transfer performance compared with Silver + water dusty nanofluid. Improvement in thermal relaxation boosts temperature distribution in both fluid and dust phase. Keywords: Graphene nano particles, Silver nano particles, Stretching cylinder, Dusty fluid, Cattaneo-Christov heat flux, MHD
MHD Integrated Topping Cycle Project
1993-04-01
Manufacture, assembly, and checkout of combustion subsystem hardware was completed and the hardware was delivered to CDIF along with the water electrical isolators. A successful nozzle proof test was concluded; its purpose was to evaluate adequacy of the nozzle structure and sealing of sidewall-to-electrode wall joints, water tubes, and stud and wire penetrations at operating pressure. Design modifications to spare channel inlet frame were made to enable iron oxide injection. Results of tests in the CDIF 1A1 channel which compared effect of different cathode wall iron oxide injection locations indicated that injection through the side port may be more effective, particularly if one of the two ports becomes clogged. Design confirmation testing of a pneumatically driven ram to clear a plugged iron oxide injector tip was performed. Manufacture of spare and replacement parts for 1A4 channel and diffuser was begun. Construction of the cathode power cabinets and associated control system was completed. Hot-fire checkout series was completed for the combustion subsystem; 16.8 thermal hours were accumulated during seven tests. This test series demonstrated adequacy of overall cooling of combustion subsystem and provided an initial evaluation of heat losses and slagging characteristics. Several major facility activities at the CDIF were accomplished including installation and testing of new iron oxide pumps, initial on-line checkout of coal feed system modifications, modification of seed system including replacement of silo rotary feeder, installation of new filter receiver on the silo, conversion of fly ash bin to dust collector, removal of all of the electrical wiring (used for 1A1 channel) between the channel and HVR in order to install 1A4 wiring, and installation of the 1A4 channel.
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Energy Technology Data Exchange (ETDEWEB)
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.
Stability of ideal MHD configurations. I. Realizing the generality of the G operator
Keppens, R.; Demaerel, T.
2016-12-01
A field theoretical approach, applied to the time-reversible system described by the ideal magnetohydrodynamic (MHD) equations, exposes the full generality of MHD spectral theory. MHD spectral theory, which classified waves and instabilities of static or stationary, usually axisymmetric or translationally symmetric configurations, actually governs the stability of flowing, (self-)gravitating, single fluid descriptions of nonlinear, time-dependent idealized plasmas, and this at any time during their nonlinear evolution. At the core of this theory is a self-adjoint operator G , discovered by Frieman and Rotenberg [Rev. Mod. Phys. 32, 898 (1960)] in its application to stationary (i.e., time-independent) plasma states. This Frieman-Rotenberg operator dictates the acceleration identified by a Lagrangian displacement field ξ , which connects two ideal MHD states in four-dimensional space-time that share initial conditions for density, entropy, and magnetic field. The governing equation reads /d 2 ξ d t 2 = G [ ξ ] , as first noted by Cotsaftis and Newcomb [Nucl. Fusion, Suppl. Part 2, 447 and 451 (1962)]. The time derivatives at left are to be taken in the Lagrangian way, i.e., moving with the flow v. Physically realizable displacements must have finite energy, corresponding to being square integrable in the Hilbert space of displacements equipped with an inner product rule, for which the G operator is self-adjoint. The acceleration in the left-hand side features the Doppler-Coriolis operator v . ∇ , which is known to become an antisymmetric operator when restricting attention to stationary equilibria. Here, we present all derivations needed to get to these insights and connect results throughout the literature. A first illustration elucidates what can happen when self-gravity is incorporated and presents aspects that have been overlooked even in simple uniform media. Ideal MHD flows, as well as Euler flows, have essentially 6 + 1 wave types, where the 6 wave modes
Priority pollutant analysis of MHD-derived combustion products
Parks, Katherine D.
An important factor in developing Magnetohydrodynamics (MHD) for commercial applications is environmental impact. Consequently, an effort was initiated to identify and quantify any possible undesirable minute chemical constituents in MHD waste streams, with special emphasis on the priority pollutant species. This paper discusses how priority pollutant analyses were used to accomplish the following goals at the University of Tennessee Space Institute (UTSI): comparison of the composition of solid combustion products collected from various locations along a prototypical MHD flow train during the firing of Illinois No. 6 and Montana Rosebud coals; comparison of solid waste products generated from MHD and conventional power plant technologies; and identification of a suitable disposal option for various MHD derived combustion products. Results from our ongoing research plans for gas phase sampling and analysis of priority pollutant volatiles, semi-volatiles, and metals are discussed.
Preliminary results of MHD stability in HL-1 tokamak
International Nuclear Information System (INIS)
Zheng Yongzhen; Ma Tengcai; Xiao Zhenggui Cai Renfang
1987-01-01
In this paper, MHD activities of HL-1 tokamak plasma are studied with Fourier transform and correlatio analysis. The poloidal modes m = 1, 2, 3,4 and toroidal modes n of MHD magnetic fluctuation signals are detected. Methods for suppressing MHD instabilities are suggested and tested, after MHD instabilities are studied in HL-1. The effects of MHD characteristics in the beginning stage of discharge on the whole process of discharge are analyzed. The disruption, in HL-1 device could be divided into three kinds: internal disruption, minor disruption and major disruption. The result shows that HL-1 will have a better operation condition if internal disruption appears. In is end, the stable operation region of HL-1 tokamak is also given
MHD simulations of coronal dark downflows considering thermal conduction
Zurbriggen, E.; Costa, A.; Esquivel, A.; Schneiter, M.; Cécere, M.
2017-10-01
While several scenarios have been proposed to explain supra-arcade downflows (SADs) observed descending through turbulent hot regions, none of them have systematically addressed the consideration of thermal conduction. The SADs are known to be voided cavities. Our model assumes that SADs are triggered by bursty localized reconnection events that produce non-linear waves generating the voided cavity. These subdense cavities are sustained in time because they are hotter than their surrounding medium. Due to the low density and large temperature values of the plasma we expect the thermal conduction to be an important process. Our main aim here is to study if it is possible to generate SADs in the framework of our model considering thermal conduction. We carry on 2D MHD simulations including anisotropic thermal conduction, and find that if the magnetic lines envelope the cavities, they can be isolated from the hot environment and be identified as SADs.
Resistive MHD studies of high-β-tokamak plasmas
International Nuclear Information System (INIS)
Lynch, V.E.; Carreras, B.A.; Hicks, H.R.; Holmes, J.A.; Garcia, L.
1981-01-01
Numerical calculations have been performed to study the MHD activity in high-β tokamaks such as ISX-B. These initial value calculations built on earlier low β techniques, but the β effects create several new numerical issues. These issues are discussed and resolved. In addition to time-stepping modules, our system of computer codes includes equilibrium solvers (used to provide an initial condition) and output modules, such as a magnetic field line follower and an X-ray diagnostic code. The transition from current driven modes at low β to predominantly pressure driven modes at high β is described. The nonlinear studies yield X-ray emissivity plots which are compared with experiment
Chernoff, D. F.; Hollenbach, David J.; Mckee, Christopher F.
1990-01-01
Researchers survey shock solutions of a partially ionized gas with a magnetic field. The gas is modeled by interacting neutral, ion, electron and charged grain components. They employ a small neutral-ion chemical network to follow the dissociation and ionization of the major species. Cooling by molecular hydrogen (rotational, vibrational and dissociation), grains and dipole molecules is included. There are three basic types of solutions (C, C asterisk, and J) and some more complicated flows involving combinations of the basic types. The initial preshock conditions cover hydrogen nuclei densities of 1 less than n less than 10(exp 10) cm(-3) and shock velocities of 5 less than v(sub s) less than 60 km/s. The magnetic field is varied over 5 decades and the sensitivity of the results to grain parameters, UV and cosmic ray fluxes is ascertained. The parameter space is quite complicated, but there exist some simple divisions. When the initial ionization fraction is small (chi sub i less than 10(-5)), there is a sharp transition between fully C solutions at low velocity and strong J solutions at high velocity. When the initial ionization fraction is larger, C asterisk and/or very weak J shocks are present at low velocities in addition to the C solutions. The flow again changes to strong J shocks at high velocities. When the ionization fraction is large and the flow is only slightly greater than the bulk Alfven velocity, there is a complicated mixture of C, C asterisk and J solutions.
Badia, Santiago; Martín, Alberto F.; Planas, Ramon
2014-10-01
The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.
Transient behavior of high-interaction MHD generator following external loading faults
International Nuclear Information System (INIS)
Ishikawa, Motoo
1983-01-01
Transient behavior consequent to external loading faults is studied numerically on four configurations of high-interaction MHD generators-subsonic Faraday, supersonic Faraday, subsonic diagonal and supersonic diagonal, to provide a variable data base to serve in selecting the type of large-scale MHD generator. Time-dependent one-dimensional Navier-Stokes equations are solved with the 1969 MacCormack method, in combination with the Maxwell equations and the generalized Ohm's law. An artificial viscosity term is added to the Navier-Stokes equations to maintain numerical stability. It is shown that, with both supersonic and subsonic flows, the Faraday generator is liable to sustain more harmful effect from short than from open faults of the external loading circuit. For large-scale diagonal types, on the other hand, open faults are more dangerous. With subsonic flow, a shock wave propagating upstream is induced by short fault in the Faraday, and by open fault in the diagonal-type generator. In the case of supersonic flow, propagation upstream of the disturbance is completely obstructed. Larger electrical stress is foreseen for Faraday than for diagonal configuration. (author)
Analysis of voltage-drop near cold-electrodes of a combustion MHD generator
International Nuclear Information System (INIS)
Satyamurthy, P.; Venkatramani, N.; Rohatgi, V.K.
1983-01-01
In this paper turbulent compressible boundary layer equations for mass, momentum and energy are solved near the cold electrode wall of a combustion MHD generator. Arcs are simulated by freezing the electron temperature (and hence electrical conductivity) to a temperature called Tsub(arc) when gas temperature is less than Tsub(arc). Theoretical near electrode drop for various current densities along the flow direction is analysed for various Tsub(arc) temperatures and compared with experimentally obtained near electrode drop. It is found that the Tsub(arc) temperature increases as a square root along the flow direction and has linear dependency on current density. (author)
Hall effects on unsteady MHD flow between two rotating disks with non-coincident parallel axes
Energy Technology Data Exchange (ETDEWEB)
Barik, R.N., E-mail: barik.rabinarayan@rediffmail.com [Department of Mathematics, Trident Academy of Technology, Bhubaneswar (India); Dash, G.C., E-mail: gcdash@indiatimes.com [Department of Mathematics, S.O.A. University, Bhubaneswar (India); Rath, P.K., E-mail: pkrath_1967@yahoo.in [Department of Mathematics, B.R.M. International Institute of Technology, Bhubaneswar (India)
2013-01-15
Hall effects on the unsteady MHD rotating flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes have been studied. There exists an axisymmetric solution to this problem. The governing equations are solved by applying Laplace transform method. It is found that the torque experienced by the disks decreases with an increase in either the Hall parameter, m or the rotation parameter, S{sup 2}. Further, the axis of rotation has no effect on the fluid flow. (author)
Hall effects on unsteady MHD flow between two rotating disks with non-coincident parallel axes
International Nuclear Information System (INIS)
Barik, R.N.; Dash, G.C.; Rath, P.K.
2013-01-01
Hall effects on the unsteady MHD rotating flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes have been studied. There exists an axisymmetric solution to this problem. The governing equations are solved by applying Laplace transform method. It is found that the torque experienced by the disks decreases with an increase in either the Hall parameter, m or the rotation parameter, S 2 . Further, the axis of rotation has no effect on the fluid flow. (author)
Calculation of three-dimensional MHD equilibria with islands and stochastic regions
International Nuclear Information System (INIS)
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
Numerical analysis of three-dimensional MHD shock interactions in an inhomogeneous medium
International Nuclear Information System (INIS)
Prndergast, M.; Wu, S.T.
1987-01-01
Study of the formation and propagation of solar-originated shock waves in heliospheric space has attracted significant attention in the past decade. This attention is important because the propagation of shocks in heliospheric space has been thought of as one of the major physical processes for solar wind and cosmic ray modulations and their subsequent influence on the earth's environment. A version of the two step Lax-Wendroff difference method is used to seek solutions of the unsteady magnetohydrodynamic (MHD) equations for the study of a solar flare generated shock wave propagating through an inhomogeneous medium. 8 references
Effect of external circuit on heat transfer in MHD Couette flow
International Nuclear Information System (INIS)
Soundalgekar, V.M.
1982-01-01
An exact solution of energy equation in fully-developed MHD Coutte flow has been derived. Temperature profiles are shown in open- and short-circuit cases. It has been observed that in short circuit case, temperature and Nusselt number (Nu) increase with increasing M, whereas in open-circuit case, with increasing M, the temperature decreases. Also in open-circuit case, Nu increases with increasing M when M is small, but at large values of M, Nu decreases with increasing M. (author)
Two dimensional analysis for magnetic flux distribution in electromagnet used for MHD applications
International Nuclear Information System (INIS)
Desai, S.V.; Venkatramani, N.; Rohatgi, V.K.
1984-01-01
Magnetic flux densities in air and iron region of iron core MHD electromagnet, are calculated based on concept of magnetic vector potential. Numerical solution to the problem is obtained by converting partial differential equations into finite difference form with simplifying assumptions. A computer progrm is developed, giving solution by finite difference method. Over-relaxation technique based on Stoke's theorem is applied. Magnetic induction along the transverse axis of the magnet and plot for magnetic induction lines for current = 2420 A is presented. (author)
New method for computing ideal MHD normal modes in axisymmetric toroidal geometry
International Nuclear Information System (INIS)
Wysocki, F.; Grimm, R.C.
1984-11-01
Analytic elimination of the two magnetic surface components of the displacement vector permits the normal mode ideal MHD equations to be reduced to a scalar form. A Galerkin procedure, similar to that used in the PEST codes, is implemented to determine the normal modes computationally. The method retains the efficient stability capabilities of the PEST 2 energy principle code, while allowing computation of the normal mode frequencies and eigenfunctions, if desired. The procedure is illustrated by comparison with earlier various of PEST and by application to tilting modes in spheromaks, and to stable discrete Alfven waves in tokamak geometry
Directory of Open Access Journals (Sweden)
Muhammad Mubashir Bhatti
2016-05-01
Full Text Available In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations with the help of similarity variables. The solution of the resulting nonlinear differential equations is solved numerically with the help of the successive linearization method and Chebyshev spectral collocation method. The influence of all the emerging parameters is discussed with the help of graphs and tables. It is observed that the influence of magnetic field and fluid parameters oppose the flow. It is also analyzed that thermal radiation effects and the Prandtl number show opposite behavior on temperature profile. Furthermore, it is also observed that entropy profile increases for all the physical parameters.
Energy Technology Data Exchange (ETDEWEB)
NONE
1970-07-01
Compiled are the results of studies conducted in fiscal 1970 on MHD (magnetohydrodynamic) power generation. In the operation test and modification of the 1000kW-class MHD power generator, modification is carried out involving the combustion system, seed collecting method, and power generation channel, and reviews through experiments are conducted about the analysis and control of the boundary layer structure. In the operation test of the MHD power generator designed for prolonged operation, a test operation for resistance to heat and seeds continues more than 100 hours using a cold wall type power generation channel constituted of water cooled ceramics, and the ceramics are analyzed for failure and loss. Studies are also conducted involving MHD power generator heat exchangers, seed collecting methods, electrode materials for MHD power generators, heat-resistant materials for MHD power generators, thermal performance rating for MHD power plants, etc. In the research and development of superconductive electromagnets, superconductive electromagnets are developed and tested for 1000kW-class MHD power generators, and studies are conducted on turbine type helium liquefiers, superinsulated superconductive electromagnetic field generators, etc. (NEDO)
Resistive MHD studies of TFTR discharges
International Nuclear Information System (INIS)
Hughes, M.H.; Phillips, M.W.; Sabbagh, S.A.; Budny, R.V.
1991-01-01
MHD instabilities, thought to be resistive in character, are frequently observed in the supershot operating regime of TFTR (var-epsilon β p ≤ 0.7). These instabilities are always accompanied by substantial degradation of the confinement. Similarly of interest are recent experiments at much larger β p (var-epsilon β p ≤ 1.6), achieved through ramping the current during the beam heating phase of the discharge. In this latter regime the confinement can exceed three times the corresponding L-mode value and the β value normalized to I/aB can be as large as 4.7. Representative discharges from each of these operating regimes have been analyzed using a linear resistive MHD stability code with equilibrium pressure and q profiles obtained initially from the TRANSP analysis code. The main difference between the two types of discharge, as far as stability is concerned is shown to be the shape of the current density profile. The sensitivity to the assumed parameters is discussed. 1 ref
Energy Technology Data Exchange (ETDEWEB)
Janyszek, H [Uniwersytet Mikolaja Kopernika, Torun (Poland). Instytut Fizyki
1974-01-01
A new modified quasirelativistic equation (different from that of Breit) for N charged Dirac particles in the external stationary electromagnetic field is proposed. This equation is an amplified quantum-mechanical Bethe-Salpeter equation obtained by adding (in a semi-phenomenological manner) terms which take into account radiative corrections. The application of this approximate equations is limited to third order terms in the fine structure constant ..cap alpha...
Nonlinear equilibrium in Tokamaks including convective terms and viscosity
International Nuclear Information System (INIS)
Martin, P.; Castro, E.; Puerta, J.
2003-01-01
MHD equilibrium in tokamaks becomes very complex, when the non-linear convective term and viscosity are included in the momentum equation. In order to simplify the analysis, each new term has been separated in type gradient terms and vorticity depending terms. For the special case in which the vorticity vanishes, an extended Grad-Shafranov type equation can be obtained. However now the magnetic surface is not isobars or current surfaces as in the usual Grad-Shafranov treatment. The non-linear convective terms introduces gradient of Bernoulli type kinetic terms . Montgomery and other authors have shown the importance of the viscosity terms in tokamaks [1,2], here the treatment is carried out for the equilibrium condition, including generalized tokamaks coordinates recently described [3], which simplify the equilibrium analysis. Calculation of the new isobar surfaces is difficult and some computation have been carried out elsewhere for some particular cases [3]. Here, our analysis is extended discussing how the toroidal current density, plasma pressure and toroidal field are modified across the midplane because of the new terms (convective and viscous). New calculations and computations are also presented. (Author)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Rashidi
2010-01-01
Full Text Available The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Padé method was used which is a combination of differential transform method (DTM and Padé approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solutions obtained by the DTM and the DTM-Padé with numerical solution (fourth-order Runge–Kutta revealed that the DTM-Padé method is an excellent method for solving MHD boundary-layer equations.
Sakurai, Takashi; Goossens, Marcel; Hollweg, Joseph V.
1991-01-01
The present method of addressing the resonance problems that emerge in such MHD phenomena as the resonant absorption of waves at the Alfven resonance point avoids solving the fourth-order differential equation of dissipative MHD by recourse to connection formulae across the dissipation layer. In the second part of this investigation, the absorption of solar 5-min oscillations by sunspots is interpreted as the resonant absorption of sounds by a magnetic cylinder. The absorption coefficient is interpreted (1) analytically, under certain simplifying assumptions, and numerically, under more general conditions. The observed absorption coefficient magnitude is explained over suitable parameter ranges.
MHD stability limits in the TCV Tokamak
International Nuclear Information System (INIS)
Reimerdes, H.
2001-07-01
Magnetohydrodynamic (MHD) instabilities can limit the performance and degrade the confinement of tokamak plasmas. The Tokamak a Configuration Variable (TCV), unique for its capability to produce a variety of poloidal plasma shapes, has been used to analyse various instabilities and compare their behaviour with theoretical predictions. These instabilities are perturbations of the magnetic field, which usually extend to the plasma edge where they can be detected with magnetic pick-up coils as magnetic fluctuations. A spatially dense set of magnetic probes, installed inside the TCV vacuum vessel, allows for a fast observation of these fluctuations. The structure and temporal evolution of coherent modes is extracted using several numerical methods. In addition to the setup of the magnetic diagnostic and the implementation of analysis methods, the subject matter of this thesis focuses on four instabilities, which impose local and global stability limits. All of these instabilities are relevant for the operation of a fusion reactor and a profound understanding of their behaviour is required in order to optimise the performance of such a reactor. Sawteeth, which are central relaxation oscillations common to most standard tokamak scenarios, have a significant effect on central plasma parameters. In TCV, systematic scans of the plasma shape have revealed a strong dependence of their behaviour on elongation κ and triangularity δ, with high κ, and low δ leading to shorter sawteeth with smaller crashes. This shape dependence is increased by applying central electron cyclotron heating. The response to additional heating power is determined by the role of ideal or resistive MHD in triggering the sawtooth crash. For plasma shapes where additional heating and consequently, a faster increase of the central pressure shortens the sawteeth, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The observed decrease
Two-fluid turbulence including electron inertia
Energy Technology Data Exchange (ETDEWEB)
Andrés, Nahuel, E-mail: nandres@iafe.uba.ar; Gómez, Daniel [Instituto de Astronomía y Física del Espacio, CC. 67, suc. 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, 1428 Buenos Aires (Argentina); Gonzalez, Carlos; Martin, Luis; Dmitruk, Pablo [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, 1428 Buenos Aires (Argentina)
2014-12-15
We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure, and electron inertia. According to this description, each plasma species introduces a new spatial scale: the ion inertial length λ{sub i} and the electron inertial length λ{sub e}, which are not present in the traditional MHD description. In the present paper, we seek for possible changes in the energy power spectrum in fully developed turbulent regimes, using numerical simulations of the two-fluid equations in two-and-a-half dimensions. We have been able to reproduce different scaling laws in different spectral ranges, as it has been observed in the solar wind for the magnetic energy spectrum. At the smallest wavenumbers where plain MHD is valid, we obtain an inertial range following a Kolmogorov k{sup −5∕3} law. For intermediate wavenumbers such that λ{sub i}{sup −1}≪k≪λ{sub e}{sup −1}, the spectrum is modified to a k{sup −7∕3} power-law, as has also been obtained for Hall-MHD neglecting electron inertia terms. When electron inertia is retained, a new spectral region given by k>λ{sub e}{sup −1} arises. The power spectrum for magnetic energy in this region is given by a k{sup −11∕3} power law. Finally, when the terms of electron inertia are retained, we study the self-consistent electric field. Our results are discussed and compared with those obtained in the solar wind observations and previous simulations.
MHD generator performance analysis for the Advanced Power Train study
Pian, C. C. P.; Hals, F. A.
1984-01-01
Comparative analyses of different MHD power train designs for early commercial MHD power plants were performed for plant sizes of 200, 500, and 1000 MWe. The work was conducted as part of the first phase of a planned three-phase program to formulate an MHD Advanced Power Train development program. This paper presents the results of the MHD generator design and part-load analyses. All of the MHD generator designs were based on burning of coal with oxygen-enriched air preheated to 1200 F. Sensitivities of the MHD generator design performance to variations in power plant size, coal type, oxygen enrichment level, combustor heat loss, channel length, and Mach number were investigated. Basd on these sensitivity analyses, together with the overall plant performance and cost-of-electricity analyses, as well as reliability and maintenance considerations, a recommended MHD generator design was selected for each of the three power plants. The generators for the 200 MWe and 500 MWe power plant sizes are supersonic designs. A subsonic generator design was selected for the 1000 MWe plant. Off-design analyses of part-load operation of the supersonic channel selected for the 200 MWe power plant were also conductd. The results showed that a relatively high overall net plant efficiency can be maintained during part-laod operation with a supersonic generator design.
Energy Technology Data Exchange (ETDEWEB)
None
1979-01-01
Progress is reported on the following tasks: characterization of coal for open-cycle MHD power generation systems; compressive creep and strength studies of MHD preheater materials; preparation of coals for utilization in direct coal-fired MHD generation; characterization of volatile matter in coal; MHD materials evaluation; operability of the Moderate Temperature Slag Flow Facility; slag-seed equilibria and separations related to the MHD system; thermionic emission of coal and electrode materials; MHD instrumentation, consolidated inversion simulator, and data acquisition; combined MHD-steam plant cycle analysis and control; and slag physical properties - electrical and thermal conductivity. (WHK)
International Nuclear Information System (INIS)
Reiman, A.; Monticello, D.; Pomphrey, N.
1993-01-01
The three-dimensional MHD equilibrium equation is a mixed elliptic-hyperbolic partial differential equation. Unlike more familiar equations of this sort, the source term in the elliptic part of the equation is dependent on the time-asymptotic solution of the hyperbolic part, because the pressure and the force-free part of the current are constant along magnetic field lines. The equations for the field line trajectories can be put in the form of Hamilton's equations for a one-dimensional time-dependent system. The authors require an accurate solution for the KAM surfaces of this nonintegrable Hamiltonian. They describe a new algorithm they have developed for this purpose, and discuss its relationship to previously developed algorithms for computing KAM surfaces. They also discuss the numerical issues that arise in self-consistently coupling the output of this algorithm to the elliptic piece of the equation to calculate the magnetic field driven by the current. For nominally axisymmetric devices, they describe how the code is used to directly calculate the saturated state of nonaxisymmetric instabilities by following the equilibrium solution through a bifurcation. They argue that this should be the method of choice for evaluating stability to tearing modes in toroidal magnetic confinement devices
Energy Technology Data Exchange (ETDEWEB)
Bates, J.L.; Marchant, D.D.; Daniel, J.L.
1978-10-01
The objectives of this program are directed toward the development and characterization of high temperature ceramics for open-cycle, coal-fired MHD power generators. The current activities are directed to electrode and insulator materials, and include (1) determination of the effects of alkali seed on the behavior of ceramics in a dc electric field; (2) development and testing of improved high temperature ceramic electrodes and insulators with controlled composition, microstructure, and properties; and (3) characterization and evaluation of materials utilized in channels being tested for MHD power generator development. Research is reported on (1) evaluation of metal electrodes from 250 hour MHD test, (2) characterization and properties of USSR MgO insulating wall material, (3) thermal diffusivity/thermal conductivity of electrode and insulator materials, (4) coprecipitation of ceramic powders, (5) properties of yttria chromites, and (6) rare earth hafnates. (WHK)
Shiraishi, Junya; Miyato, Naoaki; Matsunaga, Go
2016-05-10
It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle's Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas.
Thermal energy creation and transport and X-ray/EUV emission in a thermodynamic MHD CME simulation
Reeves, K.; Mikic, Z.; Torok, T.; Linker, J.; Murphy, N. A.
2017-12-01
We model a CME using the PSI 3D numerical MHD code that includes coronal heating, thermal conduction and radiative cooling in the energy equation. The magnetic flux distribution at 1 Rs is produced by a localized subsurface dipole superimposed on a global dipole field, mimicking the presence of an active region within the global corona. We introduce transverse electric fields near the neutral line in the active region to form a flux rope, then a converging flow is imposed that causes the eruption. We follow the formation and evolution of the current sheet and find that instabilities set in soon after the reconnection commences. We simulate XRT and AIA EUV emission and find that the instabilities manifest as bright features emanating from the reconnection region. We examine the quantities responsible for plasma heating and cooling during the eruption, including thermal conduction, radiation, adiabatic compression and expansion, coronal heating and ohmic heating due to dissipation of currents. We find that the adiabatic compression plays an important role in heating the plasma around the current sheet, especially in the later stages of the eruption when the instabilities are present. Thermal conduction also plays an important role in the transport of thermal energy away from the current sheet region throughout the reconnection process.
Mechanism of power generation - the MHD way
International Nuclear Information System (INIS)
Rangachari, S.; Ramash, V.R.; Subramanian, C.K.
1975-01-01
The basic physical principles of magnetohydrodynamics and the application of this principle for power generation (direct energy conversion) are explained. A magnetohydrodynamic generator (MHDG) is described both in the Faraday and Hall modes. The advantages of the Faraday mode and the Hall mode for different geometries of the generator are mentioned. The conductor used is a fluid - an ionised gas (plasma) or a liquid metal at high temperature. The difficulties in maintaining high temperature and high velocity for the gas and very low temperature at the same time side by side for superconducting magnets to produce a strong magnetic field, are pointed out. The most commonly used gas is purified air. The advantages of MHD generators and the present power crisis have compelled further research in this field in spite of the high costs involved. (A.K.)
MHD simulation of the Bastille day event
Energy Technology Data Exchange (ETDEWEB)
Linker, Jon, E-mail: linkerj@predsci.com; Torok, Tibor; Downs, Cooper; Lionello, Roberto; Titov, Viacheslav; Caplan, Ronald M.; Mikić, Zoran; Riley, Pete [Predictive Science Inc., 9990 Mesa Rim Road, Suite 170, San Diego CA, USA 92121 (United States)
2016-03-25
We describe a time-dependent, thermodynamic, three-dimensional MHD simulation of the July 14, 2000 coronal mass ejection (CME) and flare. The simulation starts with a background corona developed using an MDI-derived magnetic map for the boundary condition. Flux ropes using the modified Titov-Demoulin (TDm) model are used to energize the pre-event active region, which is then destabilized by photospheric flows that cancel flux near the polarity inversion line. More than 10{sup 33} ergs are impulsively released in the simulated eruption, driving a CME at 1500 km/s, close to the observed speed of 1700km/s. The post-flare emission in the simulation is morphologically similar to the observed post-flare loops. The resulting flux rope that propagates to 1 AU is similar in character to the flux rope observed at 1 AU, but the simulated ICME center passes 15° north of Earth.
3-D nonlinear evolution of MHD instabilities
International Nuclear Information System (INIS)
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
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.
On axisymmetric resistive MHD equilibria with flow free of Pfirsch-Schlüter diffusion
Throumoulopoulos, George N.; Tasso, Henri
2002-11-01
The equilibrium of an axisymmetric magnetically confined plasma with anisotropic electrical conductivity and flows parallel to the magnetic field is investigated within the framework of the MHD theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order partial differential equation for the poloidal magnetic flux function along with a Bernoulli equation for the density identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the conductivities σ_allel and σ_⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic conductivity and parallel flows (see [1]) the equilibrium is compatible with non-vanishing poloidal currents. For incompressible flows exact solutions of the above mentioned set of equations can be constructed with σ_allel and σ_⊥ profiles compatible with collisional conductivity profiles, i.e. profiles peaked close to the magnetic axis, vanishing on the boundary and such that σ_allel> σ_⊥. In particular, an exact equilibrium describing a toroidal plasma of arbitrary aspect ratio being contained within a perfectly conducting boundary of rectangular cross-section and peaked toroidal current density profile vanishing on the boundary is further considered. For this equilibrium in the case of vanishing flows the difference σ_allel-σ_⊥ for the reversed field pinch scaling Bp Bt (where Bp and Bt are the poloidal and toroidal magnetic field components) is nearly two times larger than that for the tokamak scaling B_p 0.1 B_t. [1] G. N. Throumoulopoulos, H. Tasso, J. Plasma Physics 64, 601 (2000).
Study of the processes resulting from the use of alkaline seed in natural gas-fired MHD facilities
International Nuclear Information System (INIS)
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 2 CO 3 on the heat exchange surface are also included
Energy Technology Data Exchange (ETDEWEB)
NONE
1980-03-01
Examination was conducted in detail on an MHD generation system by coal combustion, with the results reported. Concerning a gas table calculation program in coal combustion, it was prepared assuming 100% slag removal ratio in the combustor as the primary approximation. A combustor for MHD generation needs to efficiently burn fuel using high temperature pre-heated air as the oxidant, to fully dissociate/electrolytically dissociate seed, and to supply to the generation channel a high speed combustion gas plasma having a high electrical conductivity which is required for MHD generation. This year, an examination was conducted on technological problems in burning coal in an MHD combustor. As for the NOx elimination system in an MHD generation plant, an examination was made if the method studied so far in MHD generation using heavy oil as the fuel is applicable to coal. Also investigated and reviewed were various characteristics, change in physical properties, recovery method, etc., in a mixed state of seed and slag in the case of coal combustion MHD. (NEDO)
Energy Technology Data Exchange (ETDEWEB)
NONE
1969-07-01
Compiled are the results of studies conducted in fiscal 1969 on MHD (magnetohydrodynamic) power generation. In the operation test and modification of the 1,000kW-class MHD power generator, the operation test continues from the preceding fiscal year using high-temperature air as oxidant, and the growth of boundary layer in the channel is determined. In the operation test of the MHD power generator designed for prolonged operation, insulation walls, electrode materials, and structures capable of prolonged operation are developed and tested. In the research of MHD power generator heat exchangers, studies are made about the bulkhead type and heat accumulator types (stationary type, rotary type, and falling-grain type). In addition, studies are conducted about seed collecting methods, MHD power generator electrode materials, heat-resisting insulators, and thermal performance rating. In the research and development of superconductive electromagnets, studies are conducted about superconductive electromagnets for 1kW MHD power generators, ferromagnetic superconductive electromagnets for 1,000kW-class MHD power generators, 45-kilogauss col type superconductive electromagnets, turbine type helium liquefier, high current density col type superconductive electromagnets, superinsulated magnetic field generators, etc. (NEDO)
MHD stability limits in the TCV Tokamak
Energy Technology Data Exchange (ETDEWEB)
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
Magnetohydrodynamic (MHD) instabilities can limit the performance and degrade the confinement of tokamak plasmas. The Tokamak a Configuration Variable (TCV), unique for its capability to produce a variety of poloidal plasma shapes, has been used to analyse various instabilities and compare their behaviour with theoretical predictions. These instabilities are perturbations of the magnetic field, which usually extend to the plasma edge where they can be detected with magnetic pick-up coils as magnetic fluctuations. A spatially dense set of magnetic probes, installed inside the TCV vacuum vessel, allows for a fast observation of these fluctuations. The structure and temporal evolution of coherent modes is extracted using several numerical methods. In addition to the setup of the magnetic diagnostic and the implementation of analysis methods, the subject matter of this thesis focuses on four instabilities, which impose local and global stability limits. All of these instabilities are relevant for the operation of a fusion reactor and a profound understanding of their behaviour is required in order to optimise the performance of such a reactor. Sawteeth, which are central relaxation oscillations common to most standard tokamak scenarios, have a significant effect on central plasma parameters. In TCV, systematic scans of the plasma shape have revealed a strong dependence of their behaviour on elongation {kappa} and triangularity {delta}, with high {kappa}, and low {delta} leading to shorter sawteeth with smaller crashes. This shape dependence is increased by applying central electron cyclotron heating. The response to additional heating power is determined by the role of ideal or resistive MHD in triggering the sawtooth crash. For plasma shapes where additional heating and consequently, a faster increase of the central pressure shortens the sawteeth, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The
Flow Reversal of Fully-Developed Mixed MHD Convection in Vertical Channels
International Nuclear Information System (INIS)
Saleh, H.; Hashim, I.
2010-01-01
The present analysis is concerned with flow reversal phenomena of the fully-developed laminar combined free and forced MHD convection in a vertical parallel-plate channel. The effect of viscous dissipation is taken into account. Flow reversal adjacent to the cold (or hot) wall is found to exist within the channel as Gr/Re is above (or below) a threshold value. Parameter zones for the occurrence of reversed flow are presented. (fundamental areas of phenomenology(including applications))
Influence of hot beam ions on MHD ballooning modes in tokamaks
International Nuclear Information System (INIS)
Rewoldt, G.; Tang, W.M.
1984-01-01
It has recently been proposed that the presence of high-energy ions from neutral-beam injection can have a strong stabilizing effect on kinetically modified ideal-MHD ballooning modes in tokamaks. To assess realistically the importance of such effects, a comprehensive kinetic stability analysis, which takes into account the integral equation nature of the basic problem, has been applied to this investigation. In the collisionless limit, the effect of adding small fractions of hot beam ions is indeed found to be strongly stabilizing. On the other hand, for somewhat larger fractions of hot ions, a different, beam-driven root of the mode equations is found to occur with a growth rate comparable in magnitude to the growth rate of the usual MHD ballooning mode in the absence of hot ions. This implies that there should be an optimal density of hot particles which minimizes the strength of the relevant instabilities. Employing non-Maxwellian equilibrium distribution functions to model the beam species makes a quantitative, but not qualitative, difference in the results. Adding collisions to the calculation tends to reduce considerably the stabilizing effect of the hot ions. (author)
Influence of the solar wind and IMF on Jupiter's magnetosphere: Results from global MHD simulations
Sarkango, Y.; Jia, X.; Toth, G.; Hansen, K. C.
2017-12-01
Due to its large size, rapid rotation and presence of substantial internal plasma sources, Jupiter's magnetosphere is fundamentally different from that of the Earth. How and to what extent do the external factors, such as the solar wind and interplanetary magnetic field (IMF), influence the internally-driven magnetosphere is an open question. In this work, we solve the 3D semi-relativistic magnetohydrodynamic (MHD) equations using a well-established code, BATSRUS, to model the Jovian magnetosphere and study its interaction with the solar wind. Our global model adopts a non-uniform mesh covering the region from 200 RJ upstream to 1800 RJ downstream with the inner boundary placed at a radial distance of 2.5 RJ. The Io plasma torus centered around 6 RJ is generated in our model through appropriate mass-loading terms added to the set of MHD equations. We perform systematic numerical experiments in which we vary the upstream solar wind properties to investigate the impact of solar wind events, such as interplanetary shock and IMF rotation, on the global magnetosphere. From our simulations, we extract the location of the magnetopause boundary, the bow shock and the open-closed field line boundary (OCB), and determine their dependence on the solar wind properties and the IMF orientation. For validation, we compare our simulation results, such as density, temperature and magnetic field, to published empirical models based on in-situ measurements.
Energy Technology Data Exchange (ETDEWEB)
Vlaykov, Dimitar G., E-mail: Dimitar.Vlaykov@ds.mpg.de [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, D-37077 Göttingen (Germany); Grete, Philipp [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany); Schmidt, Wolfram [Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029 Hamburg (Germany); Schleicher, Dominik R. G. [Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C (Chile)
2016-06-15
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However, the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator [W. K. Yeo (CUP, 1993)] and require no assumptions about the nature of the flow or magnetic field. Thus, the scope of their applicability ranges from the sub- to the hyper-sonic and -Alfvénic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular, the anisotropy of the flow. Their properties are a priori validated in Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.
Energy Technology Data Exchange (ETDEWEB)
NONE
1990-07-01
Experimental disk MHD facilities are predesigned, and commercial-scale (1,000 MWt) MHD/steam systems are investigated. The predesigns of the disk MHD facilities indicate that enthalpy extraction is 8.7% for a 10 MWt open cycle MHD generator, and increases to 37% for a 5 MWt closed cycle MHD generator. Commercial (1,000 MWt) MHD/steam systems are studied for 4 types. Of these types, the open cycle disk MHD generator shows the lowest efficiency of 42.8%, while the closed cycle disk MHD generator the highest efficiency of 50.0%. The open cycle linear generator, although showing an efficiency of 49.4%, may be the lowest-cost type, when the necessary heat source, heat exchangers and the like are taken into consideration. For the design of superconducting magnet, it is necessary to further investigate whether the one for the test facility is applicable to the commercial systems. (NEDO)
Conversion software for ANSYS APDL 2 FLUENT MHD magnetic file
International Nuclear Information System (INIS)
Ghita, G.; Ionescu, S.; Prisecaru, I.
2016-01-01
The present paper describes the improvements made to the conversion software for ANSYS APDL 2 FLUENT MHD Magnetic File which is able to extract the data from ANSYS APDL file and write down a file containing the magnetic field data in FLUENT magneto hydro dynamics (MHD) format. The MHD module has some features for the uniform and non uniform magnetic field but it is limited for sinusoidal or pulsed, square wave, having a fixed duty cycle of 50%. The present software, ANSYS APDL 2 FLUENT MHD Magnetic File, suffered major modifications in comparison with the last one. The most important improvement consists in a new graphical interface, which has 3D graphical interface for the input file but also for the output file. Another improvement has been made for processing time, the new version is two times faster comparing with the old one. (authors)
Numerical Simulation of 3D Viscous MHD Flows
National Research Council Canada - National Science Library
Golovachov, Yurii P; Kurakin, Yurii A; Schmidt, Alexander A; Van Wie, David M
2003-01-01
.... Flows in hypersonic intakes are considered. Preliminary results showed that local MHD interaction in the inlet part of the intake model was the most effective for control over plasma flow field...
Diagnostic development and support of MHD (magnetohydrodynamics) test facilities
Energy Technology Data Exchange (ETDEWEB)
1989-07-01
Mississippi State University (MSU) is developing diagnostic instruments for Magnetohydrodynamics (MHD) power train data acquisition and for support of MHD component development test facilities. Microprocessor-controlled optical instruments, initially developed for HRSR support, are being refined, and new systems to measure temperatures and gas-seed-slag stream characteristics are being developed. To further data acquisition and analysis capabilities, the diagnostic systems are being interfaced with MHD Energy Center computers. Technical support for the diagnostic needs of the national MHD research effort is being provided. MSU personnel will also cooperate with government agencies and private industries to improve the transformation of research and development results into processes, products and services applicable to their needs.
Unsteady MHD free convective flow past a vertical porous plate ...
African Journals Online (AJOL)
user
International Journal of Engineering, Science and Technology .... dimensional MHD boundary layer on the body with time varying temperature. ... flow of an electrically conducting fluid past an infinite vertical porous flat plate coinciding with.
Generalized similarity method in unsteady two-dimensional MHD ...
African Journals Online (AJOL)
user
International Journal of Engineering, Science and Technology. Vol. 1, No. 1, 2009 ... temperature two-dimensional MHD laminar boundary layer of incompressible fluid. ...... Φ η is Blasius solution for stationary boundary layer on the plate,. ( ). 0.
Combined effects of radiation and chemical reaction on MHD flow ...
African Journals Online (AJOL)
(2016) have studied unsteady MHD flow in porous media over exponentially accelerated plate ... boundary layer flow of heat and mass transfer over a moving vertical plate with suction. ... flow considering free convection over a porous plate.
International Nuclear Information System (INIS)
Charlton, L.A.; Carreras, B.A.; Holmes, J.A.; Lynch, V.E.
1988-01-01
The linear stability and nonlinear evolution of the resistive m = 1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta
FLIP-MHD: A particle-in-cell mehtod for magnetohydrodynamics
International Nuclear Information System (INIS)
Brackbill, J.U.
1990-01-01
A particle-in-cell (PIC) method, FLIP is extended to magnetohydrodynamic (MHD) flow in two dimensions. Particles are used to reduce computational diffusion of the magnetic field. FLIP is an extension of ''classical'' PIC, where particles have mass, but every other property of the fluid is stored on a grid. In FLIP, particles have every property of the fluid, so that they provide a complete Lagrangian description not only to resolve contact discontinuities but also to reduce computational diffusion of linear and angular momentum. The interactions among the particles are calculated on a grid, for convenience and economy. The present study extends FLIP to MHD, by including information about the magnetic field among the attributes of the particles. 6 refs
A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG
Griffiths, M. K.; Fedun, V.; Erdélyi, R.
2015-03-01
Parallelization techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs), possessing hundreds of processor cores. The opportunity has been recognized by the computational sciences and engineering communities, who have recently harnessed successfully the numerical performance of GPUs. For example, parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Here, we describe the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1-3D MHD code capable of modelling magnetized and gravitationally stratified plasma. The objective of this paper is to present the numerical methods and techniques used for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the performance benchmarks and validation results demonstrating that the code successfully simulates the physics for a range of test scenarios including a full 3D realistic model of wave propagation in the solar atmosphere.
Neoclassical viscous stress tensor for non-linear MHD simulations with XTOR-2F
International Nuclear Information System (INIS)
Mellet, N.; Maget, P.; Meshcheriakov, D.; Lütjens, H.
2013-01-01
The neoclassical viscous stress tensor is implemented in the non-linear MHD code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), allowing consistent bi-fluid simulations of MHD modes, including the metastable branch of neoclassical tearing modes (NTMs) (Carrera et al 1986 Phys. Fluids 29 899–902). Equilibrium flows and bootstrap current from the neoclassical theory are formally recovered in this Chew–Goldberger–Low formulation. The non-linear behaviour of the new model is verified on a test case coming from a Tore Supra non-inductive discharge. A NTM threshold that is larger than with the previous model is obtained. This is due to the fact that the velocity is now part of the bootstrap current and that it differs from the theoretical neoclassical value. (paper)
Influence of MHD effects and edge conditions on ITER helium ash accumulation and sustained ignition
International Nuclear Information System (INIS)
Redi, M.H.; Cohen, S.A.
1990-06-01
Dilution of reacting species by build-up of helium ash and its effect on ignition in the ITER tokamak have been studies in a series of simulations with the one-dimensional BALDUR transport code. Thermal diffusivities, obtained from ITER scaling laws and with radial variations observed in JET, gave τ E ∼ 2--4 sec. Refueling of deuterium and tritium maintained constant electron density, while carbon recycling was 100% and the helium ash recycling was varied from 1.0 to 0.5. Including MHD effects, specifically sawteeth and beta limits, we find that ignition can be sustained for 200 seconds with R helium = 0.95. These simulations, the only non-zero-dimensional, time-dependent simulations thus far made for ITER plasmas, emphasize that edge plasma conditions, MHD behavior, and helium particle transport are critical synergistic issues for sustained ignition. 27 refs., 2 figs., 1 tab
MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts
International Nuclear Information System (INIS)
Sidorenkov, S.I.; Hua, T.Q.; Araseki, H.
1994-01-01
Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. Argonne National Laboratory and The Efremov Institute have jointly defined several benchmark problems for code validation. The problems, described in this paper, are based on two series of rectangular duct experiments conducted at ANL; one of the series is a joint ANL/Efremov experiment. The geometries consist of variation of aspect ratio and wall thickness (thus wall conductance ratio). The transverse magnetic fields are uniform and nonuniform in the axial direction
Observation of SOL Current Correlated with MHD Activity in NBI-heated DIII-D Tokamak Discharges
International Nuclear Information System (INIS)
Takahashi, H.; Fredrickson, E.D.; Schaffer, M.J.; Austin, M.E.; Evans, T.E.; Lao, L.L.; Watkins, J.G.
2004-01-01
This work investigates the potential roles played by the scrape-off-layer current (SOLC) in MHD activity of tokamak plasmas, including effects on stability. SOLCs are found during MHD activity that are: (1) slowly growing after a mode-locking-like event, (2) oscillating in the several kHz range and phase-locked with magnetic and electron temperature oscillations, (3) rapidly growing with a sub-ms time scale during a thermal collapse and a current quench, and (4) spiky in temporal behavior and correlated with spiky features in Da signals commonly identified with the edge localized mode (ELM). These SOLCs are found to be an integral part of the MHD activity, with a propensity to flow in a toroidally non-axisymmetric pattern and with magnitude potentially large enough to play a role in the MHD stability. Candidate mechanisms that can drive these SOLCs are identified: (a) toroidally non-axisymmetric thermoelectric potential, (b) electromotive force (EMF) from MHD activity, and (c) flux swing, both toroidal and poloidal, of the plasma column. An effect is found, stemming from the shear in the field line pitch angle, that mitigates the efficacy of a toroidally non-axisymmetric SOLC to generate a toroidally non-axisymmetric error field. Other potential magnetic consequences of the SOLC are identified: (i) its error field can introduce complications in feedback control schemes for stabilizing MHD activity and (ii) its toroidally non-axisymmetric field can be falsely identified as an axisymmetric field by the tokamak control logic and in equilibrium reconstruction. The radial profile of a SOLC observed during a quiescent discharge period is determined, and found to possess polarity reversals as a function of radial distance
Electrode materials for an open-cycle MHD generator channel
International Nuclear Information System (INIS)
Telegin, G.P.; Romanov, A.I.; Akopov, F.A.; Gokhshtejn, Ya.P.; Rekov, A.I.
1983-01-01
The results of investigations, technological developments and tests of high temperature materials for MHD electrodes on the base of zirconium dioxide, stabilized with oxides of calcium, yttrium, neodymium, and dioxide of cerium, chromites, tamping masses from stabilized dioxide of zirconium, cermets are considered. It is established that binary and ternary solutions on the base of zirconium dioxide and alloyed chromites are the perspective materials for the MHD electrodes on pure fuel
Relativistic modeling capabilities in PERSEUS extended MHD simulation code for HED plasmas
Energy Technology Data Exchange (ETDEWEB)
Hamlin, Nathaniel D., E-mail: nh322@cornell.edu [438 Rhodes Hall, Cornell University, Ithaca, NY, 14853 (United States); Seyler, Charles E., E-mail: ces7@cornell.edu [Cornell University, Ithaca, NY, 14853 (United States)
2014-12-15
We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest hybrid X-pinch simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as X-pinches and laser-plasma interactions. By suitable formulation of the relativistic generalized Ohm’s law as an evolution equation, we have reduced the recovery of primitive variables, a major technical challenge in relativistic codes, to a straightforward algebraic computation. Our code recovers expected results in the non-relativistic limit, and reveals new physics in the modeling of electron beam acceleration following an X-pinch. Through the use of a relaxation scheme, relativistic PERSEUS is able to handle nine orders of magnitude in density variation, making it the first fluid code, to our knowledge, that can simulate relativistic HED plasmas.
Reminimization of energy integral and stability limit for non-ideal MHD (magnetohydrodynamic) plasma
International Nuclear Information System (INIS)
Kondoh, Y.
1988-03-01
The stability condition of relaxed states is derived from the energy principle for the non-ideal MHD plasma. An Euler equation for the reminimization of energy integral is derived and shown to give the marginal stable, non-singular perturbations for the stability condition. An extended stability limit for the β = 0 relaxed states is derived from the stability condition, with use of the eigenvalue analysis for the Euler equation. By using the perturbation method, the extended stability limit is solved in the 1st order approximation to explain the deviation of the experimental stability limit from the idealized stability limit by Taylor. A procedure to get overall stability limit against both the non-singular and the singular perturbations is discussed. 25 refs
MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect
Zokri, S. M.; Arifin, N. S.; Salleh, M. Z.; Kasim, A. R. M.; Mohammad, N. F.; Yusoff, W. N. S. W.
2017-09-01
This study investigates the influence of viscous dissipation on magnetohydrodynamic (MHD) flow of Jeffrey nanofluid over a stretching sheet with convective boundary conditions. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by utilizing the similarity transformation variables. The Runge-Kutta Fehlberg method is used to solve the problem numerically. The numerical solutions obtained are presented graphically for several dimensionless parameters such as Brownian motion, Lewis number and Eckert number on the specified temperature and concentration profiles. It is noted that the temperature profile is accelerated due to increasing values of Brownian motion parameter and Eckert number. In contrast, both the Brownian motion parameter and Lewis number have caused the deceleration in the concentration profiles.
A hybrid LLR-MHD model of kink perturbations in EXTRAP
International Nuclear Information System (INIS)
Lehnert, B.
1987-07-01
In high-beta systems, such as Extrap and other Z-pinch configurations, kinetic large Larmor radius (LLR) phenomena introduce strong phase-mixing and dispersive effects and a corresponding 'kinetic damping' which cannot be treated in terms of MHD theory. In this paper a first attempt is made to include these effects by proposing a hybrid LLR-MHD model in which the kinetic phenomena enter as constraints on the possible forms of the plasma perturbations. The latter then become restricted to a limited class which can be treated in terms of MHD theory. The present model does not claim to produce stability conditions which are exact in all details, but should merely provide a picture of the general relationship between the basic plasma parameters in a state of marginal stability. For kink perturbations in Extrap stability relations have thus been obtained between the pinch and conductor currents, the pinch radius and the axial conductor distance, and the number of contained ion Larmor radii. These relations appear to be consistent with so far obtained experimental data. A short discussion on the effects of a superimposed axial magnetic field has been included. At this stage only experiments can verify whether or not the present simple model becomes relevant to Extrap stability. (author)
Ideal MHD stability and characteristics of edge localized modes on CFETR
Li, Ze-Yu; Chan, V. S.; Zhu, Yi-Ren; Jian, Xiang; Chen, Jia-Le; Cheng, Shi-Kui; Zhu, Ping; Xu, Xue-Qiao; Xia, Tian-Yang; Li, Guo-Qiang; Lao, L. L.; Snyder, P. B.; Wang, Xiao-Gang; the CFETR Physics Team
2018-01-01
Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for the China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario (R = 5.7 m, B T = 5 T) derived from multi-code integrated modeling, with key parameters {{β }N},{{β }T},{{β }p} varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for the engineering design. The long wavelength low-n global ideal MHD stability of the CFETR baseline scenario, including the wall stabilization effect, is evaluated by GATO. It is found that the low-n core modes are stable with a wall at r/a = 1.2. An investigation of intermediate wavelength ideal MHD modes (peeling ballooning modes) is also carried out by multi-code benchmarking, including GATO, ELITE, BOUT++ and NIMROD. A good agreement is achieved in predicting edge-localized instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT++. A mix of grassy and type I ELMs is identified. When the size and magnetic field of CFETR are increased (R = 6.6 m, B T = 6 T), collisionality correspondingly increases and the instability is expected to shift to grassy ELMs.
International Nuclear Information System (INIS)
Hayat, Tasawar; Imtiaz, Maria; Alsaedi, Ahmed; Almezal, Saleh
2016-01-01
This paper investigates the steady two-dimensional magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid over a stretching surface with homogeneous–heterogeneous reactions. Characteristics of relaxation time for heat flux are captured by employing new heat flux model proposed by Christov. A system of ordinary differential equations is obtained by using suitable transformations. Convergent series solutions are derived. Impacts of various pertinent parameters on the velocity, temperature and concentration are discussed. Analysis of the obtained results shows that fluid relaxation and retardation time constants have reverse behavior on the velocity and concentration fields. Also temperature distribution decreases for larger values of thermal relaxation time. - Highlights: • Cattaneo–Christov heat flux model is used to study the MHD flow of an Oldroyd-B fluid. • Velocity is decreasing function of Hartman number. • Increasing values of the strengths of homogeneous and heterogeneous reaction parameters decrease the wall concentration.
Present state of research and development of MHD power generation
International Nuclear Information System (INIS)
Ikeda, Shigeru
1978-01-01
MHD power generation can obtain electric energy directly from the heat energy of high speed plasma flow, and the power generating plant of 1 million kW can be realized by this method. When the MHD power generation method is combined before conventional thermal power generation method, the thermal efficiency can be raised to about 60% as compared with 38% in thermal power generation plants. The research and development of MHD power generation are in progress in USA and USSR. The research and development in Japan are in the second stage now after the first stage project for 10 years, and the Mark 7 generator with 100 kW electric output for 200 hr continuous operation is under construction. The MHD power generation is divided into three types according to the conductive fluids used, namely combustion type for thermal power generation, unequilibrated type and liquid metal type for nuclear power generation. The principle of MHD power generation and the constitution of the plant are explained. In Japan, the Mark 2 generator generated 1,180 kW for 1 min in 1971, and the Mark 3 generator generated 1.9 kW continuously for 110 hr in 1967. The MHD generator with superconducting magnet succeeded in 1969 to generate 25 kW for 6 min. The second stage project aimes at collecting design data and obtaining operational experience for the construction of 10 MW class pilot plant, and the Mark 7 and 8 generators are planned. (Kako, I.)
Partial differential equations and their applications
International Nuclear Information System (INIS)
Gauthier-Villars
1998-01-01
This book is dedicated to the French mathematician J.L.Lions. It represents a compilation of articles from about 80 authors. The topics treated are diverse but the more or less commune matter is the study of the characteristics of some partial differential equations. Stability, optimal approximation, numerical resolution, particular applications are among the subjects reviewed. An article deals with the MHD stability of fusion plasmas in tokamaks, another presents the scientific and technical challenges of nuclear energy in France. The latter that contains no equations can be considered as an enjoyable break in a sea of about 40 mathematical articles. (A.C.)
Regularity criteria for the 3D magneto-micropolar fluid equations via ...
Indian Academy of Sciences (India)
We consider sufficient conditions to ensure the smoothness of solutions to 3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier–Stokes and MHD equations.
Directory of Open Access Journals (Sweden)
WU Renchao
2016-06-01
Full Text Available In this paper, we consider three dimensional compressible viscous magnetohydro dynamic equations(MHD with external potentialforce. We first derive the corresponding non-constantstationary solutions. Then we show global well-posedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that rescribed initial data is close to the stationary solution.
Energy Technology Data Exchange (ETDEWEB)
Finan, C.H. III
1980-12-01
Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are solved simultaneously to avoid syncronization errors.
CAFE: A NEW RELATIVISTIC MHD CODE
Energy Technology Data Exchange (ETDEWEB)
Lora-Clavijo, F. D.; Cruz-Osorio, A. [Instituto de Astronomía, Universidad Nacional Autónoma de México, AP 70-264, Distrito Federal 04510, México (Mexico); Guzmán, F. S., E-mail: fdlora@astro.unam.mx, E-mail: aosorio@astro.unam.mx, E-mail: guzman@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo. Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán, México (Mexico)
2015-06-22
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin–Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin–Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Electromagnetic properties of a modular MHD thruster
Kom, C. H.; Brunet, Y.
1999-04-01
The magnetic field of an annular MHD thruster made of independent superconducting modules has been studied with analytical and numerical methods. This configuration allows to obtain large magnetized volumes and high induction levels with rapidly decreasing stray fields. When some inductors are out of order, the thruster remains still operational, but the stray fields increase in the vicinity of the failure. For given structural materials and superconductors, it is possible to determine the size of the conductor in order to reduce the electromagnetic forces and the peak field supported by the conductors. For an active field of 10 T in a 6 m ray annular active channel of a thruster with 24 modules, the peak field is exactly 15.6 T in the Nb3Sn conductors and the structure has to sustain 10^8 N/m forces. The necessity to place some magnetic or superconducting shield is discussed, particularly when the thruster is in a degraded regime. Nous présentons une étude analytique et numérique du champ magnétique d'un propulseur MHD naval annulaire, constitué de secteurs inducteurs supraconducteurs. Cette configuration nécessite des champs magnétiques élevés dans des volumes importants, et permet une décroissance rapide des champs de fuite. Lorsque quelques inducteurs sont en panne, le propulseur reste toujours opérationnel, mais les champs de fuite sont importants aux environs des modules hors service. Étant donné un matériau supraconducteur, il est possible de déterminer la forme des inducteurs dans le but de réduire à la fois les forces électromagnétiques et le surchamp supporté par le bobinage. Pour un propulseur annulaire constitué de 24 modules inducteurs, et un champ actif de 10 T au centre de la partie active du canal (r = 6 m) on obtient avec du Nb3Sn un champ maximun sur le conducteur de 15,5 T et la structure supporte une force de 10^8 N/m. De plus, la nécessité de placer des écrans magnétique ou supraconducteur en régime dégradé (mise
Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions
International Nuclear Information System (INIS)
Lin, Hongxia; Du, Lili
2013-01-01
In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations. (paper)
Energy Technology Data Exchange (ETDEWEB)
NONE
1981-03-01
'Research on MHD generation system' was implemented by its expert committee in the electric joint study group, with the results of fiscal 1980 reported. This year, a detailed conceptual design was carried out on a coal fired MHD generation system, with points for the technological development concretely examined. In addition, investigation was conducted on the progress of MHD generation technology, development situation of other generation systems, state of energy resources, etc., in various foreign countries. In the conceptual design of the coal fired MHD generation plant, the system structure of a 2,000 MWt class commercial MHD generation plant was explained, as were the conceptual design of the structural elements and proposals for a 500 MWt class demonstration plant and an 100 MWt class experimental plant, for example. In the overseas trend of R and D on MHD generation, investigations were made concerning the U.S., Soviet Union, and China, with details compiled for such items as generation plants, combustors, generation channels, heat resisting materials, superconducting magnets, heat exchangers, seed slags, inverters, boilers and environments, and commercial plants. (NEDO)
NON-IDEAL MHD EFFECTS AND MAGNETIC BRAKING CATASTROPHE IN PROTOSTELLAR DISK FORMATION
International Nuclear Information System (INIS)
Li Zhiyun; Krasnopolsky, Ruben; Shang Hsien
2011-01-01
Dense, star-forming cores of molecular clouds are observed to be significantly magnetized. A realistic magnetic field of moderate strength has been shown to suppress, through catastrophic magnetic braking, the formation of a rotationally supported disk (RSD) during the protostellar accretion phase of low-mass star formation in the ideal MHD limit. We address, through two-dimensional (axisymmetric) simulations, the question of whether realistic levels of non-ideal effects, computed with a simplified chemical network including dust grains, can weaken the magnetic braking enough to enable an RSD to form. We find that ambipolar diffusion (AD), the dominant non-ideal MHD effect over most of the density range relevant to disk formation, does not enable disk formation, at least in two dimensions. The reason is that AD allows the magnetic flux that would be dragged into the central stellar object in the ideal MHD limit to pile up instead in a small circumstellar region, where the magnetic field strength (and thus the braking efficiency) is greatly enhanced. We also find that, on the scale of tens of AU or more, a realistic level of Ohmic dissipation does not weaken the magnetic braking enough for an RSD to form, either by itself or in combination with AD. The Hall effect, the least explored of these three non-ideal MHD effects, can spin up the material close to the central object to a significant, supersonic rotation speed, even when the core is initially non-rotating, although the spun-up material remains too sub-Keplerian to form an RSD. The problem of catastrophic magnetic braking that prevents disk formation in dense cores magnetized to realistic levels remains unresolved. Possible resolutions of this problem are discussed.
Heat transfer enhancement of free surface MHD-flow by a protrusion wall
International Nuclear Information System (INIS)
Hulin Huang; Bo Li
2010-01-01
Due to the magnetohydrodynamic (MHD) effect on the flow, which degrades heat transfer coefficients by pulsation suppression of external magnetic field on the flow, a hemispherical protrusion wall is applied to free surface MHD-flow system as a heat transfer enhancement, because the hemispherical protrusion wall has some excellent characteristics including high heat transfer coefficients, low friction factors and high overall thermal performances. So, the characteristics of the fluid flow and heat transfer of the free surface MHD-flow with hemispherical protrusion wall are simulated numerically and the influence of some parameters, such as protrusion height δ/D, and Hartmann number, are also discussed in this paper. It is found that, in the range of Hartmann number 30 ≤ Ha ≤ 70, the protrusion wall assemblies can achieve heat transfer enhancements (Nu/Nu 0 ) of about 1.3-2.3 relative to the smooth channel, while the friction loss (f/f 0 ) increases by about 1.34-1.45. Thus, the high Nusselt number can be obtained when the protrusion wall with a radically lower friction loss increase, which may help get much higher overall thermal performances.
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
Energy Technology Data Exchange (ETDEWEB)
Ramakanth Munipalli; P.-Y.Huang; C.Chandler; C.Rowell; M.-J.Ni; N.Morley; S.Smolentsev; M.Abdou
2008-06-05
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as “canonical”,) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
New Developments in Modeling MHD Systems on High Performance Computing Architectures
Germaschewski, K.; Raeder, J.; Larson, D. J.; Bhattacharjee, A.
2009-04-01
Modeling the wide range of time and length scales present even in fluid models of plasmas like MHD and X-MHD (Extended MHD including two fluid effects like Hall term, electron inertia, electron pressure gradient) is challenging even on state-of-the-art supercomputers. In the last years, HPC capacity has continued to grow exponentially, but at the expense of making the computer systems more and more difficult to program in order to get maximum performance. In this paper, we will present a new approach to managing the complexity caused by the need to write efficient codes: Separating the numerical description of the problem, in our case a discretized right hand side (r.h.s.), from the actual implementation of efficiently evaluating it. An automatic code generator is used to describe the r.h.s. in a quasi-symbolic form while leaving the translation into efficient and parallelized code to a computer program itself. We implemented this approach for OpenGGCM (Open General Geospace Circulation Model), a model of the Earth's magnetosphere, which was accelerated by a factor of three on regular x86 architecture and a factor of 25 on the Cell BE architecture (commonly known for its deployment in Sony's PlayStation 3).
Some effects of MHD activity on impurity transport in the PBX tokamak
International Nuclear Information System (INIS)
Ida, K.; Fonck, R.J.; Hulse, R.A.; LeBlanc, B.
1985-10-01
The effects of MHD activity on intrinsic impurity transport are studied in ohmic discharges of the Princeton Beta Experiment (PBX) by measuring of the Z/sub eff/ profile from visible bremsstrahlung radiation and the spectral line intensities from ultraviolet spectroscopy. A diffusive/convective transport model, including an internal disruption model, is used to simulate the data. The Z/sub eff/ profile with no MHD activity is fitted with a strong inward convection, characterized by a peaking parameter c/sub v/ (= -a 2 v/2rD) = 11 (3.5, +4.5). At the onset of MHD activity (a large m = 1 n = 1 oscillation followed by sawteeth), this strongly peaked profile is flattened and subsequently reaches a new quasi-equilibrium shape. This profile is characterized by reduced convection [c/sub v/ = 3.6 (-1.1, +1.6), D = 1.4 (-0.7, +5.6) x 10 4 cm 2 /s], in addition to the particle redistribution which accompanies the sawtooth internal disruptions. 10 figs
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
International Nuclear Information System (INIS)
Munipalli, Ramakanth; Huang, P.-Y.; Chandler, C.; Rowell, C.; Ni, M.-J.; Morley, N.; Smolentsev, S.; Abdou, M.
2008-01-01
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as 'canonical',) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
Energy Technology Data Exchange (ETDEWEB)
Boulbe, C
2007-10-15
Interaction between a plasma and a magnetic field appears and has an important role in various domains such as thermonuclear fusion by magnetic confinement or astrophysical plasmas for example. In evolution, these interactions are described by the equations of magnetohydrodynamics (MHD). At equilibrium, the MHD equations result in the magnetostatic equations involving the magnetic field and the kinetic pressure of the plasma. The magnetostatic equations form a system of 3-dimensional non linear partial differential equations involving a magnetic field and a kinetic plasma pressure. When the pressure is supposed negligible, the magnetic field is known as Beltrami field. In a first time, we propose to solve numerically the Beltrami field problem using a fixed point iterative algorithm associated with finite element methods. This iterative strategy is extended in a second time to the computation of magnetostatic configurations with pressure. In the sequel, we interest in the approximation of ideal MHD equations. This system forms a nonlinear hyperbolic conservation law. We propose to use a finite volume approach, in which fluxes are calculated by a Roe's method on a tetrahedral mesh. Fluxes of the magnetic field are modified in order to satisfy the constraint of divergence free imposed on it. The proposed methods have been implemented in two new 3-dimensional codes called TETRAFFF for equilibrium, and TETRAMHD for MHD. The obtained numerical results confirm the high performance of these methods. (author)
The structure of ideal MHD Alfven modes
International Nuclear Information System (INIS)
Turnbull, A.D.; Chu, M.S.; Lao, L.L.; Greene, J.M.; Strait, E.J.; Chance, M.S.
1991-01-01
Continuum Alfven modes have undergone a resurgence in interest with the recent realization that so-called Toroidicity-Induced Alfven Eigenmodes (TAE modes) can be destabilized either by energetic beam ions in a strongly heated plasma or by alpha particles in a burning plasma. The GATO Ideal MHD Stability code, which minimizes the potential energy according to a variational formulation, has now been modified to isolate and calculate stable continuum eigenmodes. The existence of the TAE mode and its associated gap has been verified, using this code, for a circular cross-section, finite aspect ratio equilibrium. Moreover, the eigenfrequencies and eigenmodes obtained from this variational calculation are found to be in extremely good quantitative agreement with those obtained from the non-variational NOVA code. A systematic survey of the stable continuum has further revealed a surprising diversity in the structure of the continuum Alfven modes; the logarithmic singularity can be so broad, in some cases, as to occupy the whole cross-section. This has important implications for heating experiments which aim to locally excite the plasma by rf waves in the Alfven frequency range. The structure of several representative examples is discussed. The Alfven continuum, in general, and the TAE mode and its associated gap, in particular, are also found to be strongly modified by cross-sectional shaping. The dependence of the spectrum on various shaping factors is explored
Perturbed solutions of fixed boundary MHD equilibria
International Nuclear Information System (INIS)
Portone, A.
2004-01-01
In this study, the fixed boundary plasma MHD equilibrium problem is solved by the finite element method; then, by perturbing the flux at the plasma boundary nodes, linear formulae are derived linking the variation of several plasma parameters of interest to the variation of the currents flowing in the external circuits. On the basis of these formulae it is shown how it is possible to efficiently solve two central problems in plasma engineering, namely (1) the optimization of the currents in a given set of coils necessary to maintain a specified equilibrium configuration and (2) the derivation of a linear dynamic model describing the plasma axisymmetric displacement (n = 0 mode) about a given magnetic configuration. A case study-based on the ITER reference equilibrium magnetic configuration at burn-is analysed both in terms of equilibrium currents optimality as well as axisymmetric stability features. The results obtained by these formulae are also compared with the predictions of a non-linear free boundary code and of a linear, dynamic model. As shown, the formulae derived here are in good agreement with such predictions, confirming the validity of the present approach. (author)
On the hierarchy of partially invariant submodels of differential equations
Energy Technology Data Exchange (ETDEWEB)
Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru
2008-07-04
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V.
2008-07-01
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
On the hierarchy of partially invariant submodels of differential equations
International Nuclear Information System (INIS)
Golovin, Sergey V
2008-01-01
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given
Performance of MHD coatings in flowing Li at 700 deg
International Nuclear Information System (INIS)
Pint, B.; Pawel, S.J.; Howell, M.; Moser, J.L.; Garner, G.W.; Santella, M.L.; Tortorelli, P.F.; Di Stefano, J.R.
2007-01-01
Full text of publication follows: A thermal convection loop was constructed from V-4Cr-4Ti tubing and operated in vacuum at a maximum Li temperature of 700 deg. C for ∼1000 h.. Due to slow Li flow (∼1 cm/s) in the loop, the temperature gradient was ∼340 deg. C. Specimens in the hot and cold legs of the loop included V-4Cr-4Ti spacers, tensile specimens (SS-3 type) and coupons coated by physical vapor deposition with yttria and over coated with unalloyed vanadium. Based on prior work, the multi-layer electrically-insulating coatings were developed to reduce the magneto hydrodynamic (MHD) force expected in the first wall of a lithium cooled blanket in a magnetic confinement fusion reactor. Characterization of the specimens after exposure will include: (1) mass change and chemistry change as a function of location in the temperature gradient, (2) the effect of Li exposure on the tensile properties of V-4Cr-4Ti and (3) characterization of the properties and microstructure of the coatings after exposure. Of particular interest will be the coating resistivity after exposure and any degradation of the thin (∼10 μm) vanadium overlayer. Chemistry of the Li before and after the experiment will be compared in order to assess any mass transfer effects. (authors)
Coal-fired MHD combustor development project: Phase 3D
1985-05-01
This fourth quarterly technical progress report of the Coal-Fired MHD Combustor Development Project (Phase 3D) presents the accomplishments during the period February 1 to April 30, 1985. The scope of work covered by this quarterly report encompasses development work on the 50 MW/sub t/ combustor related to test support at the CDIF, assembly and checkout of first and second stage hardware, second stage design verification testing, designs for a continuous slag rejector and low preheat inlet section, and planning for power train testing. Progress includes the following: assembly and checkout of the second first stage, two second stages, and PEM was completed and the hardware was shipped to CDIF and FETS; integration of first and second stage hardware on the FETS Cell No. 2 test stand was completed, cold flow functional tests were performed, and hot fire checkout testing was initiated; assembly of the continuous slag rejector test set-up was 70% completed; the low preheat air inlet section Preliminary Design Review was held (work on the detail design was initiated and is 85% complete); and the Users' Manual was updated to include material for the second stage and final revisions to the power train test plan were made.
Directory of Open Access Journals (Sweden)
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
A MHD channel study for the ETF conceptual design
Wang, S. Y.; Staiger, P. J.; Smith, J. M.
1981-01-01
The procedures and computations used to identify an MHD channel for a 540 mW(I) EFT-scale plant are presented. Under the assumed constraints of maximum E(x), E(y), J(y) and Beta; results show the best plant performance is obtained for active length, L is approximately 12 M, whereas in the initial ETF studies, L is approximately 16 M. As MHD channel length is reduced from 16 M, the channel enthalpy extraction falls off, slowly. This tends to reduce the MHD power output; however, the shorter channels result in lower heat losses to the MHD channel cooling water which allows for the incorporation of more low pressure boiler feedwater heaters into the system and an increase in steam plant efficiency. The net result of these changes is a net increase in the over all MHD/steam plant efficiency. In addition to the sensitivity of various channel parameters, the trade-offs between the level of oxygen enrichment and the electrical stress on the channel are also discussed.
Further analysis of MHD acceleration for a hypersonic wind tunnel
International Nuclear Information System (INIS)
Christiansen, M.J.; Schmidt, H.J.; Chapman, J.N.
1995-01-01
A previously completed MHD study of the use of an MHD accelerator with seeded air from a state-of-the-art arc heater, was generally hailed as showing that the system studied has some promise of meeting the most critical hypersonic testing requirements. However, some concerns existed about certain aspects of the results. This paper discusses some of these problems and presents analysis of potential solutions. Specifically the problems addressed are; reducing the amount of seed in the flow, reducing test chamber temperatures, and reducing the oxygen dissociation. Modeling techniques are used to study three design variables of the MHD accelerator. The accelerator channel inlet Mach number, the accelerator channel divergence angle, and the magnetic field strength are all studied. These variables are all optimized to meet the goals for seed, temperature, and dissociated oxygen reduction. The results of this paper are encouraging, showing that all three goals can be met. General relationships are observed as to how the design variables affect the performance of the MHD accelerator facility. This paper expands on the results presented in the UTSI report and further supports the feasibility of MHD acceleration as a means to provide hypersonic flight simulation
Results from a large-scale MHD propulsion experiment
International Nuclear Information System (INIS)
Petrick, M.; Libera, J.; Bouillard, J.X.; Pierson, E.S.; Hill, D.
1992-01-01
This paper reports on magnetohydrodynamic (MHD) thrusters which 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 electromagnet (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 2T (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 (>6 T) practical MHD propulsion systems appear possible
Experimental and analytical investigation of an MHD channel window frame
International Nuclear Information System (INIS)
Srinivasan, M.G.; Krajcinovic, D.
1977-01-01
A common design of magnetohydrodynamic (MHD) generator channel emphasizes a series of mutually connected window frames providing the support for electrodes and containing the jet of ionized gases. Structurally, a window frame is a rectangular frame with a cross section in the form of a quadrilateral weakened by one or more holes forming the cooling system. Window frames are joined together to make a beam with a box cross section by means of shear pins. A typical window frame is subjected to a rather severe environment characterized by large pressure and high temperatures. The main sources of stresses and strains would include static and dynamic gas pressures and thermal fields characterized by large gradients across the thickness of frame members. The authors consider only the stresses associated with thermal fields. The actual problem is still a very complex one involving analysis of the heat conduction through the electrode-frame system heated by the gas and cooled by the coolant fluid and determination of stresses (elastic and plastic) in a frame with an irregular cross section. In order to obtain a reasonable qualitative and quantitative insight into the phenomenon, three distinctly different approaches have been used: a large elasto-plastic finite element program was used to determine the stresses in the actual frame, an experiment was performed to establish the stress concentrations around holes needed for the passage of coolant, and a two-bar model was used in order to assess the time dependent behavior of the structure for various loading conditions. (Auth.)
Numerical MHD study for plasmoid instability in uniform resistivity
Shimizu, Tohru; Kondoh, Koji; Zenitani, Seiji
2017-11-01
The plasmoid instability (PI) caused in uniform resistivity is numerically studied with a MHD numerical code of HLLD scheme. It is shown that the PI observed in numerical studies may often include numerical (non-physical) tearing instability caused by the numerical dissipations. By increasing the numerical resolutions, the numerical tearing instability gradually disappears and the physical tearing instability remains. Hence, the convergence of the numerical results is observed. Note that the reconnection rate observed in the numerical tearing instability can be higher than that of the physical tearing instability. On the other hand, regardless of the numerical and physical tearing instabilities, the tearing instability can be classified into symmetric and asymmetric tearing instability. The symmetric tearing instability tends to occur when the thinning of current sheet is stopped by the physical or numerical dissipations, often resulting in the drastic changes in plasmoid chain's structure and its activity. In this paper, by eliminating the numerical tearing instability, we could not specify the critical Lundquist number Sc beyond which PI is fully developed. It suggests that Sc does not exist, at least around S = 105.
Influence of slag-seed interaction on MHD generator performance
International Nuclear Information System (INIS)
Luongo, C.A.; Kruger, C.M.
1984-01-01
An overview of past work in the field of slag/seed interaction is presented. The ideal solution model for the slag and its failure to lead to accurate predictions are discussed. The non-ideal solution model is introduced. Data on potassium vapor pressure over slags taken at the National Bureau of Standards and Montana State University were compiled and compared. Large disagreement between these sources was observed. The shortcomings of the complete thermodynamic equilibrium models led to over predictions in the fraction of seed lost to the slag. A model including non-equilibrium effects is introduced. The heat/mass transfer analogy is invoked to calculate the mass transfer rate of potassium towards the slag. Using typical conditions for a large MHD generator, an integral method is used to evaluate the potassium concentration boundary layer thickness. The calculations are performed with the slag runoff (ash rejection) as a parameter. The increase in boundary layer resistance due to potassium depletion is calculated
MHD modeling of coronal loops: the transition region throat
Guarrasi, M.; Reale, F.; Orlando, S.; Mignone, A.; Klimchuk, J. A.
2014-04-01
Context. The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross-sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. Aims: The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. Methods: We study the area response with a time-dependent 2D magnetohydrodynamic (MHD) loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal conduction, and radiation from optically thin plasma. We run a simulation for a loop 50 Mm long and quasi-statically heated to about 4 MK. Results: We find that the area can change substantially with the quasi-steady heating rate, e.g., by ~40% at 0.5 MK as the loop temperature varies between 1 MK and 4 MK, and, therefore, affects the interpretation of the differential emission measure vs. temperature (DEM(T)) curves. The movie associated to Fig. 4 is available in electronic form at http://www.aanda.org
3D MHD MODELING OF TWISTED CORONAL LOOPS
Energy Technology Data Exchange (ETDEWEB)
Reale, F.; Peres, G. [Dipartimento di Fisica and Chimica, Università di Palermo, Piazza del Parlamento 1, I-90134 Palermo (Italy); Orlando, S. [INAF-Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, I-90134 Palermo (Italy); Guarrasi, M. [CINECA—Interuniversity consortium, via Magnanelli 6/3, I-40033, Casalecchio di Reno, Bologna (Italy); Mignone, A. [Dipartimento di Fisica Generale, Università di Torino, via Pietro Giuria 1, I-10125, Torino (Italy); Hood, A. W.; Priest, E. R., E-mail: fabio.reale@unipa.it [School of Mathematics and Statistics, University of St. Andrews, St. Andrews, KY16 9SS (United Kingdom)
2016-10-10
We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube in the solar atmosphere extending from the high- β chromosphere to the low- β corona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ∼30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and X-ray bands. The plasma confined in the flux tube is heated to active region temperatures (∼3 MK) after ∼2/3 hr. Upflows from the chromosphere up to ∼100 km s{sup −1} fill the core of the flux tube to densities above 10{sup 9} cm{sup −3}. More heating is released in the low corona than the high corona and is finely structured both in space and time.
Active MHD control experiments in RFX-mod
International Nuclear Information System (INIS)
Ortolani, Sergio
2006-01-01
The RFX reversed field pinch experiment has been modified (RFX-mod) to address specific issues of active control of MHD instabilities. A thin shell (τ Bv ∼50 ms) has replaced the old thick one (τ Bv ∼500 ms) and 192 (4 poloidal x 48 toroidal) independently powered saddle coils surround the thin shell forming a cage completely covering the torus. This paper reports the results obtained during the first year of operation. The system has been used with various control scenarios including experiments on local radial field cancellation over the entire torus surface to mimic an ideal wall ('virtual shell') and on single and multiple mode feedback control. Successful virtual shell operation has been achieved leading to: a 3-fold increase in pulse length and well controlled 300 ms pulses(∼6 shell times) up to ∼1 MA plasma current; one order of magnitude reduction of the dominant radial field perturbations at the plasma edge and correspondingly 100% increase in global energy confinement time. Robust feedback stabilization of resistive wall modes has been demonstrated in conditions where rotation does not play a role and multiple unstable modes are present
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Influence of hot beam ions on MHD ballooning modes in tokamaks
International Nuclear Information System (INIS)
Rewoldt, G.; Tang, W.M.
1984-07-01
It has recently been proposed that the presence of high energy ions from neutral beam injection can have a strong stabilizing effect on kinetically-modified ideal MHD ballooning modes in tokamaks. In order to assess realistically the importance of such effects, a comprehensive kinetic stability analysis, which takes into account the integral equation nature of the basic problem, has been applied to this investigation. In the collisionless limit, the effect of adding small fractions of hot beam ions is indeed found to be strongly stabilizing. On the other hand, for somewhat larger fractions of hot ions, a new beam-driven mode is found to occur with a growth rate comparable in magnitude to the growth rate of the MHD ballooning mode in the absence of hot ions. This implies that there should be an optimal density of hot particles which minimizes the strength of the relevant instabilities. Employing non-Maxwellian equilibrium distribution functions to model the beam species makes a quantitative, but not qualitative, difference in the results. Adding collisions to the calculation tends to reduce considerably the stabilizing effect of the hot ions
CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel
2017-08-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
Energy Technology Data Exchange (ETDEWEB)
Anninos, Peter; Lau, Cheuk [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States); Bryant, Colton [Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois, 60208 (United States); Fragile, P. Chris [Department of Physics and Astronomy, College of Charleston, 66 George Street, Charleston, SC 29424 (United States); Holgado, A. Miguel [Department of Astronomy and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801 (United States); Nemergut, Daniel [Operations and Engineering Division, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States)
2017-08-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
International Nuclear Information System (INIS)
Anninos, Peter; Lau, Cheuk; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Nemergut, Daniel
2017-01-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
MHD equilibrium and pressure driven instability in L=1 heliotron plasmas
International Nuclear Information System (INIS)
Nakamura, Y.; Suzuki, Y.; Yamagishi, O.; Kondo, K.; Nakajima, N.; Hayashi, T.; Monticello, D.A.; Reiman, A.H.
2003-01-01
Free boundary MHD equilibrium properties of Heliotron J are investigated by VMEC, HINT and PIES codes, and ideal MHD stability properties are studied by the Mercier criterion, the ballooning mode equation and the CAS3D global stability code. It is shown by the equilibrium calculations that the change of the plasma boundary shape is substantial in a low shear helical system even if the beta is relatively low. Preliminary comparison between PIES results and HINT results shows that the beta value at which the magnetic island begin to be perceptible is almost the same in both codes, but the island width seems to be different. From the stability analysis, good correlation is found between local and global analyses for the three dimensional(3D) or helical ballooning mode whose mode structure shows strong poloidal and toroidal mode (helical mode) coupling. In the helical ballooning mode, the Eigenmode is localized within a flux tube. It is also found that the positive shear of the rotational transform is favorable for the 3D ballooning mode stability in a low shear helical system. (author)
Test Particle Energization and the Anisotropic Effects of Dynamical MHD Turbulence
González, C. A.; Dmitruk, P.; Mininni, P. D.; Matthaeus, W. H.
2017-11-01
In this paper, we analyze the effect of dynamical three-dimensional magnetohydrodynamic (MHD) turbulence on test particle acceleration and compare how this evolving system affects particle energization by current sheet interaction, as opposed to frozen-in-time fields. To do this, we analyze the ensemble particle acceleration for static electromagnetic fields extracted from direct numerical simulations of the MHD equations, and compare it with the dynamical fields. We show that a reduction in particle acceleration in the dynamical model results from particle trapping in field lines, which forces the particles to be advected by the flow and suppresses long exposures to the strong electric field gradients that take place between structures and generate (among other effects) an efficient particle acceleration in the static case. In addition, we analyze the effect of anisotropy caused by the mean magnetic field. It is well known that for sufficiently strong external fields, the system experiences a transition toward a two-dimensional flow. This causes an increment in the size of the coherent structures, resulting in a magnetized state of the particles and a reduction in particle energization.
A review on application of MHD theory to plasma boundary problems in tokamaks
International Nuclear Information System (INIS)
Itoh, Kimitaka.
1992-08-01
A survey is made on the problems of the edge plasmas, to which the analyses based on the MHD theory have been successfully applied. Also discussed are the efforts to extend the model equation to more general (and important as well) problems such as H-mode physics. An overview is first made on the advantages of the MHD picture, and the necessary supplementary physics are examined. Next, one- and two-dimensional models of the spatial structure of the edge plasma is discussed. The results on the stationary structure, both analytical and numerical, are reviewed: Typical example as well as the scaling law are shown. The instabilities associated with edge plasma is next reviewed. The surface kink mode, ballooning mode, interchange mode, resistive interchange mode and thermal instability are discussed. Role of the geometry such as the location of the X-point is studied. Influences of the atomic processes, and those of the radial electric field are also discussed. The analysis of the H-mode transition physics is finally discussed. The boundary plasma is a nonlinear media which possesses the possibility for bifurcation in which the radial electric field plays a key role. The model of the ion viscosity is also studied. Transition physics is developed. Analysis on the self-generating oscillation is shown and the relation with ELMs is discussed. After reviewing these problems, several comments are made to what directions the study can be deepened. (author) 53 refs
International Nuclear Information System (INIS)
1968-01-01
Proceedings of a Symposium on Magnetohydrodynamic Electrical Power Generation held by the IAEA at Warsaw, 24-30 July 1968. The meeting was attended by some 300 participants from 21 countries and three international organizations. In contrast to the Symposium held two years ago, much more emphasis was placed on the economic aspects of using MHD generators in large-scale power generation. Among closed- cycle systems, the prospects of linking an ultra-high-temperature reactor with an MHD generator were explored, and the advantages gained by having a liquid-metal generator as a 'topper' in a conventional steam generating plant were presented. Comments were made about the disproportionate effect of end and boundary conditions in experimental MHD generators on the main plasma parameters, and estimates were made of the interrelationship to be expected in real generators. The estimates will have to await confirmation until results are obtained on large-scale prototype MHD systems. Progress in materials research, in design and construction of auxiliary equipment such as heat exchangers, supercooled magnets (which are- now commercially available), etc., is accompanied by sophisticated ideas of plant design. The Proceedings are complemented by three Round Table Discussions in which chosen experts from various countries discuss the outlook for closed-cycle gas, closed-cycle liquid-metal and open-cycle MHD, and give their views as to the most fruitful course to follow to achieve economic full-scale power generation. Contents: (Vol. I) 1. Closed-Cycle MHD with Gaseous Working Fluids: (a) Diagnostics (3 papers); (b) Steady-state non-equilibrium ionization (8 papers); (c) Transient non-equilibrium ionization (7 papers); (d) Pre-ionization and gas discharge (4 papers); (e) Fields and flow in MHD channels (10 papers); (0 Instabilities (8 papers); (g) Generator design and performance studies (6 papers); (Vol. II) (h) Shock waves (6 papers); (i) Power generation experiments (13 papers
Directory of Open Access Journals (Sweden)
Uday Singh Rajput
2017-11-01
Full Text Available Effects of rotation and radiation on unsteady MHD flow past a vertical plate with variable wall temperature and mass diffusion in the presence of Hall current is studied here. Earlier we studied chemical reaction effect on unsteady MHD flow past an exponentially accelerated inclined plate with variable temperature and mass diffusion in the presence of Hall current. We had obtained the results which were in agreement with the desired flow phenomenon. To study further, we are changing the model by considering radiation effect on fluid, and changing the geometry of the model. Here in this paper we are taking the plate positioned vertically upward and rotating with velocity Ω . Further, medium of the flow is taken as porous. The plate temperature and the concentration level near the plate increase linearly with time. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations under consideration have been solved by Laplace transform technique. The model contains equations of motion, diffusion equation and equation of energy. To analyze the solution of the model, desirable sets of the values of the parameters have been considered. The governing equations involved in the flow model are solved by the Laplace-transform technique. The results obtained have been analyzed with the help of graphs drawn for different parameters. The numerical values obtained for the drag at boundary and Nusselt number have been tabulated. We found that the values obtained for velocity, concentration and temperature are in concurrence with the actual flow of the fluid
International Nuclear Information System (INIS)
Niemann, R.C.; Mataya, K.F.; Smith, R.P.; McWilliams, D.A.; Borden, R.; Streeter, M.H.; Wickson, R.; Privalov, N.P.
1978-01-01
In order to facilitate the rapid development of MHD technology for the generation of electrical energy, the U.S. and U.S.S.R. are jointly conducting research within the framework of the Program of Scientific and Technical Cooperation. The Institute for High Temperature (IVTAN) of the U.S.S.R. has designed and fabricated a special MHD facility which uses as its base much of the equipment of the existing U-25 Facility. The new MHD fow train consisting of a combustor, magnet, channel, and diffuser is named U-25B. The U.S. has provided a superconducting magnet system for the U-25B MHD Facility. As a result of these joint efforts, a unique and broad range of experimental test conditions similar to those that will exist in operation of commercial MHD generators has been created. The United States Superconducting Magnet System (U.S. SCMS) was designed, fabricated, and delivered to the U-25B Facility by the Argonne National Laboratory (ANL) under the sponsorship of the U.S. Department of Energy. The following description focuses on the cryogenic-related aspects of the magnet system commissioning and operation in the U.S.S.R
Helium refrigerator-liquefier system for MHD generator
International Nuclear Information System (INIS)
Akiyama, Y.; Ishii, H.; Mori, Y.; Yamamoto, M.; Wada, R.; Ando, M.
1974-01-01
MHD power generators have been investigated in the Electro-Technical Laboratory as one of the National Research and Development Programmes. A helium refrigerator-liquefier system has been developed to cool the superconducting magnet for a 1000 kW class MHD power generator. The turboexpander with low temperature gas bearings and an alternator had been developed for the MHD project at the Electro-Technical Laboratory previously. The liquefaction capacity is 250 iota/h and the refrigeration power is 2.9 kW at 20 K. The superconducting magnet is 50 tons and the cryostat has a liquid helium volume of 2700 iota. The evaporation rate is 60 to 80 iota/h. It takes, in all 2 to 3 weeks to fill the cryostat with liquid helium. (author)
Diagnostic development and support of MHD test facilities
Energy Technology Data Exchange (ETDEWEB)
1990-01-01
The Diagnostic Instrumentation and Analysis Laboratory (DIAL) at Mississippi State University (MSU) is developing diagnostic instruments for MHD power train data acquisition and for support of MHD component development test facilities. Microprocessor-controlled optical instruments, initially developed for Heat Recovery/Seed Recovery support, are being refined, and new systems to measure temperatures and gas-seed-slag stream characteristics are being developed. To further data acquisition and analysis capabilities, the diagnostic systems are being interfaced with DIAL's computers. Technical support for the diagnostic needs of the national MHD research effort is being provided. DIAL personnel will also cooperate with government agencies and private industries to improve the transformation of research and development results into processes, products and services applicable to their needs. 25 figs., 6 tabs.
Pseudo-MHD ballooning modes in tokamak plasmas
International Nuclear Information System (INIS)
Callen, J.D.; Hegna, C.C.
1996-08-01
The MHD description of a plasma is extended to allow electrons to have both fluid-like and adiabatic-regime responses within an instability eigenmode. In the resultant open-quotes pseudo-MHDclose quotes model, magnetic field line bending is reduced in the adiabatic electron regime. This makes possible a new class of ballooning-type, long parallel extent, MHD-like instabilities in tokamak plasmas for α > s 2 (2 7/3 /9) (r p /R 0 ) or-d√Β/dr > (2 1/6 /3)(s/ R 0q ), which is well below the ideal-MHD stability boundary. The marginally stable pressure profile is similar in both magnitude and shape to that observed in ohmically heated tokamak plasmas
Numerical study of the axisymmetric ideal MHD stability of Extrap
International Nuclear Information System (INIS)
Benda, M.
1993-04-01
A numerical study of the free-boundary axisymmetric (n=0) ideal magnetohydrodynamical (MHD) motions of the Extrap device is presented. The dependence of stability on current profiles in the plasma and currents in the external conductors is investigated. Results are shown for linear growth-rates and nonlinear saturation amplitudes and their dependence on plasma radius as well as on the conducting shell radius. A method combined of two different algorithms has been developed and tested. The interior region of the plasma is simulated by means of a Lagrangian Finite Element Method (FEM) for ideal magnetohydrodynamics, The method is based on a nonlinear radiation principle for the Lagrangian description of ideal MHD. The Boundary Element Method (BEM) is used together with the Lagrangian FEM to simulate nonlinear motion of an ideal MHD plasma behaviour in a vacuum region under the influence of external magnetic fields. 31 refs
Diagnostic development and support of MHD test facilities
International Nuclear Information System (INIS)
Shepard, W.S.; Cook, R.L.
1990-01-01
The Diagnostic Instrumentation and Analysis Laboratory (DIAL) at Mississippi State University (MSU) is developing diagnostic instruments for MHD power train data acquisition and for support of MHD component development test facilities. Microprocessor-controlled optical instruments, initially developed for Heat Recovery/ Seed Recovery support, are being refined, and new systems to measure temperatures and gas-seed-slag stream characteristics are being developed. To further data acquisition and analysis capabilities, the diagnostic systems are being interfaced with DIAL's computers. Technical support for the diagnostic needs of the national MHD research effort is being provided. DIAL personnel will also cooperate with government agencies and private industries to improve the transformation of research and development results into processes, products and services applicable to their needs
Directory of Open Access Journals (Sweden)
Asma Khalid
2018-06-01
Full Text Available The intention here is to investigate the effects of wall couple stress with energy and concentration transfer in magnetohydrodynamic (MHD flow of a micropolar fluid embedded in a porous medium. The mathematical model contains the set of linear conservation forms of partial differential equations. Laplace transforms and convolution technique are used for computation of exact solutions of velocity, microrotations, temperature and concentration equations. Numerical values of skin friction, couple wall stress, Nusselt and Sherwood numbers are also computed. Characteristics for the significant variables on the physical quantities are graphically discussed. Comparison with previously published work in limiting sense shows an excellent agreement. Keywords: Micropolor fluid, Microrotation, MHD, Porosity, Wall couple stress, Exact solutions
A performance analysis for MHD power cycles operating at maximum power density
International Nuclear Information System (INIS)
Sahin, Bahri; Kodal, Ali; Yavuz, Hasbi
1996-01-01
An analysis of the thermal efficiency of a magnetohydrodynamic (MHD) power cycle at maximum power density for a constant velocity type MHD generator has been carried out. The irreversibilities at the compressor and the MHD generator are taken into account. The results obtained from power density analysis were compared with those of maximum power analysis. It is shown that by using the power density criteria the MHD cycle efficiency can be increased effectively. (author)
Salient issues of edge physics pertaining to loss of confinement: A resistive MHD analysis
International Nuclear Information System (INIS)
Thayer, D.R.
1990-01-01
In general we have made significant contributions towards the ultimate goal of creating a complete theory of edge turbulence and transport in magnetic fusion devices. Our main focus has been to utilize a resistive MHD model. This analysis includes: (1) ''rippling'' type models in which the current fluctuations are decoupled and the resistivity fluctuations are fundamental, and (2) ''drift'' type models in which the ambient current can be small (no resistivity fluctuations needed) and the current fluctuations are fundamental. In these turbulence frameworks, the important atomic physics based edge sources have been included (impurity radiation, ionization, and charge exchange effects)
Numerical study of shock waves in non-ideal magnetogasdynamics (MHD
Directory of Open Access Journals (Sweden)
Addepalli Ramu
2016-01-01
Full Text Available One-dimensional unsteady adiabatic flow of strong converging shock waves in cylindrical or spherical symmetry in MHD, which is propagating into plasma, is analyzed. The plasma is assumed to be non-ideal gas whose equation of state is of Mie–Gruneisen type. Suitable transformations reduce the governing equations into ordinary differential equations of Poincare type. In the present work, McQueen and Royce equations of state (EOS have been considered with suitable material constants and the spherical and cylindrical cases are worked out in detail to investigate the behavior and the influence on the shock wave propagation by energy input and β(ρ/ρ0, the measure of shock strength. The similarity solution is valid for adiabatic flow as long as the counter pressure is neglected. The numerical technique applied in this paper provides a global solution to the implosion problem for the flow variables, the similarity exponent α for different Gruneisen parameters. It is shown that increasing β(ρ/ρ0 does not automatically decelerate the shock front but the velocity and pressure behind the shock front increases quickly in the presence of the magnetic field and decreases slowly and become constant. This becomes true whether the piston is accelerated, is moving at constant speed or is decelerated. These results are presented through the illustrative graphs and tables. The magnetic field effects on the flow variables through a medium and total energy under the influence of strong magnetic field are also presented.
Characterizing electrostatic turbulence in tokamak plasmas with high MHD activity
Energy Technology Data Exchange (ETDEWEB)
Guimaraes-Filho, Z O; Santos Lima, G Z dos; Caldas, I L; Nascimento, I C; Kuznetsov, Yu K [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66316, 05315-970, Sao Paulo, SP (Brazil); Viana, R L, E-mail: viana@fisica.ufpr.b [Departamento de Fisica, Universidade Federal do Parana, Caixa Postal 19044, 81531-990, Curitiba, PR (Brazil)
2010-09-01
One of the challenges in obtaining long lasting magnetic confinement of fusion plasmas in tokamaks is to control electrostatic turbulence near the vessel wall. A necessary step towards achieving this goal is to characterize the turbulence level and so as to quantify its effect on the transport of energy and particles of the plasma. In this paper we present experimental results on the characterization of electrostatic turbulence in Tokamak Chauffage Alfven Bresilien (TCABR), operating in the Institute of Physics of University of Sao Paulo, Brazil. In particular, we investigate the effect of certain magnetic field fluctuations, due to magnetohydrodynamical (MHD) instabilities activity, on the spectral properties of electrostatic turbulence at plasma edge. In some TCABR discharges we observe that this MHD activity may increase spontaneously, following changes in the edge safety factor, or after changes in the radial electric field achieved by electrode biasing. During the high MHD activity, the magnetic oscillations and the plasma edge electrostatic turbulence present several common linear spectral features with a noticeable dominant peak in the same frequency. In this article, dynamical analyses were applied to find other alterations on turbulence characteristics due to the MHD activity and turbulence enhancement. A recurrence quantification analysis shows that the turbulence determinism radial profile is substantially changed, becoming more radially uniform, during the high MHD activity. Moreover, the bicoherence spectra of these two kinds of fluctuations are similar and present high bicoherence levels associated with the MHD frequency. In contrast with the bicoherence spectral changes, that are radially localized at the plasma edge, the turbulence recurrence is broadly altered at the plasma edge and the scrape-off layer.
Spectrum of resistive MHD modes in cylindrical plasmas
International Nuclear Information System (INIS)
Ryu, C.M.; Grimm, R.C.
1983-07-01
A numerical study of the normal modes of a compressible resistive MHD fluid in cylindrical geometry is presented. Resistivity resolves the shear Alfven and slow magnetosonic continua of ideal MHD into discrete spectra and gives rise to heavily damped modes whose frequencies lie on specific lines in the complex plane. Fast magnetosonic waves are less affected but are also damped. Overstable modes arise from the shear Alfven spectrum. The stabilizing effect of favorable average curvature is shown. Eigenfunctions illustrating the nature of typical normal modes are displayed
High pressure MHD coal combustors investigation, phase 2
Iwata, H.; Hamberg, R.
1981-05-01
A high pressure MHD coal combustor was investigated. The purpose was to acquire basic design and support engineering data through systematic combustion experiments at the 10 and 20 thermal megawatt size and to design a 50 MW/sub t/ combustor. This combustor is to produce an electrically conductive plasma generated by the direct combustion of pulverized coal with hot oxygen enriched vitiated air that is seeded with potassium carbonate. Vitiated air and oxygen are used as the oxidizer, however, preheated air will ultimately be used as the oxidizer in coal fired MHD combustors.
Temperature oscillating regimes in Tore Supra diagnosed by MHD activity
International Nuclear Information System (INIS)
Maget, P.; Imbeaux, F.; Giruzzi, G.; Udintsev, V.S.; Huysmans, G.T.A.; Segui, J.-L.; Goniche, M.; Moreau, Ph.; Sabot, R.; Garbet, X.
2006-01-01
This paper describes what we can learn on the regimes of spontaneous electron temperature oscillations discovered in Tore Supra from the analysis of MHD activity. Since the first observations of this oscillating behaviour of plasma equilibrium, and its interpretation as a predator-prey system involving lower hybrid waves power deposition and electron confinement, analysis of MHD modes has confirmed the reality of safety factor profile oscillations. This points towards the importance of rational values of the safety factor in the transition to transport barriers in reversed magnetic shear plasmas
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
MHD instabilities in astrophysical plasmas: very different from MHD instabilities in tokamaks!
Goedbloed, J. P.
2018-01-01
The extensive studies of MHD instabilities in thermonuclear magnetic confinement experiments, in particular of the tokamak as the most promising candidate for a future energy producing machine, have led to an ‘intuitive’ description based on the energy principle that is very misleading for most astrophysical plasmas. The ‘intuitive’ picture almost directly singles out the dominant stabilizing field line bending energy of the Alfvén waves and, consequently, concentrates on expansion schemes that minimize that contribution. This happens when the wave vector {{k}}0 of the perturbations, on average, is perpendicular to the magnetic field {B}. Hence, all macroscopic instabilities of tokamaks (kinks, interchanges, ballooning modes, ELMs, neoclassical tearing modes, etc) are characterized by satisfying the condition {{k}}0 \\perp {B}, or nearly so. In contrast, some of the major macroscopic instabilities of astrophysical plasmas (the Parker instability and the magneto-rotational instability) occur when precisely the opposite condition is satisfied: {{k}}0 \\parallel {B}. How do those instabilities escape from the dominance of the stabilizing Alfvén wave? The answer to that question involves, foremost, the recognition that MHD spectral theory of waves and instabilities of laboratory plasmas could be developed to such great depth since those plasmas are assumed to be in static equilibrium. This assumption is invalid for astrophysical plasmas where rotational and gravitational accelerations produce equilibria that are at best stationary, and the associated spectral theory is widely, and incorrectly, believed to be non-self adjoint. These complications are addressed, and cured, in the theory of the Spectral Web, recently developed by the author. Using this method, an extensive survey of instabilities of astrophysical plasmas demonstrates how the Alfvén wave is pushed into insignificance under these conditions to give rise to a host of instabilities that do not
MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1997-10-01
A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)
International Nuclear Information System (INIS)
Witalis, E.A.
1965-12-01
Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given
Energy Technology Data Exchange (ETDEWEB)
Witalis, E A
1965-12-15
Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given.
Krishna, M. Veera; Swarnalathamma, B. V.
2017-07-01
We considered the transient MHD flow of a reactive second grade fluid through porous medium between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The governing equations are solved by Laplace transform technique. The effects of the pertinent parameters on the velocity, temperature are discussed in detail. The shear stress and Nusselt number at the plates are also obtained analytically and computationally discussed with reference to governing parameters.
Ferdows, M.; Khan, M.S.; Alam, M.M.; Sun, S.
2012-01-01
Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed. 2012 M. Ferdows et al.
3D MHD Flux emergence experiments
DEFF Research Database (Denmark)
Hood, A.W.; Archontis, V.; Mactaggart, David
2012-01-01
This paper reviews some of the many 3D numerical experiments of the emergence of magnetic fields from the solar interior and the subsequent interaction with the pre-existing coronal magnetic field. The models described here are idealised, in the sense that the internal energy equation only involves...
Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder
Nagendramma, V.; Leelarathnam, A.; Raju, C. S. K.; Shehzad, S. A.; Hussain, T.
2018-06-01
An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence.
Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate
Ramli, Norshafira; Ahmad, Syakila; Pop, Ioan
2017-08-01
In this study, the problem of MHD flow and heat transfer of ferrofluids over a moving flat plate with slip effect and uniform heat flux is considered. The governing ordinary differential equations are solved via shooting method. The effect of slip parameter on the dimensionless velocity, temperature, skin friction and Nusselt numbers are numerically studied for the three selected ferroparticles; magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Mn-Zn ferrite (Mn-ZnFe2O4) with water-based fluid. The results indicate that dual solutions exist for a plate moving towards the origin. It is found that the slip process delays the boundary layer separation. Moreover, the velocity and thermal boundary-layer thicknesses decrease in the first solution while increase with the increase of the value of slip parameters in second solution.
Ideal MHD equilibrium of a weakly toroidal plasma column with elongated cross-section
International Nuclear Information System (INIS)
Heesch, E.J.M. van; Schuurman, W.
1980-07-01
Solutions are obtained of the ideal MHD equations describing the equilibrium of a weakly toroidal plasma with an elliptic cross-section surrounded by a force-free magnetic field with constant ratio between current density and magnetic field strength. The force-free field parameter causes the stagnation points to recede along the major axis of the ellipse. Above a certain value of the force-free field parameter, stagnation points do not exist, so that the compression ratio of the plasma column is no longer limited. The analysis was carried out to first order in the force-free field parameter as well as to second order for an estimate of the error
MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow
International Nuclear Information System (INIS)
Jirkovsky, L.; Bo-ot, L. Ma.; Chiang, C. M.
2010-01-01
We derive higher order magneto-hydrodynamic (MHD) equations from a microscopic picture using projection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number. (physics of gases, plasmas, and electric discharges)
Hanumagowda, B. N.; Salma, A.; Nagarajappa, C. S.
2018-04-01
The theoretical discussion is carried out for understanding the combined study of MHD, rough surface and couple-stress in the presence of applied magnetic field between two curved circular plates is present analysis. Modified Reynolds Equations accounting for rough surface using stochastic model of Christensen are mathematically formulated. The close form derivations for pressure, load-supporting capacity and response-film time are obtained. Our results shows that, there is an significant increase (decrease) for pressure, load-supporting capacity and squeeze film time due to the effect of azimuthal (radial) roughness parameter when compared to the Hanumagowda.et.al [14] and numerical data of load supporting capacity and response time are given in Table for engineering applications.
Non-disruptive MHD dynamics in inward-shifted LHD configurations
International Nuclear Information System (INIS)
Miura, H.; Ichiguchi, K.; Nakajima, N.; Hayashi, T.; Carreras, B.A.
2005-01-01
Two kinds of nonlinear simulations are conducted to study behaviors of the pressure-driven modes in the Large Helical Device (LHD) plasma with the vacuum magnetic axis located at R ax =3.6 m (so called inward-shifted configuration). One is the three-field reduced magnetohydrodynamic (RMHD) simulations. The other is the direct numerical simulations (DNS) of fully three-dimensional (3D) compressible MHD equations. The RMHD results suggest that the plasma behavior depends on the strength of the interaction between the unstable modes with different helicity. Similar plasma behaviors are also obtained in the DNS. In addition to some basic coincidence between RMHD and DNS, substantial toroidal flow generation is observed in the DNS. It is shown that toroidal flow can become stronger than the poloidal flow. (author)
Non-disruptive MHD dynamics in inward-shifted LHD configurations
International Nuclear Information System (INIS)
Miura, H.; Ichiguchi, K.; Nakajima, N.; Hayashi, T.; Carreras, B.A.
2005-01-01
Two kinds of nonlinear simulations are conducted to study behaviors of the pressure-driven modes in the Large Helical Device (LHD) plasma with the vacuum magnetic axis located at R ax = 3.6m (so called inward-shifted configuration). One is the three-field reduced magnetohydrodynamic (RMHD) simulations. The other is the direct numerical simulations (DNS) of fully three-dimensional (3D) compressible MHD equations. The RMHD results suggest that the plasma behavior depends on the strength of the interaction between the unstable modes with different helicity. Similar plasma behaviors are also obtained in the DNS. In addition to some basic coincidence between RMHD and DNS, substantial toroidal flow generation is observed in the DNS. It is shown that toroidal flow can become stronger than the poloidal flow. (author)
International Nuclear Information System (INIS)
Niemann, R.C.; Mataya, K.F.; McWilliams, D.A.; Borden, R.; Streeter, M.H.; Wickson, R.; Smelser, P.; Privalov, N.P.
1978-01-01
The design features and accumulated operating experience, from a cryogenics point of view, of the United States Superconducting Magnet System (U.S. SCMS) are presented. The principal cryogenic system design parameters are enumerated. Details of the cryogenic aspects of magnetic system commissioning, standby mode, and operation with MHD generators are discussed. Included are system operation, problems encountered and corrective actions taken, and measured operating parameters which include liquid helium boiloff, cryostat pressure and level versus time, etc. The aspects of the transition between operation in the laboratory and in an MHD plant are elaborated
International Nuclear Information System (INIS)
Kersale, Evy
2000-01-01
The first part of this work proposes a new version of the mathematical formalism used to describe pressure-driven instabilities in magnetized accretion-ejection structures. Such processes, occurring in magnetically confined plasmas, pose very stringent limits to thermonuclear fusion devices but their influence in astrophysical objects has rarely been considered. In a framework which eliminates fast magnetosonic waves one develops a system of equations allowing us to follow both ballooning and interchange modes. An application of this result to a cylindrical jet being subject to solid rotation shows that the inner parts of such structures are destabilized by magnetic shear. Furthermore, while clarifying somewhat previous studies, one finds that jets confined by a dominant toroidal magnetic field are generically unstable with respect to interchange modes. Moreover, one has written a numerical code to solve the MHD partial differential equations. Starting with a basic algorithm, one has assessed the effects of the geometry, boundary conditions and artificial dissipation on numerical computation. The code has been tested by solving classical hydrodynamic and MHD Riemann problems. A new mechanism of ultra high energy cosmic ray production in gamma-ray bursts composes the last part of this work. In these objects, particles are accelerated up to energies of the order of 10 21 eV, by means of relativistic Alfven perturbations crossings. A stream instability involving a highly relativistic shell of plasma, the fireball, and baryons going through it produces such Alfven fronts. Then, Brillouin-like backscattering processes redistribute the available energy between the forward and backward Alfven waves and the magnetosonic ones. (author) [fr
Arc damage characteristics of inter-anode insulators in MHD generator
International Nuclear Information System (INIS)
Kato, Ken; Takano, Kiyonami
1990-01-01
The inter-anode arc caused by a Hall field is driven by a magnetic field into the anode-wall in an MHD generator, which limits the lifetime and performance of the generator. The arc damage to inter-anode insulators of an MHD generator has been studied experimentally, in order to obtain basic data for the design of the inter-anode insulation. The experiment was conducted using a pair of electrodes with an insulator between them. Arc currents was supplied from a DC power source and magnetic field was applied perpendicular to the arc current. Experimental parameters are the insulator thickness, arc current, magnetic field and insulator materials. Quartz glass, boron nitride, magnesia, alumina, silicon carbide, silicon nitride etc. were tested and evaluated. The following conclusions are evident from the experiments. Boron nitride and quartz glass are the most promising inter-anode insulators. Boron nitride has a higher arc voltage and longer cutting time than quartz glass, and it is the best material. Cutting time is approximately proportional to the -0.4 th power of the magnetic field. Loss of insulator is approximately proportional to the 0.7 th power of the arc current. The arc voltage increases linearly with the inter anode gap length. It also increases with magnetic field, but decreases with increase of arc current. An equation which approximates to such relations of arc voltage versus inter-anode gap length, arc current and magnetic field has been obtained. The standard deviation of the error of this equation is 12 % for boron nitride and 15 % for quartz glass. (author)
Construction program for a large superconducting MHD magnet system at the coal-fired flow facility
International Nuclear Information System (INIS)
Wang, S.T.; Genens, L.; Gonczy, J.; Ludwig, H.; Lieberg, M.; Kraft, E.; Gacek, D.; Huang, Y.C.; Chen, C.J.
1980-01-01
The Argonne National Laboratory has designed and is constructing a 6 T large aperture superconducting MHD magnet for use in the Coal-Fired Flow Facility (CFFF) at the University of Tennessee Space Institute (UTSI) at Tullahoma, Tennessee. The magnet system consists of the superconducting magnet, a magnet power supply, an integrated instrumentation for operation, control and protection, and a complete cryogenic facility including a CTI Model 2800 helium refrigerator/liquefier with two compressors, helium gas handling system and a 7500 liter liquid helium dewar. The complete system will be tested at Argonne, IL in 1981. The magnet design is reviewed, and the coil fabrication programs are described in detail
Multi-scale MHD analysis of heliotron plasma in change of background field
International Nuclear Information System (INIS)
Ichiguchi, K.; Sakakibara, S.; Ohdachi, S.; Carreras, B.A.
2012-11-01
A partial collapse observed in the Large Helical Device (LHD) experiments shifting the magnetic axis inwardly with a real time control of the background field is analyzed with a magnetohydrodynamics (MHD) numerical simulation. The simulation is carried out with a multi-scale simulation scheme. In the simulation, the equilibrium also evolves including the change of the pressure and the rotational transform due to the perturbation dynamics. The simulation result agrees with the experiments qualitatively, which shows that the mechanism is attributed to the destabilization of an infernal-like mode. The destabilization is caused by the change of the background field through the enhancement of the magnetic hill. (author)
Losses of runaway electrons in MHD-active plasmas of the COMPASS tokamak.
Czech Academy of Sciences Publication Activity Database
Ficker, Ondřej; Mlynář, Jan; Vlainic, Milos; Čeřovský, Jaroslav; Urban, Jakub; Vondráček, Petr; Weinzettl, Vladimír; Macúšová, Eva; Decker, J.; Gospodarczyk, M.; Martin, P.; Nardon, E.; Papp, G.; Plyusnin, V.V.; Reux, C.; Saint-Laurent, F.; Sommariva, C.; Cavalier, Jordan; Havlíček, Josef; Havránek, Aleš; Hronová-Bilyková, Olena; Imríšek, Martin; Markovič, Tomáš; Varju, Jozef; Papřok, Richard; Pánek, Radomír; Hron, Martin
2017-01-01
Roč. 57, č. 7 (2017), č. článku 076002. ISSN 0029-5515 R&D Projects: GA MŠk LG14002; GA MŠk(CZ) LM2015045; GA MŠk(CZ) 8D15001 EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : tokamaks * runaway electrons * MHD instabilities * disruptions Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 3.307, year: 2016
Scaling of the MHD perturbation amplitude required to trigger a disruption and predictions for ITER
Czech Academy of Sciences Publication Activity Database
de Vries, P.C.; Pautasso, G.; Nardon, E.; Cahyna, Pavel; Gerasimov, S.; Havlíček, Josef; Hender, T.C.; Huijsmans, G.T.A.; Lehnen, M.; Maraschek, M.; Markovič, Tomáš; Snipes, J.A.
2016-01-01
Roč. 56, č. 2 (2016), č. článku 026007. ISSN 0029-5515 R&D Projects: GA MŠk(CZ) LM2011021 EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : disruptions * locked modes * MHD instabilities * ITER * COMPASS tokamak Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 3.307, year: 2016 http://iopscience.iop.org/article/10.1088/0029-5515/56/2/026007/meta
Simulations of MHD flows with moving interfaces
Gerbeau, J F; Le Bris, C
2003-01-01
We report on the numerical simulation of a two-fluid magnetohydrodynamics problem arising in the industrial production of aluminium. The motion of the two non-miscible fluids is modeled through the incompressible Navier-Stokes equations coupled with the Maxwell equations. Stabilized finite elements techniques and an arbitrary Lagrangian-Eulerian formulation (for the motion of the interface separating the two fluids) are used in the numerical simulation. With a view to justifying our strategy, details on the numerical analysis of the problem, with a special emphasis on conservation and stability properties and on the surface tension discretization, as well as results on tests cases are provided. Examples of numerical simulations of the industrial case are eventually presented.