Ideal Magnetohydrodynamics Stability Spectrum with a Resistive Wall
Energy Technology Data Exchange (ETDEWEB)
Smith, S. P. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Jardin, S. C. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2008-05-01
We show that the eigenvalue equations describing a cylindrical ideal magnetophydrodynamicsw (MHD) plasma interacting with a thin resistive wall can be put into the standard mathematical form: Α•χ = λΒ• χ. This is accomplished by using a finite element basis for the plasma, and by adding an extra degree of freedom corresponding to the electrical current in the thin wall. The standard form allows the use of linear eigenvalue solvers, without additional interations, to compute the complete spectrum of plasma modes in the presence of a surrounding restrictive wall at arbitrary separation. We show that our method recovers standard results in the limits of (1) an infinitely resistive wall (no wall), and (2) a zero resistance wall (ideal wall).
Institute of Scientific and Technical Information of China (English)
Shi Bing-Ren; Qu Wen-Xiao
2006-01-01
A ballooning mode equation for tokamak plasma, with the toroidicity and the Shafranov shift effects included, is derived for a shift circular flux tokamak configuration. Using this equation, the stability of the plasma configuration with an internal transport barrier (IT2 against the high n (the toroidal mode number) ideal magnetohydrodynamic (MHD) ballooning mode is analysed. It is shown that both the toroidicity and the Shafranov shift effects are stabilizing.In the ITB region, these effects give rise to a low shear stable channel between the first and the second stability regions.Out of the ITB region towards the plasma edge, the stabilizing effect of the Shafranov shift causes the unstable zone to be significantly narrowed.
Elements of magnetohydrodynamic stability theory
Energy Technology Data Exchange (ETDEWEB)
Spies, G O
1976-11-01
The nonlinear equations of ideal magnetohydrodynamics are discussed along with the following topics: (1) static equilibrium, (2) strict linear theory, (3) stability of a system with one degree of freedom, (4) spectrum and variational principles in magnetohydrodynamics, (5) elementary proof of the modified energy principle, (6) sufficient stability criteria, (7) local stability, and (8) normal modes. (MOW)
Nesterenko, Mikhail
2009-01-01
We define and explore the concept of ideal stabilization. The program is ideally stabilizing if its every state is legitimate. Ideal stabilization allows the specification designer to prescribe with arbitrary degree of precision not only the fault-free program behavior but also its recovery operation. Specifications may or may not mention all possible states. We identify approaches to designing ideal stabilization to both kinds of specifications. For the first kind, we state the necessary condition for an ideally stabilizing solution. On the basis of this condition we prove that there is no ideally stabilizing solution to the leader election problem. We illustrate the utility of the concept by providing examples of well-known programs and proving them ideally stabilizing. Specifically, we prove ideal stabilization of the conflict manager, the alternator, the propagation of information with feedback and the alternating bit protocol.
Parametric resonance in ideal magnetohydrodynamics
Zaqarashvili
2000-08-01
We show that an external nonelectromagnetic periodic inhomogeneous force sets up a parametric resonance in an ideal magnetohydrodynamics. Alfven waves with certain wavelengths grow exponentially in amplitude. Nonlinear interaction between the resonant harmonics produces the long-term modulation of amplitudes. The mechanism of the energy transformation from an external nonelectromagnetic force to magnetic oscillations of the system presented here can be used in understanding the physical background of the gravitational action on the magnetized medium. Future application of this theory to several astrophysical problems is briefly discussed.
Computational Methods for Ideal Magnetohydrodynamics
Kercher, Andrew D.
Numerical schemes for the ideal magnetohydrodynamics (MHD) are widely used for modeling space weather and astrophysical flows. They are designed to resolve the different waves that propagate through a magnetohydro fluid, namely, the fast, Alfven, slow, and entropy waves. Numerical schemes for ideal magnetohydrodynamics that are based on the standard finite volume (FV) discretization exhibit pseudo-convergence in which non-regular waves no longer exist only after heavy grid refinement. A method is described for obtaining solutions for coplanar and near coplanar cases that consist of only regular waves, independent of grid refinement. The method, referred to as Compound Wave Modification (CWM), involves removing the flux associated with non-regular structures and can be used for simulations in two- and three-dimensions because it does not require explicitly tracking an Alfven wave. For a near coplanar case, and for grids with 213 points or less, we find root-mean-square-errors (RMSEs) that are as much as 6 times smaller. For the coplanar case, in which non-regular structures will exist at all levels of grid refinement for standard FV schemes, the RMSE is as much as 25 times smaller. A multidimensional ideal MHD code has been implemented for simulations on graphics processing units (GPUs). Performance measurements were conducted for both the NVIDIA GeForce GTX Titan and Intel Xeon E5645 processor. The GPU is shown to perform one to two orders of magnitude greater than the CPU when using a single core, and two to three times greater than when run in parallel with OpenMP. Performance comparisons are made for two methods of storing data on the GPU. The first approach stores data as an Array of Structures (AoS), e.g., a point coordinate array of size 3 x n is iterated over. The second approach stores data as a Structure of Arrays (SoA), e.g. three separate arrays of size n are iterated over simultaneously. For an AoS, coalescing does not occur, reducing memory efficiency
Paz-Soldan, C; Bergerson, W F; Brookhart, M I; Hannum, D A; Kendrick, R; Fiksel, G; Forest, C B
2010-12-01
The rotating wall machine, a basic plasma physics experimental facility, has been constructed to study the role of electromagnetic boundary conditions on current-driven ideal and resistive magnetohydrodynamic instabilities, including differentially rotating conducting walls. The device, a screw pinch magnetic geometry with line-tied ends, is described. The plasma is generated by an array of 19 plasma guns that not only produce high density plasmas but can also be independently biased to allow spatial and temporal control of the current profile. The design and mechanical performance of the rotating wall as well as diagnostic capabilities and internal probes are discussed. Measurements from typical quiescent discharges show the plasma to be high β (≤p>2μ(0)/B(z)(2)), flowing, and well collimated. Internal probe measurements show that the plasma current profile can be controlled by the plasma gun array.
Variational Integrators for Ideal and Reduced Magnetohydrodynamics
Kraus, Michael; Maj, Omar; Tassi, Emanuele; Grasso, Daniela
2016-10-01
Ideal and reduced magnetohydrodynamics are simplified sets of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their geometrical character. The resulting integrators preserve important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As these integrators are free of numerical resistivity, the magnetic field line topology is preserved and spurious reconnection is absent in the ideal case. Only when effects of finite electron mass are added, magnetic reconnection takes place. The excellent conservation properties of the methods are exemplified with numerical examples in 2D. We conclude with an outlook towards the treatment of general geometries in 3D and full magnetohydrodynamics.
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Converging cylindrical shocks in ideal magnetohydrodynamics
Pullin, D. I.
2014-09-01
We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R = √μ0/p0 I/(2π) where I is the current, μ0 is the permeability, and p0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field then
Converging cylindrical shocks in ideal magnetohydrodynamics
Pullin, D. I.; Mostert, W.; Wheatley, V.; Samtaney, R.
2014-09-01
We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R=sqrt{μ _0/p_0} I/(2 π ) where I is the current, μ0 is the permeability, and p0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field
Remarks on the Regularity to 3-D Ideal Magnetohydrodynamic Equations
Institute of Scientific and Technical Information of China (English)
Quan Sen JIU; Cheng HE
2004-01-01
In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T]. Five sufficient conditions are given. Our results are motivated by two main ideas: one is to control the accumulation of vorticity alone; the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.
Magnetohydrodynamic stability of tokamaks
Zohm, Hartmut
2014-01-01
This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong lin
On the convexity of Relativistic Ideal Magnetohydrodynamics
Ibáñez, José-María; Aloy, Miguel-Ángel; Martí, José-María; Miralles, Juan-Antonio
2015-01-01
We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis ...
High—Order Gas—Kinetic Methods for Ideal Magnetohydrodynamics
Institute of Scientific and Technical Information of China (English)
HuazhongTANG
1999-01-01
This article is to study extension of gas-kinetic theory based flux splitting methods to ideal magnetohydrodynamics(MHD) equations,Uniform high-order gas-kinetic methods are presented,based on TVD type RUnge-Kutta time discretization and technique of the initial reconstruction.The numerical results have been given to show robustness of our schemes.
Servidio, S; Matthaeus, W H; Carbone, V
2008-10-01
We explore the problem of the ergodicity of magnetohydrodynamics and Hall magnetohydrodynamics in three-dimensional, ideal Galerkin systems that are truncated to a finite number of Fourier modes. We show how single Fourier modes follow the Gibbs ensemble prediction, and how the ergodicity of the phase space is restored for long-time Galerkin solutions. Running time averages and two-time correlation functions show, at long times, a convergence towards zero of time averaged single Fourier modes. This suggests a delayed approach to, rather than a breaking of, ergodicity. Finally, we present some preliminary ideas concerning the origin of the associated time scales.
Current-sheet formation in 3D ideal incompressible magnetohydrodynamics
Grauer; Marliani
2000-05-22
The evolution of current density and vorticity in the ideal, inviscid incompressible magnetohydrodynamic equations in three dimensions is studied numerically. Highly effective resolutions are obtained by adaptive structured mesh refinement techniques. We report on results for three different initial conditions showing similar behavior: in the early stage of the evolution a fast increase in vorticity and current density is observed. Thereafter, the evolution towards nearly two-dimensional current sheets results in a depletion of nonlinearity.
On stability criteria for kinetic magnetohydrodynamics
Ramos, J. J.
2016-12-01
The existence of a potential energy functional in the zero-Larmor-radius collisionless plasma theory of Kruskal & Oberman (Phys. Fluids, vol. 1, 1958 p. 275), Rosenbluth & Rostoker (Phys. Fluids, vol. 2, 1959, p. 23) allows us to derive easily sufficient conditions for linear stability. However, this kinetic magnetohydrodynamics (KMHD) theory does not have a self-adjointness property, making it difficult to derive necessary conditions. In particular, the standard methods to prove that an instability follows if some trial perturbation makes the incremental potential energy negative, which rely on the self-adjointness of the force operator or on the existence of a complete basis of normal modes, are not applicable to KMHD. This paper investigates KMHD linear stability criteria based on the time evolution of initial-value solutions, without recourse to the classic bounds or comparison theorems of Kruskal-Oberman and Rosenbluth-Rostoker for the KMHD potential energy. The adopted approach does not solve the kinetic equations by integration along characteristics and does not require that the particle orbits be periodic or nearly periodic. Most importantly, the investigation of a necessary condition for stability does not require the self-adjointness of the force operator or the existence of a complete basis of normal modes. It is thereby shown that stability in isothermal ideal-MHD is a sufficient condition for stability in KMHD and that, with a proviso on the long-time behaviour of oscillations about stable equilibria, stability in the double-adiabatic fluid theory, including the variation of the parallel fluid displacement, would be a necessary condition for stability in KMHD.
Optimal modes of operation of two idealized magnetohydrodynamic devices
Energy Technology Data Exchange (ETDEWEB)
Okulov, N.A.
1984-01-01
A conduction channel and a conduction cylinder, idealized devices, which model the operation of conduction magnetohydrodynamic (MGD) generators (pump) and magnetohydrodynamic propulsion devices, are examined. It is shown that it is sufficient to know the operational characteristics in the idle (kh.kh.) and short circuiting (KZ) modes alone in order to determine the operational characteristics of a conduction channel in the optimal mode, that is, in a mode of most complete energy conversion. The mode with which the required speed of movement is supported with minimal expenditures of energy is called the optimal mode of operation of a conduction cylinder. It is established that the characteristics of the corresponding optimal movement are expressed through the characteristics of the so called basis movements, whose number is one less than the number of electrodes.
Morrison, Philip J; Tronko, Natalia
2013-01-01
Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical {\\delta}W criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of {\\delta}W is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instabili...
Can non-ideal magnetohydrodynamics solve the magnetic braking catastrophe?
Wurster, James; Bate, Matthew R
2015-01-01
We investigate whether or not the low ionisation fractions in molecular cloud cores can solve the `magnetic braking catastrophe', where magnetic fields prevent the formation of circumstellar discs around young stars. We perform three-dimensional smoothed particle non-ideal magnetohydrodynamics (MHD) simulations of the gravitational collapse of one solar mass molecular cloud cores, incorporating the effects of ambipolar diffusion, Ohmic resistivity and the Hall effect alongside a self-consistent calculation of the ionisation chemistry assuming 0.1 micron grains. When including only ambipolar diffusion or Ohmic resistivity, discs do not form in the presence of strong magnetic fields, similar to the cases using ideal MHD. With the Hall effect included, disc formation depends on the direction of the magnetic field with respect to the rotation vector of the gas cloud. When the vectors are aligned, strong magnetic braking occurs and no disc is formed. When the vectors are anti-aligned, a disc with radius of 13AU ca...
A simple ideal magnetohydrodynamical model of vertical disruption events in tokamaks
Fitzpatrick, R.
2009-01-01
A simple model of axisymmetric vertical disruption events (VDEs) in tokamaks is presented in which the halo current force exerted on the vacuum vessel is calculated directly from linear, marginally stable, ideal-magnetohydrodynamical (MHD) stability analysis. The basic premise of the model is that the halo current force modifies pressure balance at the edge of the plasma, and therefore also modifies ideal-MHD plasma stability. In order to prevent the ideal vertical instability, responsible for the VDE, from growing on the very short Alfvén time scale, the halo current force must adjust itself such that the instability is rendered marginally stable. The model predicts halo currents which are similar in magnitude to those observed experimentally. An approximate nonaxisymmetric version of the model is developed in order to calculate the toroidal peaking factor for the halo current force.
Field topologies in ideal and near ideal magnetohydrodynamics and vortex dynamics
Low, B C
2014-01-01
Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near ideal MHD are reviewed in two parts. The first part gives a physically complete description of the frozen in field topology, taking magnetic flux conservation as fundamental and treating four topics, Eulerian and Lagrangian descriptions of MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics in comparison to ideal MHD. A corollary clarifies the challenge of achieving a high degree of the frozen in condition in numerical MHD. The second part treats field topology breakage centered on the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, i.e., electric current sheets of zero thickness. A similar incompatibil...
Energy Technology Data Exchange (ETDEWEB)
Aiba, N. [Japan Atomic Energy Agency, Rokkasho, Aomori 039-3212 (Japan); Hirota, M. [Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577 (Japan)
2015-08-15
In a rotating toroidal plasma surrounded by a resistive wall, it is shown that linear magnetohydrodynamic (MHD) instabilities can be excited by interplay between the resistive wall mode (RWM) and stable ideal MHD modes, where the RWM can couple with not only a stable external kink mode but also various stable Alfvén eigenmodes that abound in a toroidal plasma. The RWM growth rate is shown to peak repeatedly as the rotation frequency reaches specific values for which the frequencies of the ideal MHD modes are Doppler-shifted to the small RWM frequency. Such destabilization can be observed even when the RWM in a static plasma is stable. A dispersion relation clarifies that the unstable mode changes from the RWM to the ideal MHD mode destabilized by wall resistivity when the rotation frequency passes through these specific values. The unstable mode is excited at these rotation frequencies even though plasma rotation also tends to stabilize the RWM from the combination of the continuum damping and the ion Landau damping.
Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus
Energy Technology Data Exchange (ETDEWEB)
Weitzner, Harold [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-02-15
An alternative representation of an ideal magnetohydrodynamic equilibrium is developed. The representation is a variation of one given by A. Salat, Phys. Plasmas 2, 1652 (1995). The system of equations is used to study the possibility of non-symmetric equilibria in a topological torus, here an approximate rectangular parallelopiped, with periodicity in two of the three rectangular coordinates. An expansion is carried out in the deviation of pressure surfaces from planes. Resonances are manifest in the process. Nonetheless, provided the magnetic shear is small, it is shown that it is possible to select the magnetic fields and flux surfaces in such a manner that no singularities appear on resonant surfaces. One boundary surface of the parallelopiped is not arbitrary but is dependent on the equilibrium in question. A comparison of the solution sets of axisymmetric and non-axisymmetric equilibria suggests that the latter have a wider class of possible boundary shapes but more restrictive rotational transform profiles. No proof of convergence of the series is given.
Analytical study of magnetohydrodynamic propulsion stability
Abdollahzadeh Jamalabadi, M. Y.
2014-09-01
In this paper an analytical solution for the stability of the fully developed flow drive in a magneto-hydro-dynamic pump with pulsating transverse Eletro-magnetic fields is presented. To do this, a theoretical model of the flow is developed and the analytical results are obtained for both the cylindrical and Cartesian configurations that are proper to use in the propulsion of marine vessels. The governing parabolic momentum PDEs are transformed into an ordinary differential equation using approximate velocity distribution. The numerical results are obtained and asymptotic analyses are built to discover the mathematical behavior of the solutions. The maximum velocity in a magneto-hydro-dynamic pump versus time for various values of the Stuart number, electro-magnetic interaction number, Reynolds number, aspect ratio, as well as the magnetic and electrical angular frequency and the shift of the phase angle is presented. Results show that for a high Stuart number there is a frequency limit for stability of the fluid flow in a certain direction of the flow. This stability frequency is dependent on the geometric parameters of a channel.
Analytical Study of Magnetohydrodynamic Propulsion Stability
Institute of Scientific and Technical Information of China (English)
M.Y.Abdollahzadeh Jamalabadi
2014-01-01
In this paper an analytical solution for the stability of the fully developed flow drive in a magneto-hydro-dynamic pump with pulsating transverse Eletro-magnetic fields is presented. To do this, a theoretical model of the flow is developed and the analytical results are obtained for both the cylindrical and Cartesian configurations that are proper to use in the propulsion of marine vessels. The governing parabolic momentum PDEs are transformed into an ordinary differential equation using approximate velocity distribution. The numerical results are obtained and asymptotic analyses are built to discover the mathematical behavior of the solutions. The maximum velocity in a magneto-hydro-dynamic pump versus time for various values of the Stuart number, electro-magnetic interaction number, Reynolds number, aspect ratio, as well as the magnetic and electrical angular frequency and the shift of the phase angle is presented. Results show that for a high Stuart number there is a frequency limit for stability of the fluid flow in a certain direction of the flow. This stability frequency is dependent on the geometric parameters of a channel.
Magnetohydrodynamic stability of broad line region clouds
Krause, Martin; Burkert, Andreas
2012-01-01
Hydrodynamic stability has been a longstanding issue for the cloud model of the broad line region in active galactic nuclei. We argue that the clouds may be gravitationally bound to the supermassive black hole. If true, stabilisation by thermal pressure alone becomes even more difficult. We further argue that if magnetic fields should be present in such clouds at a level that could affect the stability properties, they need to be strong enough to compete with the radiation pressure on the cloud. This would imply magnetic field values of a few Gauss for a sample of Active Galactic Nuclei we draw from the literature. We then investigate the effect of several magnetic configurations on cloud stability in axi-symmetric magnetohydrodynamic simulations. For a purely azimuthal magnetic field which provides the dominant pressure support, the cloud first gets compressed by the opposing radiative and gravitational forces. The pressure inside the cloud then increases, and it expands vertically. Kelvin-Helmholtz and colu...
Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics
Low, B. C.
2015-01-01
Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics: Eulerian and Lagrangian descriptions of three dimensional (3D) MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clarifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low- β limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results in sheet dissipation, resistive heating and topological changes in the field notwithstanding the small resistivity. Strong Faraday induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun's corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit
On stability and instability criteria for magnetohydrodynamics.
Friedlander, Susan; Vishik, Misha M.
1995-06-01
It is shown that for most, but not all, three-dimensional magnetohydrodynamic (MHD) equilibria the second variation of the energy is indefinite. Thus the class of such equilibria whose stability might be determined by the so-called Arnold criterion is very restricted. The converse question, namely conditions under which MHD equilibria will be unstable is considered in this paper. The following sufficient condition for linear instability in the Eulerian representation is presented: The maximal real part of the spectrum of the MHD equations linearized about an equilibrium state is bounded from below by the growth rate of an operator defined by a system of local partial differential equations (PDE). This instability criterion is applied to the case of axisymmetric toroidal equilibria. Sufficient conditions for instability, stronger than those previously known, are obtained for rotating MHD. (c) 1995 American Institute of Physics.
Two Special Solutions of the Non-ideal Magnetohydrodynamics
Institute of Scientific and Technical Information of China (English)
FENG Xue-Shang; LIU Yong; WEI Feng-Si; YE Zhan-Yin
2000-01-01
A special transformation is found to solve the Magnetohydrodynamic equations, by which two classes of exact analytic time-dependent solutions of magnetic annihilation for incompressible magnetic fluid have been obtained.The solutions derived here possesses scaling property with time t as the scale factor. We find that the current can perform the soliton-like behaviour in the case of asymmetric inflow. The relevant evolution characteristics in the process of magnetic annihilation are also revealed.
Stability of an impulsively accelerated density interface in magnetohydrodynamics.
Wheatley, V; Pullin, D I; Samtaney, R
2005-09-16
In the framework of ideal incompressible magnetohydrodynamics, we examine the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This is accomplished by analytically solving the linearized initial value problem, which is a model for the Richtmyer-Meshkov instability. We find that the initial growth rate of the interface is unaffected by the presence of a magnetic field, but for a finite magnetic field the interface amplitude asymptotes to a constant value. Thus the instability of the interface is suppressed. The interface behavior from the analytical solution is compared to the results of both linearized and nonlinear compressible numerical simulations.
Emergence of high peaks in the axial velocity for an ideal magnetohydrodynamic disk configuration.
Montani, Giovanni; Carlevaro, Nakia
2010-08-01
We study the profile of a thin disk configuration as described by an axisymmetric ideal magnetohydrodynamics steady equilibrium. We consider the disk like a differentially rotating system dominated by the Keplerian term, but allowing for a nonzero radial and vertical matter flux. As a result, the steady state allows for the existence of local peaks for the vertical velocity of the plasma particles, though it prevents the radial matter accretion rate. This ideal magnetohydrodynamics scheme is therefore unable to solve the angular momentum-transport problem, but we suggest that it provides a mechanism for the generation of matter-jet seeds.
Nonlinear tearing mode study using the almost ideal magnetohydrodynamics (MHD) constraint
Energy Technology Data Exchange (ETDEWEB)
Ren, C.; Callen, J.D. [Univ. of Wisconsin, Madison, WI (United States); Jensen, T.H. [General Atomics, San Diego, CA (United States)
1998-12-31
The tearing mode is an important resistive magnetohydrodynamics (MHD) mode. It perturbs the initial equilibrium magnetic flux surfaces through magnetic field line reconnection to form new flux surfaces with magnetic islands. In the study of the tearing mode, usually the initial equilibria are one dimensional with two ignorable coordinates and the perturbed equilibria are two dimensional with one ignorable coordinate. The tearing mode can be linearly unstable and its growth saturates at a fine amplitude. The neoclassical tearing mode theory shows that the mode can be nonlinearly driven by the bootstrap current even when it is linearly stable to the classical tearing mode. It is important to study the nonlinear behavior of the tearing mode. As an intrinsically nonlinear approach, the use of the almost ideal MHD constraint is suited to study the nonlinear properties of the tearing mode. In this paper, as a validation of the method, the authors study two characteristics of the tearing mode using the almost ideal MHD constraint: (1) the linear stability condition for the initial one dimensional equilibrium; and (2) the final saturation level for the unstable case. In this work, they only consider the simplest case where no gradient of pressure or current density exists at the mode resonant surface.
Christlieb, Andrew J; Tang, Qi
2013-01-01
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vecto...
On the behavior of hyperbolic neutral points in two-dimensional ideal magnetohydrodynamics.
Cordoba, D; Marliani, C
1999-03-16
We study ideal incompressible magnetohydrodynamics in two dimensions. We obtain an exponential estimate on the closing of the angle at hyperbolic saddle points of the magnetic stream function under the assumption that the velocity remains bounded. The analytic results are supported by numerical simulations. These results give evidence against a standard scenario for singularity formation for these equations.
The impact of non-ideal magnetohydrodynamics on binary star formation
Wurster, James; Price, Daniel J.; Bate, Matthew R.
2017-04-01
We investigate the effect of non-ideal magnetohydrodynamics (MHD) on the formation of binary stars using a suite of three-dimensional smoothed particle magnetohydrodynamics simulations of the gravitational collapse of 1 M⊙, rotating, perturbed molecular-cloud cores. Alongside the role of Ohmic resistivity, ambipolar diffusion and the Hall effect, we also examine the effects of magnetic field strength, orientation and amplitude of the density perturbation. When modelling sub-critical cores, ideal MHD models do not collapse whereas non-ideal MHD models collapse to form single protostars. In supercritical ideal MHD models, increasing the magnetic field strength or decreasing the initial-density perturbation amplitude decreases the initial binary separation. Strong magnetic fields initially perpendicular to the rotation axis suppress the formation of binaries and yield discs with magnetic fields ˜10 times stronger than if the magnetic field was initially aligned with the rotation axis. When non-ideal MHD is included, the resulting discs are larger and more massive, and the binary forms on a wider orbit. Small differences in the supercritical cores caused by non-ideal MHD effects are amplified by the binary interaction near periastron. Overall, the non-ideal effects have only a small impact on binary formation and early evolution, with the initial conditions playing the dominant role.
Magnetohydrodynamic stability of stochastically driven accretion flows
Nath, Sujit K; Chattopadhyay, Amit K
2013-01-01
We investigate the evolution of magnetohydrodynamic/hydromagnetic perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable, but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations/experiments. The mismatch seems to have been resolved, atleast in certain regimes, in the presence of weak magnetic field revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It ...
Christlieb, Andrew J.; Rossmanith, James A.; Tang, Qi
2014-07-01
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vector potential satisfies is solved using a version of FD-WENO developed for Hamilton-Jacobi equations. The resulting numerical method is endowed with several important properties: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as point values on the same mesh (i.e., there is no mesh staggering); (2) both the spatial and temporal orders of accuracy are fourth-order; (3) no spatial integration or multidimensional reconstructions are needed in any step; and (4) special limiters in the magnetic vector potential update are used to control unphysical oscillations in the magnetic field. Several 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to show high-resolution on test problems that involve shocks.
Magnetohydrodynamic stability of stochastically driven accretion flows.
Nath, Sujit Kumar; Mukhopadhyay, Banibrata; Chattopadhyay, Amit K
2013-07-01
We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.
Evidence for a singularity in ideal magnetohydrodynamics implications for fast reconnection
Kerr, R M; Kerr, Robert M.; Brandenburg, Axel
1998-01-01
Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics (MHD) is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. The magnetic curvature force causes the flux rings to shrink until they come into contact. This produces a current sheet between them. In the ideal compressible calculations, the evidence for a singularity in a finite time $t_c$ is that the peak current density behaves like $|J|_\\infty \\sim 1/(t_c-t)$ for a range of sound speeds (or plasma betas). For the incompressible calculations consistency with the compressible calculations is noted and evidence is presented that there is convergence to a self-similar state. In the resistive reconnection calculations the magnetic helicity is nearly conserved and energy is dissipated.
THE SMALL-SCALE DYNAMO AND NON-IDEAL MAGNETOHYDRODYNAMICS IN PRIMORDIAL STAR FORMATION
Energy Technology Data Exchange (ETDEWEB)
Schober, Jennifer; Federrath, Christoph; Glover, Simon; Klessen, Ralf S. [Zentrum fuer Astronomie der Universitaet Heidelberg, Institut fuer Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg (Germany); Schleicher, Dominik [Institut fuer Astrophysik, Georg-August-Universitaet Goettingen, Friedrich-Hund-Platz, D-37077 Goettingen (Germany); Banerjee, Robi, E-mail: schober@stud.uni-heidelberg.de, E-mail: christoph.federrath@monash.edu, E-mail: glover@uni-heidelberg.de, E-mail: klessen@uni-heidelberg.de, E-mail: dschleic@astro.physik.uni-goettingen.de, E-mail: banerjee@hs.uni-hamburg.de [Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg (Germany)
2012-08-01
We study the amplification of magnetic fields during the formation of primordial halos. The turbulence generated by gravitational infall motions during the formation of the first stars and galaxies can amplify magnetic fields very efficiently and on short timescales up to dynamically significant values. Using the Kazantsev theory, which describes the so-called small-scale dynamo-a magnetohydrodynamical process converting kinetic energy from turbulence into magnetic energy-we can then calculate the growth rate of the small-scale magnetic field. Our calculations are based on a detailed chemical network and we include non-ideal magnetohydrodynamical effects such as ambipolar diffusion and Ohmic dissipation. We follow the evolution of the magnetic field up to larger scales until saturation occurs on the Jeans scale. Assuming a weak magnetic seed field generated by the Biermann battery process, both Burgers and Kolmogorov turbulence lead to saturation within a rather small density range. Such fields are likely to become relevant after the formation of a protostellar disk and, thus, could influence the formation of the first stars and galaxies in the universe.
Masson, J.; Chabrier, G.; Hennebelle, P.; Vaytet, N.; Commerçon, B.
2016-03-01
Angular momentum transport and the formation of rotationally supported structures are major issues in our understanding of protostellar core formation. Whereas purely hydrodynamical simulations lead to large Keplerian disks, ideal magnetohydrodynamics (MHD) models yield the opposite result, with essentially no disk formation. This stems from the flux-freezing condition in ideal MHD, which leads to strong magnetic braking. In this paper, we provide a more accurate description of the evolution of the magnetic flux redistribution by including resistive terms in the MHD equations. We focus more particularly on the effect of ambipolar diffusion on the properties of the first Larson core and its surrounding structure, exploring various initial magnetisations and magnetic field versus rotation axis orientations of a 1 M⊙ collapsing prestellar dense core. We used the non-ideal magnetohydrodynamics version of the adaptive mesh refinement code RAMSES to carry out these calculations. The resistivities required to calculate the ambipolar diffusion terms were computed using a reduced chemical network of charged, neutral, and grain species. Including ambipolar diffusion leads to the formation of a magnetic diffusion barrier (also known as the decoupling stage) in the vicinity of the core, which prevents accumulation of magnetic flux in and around the core and amplification of the field above 0.1 G. The mass and radius of the first Larson core, however, remain similar between ideal and non-ideal MHD models. This diffusion plateau, preventing further amplification of the field and reorganising the field topology, has crucial consequences for magnetic braking processes, allowing the formation of disk structures. Magnetically supported outflows launched in ideal MHD models are weakened or even disappear when using non-ideal MHD. In contrast to ideal MHD calculations, misalignment between the initial rotation axis and the magnetic field direction does not significantly affect the
Liu, Wei
2010-01-01
We present results from three-dimensional ideal magnetohydrodynamic simulations of unmagnetized dense plasma jet injection into a hot strongly magnetized plasma, with the aim of providing insight into core fueling of a tokamak with parameters relevant for ITER (International Thermonuclear Experimental Reactor) and NSTX (National Spherical Torus Experiment). Unmagnetized jet injection is similar to compact toroid injection but with higher possible injection density and total mass, as well as a potentially smaller footprint for the injector hardware. Our simulation results show that the unmagnetized dense jet is quickly magnetized upon injection. The penetration depth of the jet into the tokamak plasma is mostly dependent on the jet's initial kinetic energy while the jet's magnetic field determines its interior evolution. A key requirement for spatially precise fueling is for the jet's slowing-down time to be less than the time for the perturbed tokamak magnetic flux to relax due to magnetic reconnection. Thus ...
Energy Technology Data Exchange (ETDEWEB)
Liu, Wei [Los Alamos National Laboratory; Hsu, Scott [Los Alamos National Laboratory; Li, Hui [Los Alamos National Laboratory
2009-01-01
We present results from three-dimensional ideal magnetohydrodynamic simulations of low {beta} compact toroid (CT) injection into a hot strongly magnetized plasma, with the aim of providing insight into CT fueling of a tokamak with parameters relevant for ITER (International Thermonuclear Experimental Reactor). A regime is identified in terms of CT injection speed and CT-to-background magnetic field ratio that appears promising for precise core fueling. Shock-dominated regimes, which are probably unfavorable for tokamak fueling, are also identified. The CT penetration depth is proportional to the CT injection speed and density. The entire CT evolution can be divided into three stages: (1) initial penetration, (2) compression in the direction of propagation and reconnection, and (3) coming to rest and spreading in the direction perpendicular to injection. Tilting of the CT is not observed due to the fast transit time of the CT across the background plasma.
Gas-Kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics
Xu, Kun
1998-01-01
A gas-kinetic solver is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of "particle" collisions in the transport process. Consequently, the artificial dissipation in the new scheme is much reduced in comparison with the MHD Flux Vector Splitting Scheme. At the same time, the new scheme is compared with the well-developed Roe-type MHD solver. It is concluded that the kinetic MHD scheme is more robust and efficient than the Roe- type method, and the accuracy is competitive. In this paper the general principle of splitting the macroscopic flux function based on the gas-kinetic theory is presented. The flux construction strategy may shed some light on the possible modification of AUSM- and CUSP-type schemes for the compressible Euler equations, as well as to the development of new schemes for a non-strictly hyperbolic system.
A simple GPU-accelerated two-dimensional MUSCL-Hancock solver for ideal magnetohydrodynamics
Bard, Christopher M.; Dorelli, John C.
2014-02-01
We describe our experience using NVIDIA's CUDA (Compute Unified Device Architecture) C programming environment to implement a two-dimensional second-order MUSCL-Hancock ideal magnetohydrodynamics (MHD) solver on a GTX 480 Graphics Processing Unit (GPU). Taking a simple approach in which the MHD variables are stored exclusively in the global memory of the GTX 480 and accessed in a cache-friendly manner (without further optimizing memory access by, for example, staging data in the GPU's faster shared memory), we achieved a maximum speed-up of ≈126 for a 10242 grid relative to the sequential C code running on a single Intel Nehalem (2.8 GHz) core. This speedup is consistent with simple estimates based on the known floating point performance, memory throughput and parallel processing capacity of the GTX 480.
A Simple GPU-Accelerated Two-Dimensional MUSCL-Hancock Solver for Ideal Magnetohydrodynamics
Bard, Christopher; Dorelli, John C.
2013-01-01
We describe our experience using NVIDIA's CUDA (Compute Unified Device Architecture) C programming environment to implement a two-dimensional second-order MUSCL-Hancock ideal magnetohydrodynamics (MHD) solver on a GTX 480 Graphics Processing Unit (GPU). Taking a simple approach in which the MHD variables are stored exclusively in the global memory of the GTX 480 and accessed in a cache-friendly manner (without further optimizing memory access by, for example, staging data in the GPU's faster shared memory), we achieved a maximum speed-up of approx. = 126 for a sq 1024 grid relative to the sequential C code running on a single Intel Nehalem (2.8 GHz) core. This speedup is consistent with simple estimates based on the known floating point performance, memory throughput and parallel processing capacity of the GTX 480.
Energy Technology Data Exchange (ETDEWEB)
Cooper, W. A.; Brunetti, D.; Duval, B. P.; Faustin, J. M.; Graves, J. P.; Kleiner, A.; Patten, H.; Pfefferlé, D.; Porte, L.; Raghunathan, M.; Reimerdes, H.; Sauter, O.; Tran, T. M., E-mail: wilfred.cooper@epfl.ch [Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne (Switzerland)
2016-04-15
Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasma-vacuum interface are computed for the first time. The structures obtained have the appearance of saturated ideal external kink/peeling modes. High edge pressure gradients yield toroidal mode number n = 1 corrugations for a high edge bootstrap current and larger n distortions when this current is small. Deformations in the plasma boundary region induce a nonaxisymmetric Pfirsch-Schlüter current driving a field-aligned current ribbon consistent with reported experimental observations. A variation in the 3D equilibrium confirms that the n = 1 mode is a kink/peeling structure. We surmise that our calculated equilibrium structures constitute a viable model for the edge harmonic oscillations and outer modes associated with a quiescent H-mode operation in shaped tokamak plasmas.
Ideal MHD Stability Prediction and Required Power for EAST Advanced Scenario
Institute of Scientific and Technical Information of China (English)
陈均杰; 李国强; 钱金平; 刘子奚
2012-01-01
The Experimental Advanced Superconducting Tokamak (EAST) is the first fully superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. The ideal magnetohydrodynamic (MHD) stability and required power for the EAST advanced tokamak (AT) scenario with negative central shear and double transport barrier (DTB) are investigated. With the equilibrium code TOQ and stability code GATO, the ideal MHD stability is analyzed. It is shown that a moderate ratio of edge transport barriers' (ETB) height to internal transport barriers' (ITBs) height is beneficial to ideal MHD stability. The normalized beta/3N limit is about 2.20 (without wall) and 3.70 (with ideal wall). With the scaling law of energy confinement time, the required heating power for EAST AT scenario is calculated. The total heating power Pt increases as the toroidal magnetic field BT or the normalized beta βN is increased.
Viscous, resistive magnetohydrodynamic stability computed by spectral techniques.
Dahlburg, R B; Zang, T A; Montgomery, D; Hussaini, M Y
1983-09-01
Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasiequilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfvén speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
Viscous, resistive magnetohydrodynamic stability computed by spectral techniques
Dahlburg, R. B.; Zang, T. A.; Montgomery, D.; Hussaini, M. Y.
1983-01-01
Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations
Helzel, Christiane; Taetz, Bertram
2010-01-01
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [SIAM J. Sci. Comp. 28, 1766 (2006)], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J. Comp. Phys. 165, 126 (2000)]. In particular, in our extension we take great care to maintain the three most ...
Alfvén waves and ideal two-dimensional Galerkin truncated magnetohydrodynamics.
Krstulovic, Giorgio; Brachet, Marc-Etienne; Pouquet, Annick
2011-07-01
We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to 4096(2), for which several quadratic invariants are preserved by the truncation and the statistical equilibria are known. Initial conditions are the Orszag-Tang vortex with a neutral X point centered on a stagnation point of the velocity field in the large scales. In MHD, we observe that the total energy spectra at intermediate times and intermediate scales correspond to the interactions of eddies and waves, E(T)(k)~k(-3/2). Moreover, no pseudodissipative range is visible for either Euler or ideal MHD in two dimensions. In the former case, this may be linked to the existence of a vanishing turbulent viscosity whereas in MHD, the numerical resolution employed may be insufficient. When imposing a uniform magnetic field to the flow, we observe a lack of saturation of the formation of small scales together with a significant slowing down of their equilibration, with however a cutoff independent partial thermalization being reached at intermediate scales.
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1996-11-01
A theory and a numerical method are presented for the asymptotic matching analysis of resistive magnetohydrodynamic stability in a negative magnetic shear configuration with two rational surfaces. The theory formulates the problem of solving both the Newcomb equations in the ideal MHD region and the inner-layer equations around rational surfaces as boundary value/eigenvalue problems to which the finite element method and the finite difference method can be applied. Hence, the problem of stability analysis is solved by a numerically stable method. The present numerical method has been applied to model equations having analytic solutions in a negative magnetic shear configuration. Comparison of the numerical solutions with the analytical ones verifies the validity of the numerical method proposed. (author)
Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries.
Brachet, M E; Bustamante, M D; Krstulovic, G; Mininni, P D; Pouquet, A; Rosenberg, D
2013-01-01
We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 6144(3) points and three different configurations on grids of 4096(3) points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.
Liu, Wei; Li, Hui; Li, Shengtai; Lynn, Alan G
2008-01-01
Nonlinear ideal magnetohydrodynamic (MHD) simulations of the propagation and expansion of a magnetic "bubble" plasma into a lower density, weakly-magnetized background plasma are presented. These simulations mimic the geometry and parameters of the Plasma Bubble Expansion Experiment (PBEX) [A. G. Lynn, Y. Zhang, S. C. Hsu, H. Li, W. Liu, M. Gilmore, and C. Watts, Bull. Amer. Phys. Soc. {\\bf 52}, 53 (2007)], which is studying magnetic bubble expansion as a model for extra-galactic radio lobes. The simulations predict several key features of the bubble evolution. First, the direction of bubble expansion depends on the ratio of the bubble toroidal to poloidal magnetic field, with a higher ratio leading to expansion predominantly in the direction of propagation and a lower ratio leading to expansion predominantly normal to the direction of propagation. Second, an MHD shock and a trailing slow-mode compressible MHD wavefront are formed ahead of the bubble as it propagates into the background plasma. Third, the bub...
Free-boundary ideal MHD stability of W7-X divertor equilibria
Nührenberg, C.
2016-07-01
Plasma configurations describing the stellarator experiment Wendelstein 7-X (W7-X) are computationally established taking into account the geometry of the test-divertor unit and the high-heat-flux divertor which will be installed in the vacuum chamber of the device (Gasparotto et al 2014 Fusion Eng. Des. 89 2121). These plasma equilibria are computationally studied for their global ideal magnetohydrodynamic (MHD) stability properties. Results from the ideal MHD stability code cas3d (Nührenberg 1996 Phys. Plasmas 3 2401), stability limits, spatial structures and growth rates are presented for free-boundary perturbations. The work focusses on the exploration of MHD unstable regions of the W7-X configuration space, thereby providing information for future experiments in W7-X aiming at an assessment of the role of ideal MHD in stellarator confinement.
Wurster, James
2016-09-01
In this paper, we introduce Nicil: Non-Ideal magnetohydrodynamics Coefficients and Ionisation Library. Nicil is a stand-alone Fortran90 module that calculates the ionisation values and the coefficients of the non-ideal magnetohydrodynamics terms of Ohmic resistivity, the Hall effect, and ambipolar diffusion. The module is fully parameterised such that the user can decide which processes to include and decide upon the values of the free parameters, making this a versatile and customisable code. The module includes both cosmic ray and thermal ionisation; the former includes two ion species and three species of dust grains (positively charged, negatively charged, and neutral), and the latter includes five elements which can be doubly ionised. We demonstrate tests of the module, and then describe how to implement it into an existing numerical code.
Wurster, James
2016-01-01
In this paper, we introduce Nicil: Non-Ideal magnetohydrodynamics Coefficients and Ionisation Library. Nicil is a stand-alone Fortran90 module that calculates the ionisation values and the coefficients of the non-ideal magnetohydrodynamics terms of Ohmic resistivity, the Hall effect, and ambipolar diffusion. The module is fully parameterised such that the user can decide which processes to include and decide upon the values of the free parameters, making this a versatile and customisable code. The module includes both cosmic ray and thermal ionisation; the former includes two ion species and three species of dust grains (positively charged, negatively charged and neutral), and the latter includes five elements which can be doubly ionised. We demonstrate tests of the module, and then describe how to implement it into an existing numerical code.
Stabilization of numerical interchange in spectral-element magnetohydrodynamics
Sovinec, C. R.
2016-08-01
Auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. The projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code Sovinec et al. [17], provided that the projections introduce numerical dissipation.
Energy Technology Data Exchange (ETDEWEB)
Klapper, I. [Department of Mathematics, University of California, Los Angeles, California 90024 (United States); Rado, A.; Tabor, M. [Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721 (United States)
1996-11-01
The ideal three-dimensional incompressible magnetohydrodynamics equations are analyzed at magnetic null points using a generalization of a method from fluid dynamics. A closed system of ordinary differential equations governing the evolution of traces of matrices associated with the fluid velocity and magnetic field gradients are derived using a model for the pressure Hessian. It is shown rigorously that the eigenvalues of the magnetic field gradient matrix are constant in time and that, in the model, a finite time singularity occurs with characteristics similar to the magnetic field-free case. {copyright} {ital 1996 American Institute of Physics.}
Christlieb, Andrew J; Seal, David C; Tang, Qi
2015-01-01
We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e. it has no internal stages to store), single-step (i.e. it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in [SINUM, 53 (2015), pp. 1833-1856], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (which has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic p...
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
Energy Technology Data Exchange (ETDEWEB)
Loizu, J. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany); Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Hudson, S. R.; Bhattacharjee, A.; Lazerson, S. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Helander, P. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany)
2015-09-15
We consider the linear and nonlinear ideal plasma response to a boundary perturbation in a screw pinch. We demonstrate that three-dimensional, ideal-MHD equilibria with continuously nested flux-surfaces and with discontinuous rotational-transform across the resonant rational-surfaces are well defined and can be computed both perturbatively and using fully nonlinear equilibrium calculations. This rescues the possibility of constructing MHD equilibria with current sheets and continuous, smooth pressure profiles. The results predict that, even if the plasma acts as a perfectly conducting fluid, a resonant magnetic perturbation can penetrate all the way into the center of a tokamak without being shielded at the resonant surface.
DEFF Research Database (Denmark)
Ruban, V.P.; Senchenko, Sergey
2004-01-01
The evolution of piecewise constant distributions of a conserved quantity related to the frozen-in canonical vorticity in effectively two-dimensional incompressible ideal EMHD flows is analytically investigated by the Hamiltonian method. The study includes the case of axisymmetric flows with zero...
Graves, J P; Chapman, I T; Coda, S; Lennholm, M; Albergante, M; Jucker, M
2012-01-10
Virtually collisionless magnetic mirror-trapped energetic ion populations often partially stabilize internally driven magnetohydrodynamic disturbances in the magnetosphere and in toroidal laboratory plasma devices such as the tokamak. This results in less frequent but dangerously enlarged plasma reorganization. Unique to the toroidal magnetic configuration are confined 'circulating' energetic particles that are not mirror trapped. Here we show that a newly discovered effect from hybrid kinetic-magnetohydrodynamic theory has been exploited in sophisticated phase space engineering techniques for controlling stability in the tokamak. These theoretical predictions have been confirmed, and the technique successfully applied in the Joint European Torus. Manipulation of auxiliary ion heating systems can create an asymmetry in the distribution of energetic circulating ions in the velocity orientated along magnetic field lines. We show the first experiments in which large sawtooth collapses have been controlled by this technique, and neoclassical tearing modes avoided, in high-performance reactor-relevant plasmas.
Morrison, P. J.; Andreussi, T.; Pegoraro, F.
2016-10-01
In a series of papers we have investigated general properties of equilibria and their stability in each of the Lagrangian, Eulerian, and Dynamically Accessible stability formulations of magnetohydrodynamics. In our latest work we compare and contrast stability results with these formulations for two applications: stratified convection and rotating pinch equilibrium configurations. The former example, emphasizes the role played entropy, while the later demonstrates the utility of a relabeling transformation that we introduced in our earlier work. Comparisons to classical works, in particular on interchange instability, are made. DOE DE-FG02-04ER-54742.
A conservative stabilized finite element method for the magneto-hydrodynamic equations
Ben Salah, Nizar; Soulaimani, Azzeddine; Habashi, Wagdi G.; Fortin, Michel
1999-03-01
This work presents a finite element solution of the 3D magneto-hydrodynamics equations. The formulation takes explicitly into account the local conservation of the magnetic field, giving rise to a conservative formulation and introducing a new scalar variable. A stabilization technique is used in order to allow equal linear interpolation on tetrahedral elements of all the variables. Numerical tests are performed in order to assess the stability and the accuracy of the resulting methods. The convergence rates are calculated for different stabilization parameters. Well-known MHD benchmark tests are calculated. Results show good agreement with analytical solutions. Copyright
Lee, E; Brachet, M E; Pouquet, A; Mininni, P D; Rosenberg, D
2008-12-01
We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal nondissipative case is studied up to the equivalent of 2048;{3} grid points for one of these flows. The temporal evolution of the logarithmic decrements delta of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta , the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.
Helzel, Christiane; Taetz, Bertram
2012-01-01
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete divergence of the magnetic field. One approach that has been shown successful in stabilizing MHD calculations are constrained transport (CT) schemes. CT schemes can be viewed as predictor-corrector methods for updating the magnetic field, where a magnetic field value is first predicted by a method that does not exactly preserve the divergence-free condition on the magnetic field, followed by a correction step that aims to control these divergence errors. In Helzel et al. (2011) the authors presented an unstaggered constrained transport method for the MHD equations on 3D Cartesian grids. In this work we generalize the method of Helzel et al. (2011) in three important ways: (1) we remove the need for operator splitting by switching to an appropriate method of lines discretization and coupling this with a non-conservative finite volume meth...
Magnetohydrodynamic stability of natural convection in a vertical porous slab
Shankar, B. M.; Kumar, Jai; Shivakumara, I. S.
2017-01-01
The stability of the conduction regime of natural convection in an electrically conducting fluid saturated porous vertical slab is investigated in the presence of a uniform external transverse magnetic field. The flow in the porous medium is described by modified Brinkman-extended Darcy equation with fluid viscosity different from effective viscosity. The boundaries of the vertical porous slab are assumed to be rigid-isothermal and electrically non-conducting. The resulting stability equations are solved numerically using Galerkin method. The critical Grashof number Gc, the critical wave number αc and the critical wave speed cc are computed for a wide range of porous parameter σp, the ratio of effective viscosity to the fluid viscosity Λ, the Prandtl number Pr and the Hartmann number M. Based on these parameters, the stability characteristics of the system are discussed in detail. The presence of advective inertia is to instill instability on the flow in a porous medium and found that the magnetic field, porous parameter and ratio of viscosities have a stabilizing effect on both stationary and oscillatory wave instabilities. Besides, the value of Pr at which transition occurs from stationary to oscillatory mode of instability decreases with increasing M ,σp and Λ .
Magnetohydrodynamic gravitational stability of a fluid jet embedded in a bounded medium
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Radwan, A.E. [Ainshams University, Faculty of Science, Mathematics Department, Cairo (Egypt); Elazab, S.S. [Ainshams University, Faculty of Girls, Mathematics Department, Cairo (Egypt); Ashour, A.A. [Al-Azhar University (Girls Branch), Faculty of Science, Mathematics Department, Nasr City, Cairo (Egypt)
2001-03-01
The magnetohydrodynamic (MHD) stability of a self-gravitating fluid cylinder embedded into a self-gravitating bounded medium has been developed. The problem is formulated and solved and, upon appropriate boundary conditions, the eigenvalue relation is derived. The latter is discussed in order to determine the stable and unstable domains and their characteristics. Some reported and previously published work is recovered as limiting cases. The self-gravitating force is destabilizing only for axisymmetric modes while it is stabilizing for the rest. The axial magnetic field has a strong stabilizing influence; but the transverse magnetic field is stabilizing or not according to restrictions. The fluid-tenuous media radii ratio plays an important role in stabilizing the model. An added feature of the present work is that it has been considered all mathematical solutions of the differential equations because singular solutions are not present at all in this case.
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Alfaisal A. Hasan
2012-01-01
Full Text Available The Magnetohydrodynamic stability of a streaming cylindrical model penetrated by varying transverse magnetic field has been discussed. The problem is formulated, the basic equations are solved, upon appropriate boundary conditions the eigenvalue relation is derived and discussed analytically, and the results are verified numerically. The capillary force is destabilizing in a small axisymmetric domain 0<<1 and stabilizing otherwise. The streaming has a strong destabilizing effect in all kinds of perturbation. The toroidal varying magnetic field interior the fluid has no direct effect at all on the stability of the fluid column. The axial exterior field has strong stabilizing effect on the model. The effect of all acting forces altogether could be identified via the numerical analysis of the stability theory of the present model.
PB3D: A new code for edge 3-D ideal linear peeling-ballooning stability
Weyens, T.; Sánchez, R.; Huijsmans, G.; Loarte, A.; García, L.
2017-02-01
A new numerical code PB3D (Peeling-Ballooning in 3-D) is presented. It implements and solves the intermediate-to-high-n ideal linear magnetohydrodynamic stability theory extended to full edge 3-D magnetic toroidal configurations in previous work [1]. The features that make PB3D unique are the assumptions on the perturbation structure through intermediate-to-high mode numbers n in general 3-D configurations, while allowing for displacement of the plasma edge. This makes PB3D capable of very efficient calculations of the full 3-D stability for the output of multiple equilibrium codes. As first verification, it is checked that results from the stability code MISHKA [2], which considers axisymmetric equilibrium configurations, are accurately reproduced, and these are then successfully extended to 3-D configurations, through comparison with COBRA [3], as well as using checks on physical consistency. The non-intuitive 3-D results presented serve as a tentative first proof of the capabilities of the code.
Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi
2016-07-01
We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free
Araki, Keisuke
2016-01-01
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Examinations of the stabilities of the hydrodynamic (HD, $\\alpha=0$) and magnetohydrodynamic (MHD, $\\alpha\\to0$) motions and the $O(\\alpha)$ Hall-term effect in terms of the Jacobi equation and the Riemannian sectional curvature tensor are presented, where {\\alpha} represents the Hall-term strength parameter. Formulations are given for the geodesic and Jacobi equations based on a linear connection with physically desirable properties, which agrees with the Levi-Civita connection. Derivations of the explicit normal-mode expressions for the Riemannian metric, Levi-Civita connection, and related formulae and equations are also provided using the generalized Els\\"asser variables (GEVs). It is very interesting that the sectional curvatures of the MHD and HMHD systems between two GEV modes were found to take both the po...
Flow stabilization of the ideal MHD resistive wall mode^1
Smith, S. P.; Jardin, S. C.; Freidberg, J. P.; Guazzotto, L.
2009-05-01
We demonstrate for the first time in a numerical calculation that for a typical circular cylindrical equilibrium, the ideal MHD resistive wall mode (RWM) can be completely stabilized by bulk equilibrium plasma flow, V, for a window of wall locations without introducing additional dissipation into the system. The stabilization is due to a resonance between the RWM and the Doppler shifted ideal MHD sound continuum. Our numerical approach introduces^2 u=φξ+ iV .∇ξ and the perturbed wall current^3 as variables, such that the eigenvalue, φ, only appears linearly in the linearized stability equations, which allows for the use of standard eigenvalue solvers. The wall current is related to the plasma displacement at the boundary by a Green's function. With the introduction of the resistive wall, we find that it is essential that the finite element grid be highly localized around the resonance radius where the parallel displacement, ξ, becomes singular. We present numerical convergence studies demonstrating that this singular behavior can be approached in a limiting sense. We also report on progress toward extending this calculation to an axisymmetric toroidal geometry. ^1Work supported by a DOE FES fellowship through ORISE and ORAU. ^2L.Guazzotto, J.P Freidberg, and R. Betti, Phys.Plasmas 15, 072503 (2008). ^3S.P. Smith and S. C. Jardin, Phys. Plasmas 15, 080701 (2008).
Linear stability of ideal MHD configurations. II. Results for stationary equilibrium configurations
Demaerel, T.; Keppens, R.
2016-12-01
In this paper, we continue exploring the consequences of the general equation of motion (EOM) governing all Lagrangian perturbations ξ about a time-dependent, ideal magnetohydrodynamic (MHD) configuration, which includes self-gravity, external gravity, pressure gradients, compressibility, inertial effects, and anisotropic Lorentz force. We here address the specific case of MHD stability for 3D stationary equilibria, where the perturbed EOM features a symmetric operator F and an antisymmetric Doppler-Coriolis operator v . ∇ . For this case, we state and prove the general properties for the solutions ξ of the governing dynamical system. For axisymmetric perturbations about axisymmetric equilibria with purely toroidal, or purely poloidal magnetic fields, specific stability theorems can be formulated. We derive a useful integral expression for the quadratic quantity given by the inner product ⟨ ξ , F [ ξ ] ⟩ . For deriving stability statements on MHD states where self-gravity is involved as well, we provide an upper bound on the perturbed self-gravitational energy associated with the displacement ξ . The resulting expression elucidates the role of potentially stabilizing versus destabilizing contributions and shows the role of gravity, entropy gradients, velocity shear, currents, Lorentz forces, inertia, and pressure gradients in offering many routes to unstable behavior in flowing gases and plasmas. These have historically mostly been studied for static v = 0 configurations, looking at stability of exactly force-balanced states, or by assuming stationarity similar to our approach here (i.e., ∂ t ≡ 0 for the state we perturb), but typically in combination with some reduced dimensionality on the configuration of interest (translational or axisymmetry). We show that in these limits, we find and generalize expressions well-known from, e.g., the study of ideal MHD stability of tokamak plasmas or from Schwarzschild's criteria controlling convection in
Andreussi, T; Pegoraro, F
2016-01-01
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi {\\it et al.}\\ [Phys.\\ Plasmas {\\bf20}, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is abse...
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
Brinkmann, R. P.
1989-01-01
This paper is a contribution to the stability analysis of current-carrying plasmas, i.e., plasma systems that are forced by external mchanisms to carry a nonrelaxing electrical current. Under restriction to translationally invariant configurations, the thermodynamic stability criterion for a multicomponent plasma is rederived within the framework of nonideal MHD. The chosen dynamics neglects scalar resistivity, but allows for other types of dissipation effects both in Ohm's law and in the equation of motion. In the second section of the paper, the thermodynamic stability criterion is compared with the ideal MHD based energy principle of Bernstein et al. With the help of Schwarz's inequality, it is shown that the former criterion is always more 'pessimistic' than the latter, i.e., that thermodynamic stability implies stability according to the MHD principle, but not vice versa. This reuslt confirms the physical plausible idea that dissipational effects tend to weaken the stability properties of current-carrying plasma equilibria by breaking the constraints of ideal MHD and allowing for possibly destabilizing effects such as magnetic field line reconfiguration.
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Haas, Fernando; Pascoal, Kellen Alves [Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91501-970 Porto Alegre, RS (Brazil); Mendonça, José Tito [IPFN, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal and Instituto de Física, Universidade de São Paulo, 05508-090 São Paulo, SP (Brazil)
2016-01-15
A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the Fermi neutrino weak force in magnetized plasmas. A fast neutrino-driven short wavelengths instability associated with the magnetosonic wave is derived. Such an instability should play a central role in strongly magnetized plasma as occurs in supernovae, where dense neutrino beams also exist. In addition, in the case of nonlinear or high frequency waves, the neutrino coupling is shown to be responsible for breaking the frozen-in magnetic field lines condition even in infinite conductivity plasmas. Simplified and ideal NMHD assumptions were adopted and analyzed in detail.
Araki, Keisuke
2017-06-01
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic and Jacobi equations based on a linear connection with physically desirable properties, which agrees with the Levi-Civita connection. Derivations of the explicit normal-mode expressions for the Riemannian metric, Levi-Civita connection, and related formulae and equations are also provided using the generalized Elsässer variables (GEVs). Examinations of the stabilities of the hydrodynamic (HD, α=0 ) and magnetohydrodynamic (MHD, α\\to0 ) motions and the O(α) Hall-term effect in terms of the Jacobi equation and the Riemannian sectional curvature tensor are presented, where α represents the Hall-term strength parameter. It is very interesting that the sectional curvatures of the MHD and HMHD systems between two GEV modes were found to take both the positive (stable) and negative (unstable) values, while that of the HD system between two complex helical waves was observed to be negative definite. Moreover, for the MHD case, negative sectional curvatures were found to occur only when mode interaction was ‘local’, i.e. the wavenumber moduli of the main flow (say p) and perturbation (say k) were relatively close to each other. However, in the nonlocal limit (k\\ll p or k\\gg p ), the sectional curvatures were always positive. This result leads to the conjecture that the MHD interactions mainly excite wavy or non-growing motions; however, some local interactions cause dynamical instability that leads to chaotic or turbulent plasma motions. Additionally, it was found that the tendencies of the O(α) effects are opposite between the ion cyclotron and whistler modes. Comparison with the energy-Casimir method is also discussed using a remarkable constant of motion which relates the Riemannian curvature to the second variation of the
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Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1996-08-01
The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)
Stabilization of the Regularity of Powers of An Ideal
Eisenbud, David
2010-01-01
When M is a finitely generated graded module over a standard graded algebra S and I is an ideal of S, it is known from work of Cutkosky, Herzog, Kodiyalam, R\\"omer, Trung and Wang that the Castelnuovo-Mumford regularity of I^mM has the form dm+e when m >> 0. We give an explicit bound on the m$for which this is true, under the hypotheses that I is generated in a single degree and M/IM has finite length, and we explore the phenomena that occur when these hypotheses are not satisfied. Finally, we prove a regularity bound for a reduced, equidimensional projective scheme of codimension 2 that is similar to the bound in the Eisenbud-Goto conjecture [1984], under the additional hypotheses that the scheme lies on a quadric and has nice singularities.
Ideal MHD stability of very high beta tokamaks
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Chance, M.S.; Jardin, S.C.; Kessel, C.; Manickam, J.; Monticello, D. (Princeton Univ., NJ (USA). Plasma Physics Lab.); Peng, Y.K.M.; Holmes, J.A.; Strickler, D.J.; Whitson, J.C. (Oak Ridge National Lab., TN (USA)); Glasser, A.H. (Los Alamos National Lab., NM (USA)); Sykes, A. (UKAEA Culham Lab., Abingdon (UK)); Ramos, J.J. (Massachusetts Inst. of Tech., Cambridge, MA (USA). Plasma Fusion Center)
1990-12-01
Achieving very high {beta} and high {beta}{sub p} simultaneously in tokamaks generally implies that the second stability region against ballooning modes must be accessed. We describe several approaches for doing this, which are characterized by the choice of constraints imposed on the equilibrium profiles and the cross-sectional shape of the plasma. The combination of high toroidal beta, restricting the current density to vanish at the edge of the plasma and maintaining a monotonic q profile, proves to be the most stringent. Consideration of equilibria with high {epsilon}{beta}{sub p} but low {beta} facilitates accessibility with peaked pressure profiles and high values of q{sub 0}. Allowing the pressure gradient and, hence, the current density to be finite at the plasma edge allows all surfaces to lie within the second stability regime. For free boundary plasmas with divertors, the divertor stabilized edge region remains in the first stability regime while the plasma core reaches into the second regime. Careful tailoring of the profiles must be used to traverse the unstable barrier commonly seen near the edge of these plasmas. The CAMINO code allows us to compute s-{alpha} curves for general tokamak geometry. These diagrams enable us to construct equilibria whose profiles are only constrained, at worst, to be marginally stable everywhere, but do not necessarily satisfy the constraints on the current or {beta}. There are theoretical indications that under certain conditions the external kinks possess a second region of stability at high q{sub 0} that is analogous to that of the ballooning modes. It is found that extremely accurate numerical means must be developed and applied to confidently establish the validity of these results. 14 refs., 5 figs., 1 tab.
Ideal MHD Stability of ITER Steady State Scenarios with ITBs
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F.M. Poli, C.E. Kessel, S. Jardin, J. Manickam, M. Chance, J. Chen
2011-07-27
One of ITER goals is to demonstrate feasibility of continuous operations using non-inductive current drive. Two main candidates have been identified for advanced operations: the long duration, high neutron fluency hybrid scenario and the steady state scenario, both operating at a plasma current lower than the reference ELMy scenario [1][2] to minimize the required current drive. The steady state scenario targets plasmas with current 7-10 MA in the flat-top, 50% of which will be provided by the self-generated, pressure-driven bootstrap current. It has been estimated that, in order to obtain a fusion gain Q > 5 at a current of 9 MA, it should be ΒN > 2.5 and H > 1.5 [3]. This implies the presence of an Internal Transport Barrier (ITB). This work discusses how the stability of steady state scenarios with ITBs is affected by the external heating sources and by perturbations of the equilibrium profiles.
Comparison of magnetic island stabilization strategies from magneto-hydrodynamic simulations
Février, O.; Maget, P.; Lütjens, H.; Beyer, P.
2017-04-01
The degradation of plasma confinement in tokamaks caused by magnetic islands motivates to better understand their possible suppression using electron cyclotron current drive (ECCD) and to investigate the various strategies relevant for this purpose. In this work, we evaluate the efficiency of several control methods through nonlinear simulations of this process with the toroidal magneto-hydro-dynamic (MHD) code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), which has been extended to incorporate in Ohm’s law a source term modeling the driven current resulting from the interaction of the EC waves with the plasma. A basic control system has been implemented in the code, allowing testing of advanced strategies that require feedback on island position or phase. We focus in particular on the robustness of the control strategies towards uncertainties that apply to the control and ECCD systems, such as the risk of misalignment of the current deposition or the possible inability to generate narrow current deposition.
Lie Group Solutions of Magnetohydrodynamics Equations and Their Well-Posedness
Directory of Open Access Journals (Sweden)
Fu-zhi Li
2016-01-01
Full Text Available Based on classical Lie Group method, we construct a class of explicit solutions of two-dimensional ideal incompressible magnetohydrodynamics (MHD equation by its infinitesimal generator. Via these explicit solutions we study the uniqueness and stability of initial-boundary problem on MHD.
A Complete 2D Stability Analysis of Fast MHD Shocks in an Ideal Gas
Trakhinin, Yuri
An algorithm of numerical testing of the uniform Lopatinski condition for linearized stability problems for 1-shocks is suggested. The algorithm is used for finding the domains of uniform stability, neutral stability, and instability of planar fast MHD shocks. A complete stability analysis of fast MHD shock waves is first carried out in two space dimensions for the case of an ideal gas. Main results are given for the adiabatic constant γ=5/3 (mono-atomic gas), that is most natural for the MHD model. The cases γ=7/5 (two-atomic gas) and γ>5/3 are briefly discussed. Not only the domains of instability and linear (in the usual sense) stability, but also the domains of uniform stability, for which a corresponding linearized stability problem satisfies the uniform Lopatinski condition, are numerically found for different given angles of inclination of the magnetic field behind the shock to the planar shock front. As is known, uniform linearized stability implies the nonlinear stability, that is local existence of discontinuous shock front solutions of a quasilinear system of hyperbolic conservation laws.
Generalized reduced magnetohydrodynamic equations
Energy Technology Data Exchange (ETDEWEB)
Kruger, S.E.
1999-02-01
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.
EFFECT OF PROFILES AND SHAPE ON IDEAL STABILITY OF ADVANCED TOKAMAK EQUILIBRIA
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MAKOWSKI,MA; CASPER,TA; FERRON,JR; TAYLOR,TS; TURNBULL,AD
2003-08-01
OAK-B135 The pressure profile and plasma shape, parameterized by elongation ({kappa}), triangularity ({delta}), and squareness ({zeta}), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P{sub 0}/
{approx} 2.0-4.5, weak negative central shear, high q{sub min} (> 2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs.
Non-axisymmetric ideal equilibrium and stability of ITER plasmas with rotating RMPs
Ham, C. J.; Cramp, R. G. J.; Gibson, S.; Lazerson, S. A.; Chapman, I. T.; Kirk, A.
2016-08-01
The magnetic perturbations produced by the resonant magnetic perturbation (RMP) coils will be rotated in ITER so that the spiral patterns due to strike point splitting which are locked to the RMP also rotate. This is to ensure even power deposition on the divertor plates. VMEC equilibria are calculated for different phases of the RMP rotation. It is demonstrated that the off harmonics rotate in the opposite direction to the main harmonic. This is an important topic for future research to control and optimize ITER appropriately. High confinement mode (H-mode) is favourable for the economics of a potential fusion power plant and its use is planned in ITER. However, the high pressure gradient at the edge of the plasma can trigger periodic eruptions called edge localized modes (ELMs). ELMs have the potential to shorten the life of the divertor in ITER (Loarte et al 2003 Plasma Phys. Control. Fusion 45 1549) and so methods for mitigating or suppressing ELMs in ITER will be important. Non-axisymmetric RMP coils will be installed in ITER for ELM control. Sampling theory is used to show that there will be significant a {{n}\\text{coils}}-{{n}\\text{rmp}} harmonic sideband. There are nine coils toroidally in ITER so {{n}\\text{coils}}=9 . This results in a significant n = 6 component to the {{n}\\text{rmp}}=3 applied field and a significant n = 5 component to the {{n}\\text{rmp}}=4 applied field. Although the vacuum field has similar amplitudes of these harmonics the plasma response to the various harmonics dictates the final equilibrium. Magnetic perturbations with toroidal mode number n = 3 and n = 4 are applied to a 15 MA, {{q}95}≈ 3 burning ITER plasma. We use a three-dimensional ideal magnetohydrodynamic model (VMEC) to calculate ITER equilibria with applied RMPs and to determine growth rates of infinite n ballooning modes (COBRA). The {{n}\\text{rmp}}=4 case shows little change in ballooning mode growth rate as the RMP is
Behaviors of helium in vanadium:Stability, diffusion, vacancy trapping and ideal tensile strength
Institute of Scientific and Technical Information of China (English)
Lijiang Gui; Yuelin Liu; Weitian Wang; Yinan Liu; Kameel Arshad; Ying Zhang; Guanghong Lu; Junen Yao
2013-01-01
The behaviors of helium in vanadium including stability, diffusion, and its interaction with vacancy as well as its effects on the ideal tensile strength was investigated by a first-principles method. The activation energy barrier of helium was calculated to be 0.09 eV, which is consistent with the experimental result. The results indicated that the vacancy can lead to a directed helium segregation into the vacancy to form a helium cluster since the vacancy provides a “lower atomic and electron density region”as a large driving force for helium binding. It is easy for a mono-vacancy to trap helium and form a HenV complex. The first-principles computational tensile test demonstrates that helium obviously decreased the tensile strength of vanadium.
Adventures in magnetohydrodynamics
Johnson, John L.
1988-03-01
The material in the report was presented in a series of three lectures presented on two days, October 29 and 30, 1987, at Nagoya University. A survey of magnetohydrodynamic theory was given as it applies to toroidal confinement. The material was broken down into four sections: (1) the derivation and justification of the MHD equations; (2) the equilibrium problem; (3) linearized stability; and (4) comments on nonlinear evolution, magnetic islands and transport theory.
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Energy Technology Data Exchange (ETDEWEB)
Gorlin, S.M.; Ljubimov, G.A.; Bitjurin, V.A.; Kovbasjuk, V.I.; Maximenko, V.I.; Medin, S.A.; Barshak, A.E.
1979-12-25
A magnetohydrodynamic device having a duct for a conducting gas to flow at an angle with the direction of the magnetic field induction vector is described. The duct is situated in the magnetic system and is provided with a plurality of electrodes adapted to interact electrically with the gas, whereas the cross-sectional shape of the duct working space is bounded by a closed contour formed by a curve inscribed into a rectangle. 1 claim.
Shift-and-inverse Lanczos algorithm for ideal MHD stability analysis
Energy Technology Data Exchange (ETDEWEB)
Chen, J.; Nakajima, N.; Okamoto, M.
1997-11-01
CAS3D and TERPSICHORE have been designed to analyze the global ideal MHD stability of three dimensional equilibria. Their critical part is to obtain the smallest eigenvalue and its corresponding eigenvector of a large but sparse real symmetric band matrix. In CAS3D the inverse iteration have been applied to do this and the spectral shift is computed by EISPACK eigensolver. It has been shown that application of such kind of software becomes very expensive in the sense of computational time and storage when matrix order and bandwidth become very large. Here this problem is resolved by using the Lanczos algorithm which is economical in CPU time and storage and particularly suitable for very large scale problems. The version of CAS3D2MN with shift-and-inverse Lanczos algorithm is called CAS3D2MNv1. Practical calculations in CAS3D2MNv1 indicate that the shift-and-inverse Lanczos recursion needs only 15 - 20 steps to calculate the smallest eigenvalue. The computation is reliable and efficient. The storage is much smaller and CPU time is saved significantly by 50 - 100 times compared with EISPACK subroutine. Finally the ballooning mode in three dimensional MHD equilibria has been mentioned briefly. (author)
Boquist, Carl W.; Marchant, David D.
1978-01-01
A ceramic-metal composite suitable for use in a high-temperature environment consists of a refractory ceramic matrix containing 10 to 50 volume percent of a continuous high-temperature metal reinforcement. In a specific application of the composite, as an electrode in a magnetohydrodynamic generator, the one surface of the electrode which contacts the MHD fluid may have a layer of varying thickness of nonreinforced refractory ceramic for electrode temperature control. The side walls of the electrode may be coated with a refractory ceramic insulator. Also described is an electrode-insulator system for a MHD channel.
Ren, Jing; Liu, Yueqiang; Liu, Yue; Medvedev, S. Yu; Wang, Zhirui; Xia, Guoliang
2016-11-01
The effects of an ideal/resistive conducting wall, the drift kinetic resonances, as well as the toroidal plasma flow, on the stability of the ideal external kink mode are numerically investigated for a reactor-relevant tokamak plasma with strongly negative triangularity (NTR) shaping. Comparison is made for a similar plasma equilibrium, but with positive triangularity (PTR). It is found that the ideal wall stabilization is less efficient for the kink stabilization in the NTR plasma due to a less ‘external’ eigenmode structure compared to the PTR plasma. The associated plasma displacement in the NTR plasma does not ‘balloon’ near the outboard mid-plane, as is normally the case for the pressure-driven kink-ballooning instability in PTR plasmas, but being more pronounced near the X-points. The toroidal flow plays a similar role for the kink stability for both NTR and PTR plasmas. The drift kinetic damping is less efficient for the ideal external kink mode in the NTR plasma, despite a somewhat larger fraction of the particle trapping near the plasma edge compared to the PTR equilibrium. However, the drift kinetic damping of the resistive wall mode (RWM) in the NTR plasma is generally as efficient as that of the PTR plasma, although the RWM window, in terms of the normalized pressure, is narrower for the NTR plasma.
Spectral analysis in magnetohydrodynamic equilibria
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Galindo, Felix [Departamento de Analisis Matematico, Universidad de Valladolid, Valladolid (Spain)
1998-12-11
It has been universally assumed that the spectrum of the magnetohydrodynamics equations, linearized around an equilibrium state, provides enough information on the short-term evolution of the plasma to study certain stability properties. We show that this is true if one takes into account viscous and resistive effects and the equilibrium satisfies certain regularity conditions. (author)
MAGNETOHYDRODYNAMIC MODELING FOR FUSION PLASMAS
Keppens, R.; Goedbloed, J. P.; Blokland, J. W. S.
2010-01-01
The magnetohydrodynamic model for fusion plasma dynamics governs the large-scale equilibrium properties, and sets the most stringent constraints on the parameter space accessible without violent disruptions. In conjunction with linear stability analysis in the complex tokamak geometry, the MHD parad
Two-wave interaction in ideal magnetohydrodynamics
T. V. Zaqarashvili; Roberts, B.
2006-01-01
The weakly nonlinear interaction of sound and linearly polarised Alfv{\\'e}n waves propagating in the same direction along an applied magnetic field is studied. It is found that a sound wave is coupled to the Alfv{\\'e}n wave with double period and wavelength when the sound and Alfv{\\'e}n speeds are equal. The Alfv{\\'e}n wave drives the sound wave through the ponderomotive force, while the sound wave returns energy back to the Alfv{\\'e}n wave through the parametric (swing) influence. As a resul...
Introduction to magnetohydrodynamics
Thompson, Ian
2016-01-01
Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.
Astrophysical Weighted Particle Magnetohydrodynamics
Gaburov, Evghenii
2010-01-01
This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD schem...
Variational Integrators for Reduced Magnetohydrodynamics
Kraus, Michael; Grasso, Daniela
2015-01-01
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws are described both at the continuous and discrete level. We verify...
Multifluid magnetohydrodynamic turbulent decay
Downes, Turlough P
2011-01-01
It is generally believed that turbulence has a significant impact on the dynamics and evolution of molecular clouds and the star formation which occurs within them. Non-ideal magnetohydrodynamic effects are known to influence the nature of this turbulence. We present the results of a suite of 512-cubed resolution simulations of the decay of initially super-Alfvenic and supersonic fully multifluid MHD turbulence. We find that ambipolar diffusion increases the rate of decay of the turbulence while the Hall effect has virtually no impact. The decay of the kinetic energy can be fitted as a power-law in time and the exponent is found to be -1.34 for fully multifluid MHD turbulence. The power spectra of density, velocity and magnetic field are all steepened significantly by the inclusion of non-ideal terms. The dominant reason for this steepening is ambipolar diffusion with the Hall effect again playing a minimal role except at short length scales where it creates extra structure in the magnetic field. Interestingl...
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
DEFF Research Database (Denmark)
Deriabine, Mikhail
2003-01-01
We consider the problem of heavy rigid body dynamics in an infinite volume of an ideal incompressible fluid performing a potential motion. If the body is axially-symmetric, then the system admits partial solutions, when the axis of symmetry is vertical, and the body sinks and rotates around its...... symmetry axis. These solutions were found by V.A.Steklov already at the end of the 19th century, and he also pointed out that in general these motions are unstable (as they are uniformly accelerated).Here we consider the more delicate question, namely we derive the conditions for stability of the rotation...
On energy conservation in extended magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Kimura, Keiji [Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Morrison, P. J. [Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712-1060 (United States)
2014-08-15
A systematic study of energy conservation for extended magnetohydrodynamic models that include Hall terms and electron inertia is performed. It is observed that commonly used models do not conserve energy in the ideal limit, i.e., when viscosity and resistivity are neglected. In particular, a term in the momentum equation that is often neglected is seen to be needed for conservation of energy.
Potential vorticity formulation of compressible magnetohydrodynamics.
Arter, Wayne
2013-01-04
Compressible ideal magnetohydrodynamics is formulated in terms of the time evolution of potential vorticity and magnetic flux per unit mass using a compact Lie bracket notation. It is demonstrated that this simplifies analytic solution in at least one very important situation relevant to magnetic fusion experiments. Potentially important implications for analytic and numerical modelling of both laboratory and astrophysical plasmas are also discussed.
Magnetohydrodynamic inertial reference system
Eckelkamp-Baker, Dan; Sebesta, Henry R.; Burkhard, Kevin
2000-07-01
Optical platforms increasingly require attitude knowledge and optical instrument pointing at sub-microradian accuracy. No low-cost commercial system exists to provide this level of accuracy for guidance, navigation, and control. The need for small, inexpensive inertial sensors, which may be employed in pointing control systems that are required to satisfy angular line-of-sight stabilization jitter error budgets to levels of 1-3 microradian rms and less, has existed for at least two decades. Innovations and evolutions in small, low-noise inertial angular motion sensor technology and advances in the applications of the global positioning system have converged to allow improvement in acquisition, tracking and pointing solutions for a wide variety of payloads. We are developing a small, inexpensive, and high-performance inertial attitude reference system that uses our innovative magnetohydrodynamic angular rate sensor technology.
Shchepetov, S. V.
2016-11-01
The stability of peeling modes in zero net current stellarator plasma is studied in high poloidal mode number m \\gg 1 approximation. The vacuum region solution is taken into account. Under these conditions in Mercier stable magnetic hill plasmas internal peeling modes are stable. External peeling modes can be unstable, but several limitations on them are found. It is shown that an analytically derived pressure gradient threshold is in reasonable agreement with the experimental observations and numerical calculations. The threshold decreases with increasing poloidal mode number m. It is shown, however, that higher modes may be stabilized due to finite ion Larmor radius effects. For the sake of definiteness, we have investigated peeling mode behavior in Mercier unstable plasma. It is shown that both external and internal peeling modes can be unstable in this regime. However, external and internal peeling modes in this case are definitely different.
Toi, K.; Ohdachi, S.; Ueda, R.; Watanabe, K. Y.; Nicolas, T.; Suzuki, Y.; Ogawa, K.; Tanaka, K.; Takemura, Y.; LHD Experiment Group
2016-09-01
Clear suppression of magnetic fluctuations associated with resistive interchange modes (RICs) is observed during long edge-localized-mode (ELM)-free phases of the H-mode plasma in an outward-shifted configuration of the Large Helical Decice, in which a steep pressure gradient is generated at the plasma edge in the magnetic hill. The ELM-free H-phase is interrupted by large amplitude ELMs which are thought to be induced through nonlinear evolution of the RICs having m = 1/n = 1 dominant component (m: poloidal mode number, n: toroidal one). The m = 1/n = 1 RIC amplitude is enhanced about 10 times compared with the H-phase level during each ELM. In most of the H-mode shots, the final ELM-free phase returns to L-phase by a large amplitude ELM. In the L-phase, the RIC amplitude is enhanced by a factor of ~3 compared with that in the H-phase, although the edge pressure gradient is reduced considerably. Linear resistive magnetohydrodynamic stability analysis is attempted using experimentally obtained equilibrium profiles. From the numerical analysis, the distance between the location of the steepest pressure gradient and the main mode resonance surface, i.e. the rotational transform ι = 1, is found to be important for a large growth of the m = 1/n = 1 RIC in the H-phase.
Impact of ideal MHD stability limits on high-beta hybrid operation
Piovesan, P.; Igochine, V.; Turco, F.; Ryan, D. A.; Cianciosa, M. R.; Liu, Y. Q.; Marrelli, L.; Terranova, D.; Wilcox, R. S.; Wingen, A.; Angioni, C.; Bock, A.; Chrystal, C.; Classen, I.; Dunne, M.; Ferraro, N. M.; Fischer, R.; Gude, A.; Holcomb, C. T.; Lebschy, A.; Luce, T. C.; Maraschek, M.; McDermott, R.; Odstrčil, T.; Paz-Soldan, C.; Reich, M.; Sertoli, M.; Suttrop, W.; Taylor, N. Z.; Weiland, M.; Willensdorfer, M.; The ASDEX Upgrade Team; The DIII-D Team; The EUROfusion MST1 Team
2017-01-01
The hybrid scenario is a candidate for stationary high-fusion gain tokamak operation in ITER and DEMO. To obtain such performance, the energy confinement and the normalized pressure {βN} must be maximized, which requires operating near or above ideal MHD no-wall limits. New experimental findings show how these limits can affect hybrid operation. Even if hybrids are mainly limited by tearing modes, proximity to the no-wall limit leads to 3D field amplification that affects plasma profiles, e.g. rotation braking is observed in ASDEX Upgrade throughout the plasma and peaks in the core. As a result, even the small ASDEX Upgrade error fields are amplified and their effects become visible. To quantify such effects, ASDEX Upgrade measured the response to 3D fields applied by 8× 2 non-axisymmetric coils as {βN} approaches the no-wall limit. The full n = 1 response profile and poloidal structure were measured by a suite of diagnostics and compared with linear MHD simulations, revealing a characteristic feature of hybrids: the n = 1 response is due to a global, marginally-stable n = 1 kink characterized by a large m = 1, n = 1 core harmonic due to q min being just above 1. A helical core distortion of a few cm forms and affects various core quantities, including plasma rotation, electron and ion temperature, and intrinsic W density. In similar experiments, DIII-D also measured the effect of this helical core on the internal current profile, providing information useful to understanding of the physics of magnetic flux pumping, i.e. anomalous current redistribution by MHD modes that keeps {{q}\\text{min}}>1 . Thanks to flux pumping, a broad current profile is maintained in DIII-D even with large on-axis current drive, enabling fully non-inductive operation at high {βN} up to 3.5-4.
Gas-Kinetic BGK Scheme for Three Dimensional Magnetohydrodynamics
Institute of Scientific and Technical Information of China (English)
Huazhong
2010-01-01
The gas-kinetic theory based flux splitting method has been successfully proposed for solving one- and two-dimensional ideal magnetohydrodynamics by Xu et al.[J. Comput. Phys., 1999; 2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter η is used to control the numerical dissipation in the flux splitting method.Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.
Han, Yujie; Luo, Zhimin; Yuwen, Lihui; Tian, Jing; Zhu, Xingrong; Wang, Lianhui
2013-02-01
A facile aqueous solution procedure has been developed to synthesize silver nanoparticles (Ag NPs) on reduced graphene oxide (RGO) (RGO/Ag NPs) with starch as an ideal reductant and stabilizer in one pot under microwave irradiation. Graphene oxide and Ag(NH3)2+ were reduced simultaneously by starch in the process of forming Ag NPs. The size of Ag NPs decorated on the RGO sheets is about 20-50 nm and the average size of Ag NPs on RGO is 34 nm calculated by X-ray diffraction. RGO and RGO/Ag NPs prepared with starch show good stability in aqueous solution. With the decoration of Ag NPs on RGO, Raman intensity of RGO increased evidently. Antimicrobial activity of RGO/Ag NPs was investigated against the gram negative bacteria Pseudomonous aeruginosa. The minimum inhibitory concentration (MIC) of RGO/Ag NPs is 0.2 wt%. The antimicrobial activity of RGO/Ag NPs is stronger than Ag NPs because of the synergic effect of RGO and Ag NPs.
BOOK REVIEW: Nonlinear Magnetohydrodynamics
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Anisotropic Diffusion in Mesh-Free Numerical Magnetohydrodynamics
Hopkins, Philip F
2016-01-01
We extend recently-developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect), and turbulent 'eddy diffusion.' We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV) as well as smoothed-particle hydrodynamics (SPH). We show the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behavior even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators ...
Global magnetohydrodynamic instabilities in the L-2M stellarator
Energy Technology Data Exchange (ETDEWEB)
Mikhailov, M. I., E-mail: mikhaylov-mi@nrcki.ru [National Research Centre Kurchatov Institute (Russian Federation); Shchepetov, S. V., E-mail: shch@fpl.gpi.ru [Russian Academy of Sciences, Prokhorov General Physics Institute (Russian Federation); Nührenberg, C.; Nührenberg, J. [Max-Planck-Institut für Plasmaphysik (Germany)
2015-12-15
Analysis of global magnetohydrodynamic (MHD) instabilities in the L-2M stellarator (Prokhorov General Physics Institute, Russian Academy of Sciences) is presented. The properties of free-boundary equilibria states are outlined, the stability conditions for small-scale modes are briefly discussed, and the number of trapped particles is estimated. All the magnetic configurations under study are stable against ballooning modes. It is shown that global ideal internal MHD modes can be found reliably only in Mercier unstable plasmas. In plasma that is stable with respect to the Mercier criterion, global unstable modes that are localized in the vicinity of the free plasma boundary and are not associated with any rational magnetic surface inside the plasma (the so-called peeling modes) can be found. The radial structure of all perturbations under study is almost entirely determined by the poloidal coupling of harmonics. The results of calculations are compared with the available experimental data.
Constructing a class of topological solitons in magnetohydrodynamics.
Thompson, Amy; Swearngin, Joe; Wickes, Alexander; Bouwmeester, Dirk
2014-04-01
We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, nt and np, respectively. The special case of nt=1 and np=1 corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for nt∈Z+ and np=1, these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity, and we estimate the soliton lifetime in such a medium as a function of the toroidal winding number.
Experiments in Magnetohydrodynamics
Rayner, J. P.
1970-01-01
Describes three student experiments in magnetohydrodynamics (MHD). In these experiments, it was found that the electrical conductivity of the local water supply was sufficient to demonstrate effectively some of the features of MHD flowmeters, generators, and pumps. (LC)
Magnetohydrodynamic fluidic system
Lee, Abraham P.; Bachman, Mark G.
2004-08-24
A magnetohydrodynamic fluidic system includes a reagent source containing a reagent fluid and a sample source containing a sample fluid that includes a constituent. A reactor is operatively connected to the supply reagent source and the sample source. MHD pumps utilize a magnetohydrodynamic drive to move the reagent fluid and the sample fluid in a flow such that the reagent fluid and the sample fluid form an interface causing the constituent to be separated from the sample fluid.
Variational integrators for reduced magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Kraus, Michael, E-mail: michael.kraus@ipp.mpg.de [Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, 85748 Garching (Germany); Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, 85748 Garching (Germany); Tassi, Emanuele, E-mail: tassi@cpt.univ-mrs.fr [Aix-Marseille Université, Université de Toulon, CNRS, CPT, UMR 7332, 163 avenue de Luminy, case 907, 13288 cedex 9 Marseille (France); Grasso, Daniela, E-mail: daniela.grasso@infm.polito.it [ISC-CNR and Politecnico di Torino, Dipartimento Energia, C.so Duca degli Abruzzi 24, 10129 Torino (Italy)
2016-09-15
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
Variational integrators for reduced magnetohydrodynamics
Kraus, Michael; Tassi, Emanuele; Grasso, Daniela
2016-09-01
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.
Magnetohydrodynamic Turbulence and the Geodynamo
Shebalin, John V.
2016-01-01
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
Current-sheet formation in incompressible electron magnetohydrodynamics
DEFF Research Database (Denmark)
Ruban, Victor P.
2002-01-01
The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonl......The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local...
A Simple Ideal MHD Model of Vertical Disruption Events in Tokamaks
Fitzpatrick, Richard
2008-11-01
A simple model of axisymmetric vertical disruption events (VDEs) in tokamaks is presented in which the halo current force exerted on the vacuum vessel is calculated directly from linear, marginally stable, ideal-magnetohydrodynamical (MHD) stability analysis. The basic premise of the model is that the halo current force modifies pressure balance at the edge of the plasma, and therefore also modifies ideal-MHD plasma stability. In order to prevent the ideal vertical instability, responsible for the VDE, from growing on the very short Alfv'en time- scale, the halo current force must adjust itself such that the instability is rendered marginally stable. The model predicts halo currents which are similar in magnitude to those observed experimentally. An approximate non-axisymmetric version of the model is developed in order to calculate the toroidal peaking factor of the halo current force.
Directory of Open Access Journals (Sweden)
Yingchao Wang
2016-01-01
Full Text Available The classification of surrounding rock stability is the critical problem in tunneling engineering. In order to decrease engineering disasters, the surrounding rock stability should be accurately evaluated. The ideal point method is applied to the classification of surrounding rock stability. Considering the complexity of surrounding rock classification, some factors such as rock uniaxial compressive strengthen, integrality coefficient of rock mass, the angle between tunnel axis and the main joint, joints condition, and seepage measurement of groundwater are selected as evaluation indices. The weight coefficients of these evaluation indices are determined by the objective and subjective weighting method, consisting with the delphi method and the information entropy theory. The objective and subjective weighting method is exact and reliable to determine the weights of evaluation indices, considering not only the expert’s experiences, but also objectivity of the field test data. A new composite model is established for evaluating the surrounding rock stability based on the ideal point method and the objective and subjective weighting method. The present model is applied to Beigu mountain tunnel in Jiangsu province, China. The result is in good agreement with practical situation of surrounding rock, which proves that the ideal point method used to classify the surrounding rock in tunnels is reasonable and effective. The present model is simple and has very strong operability, which possesses a good prospect of engineering application.
Poli, Francesca
2012-10-01
Steady state scenarios envisaged for ITER aim at optimizing the bootstrap current, while maintaining sufficient confinement and stability to provide the necessary fusion yield. Non-inductive scenarios will need to operate with Internal Transport Barriers (ITBs) in order to reach adequate fusion gain at typical currents of 9 MA. However, the large pressure gradients associated with ITBs in regions of weak or negative magnetic shear can be conducive to ideal MHD instabilities in a wide range of βN, reducing the no-wall limit. Scenarios are established as relaxed flattop states with time-dependent transport simulations with TSC [1]. Fully non-inductive configurations with current in the range of 7-10 MA and various heating mixes (NB, EC, IC and LH) have been studied against variations of the pressure profile peaking and of the Greenwald fraction. It is found that stable equilibria have qmin> 2 and moderate ITBs at 2/3 of the minor radius [2]. The ExB flow shear from toroidal plasma rotation is expected to be low in ITER, with a major role in the ITB dynamics being played by magnetic geometry. Combinations of H&CD sources that maintain reverse or weak magnetic shear profiles throughout the discharge and ρ(qmin)>=0.5 are the focus of this work. The ITER EC upper launcher, designed for NTM control, can provide enough current drive off-axis to sustain moderate ITBs at mid-radius and maintain a non-inductive current of 8-9MA and H98>=1.5 with the day one heating mix. LH heating and current drive is effective in modifying the current profile off-axis, facilitating the formation of stronger ITBs in the rampup phase, their sustainment at larger radii and larger bootstrap fraction. The implications for steady state operation and fusion performance are discussed.[4pt] [1] Jardin S.C. et al, J. Comput. Phys. 66 (1986) 481[0pt] [2] Poli F.M. et al, Nucl. Fusion 52 (2012) 063027.
Multi-region relaxed magnetohydrodynamics with flow
Dennis, G R; Dewar, R L; Hole, M J
2014-01-01
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Multi-region relaxed magnetohydrodynamics with flow
Energy Technology Data Exchange (ETDEWEB)
Dennis, G. R., E-mail: graham.dennis@anu.edu.au; Dewar, R. L.; Hole, M. J. [Research School of Physics and Engineering, Australian National University, ACT 0200 (Australia); Hudson, S. R. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States)
2014-04-15
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite, our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
Mohseni, F; Succi, S; Herrmann, H J
2015-01-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfv\\'en waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to $\\sigma^{-\\frac{1}{2}}$, $\\sigma$ being the conductivity, w...
Magnetohydrodynamics of the sun
Priest, Eric
2014-01-01
Magnetohydrodynamics of the Sun is a completely new up-to-date rewrite from scratch of the 1982 book Solar Magnetohydrodynamics, taking account of enormous advances in understanding since that date. It describes the subtle and complex interaction between the Sun's plasma atmosphere and its magnetic field, which is responsible for many fascinating dynamic phenomena. Chapters cover the generation of the Sun's magnetic field by dynamo action, magnetoconvection and the nature of photospheric flux tubes such as sunspots, the heating of the outer atmosphere by waves or reconnection, the structure of prominences, the nature of eruptive instability and magnetic reconnection in solar flares and coronal mass ejections, and the acceleration of the solar wind by reconnection or wave-turbulence. It is essential reading for graduate students and researchers in solar physics and related fields of astronomy, plasma physics and fluid dynamics. Problem sets and other resources are available at www.cambridge.org/9780521854719.
Thermoacoustic magnetohydrodynamic electrical generator
Wheatley, John C.; Swift, Gregory W.; Migliori, Albert
1986-01-01
A thermoacoustic magnetohydrodynamic electrical generator includes an intrinsically irreversible thermoacoustic heat engine coupled to a magnetohydrodynamic electrical generator. The heat engine includes an electrically conductive liquid metal as the working fluid and includes two heat exchange and thermoacoustic structure assemblies which drive the liquid in a push-pull arrangement to cause the liquid metal to oscillate at a resonant acoustic frequency on the order of 1,000 Hz. The engine is positioned in the field of a magnet and is oriented such that the liquid metal oscillates in a direction orthogonal to the field of the magnet, whereby an alternating electrical potential is generated in the liquid metal. Low-loss, low-inductance electrical conductors electrically connected to opposite sides of the liquid metal conduct an output signal to a transformer adapted to convert the low-voltage, high-current output signal to a more usable higher voltage, lower current signal.
Lectures on magnetohydrodynamical drives
Loigom, Villem
The paper deals with nonconventional types of electrical machines and drives - magnetohydrodynamical (MHD) machines and drives. In cardinal it is based on the research conducted with participation of the author in Tallinn Technical University at the Institute of Electrical Drives and Power Electronics, where the use of magnetohydrodynamical motors and drives in the metallurgical and casting industries have been studied for a long time. Major research interests include the qualities and applications of the induction MHD-drives for set in the motion (pumping, turning, dosing, mixing, etc.) non-ferrous molten metals like Al, Mg, Sn, Pb, Na, K, and their alloys. The first part of the paper describes induction MHD motors and their electrohydraulical qualities. In the second part energy conversion problems are described. Also, on the basis of the analogy between electromechanical and electrohydraulical phenomenas, static and dynamic qualities of MHD drives with induction MHD machines are discussed.
Evolution of Accretion Discs around a Kerr Black Hole using Extended Magnetohydrodynamics
Foucart, Francois; Gammie, Charles F; Quataert, Eliot
2015-01-01
Black holes accreting well below the Eddington rate are believed to have geometrically thick, optically thin, rotationally supported accretion discs in which the Coulomb mean free path is large compared to $GM/c^2$. In such an environment, the disc evolution may differ significantly from ideal magnetohydrodynamic predictions. We present non-ideal global axisymmetric simulations of geometrically thick discs around a rotating black hole. The simulations are carried out using a new code ${\\rm\\it grim}$, which evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines, and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. We find that the pressure anisotropy grows to match the ...
Future of Magnetohydrodynamic Ship Propulsion,
1983-08-16
83 FOREIGN TECHNOLOGY DIVISION FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION by A.P. Baranov DTIQ ~E tJ Approved for public release; 0.. distribution...MAGNETOHYDRODYNAMIC SHIP PROPULSION By: A.P. Baranov -,English pages: 10 Source: Sudostroyeniye, Nr. 12, December 1966, pp. 3-6 . Country of origin: USSR X...equations, etc. merged into this translation were extracted from the best quality copy available. FUTURE OF MAGNETOHYDRODYNAMIC SHIP PROPULSION A. P
Protostellar outflows with Smoothed Particle Magnetohydrodynamics (SPMHD)
Bürzle, Florian; Stasyszyn, Federico; Dolag, Klaus; Klessen, Ralf S
2011-01-01
The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D AMR/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the Smoothed Particle Hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly resolved. In this work, we use an approach where we evolve the magnetic field via the induction equation, augmented with stability correction and divergence cleaning schemes. We consider the collapse of a rotating core of one solar mass, threaded by a weak magnetic field initially parallel to the rotation axis so that the core is magnetically supercritical. We show, that Smoothed Particle Magnetohydrodynamics (SPMHD) is a...
Test particle acceleration in explosive magnetohydrodynamic reconnection
Ripperda, Bart; Xia, Chun; Keppens, Rony
2016-01-01
Magnetic reconnection is the mechanism behind many violent phenomena in the universe. We demonstrate that energy released during reconnection can lead to non-thermal particle distribution functions. We use a method in which we combine resistive magnetohydrodynamics (MHD) with relativistic test particle dynamics. Using our open-source grid-adaptive MPI-AMRVAC software, we simulate global MHD evolution combined with test particle treatments in MHD snapshots. This approach is used to evaluate particle acceleration in explosive reconnection. The reconnection is triggered by an ideal tilt instability in two-and-a-half dimensional (2.5D) scenarios and by a combination of ideal tilt and kink instabilities in three-dimensional (3D) scenarios. These instabilities occur in a system with two parallel, adjacent, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and a separation on Alfv\\'enic t...
Magnetohydrodynamics simulations on graphics processing units
Wong, Hon-Cheng; Feng, Xueshang; Tang, Zesheng
2009-01-01
Magnetohydrodynamics (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution methods for solving the ideal MHD equations are computationally expensive and Beowulf clusters or even supercomputers are often used to run the codes that implemented these methods. With the advent of the Compute Unified Device Architecture (CUDA), modern graphics processing units (GPUs) provide an alternative approach to parallel computing for scientific simulations. In this paper we present, to the authors' knowledge, the first implementation to accelerate computation of MHD simulations on GPUs. Numerical tests have been performed to validate the correctness of our GPU MHD code. Performance measurements show that our GPU-based implementation achieves speedups of 2 (1D problem with 2048 grids), 106 (2D problem with 1024^2 grids), and 43 (3D problem with 128^3 grids), respec...
Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations
Directory of Open Access Journals (Sweden)
Jianwen Zhang
2008-02-01
Full Text Available This paper is concerned with an initial boundary value problem in one-dimensional magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the case that vacuum can be allowed initially.
Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations
Directory of Open Access Journals (Sweden)
Zhang Jianwen
2008-01-01
Full Text Available This paper is concerned with an initial boundary value problem in one-dimensional magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the case that vacuum can be allowed initially.
The hydrodynamic instability of powerful cylindrical magnetohydrodynamic pumps
Energy Technology Data Exchange (ETDEWEB)
Valdmane, R.A.; Ulmanis, L.Ya.; Valdamanis, Ya.Ya.
1984-01-01
A numerical calculation is the basis for analyzing the issues of stability of the speed profile in channels of powerful cylindrical magnetohydrodynamic (MGD) pumps. A one dimensional hydraulic model is used in the calculations. The questions about stability of movement relative to transverse perturbations in speed are discussed. It is shown that at high values of the parameter epsilon and the radius of the channel the movement is unstable with respect to the transverse shifts. The results are of interest for studies of liquid metal magnetohydrodynamic generators.
Lollino, Piernicola; Andriani, Gioacchino Francesco; Fazio, Nunzio Luciano; Perrotti, Michele
2016-04-01
Strain-softening under low confinement stress, i.e. the drop of strength that occurs in the post-failure stage, represents a key factor of the stress-strain behavior of rocks. However, this feature of the rock behavior is generally underestimated or even neglected in the assessment of boundary value problems of intact soft rock masses. This is typically the case when the stability of intact rock masses is treated by means of limit equilibrium or finite element analyses, for which rigid-plastic or elastic perfectly-plastic constitutive models, generally implementing peak strength conditions of the rock, are respectively used. In fact, the aforementioned numerical techniques are characterized by intrinsic limitations that do not allow to account for material brittleness, either for the method assumptions or due to numerical stability problems, as for the case of the finite element method, unless sophisticated regularization techniques are implemented. However, for those problems that concern the stability of intact soft rock masses at low stress levels, as for example the stability of shallow underground caves or that of rock slopes, the brittle stress-strain response of rock in the post-failure stage cannot be disregarded due to the risk of overestimation of the stability factor. This work is aimed at highlighting the role of post-peak brittleness of soft rocks in the analysis of specific ideal problems by means of the use of a hybrid finite-discrete element technique (FDEM) that allows for the simulation of the rock stress-strain brittle behavior in a proper way. In particular, the stability of two ideal cases, represented by a shallow underground rectangular cave and a vertical cliff, has been analyzed by implementing a post-peak brittle behavior of the rock and the comparison with a non-brittle response of the rock mass is also explored. To this purpose, the mechanical behavior of a soft calcarenite belonging to the Calcarenite di Gravina formation, extensively
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
Solitary vortexes in magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Vainshtein, S.I.
1985-12-01
Stationary configurations in magnetohydrodynamics are investigated for the following two particular cases: (1) there is no motion, which corresponds to a state of magnetostatic equilibrium; and (2) the magnetic field intensity becomes zero, i.e., hydrodynamic vortexes are involved. It is shown that in certain cases the line-of-force topology must be sufficiently simple in order before a stationary or equilibrium state can be achieved. It is also shown that in the two-dimensional case, the magnetic surfaces of an equilibrium configuration represent coaxial cylindrical surfaces. 12 references.
Conservation of Circulation in Magnetohydrodynamics
Bekenstein, J D; Bekenstein, Jacob D.; Oron, Asaf
2000-01-01
We demonstrate, both at the Newtonian and (general) relativistic levels, theexistence of a generalization of Kelvin's circulation theorem (for pure fluids)which is applicable to perfect magnetohydrodynamics. The argument is based onthe least action principle for magnetohydrodynamic flow. Examples of the newconservation law are furnished. The new theorem should be helpful inidentifying new kinds of vortex phenomena distinct from magnetic ropes or fluidvortices.
Lutsko, James F
2016-01-01
Dense protein clusters are known to play an important role in nucleation of protein crystals from dilute solutions. While these have generally been thought to be formed from a metastable phase, the observation of similar, if not identical, clusters above the critical point for the dilute-solution/strong-solution phase transition has thrown this into doubt. Furthermore, the observed clusters are stable for relatively long times. Because protein aggregation plays an important role in some pathologies, understanding the nature of such clusters is an important problem. One mechanism for the stabilization of such structures was proposed by Pan, Vekilov and Lubchenko and was investigated using a DDFT model which confirmed the viability of the model. Here, we revisit that model and incorporate additional physics in the form of state-dependent reaction rates. We show by a combination of numerical results and general arguments that the state-dependent rates disrupt the stability mechanism. Finally, we argue that the s...
Magnetohydrodynamic process in solar activity
Directory of Open Access Journals (Sweden)
Jingxiu Wang
2014-01-01
Full Text Available Magnetohydrodynamics is one of the major disciplines in solar physics. Vigorous magnetohydrodynamic process is taking place in the solar convection zone and atmosphere. It controls the generating and structuring of the solar magnetic fields, causes the accumulation of magnetic non-potential energy in the solar atmosphere and triggers the explosive magnetic energy release, manifested as violent solar flares and coronal mass ejections. Nowadays detailed observations in solar astrophysics from space and on the ground urge a great need for the studies of magnetohydrodynamics and plasma physics to achieve better understanding of the mechanism or mechanisms of solar activity. On the other hand, the spectacular solar activity always serves as a great laboratory of magnetohydrodynamics. In this article, we reviewed a few key unresolved problems in solar activity studies and discussed the relevant issues in solar magnetohydrodynamics.
Free-boundary ideal MHD modes in W7-AS
Energy Technology Data Exchange (ETDEWEB)
Merkel, P.; Nuehrenberg, C. [Max-Planck-Institut fuer Plasmaphysik, Teilinstitut Greifswald, Greifswald (Germany); Cooper, W.A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-09-01
The CAS3D stability code may now be used to analyze the ideal magnetohydrodynamic energy principle for three-dimensional plasmas surrounded by a vacuum region, i.e. for perturbations which may deform the plasma-vacuum interface because of a non-vanishing normal component on this surface. A Green`s function technique is used here to determine the vacuum energy contribution from a surface integral with the plasma-vacuum interface as domain of integration. Assets of this procedure are that it does not require to continue either the coordinate system nor the perturbation functions into the vacuum region. The application of the CAS3D free-boundary stability code to a set of finite-{beta} W7-AS plasma configurations, computationally generated from the W7-AS coil data, shows that unstable, radially extended free-boundary modes exist in equilibria of this set, for which the local Mercier stability criterion detects stability. This is in contrast to the behaviour of the fixed-boundary modes, for which the point of marginal stability approximately coincides with the one given by the local stability analysis. Corresponding results from the TERPSICHORE and CAS3D codes are in good agreement. (author) 6 figs., 16 refs.
Magnetohydrodynamics of blood flow.
Keltner, J R; Roos, M S; Brakeman, P R; Budinger, T F
1990-10-01
The changes in hydrostatic pressure and electrical potentials across vessels in the human vasculature in the presence of a large static magnetic field are estimated to determine the feasibility of in vivo NMR spectroscopy at fields as high as 10 T.A 10-T magnetic field changes the vascular pressure in a model of the human vasculature by less than 0.2%. An exact solution to the magnetohydrodynamic equations describing a conducting fluid flowing transverse to a static magnetic field in a nonconducting, straight, circular tube is used. This solution is compared to an approximate solution that assumes that no magnetic fields are induced in the fluid and that has led previous investigators to predict significant biological effects from static magnetic fields. Experimental results show that the exact solution accurately predicts the magnetohydrodynamic slowing of 15% NaCl flowing transverse to 2.3- and 4.7-T magnetic fields for fluxes below 0.5 liter/min while the approximate solution predicts a much more retarded flow.
Spectrum of multi-region-relaxed magnetohydrodynamic modes in topologically toroidal geometry
Dewar, Robert L; Tuen,; Hole, Matthew J
2016-01-01
A general formulation of the problem of calculating the spectrum of stable and unstable eigenmodes of linearized perturbations about a magnetically confined toroidal plasma is presented. The analysis is based on a new hydromagnetic dynamical model, Multi-region Relaxed Magnetohydrodynamics (MRxMHD), which models the plasma-magnetic field system as consisting of multiple regions, containing compressible Euler fluid and Taylor-relaxed magnetic field, separated by flexible ideal-MHD current sheets. This is illustrated using a first-principles analysis of a two-region slab geometry, with periodic boundary conditions to model the outer regions of typical tokamak or reversed-field pinch plasmas. The lowest and second-lowest eigenvalues in plasmas unstable to tearing and kink-tearing modes are calculated. Very near marginal stability the lowest mode obtained using the incompressible approximation to the kinetic energy normalization of the present study is shown to correspond to the eigenvalues found in previous stud...
Beyond ideal magnetohydrodynamics: Resistive, reactive and relativistic plasmas
Andersson, N; Hawke, I; Comer, G L
2016-01-01
We develop a new framework for the modelling of charged fluid dynamics in general relativity. The model, which builds on a recently developed variational multi-fluid model for dissipative fluids, accounts for relevant effects like the inertia of both charge currents and heat and, for mature systems, the decoupling of superfluid components. We discuss how the model compares to standard relativistic magnetohydronamics and consider the connection between the fluid dynamics, the microphysics and the underlying equation of state. As illustrations of the formalism, we consider three distinct two-fluid models describing i) an Ohm's law for resistive charged flows, ii) a relativistic heat equation, and iii) an equation representing the momentum of a decoupled superfluid component. As a more complex example, we also formulate a three-fluid model which demonstrates the thermo-electric effect. This framework allows us to model neutron stars (and related systems) at a hierarchy of increasingly complex levels, and should ...
Beyond ideal magnetohydrodynamics: From fibration to 3+1 foliation
Andersson, N; Dionysopoulou, K; Comer, G L
2016-01-01
We consider a resistive multi-fluid framework from the 3+1 space-time foliation point-of-view, paying particular attention to issues relating to the use of multi-parameter equations of state and the associated inversion from evolved to primitive variables. We highlight relevant numerical issues that arise for general systems with relative flows. As an application of the new formulation, we consider a three-component system relevant for hot neutron stars. In this case we let the baryons (neutrons and protons) move together, but allow heat and electrons to exhibit relative flow. This reduces the problem to three momentum equations; overall energy-momentum conservation, a generalised Ohm's law and a heat equation. Our results provide a hierarchy of increasingly complex models and prepare the ground for new state-of-the-art simulations of relevant scenarios in relativistic astrophysics.
Anisotropic diffusion in mesh-free numerical magnetohydrodynamics
Hopkins, Philip F.
2017-04-01
We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.
Generalized shock conditions and the contact discontinuity in the Hall-magnetohydrodynamics model
Energy Technology Data Exchange (ETDEWEB)
Hameiri, Eliezer [Courant Institute of Mathematical Sciences, New York University, New York 10012 (United States)
2013-02-15
It is shown that shocks and contact discontinuities in the Hall-magnetohydrodynamics (HMHD) model must satisfy solvability conditions that replace some of the familiar Rankine-Hugoniot jump conditions when the latter do not apply due to singular behavior of fluxes of conserved quantities. Some of these conditions depend on the larger topology of the plasma and magnetic field and are not merely 'local.' The contact discontinuity which separates two adjoining plasma regions or plasma and vacuum regions is the simplest case where the new jump conditions are applicable and is discussed for a toroidal plasma with sheared magnetic field such as the tokamak, but with no initial mass flow. It is proven that a static discontinuous tokamak-like equilibrium is linearly stable in the HMHD model if it is linearly stable within the ideal magnetohydrodynamics model, provided that the electron pressure depends only on the density, and some other restrictions on the ratio of pressure to density gradients also apply. When the electron pressure does depend on two thermodynamic variables, a sufficient condition for Hall-MHD plasma stability is derived as well.
Accurate, meshless methods for magnetohydrodynamics
Hopkins, Philip F.; Raives, Matthias J.
2016-01-01
Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.
Smith, S. P.; Jardin, S. C.; Freidberg, J. P.; Guazzotto, L.
2008-11-01
The ideal MHD linear stability normal modes and frequencies for a circular cylindrical plasma (having an arbitrary equilibrium flow) interacting with a resistive wall are calculated. Projections of the plasma displacement are expanded as finite elements, using a Galerkin approach to form the inner products. A Green's function approach is taken to couple the perturbed wall currents to the plasma surface perturbations. The standard linear form, φAx=B x, is obtained by introducing an auxiliary variable, u=φξ+iV .∇ξ, and an additional degree of freedom representing the perturbed current in the resistive wall. It is shown that having projections aligned with (or perpendicular to) the equilibrium magnetic field is more important for correctly calculating the slow wave part of the spectrum than having a higher order finite element expansion with non-field-aligned projections. Investigations into the effects of axial and azimuthal flows on the resistive wall mode are also presented.
Magnetohydrodynamic Shearing Waves
Johnson, B M
2006-01-01
I consider the nonaxisymmetric linear theory of an isothermal magnetohydrodynamic (MHD) shear flow. The analysis is performed in the shearing box, a local model appropriate for a thin disk geometry. Linear perturbations in this model can be decomposed in terms of shearing waves (shwaves), which appear spatially as plane waves in a frame comoving with the shear. The time dependence of these waves cannot in general be expressed in terms of a frequency eigenvalue as in a normal mode decomposition, and numerical integration of a set of first-order amplitude equations is required for a complete characterization of their behavior. Their generic time dependence, however, is oscillatory with slowly-varying frequency and amplitude, and one can construct accurate analytic solutions by applying the Wentzel-Kramers-Brillouin method to the full set of amplitude equations. For the bulk of wavenumber space, therefore, the shwaves are well-approximated as modes with time-dependent frequencies and amplitudes. The incompressiv...
Introduction to modern magnetohydrodynamics
Galtier, Sébastien
2016-01-01
Ninety-nine percent of ordinary matter in the Universe is in the form of ionized fluids, or plasmas. The study of the magnetic properties of such electrically conducting fluids, magnetohydrodynamics (MHD), has become a central theory in astrophysics, as well as in areas such as engineering and geophysics. This textbook offers a comprehensive introduction to MHD and its recent applications, in nature and in laboratory plasmas; from the machinery of the Sun and galaxies, to the cooling of nuclear reactors and the geodynamo. It exposes advanced undergraduate and graduate students to both classical and modern concepts, making them aware of current research and the ever-widening scope of MHD. Rigorous derivations within the text, supplemented by over 100 illustrations and followed by exercises and worked solutions at the end of each chapter, provide an engaging and practical introduction to the subject and an accessible route into this wide-ranging field.
Current-sheet formation in incompressible electron magnetohydrodynamics.
Ruban, V P
2002-04-01
The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia.
Review of magnetohydrodynamic pump applications
National Research Council Canada - National Science Library
Al-Habahbeh, O.M; Al-Saqqa, M; Safi, M; Abo Khater, T
2016-01-01
Magneto-hydrodynamic (MHD) principle is an important interdisciplinary field. One of the most important applications of this effect is pumping of materials that are hard to pump using conventional pumps...
Conservation of Circulation in Magnetohydrodynamics
Bekenstein, Jacob D.; Oron, Asaf
2000-01-01
We demonstrate, both at the Newtonian and (general) relativistic levels, the existence of a generalization of Kelvin's circulation theorem (for pure fluids) which is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
Conservation of circulation in magnetohydrodynamics
Bekenstein; Oron
2000-10-01
We demonstrate at both the Newtonian and (general) relativistic levels the existence of a generalization of Kelvin's circulation theorem (for pure fluids) that is applicable to perfect magnetohydrodynamics. The argument is based on the least action principle for magnetohydrodynamic flow. Examples of the new conservation law are furnished. The new theorem should be helpful in identifying new kinds of vortex phenomena distinct from magnetic ropes or fluid vortices.
Magnetohydrodynamic Augmented Propulsion Experiment
Litchford, Ron J.; Cole, John; Lineberry, John; Chapman, Jim; Schmidt, Harold; Cook, Stephen (Technical Monitor)
2002-01-01
A fundamental obstacle to routine space access is the specific energy limitations associated with chemical fuels. In the case of vertical take-off, the high thrust needed for vertical liftoff and acceleration to orbit translates into power levels in the 10 GW range. Furthermore, useful payload mass fractions are possible only if the exhaust particle energy (i.e., exhaust velocity) is much greater than that available with traditional chemical propulsion. The electronic binding energy released by the best chemical reactions (e.g., LOX/LH2 for example, is less than 2 eV per product molecule (approx. 1.8 eV per H2O molecule), which translates into particle velocities less than 5 km/s. Useful payload fractions, however, will require exhaust velocities exceeding 15 km/s (i.e., particle energies greater than 20 eV). As an added challenge, the envisioned hypothetical RLV (reusable launch vehicle) should accomplish these amazing performance feats while providing relatively low acceleration levels to orbit (2-3g maximum). From such fundamental considerations, it is painfully obvious that planned and current RLV solutions based on chemical fuels alone represent only a temporary solution and can only result in minor gains, at best. What is truly needed is a revolutionary approach that will dramatically reduce the amount of fuel and size of the launch vehicle. This implies the need for new compact high-power energy sources as well as advanced accelerator technologies for increasing engine exhaust velocity. Electromagnetic acceleration techniques are of immense interest since they can be used to circumvent the thermal limits associated with conventional propulsion systems. This paper describes the Magnetohydrodynamic Augmented Propulsion Experiment (MAPX) being undertaken at NASA Marshall Space Flight Center (MSFC). In this experiment, a 1-MW arc heater is being used as a feeder for a 1-MW magnetohydrodynamic (MHD) accelerator. The purpose of the experiment is to demonstrate
Acceleration of particles in imbalanced magnetohydrodynamic turbulence.
Teaca, Bogdan; Weidl, Martin S; Jenko, Frank; Schlickeiser, Reinhard
2014-08-01
The present work investigates the acceleration of test particles, relevant to the solar-wind problem, in balanced and imbalanced magnetohydrodynamic turbulence (terms referring here to turbulent states possessing zero and nonzero cross helicity, respectively). These turbulent states, obtained numerically by prescribing the injection rates for the ideal invariants, are evolved dynamically with the particles. While the energy spectrum for balanced and imbalanced states is known, the impact made on particle heating is a matter of debate, with different considerations giving different results. By performing direct numerical simulations, resonant and nonresonant particle accelerations are automatically considered and the correct turbulent phases are taken into account. For imbalanced turbulence, it is found that the acceleration rate of charged particles is reduced and the heating rate diminished. This behavior is independent of the particle gyroradius, although particles that have a stronger adiabatic motion (smaller gyroradius) tend to experience a larger heating.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Solar Flares: Magnetohydrodynamic Processes
Directory of Open Access Journals (Sweden)
Kazunari Shibata
2011-12-01
Full Text Available This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 10^32 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence, local enhancement of electric current in the corona (formation of a current sheet, and rapid dissipation of electric current (magnetic reconnection that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely, while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.
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.
Strings and large scale magnetohydrodynamics
Olesen, P
1995-01-01
From computer simulations of magnetohydrodynamics one knows that a turbulent plasma becomes very intermittent, with the magnetic fields concentrated in thin flux tubes. This situation looks very "string-like", so we investigate whether strings could be solutions of the magnetohydrodynamics equations in the limit of infinite conductivity. We find that the induction equation is satisfied, and we discuss the Navier-Stokes equation (without viscosity) with the Lorentz force included. We argue that the string equations (with non-universal maximum velocity) should describe the large scale motion of narrow magnetic flux tubes, because of a large reparametrization (gauge) invariance of the magnetic and electric string fields.
Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
Pu, Shi; Rezzolla, Luciano; Rischke, Dirk H
2016-01-01
We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work [1], we consider the fluid to have a non-zero magnetization. First, we assume a constant magnetic susceptibility $\\chi_{m}$ and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with $\\chi_{m}>0$), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with $\\chi_{m}<0$), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time $\\tau$ with a power law $\\sim\\tau^{-a}$, two distinct solutions can be found depending on the values of $a$ and $\\chi_m$. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional...
Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
Pu, Shi; Roy, Victor; Rezzolla, Luciano; Rischke, Dirk H.
2016-04-01
We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a nonzero magnetization. First, we assume a constant magnetic susceptibility χm and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with χm>0 ), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with χmlaw ˜τ-a, two distinct solutions can be found depending on the values of a and χm. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the nonvanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. It is only for magnetic fields about an order of magnitude larger than expected for heavy-ion collisions that the system is substantially reheated and the lifetime of the quark phase might be extended.
Finite Larmor radius magnetohydrodynamic analysis of the ballooning modes in tokamaks*
Institute of Scientific and Technical Information of China (English)
Jiang Hai-Bin; Wang Ai-Ke; Peng Xiao-Dong
2010-01-01
In this paper,the effect of finite Larmor radius(FLR)on high n ballooning modes is studied on the basis of FLR magnetohydrodynamic(FLR-MHD)theory.A linear FLR ballooning mode equation is derived in an '(s)-α' type equilibrium of circular-flux-surfaces,which is reduced to the ideal ballooning mode equation when the FLR effect is neglected.The present model reproduces some basic features of FLR effects on ballooning mode obtained previously by kinetic ballooning mode theories.That is,the FLR introduces a real frequency into ballooning mode and has a stabilising effect on ballooning modes(e.g.,in the case of high magnetic shear(s)≥ 0.8).In particular,some new properties of FLR effects on ballooning mode are discovered in the present research.Here it is found that in a high magnetic shear region((s)≥0.8)the critical pressure gradient(αc1,FLR)of ballooning mode is larger than the ideal one(αc,IMHD)and becomes larger and larger with the increase of FLR parameter b0.However,in a low magnetic shear region,the FLR ballooning mode is more unstable than the ideal one,and the αc,FLR is much lower than the αc,IMHD.Moreover,the present results indicate that there exist some new weaker instabilities near the second stability boundary(obtained from ideal MHD theory),which means that the second stable region becomes narrow.
Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics
Bakhsh, Abeer
2016-03-09
Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability(RMI) is suppressed in ideal magnetohydrodynamics(MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2p/B^2_r) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.
Continuous magnetohydrodynamic spectra of two-dimensional coronal magnetostatic flux tubes
Belien, A. J. C.; Poedts, S.; Goedbloed, J. P.
1997-01-01
In this paper we derive the equations for the continuous ideal magnetohydrodynamic (MHD) spectrum of two-dimensional coronal loops, including gravity and expansion, in general curvilinear coordinates. The equations clearly show the coupling between Alfven and slow magnetosonic continuum waves when b
Multi-region relaxed Hall magnetohydrodynamics with flow
Lingam, Manasvi; Hudson, Stuart R
2016-01-01
The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of "ideal barriers" that prevent global relaxation, and flow. In this paper, we generalize MRxMHD with flow to include Hall effects (MRxHMHD), and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the relaxed states.
Multi-region relaxed Hall magnetohydrodynamics with flow
Lingam, Manasvi; Abdelhamid, Hamdi M.; Hudson, Stuart R.
2016-08-01
The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of "ideal barriers" that prevent global relaxation and flow. In this paper, we generalize MRxMHD with flow to include Hall effects, and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.
Magnetohydrodynamic Simulation Code CANS+: Assessments and Applications
Matsumoto, Yosuke; Kudoh, Yuki; Kawashima, Tomohisa; Matsumoto, Jin; Takahashi, Hiroyuki R; Minoshima, Takashi; Zenitani, Seiji; Miyoshi, Takahiro; Matsumoto, Ryoji
2016-01-01
We present a new magnetohydrodynamic (MHD) simulation code with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements the HLLD approximate Riemann solver, the fifth-order-monotonicity-preserving interpolation scheme, and the hyperbolic divergence cleaning method for a magnetic field. This choice of schemes significantly improved numerical accuracy and stability, and saved computational costs in multidimensional problems. Numerical tests of one- and two-dimensional problems showed the advantages of using the high-order scheme by comparing with results from a standard second-order TVD scheme. The present code enabled us to explore long-term evolution of a three-dimensional global accretion disk, in which compressible MHD turbulence saturated at much higher levels via the magneto-rotational instability than that given by the second-order scheme owing to the adoption of the high-resolution, nume...
Energy interactions in homogeneously sheared magnetohydrodynamic flows
Collard, Diane; Praturi, Divya Sri; Girimaji, Sharath
2016-11-01
We investigate the behavior of homogeneously sheared magnetohydrodynamic (MHD) flows subject to perturbations in various directions. We perform rapid distortion theory (RDT) analysis and direct numerical simulations (DNS) to examine the interplay between magnetic, kinetic, and internal energies. For perturbation wavevectors oriented along the spanwise direction, RDT analysis shows that the magnetic and velocity fields are decoupled. In the case of streamwise wavevectors, the magnetic and velocity fields are tightly coupled. The coupling is "harmonic" in nature. DNS is then used to confirm the RDT findings. Computations of spanwise perturbations indeed exhibit behavior that is impervious to the magnetic field. Computed streamwise perturbations exhibit oscillatory evolution of kinetic and magnetic energies for low magnetic field strength. As the strength of magnetic field increases, the oscillatory behavior intensifies even as the energy magnitude decays, indicating strong stabilization.
de Ruyter, Doret J.; Spiecker, Ben
2008-01-01
This article argues that sex education should include sexual ideals. Sexual ideals are divided into sexual ideals in the strict sense and sexual ideals in the broad sense. It is argued that ideals that refer to the context that is deemed to be most ideal for the gratification of sexual ideals in the strict sense are rightfully called sexual…
Generalized similarity in finite range solar wind magnetohydrodynamic turbulence.
Chapman, S C; Nicol, R M
2009-12-11
Extended or generalized similarity is a ubiquitous but not well understood feature of turbulence that is realized over a finite range of scales. The ULYSSES spacecraft solar polar passes at solar minimum provide in situ observations of evolving anisotropic magnetohydrodynamic turbulence in the solar wind under ideal conditions of fast quiet flow. We find a single generalized scaling function characterizes this finite range turbulence and is insensitive to plasma conditions. The recent unusually inactive solar minimum--with turbulent fluctuations down by a factor of approximately 2 in power--provides a test of this invariance.
Energy transfers in shell models for magnetohydrodynamics turbulence.
Lessinnes, Thomas; Carati, Daniele; Verma, Mahendra K
2009-06-01
A systematic procedure to derive shell models for magnetohydrodynamic turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross helicity, and the magnetic helicity, as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest-neighbor shells, this procedure reproduces well-known models but suggests a reinterpretation of the energy fluxes.
Dynamic multiscaling in magnetohydrodynamic turbulence
Ray, Samriddhi Sankar; Pandit, Rahul
2016-01-01
We present the first study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Dynamic multiscaling in magnetohydrodynamic turbulence.
Ray, Samriddhi Sankar; Sahoo, Ganapati; Pandit, Rahul
2016-11-01
We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Large-Scale Quasi-geostrophic Magnetohydrodynamics
Balk, Alexander M.
2014-12-01
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the "shallow water" beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra (adiabatic-type) invariant. Its presence implies energy accumulation in the 30° sector around zonal direction. With some special energy input, the extra invariant can lead to the accumulation of energy in zonal magnetic field; this happens if the input of the extra invariant is small, while the energy input is considerable.
Large Scale Quasi-geostrophic Magnetohydrodynamics
Balk, Alexander M
2014-01-01
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the "shallow water" beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra invariant. Its presence is shown to imply energy accumulation ...
Multicomponent diffusion in two-temperature magnetohydrodynamics
Ramshaw, J. D.; Chang, C. H.
1996-06-01
A recent hydrodynamic theory of multicomponent diffusion in multitemperature gas mixtures [J. D. Ramshaw, J. Non-Equilib. Thermodyn. 18, 121 (1993)] is generalized to include the velocity-dependent Lorentz force on charged species in a magnetic field B. This generalization is used to extend a previous treatment of ambipolar diffusion in two-temperature multicomponent plasmas [J. D. Ramshaw and C. H. Chang, Plasma Chem. Plasma Process. 13, 489 (1993)] to situations in which B and the electrical current density are nonzero. General expressions are thereby derived for the species diffusion fluxes, including thermal diffusion, in both single- and two-temperature multicomponent magnetohydrodynamics (MHD). It is shown that the usual zero-field form of the Stefan-Maxwell equations can be preserved in the presence of B by introducing generalized binary diffusion tensors dependent on B. A self-consistent effective binary diffusion approximation is presented that provides explicit approximate expressions for the diffusion fluxes. Simplifications due to the small electron mass are exploited to obtain an ideal MHD description in which the electron diffusion coefficients drop out, resistive effects vanish, and the electric field reduces to a particularly simple form. This description should be well suited for numerical calculations.
Magnetohydrodynamics on an unstructured moving grid
Pakmor, Ruediger; Springel, Volker
2011-01-01
Magnetic fields play an important role in astrophysics on a wide variety of scales, ranging from the Sun and compact objects to galaxies and galaxy clusters. Here we discuss a novel implementation of ideal magnetohydrodynamics (MHD) in the moving mesh code AREPO which combines many of the advantages of Eulerian and Lagrangian methods in a single computational technique. The employed grid is defined as the Voronoi tessellation of a set of mesh-generating points which can move along with the flow, yielding an automatic adaptivity of the mesh and a substantial reduction of advection errors. Our scheme solves the MHD Riemann problem in the rest frame of the Voronoi interfaces using the HLLD Riemann solver. To satisfy the divergence constraint of the magnetic field in multiple dimensions, the Dedner divergence cleaning method is applied. In a set of standard test problems we show that the new code produces accurate results, and that the divergence of the magnetic field is kept sufficiently small to closely preserv...
Accurate, Meshless Methods for Magneto-Hydrodynamics
Hopkins, Philip F
2016-01-01
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics (SPH) and adaptive mesh-refinement (AMR) schemes. Here, we extend these to include ideal magneto-hydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains div*B~0 to high accuracy. We implement these in the code GIZMO, together with a state-of-the-art implementation of SPH MHD. In every one of a large suite of test problems, the new methods are competitive with moving-mesh and AMR schemes using constrained transport (CT) to ensure div*B=0. They are able to correctly capture the growth and structure of the magneto-rotational instability (MRI), MHD turbulence, and the launching of magnetic jets, in some cases converging more rapidly than AMR codes. Compared to SPH, the MFM/MFV methods e...
Validation of Magnetospheric Magnetohydrodynamic Models
Curtis, Brian
Magnetospheric magnetohydrodynamic (MHD) models are commonly used for both prediction and modeling of Earth's magnetosphere. To date, very little validation has been performed to determine their limits, uncertainties, and differences. In this work, we performed a comprehensive analysis using several commonly used validation techniques in the atmospheric sciences to MHD-based models of Earth's magnetosphere for the first time. The validation techniques of parameter variability/sensitivity analysis and comparison to other models were used on the OpenGGCM, BATS-R-US, and SWMF magnetospheric MHD models to answer several questions about how these models compare. The questions include: (1) the difference between the model's predictions prior to and following to a reversal of Bz in the upstream interplanetary field (IMF) from positive to negative, (2) the influence of the preconditioning duration, and (3) the differences between models under extreme solar wind conditions. A differencing visualization tool was developed and used to address these three questions. We find: (1) For a reversal in IMF Bz from positive to negative, the OpenGGCM magnetopause is closest to Earth as it has the weakest magnetic pressure near-Earth. The differences in magnetopause positions between BATS-R-US and SWMF are explained by the influence of the ring current, which is included in SWMF. Densities are highest for SWMF and lowest for OpenGGCM. The OpenGGCM tail currents differ significantly from BATS-R-US and SWMF; (2) A longer preconditioning time allowed the magnetosphere to relax more, giving different positions for the magnetopause with all three models before the IMF Bz reversal. There were differences greater than 100% for all three models before the IMF Bz reversal. The differences in the current sheet region for the OpenGGCM were small after the IMF Bz reversal. The BATS-R-US and SWMF differences decreased after the IMF Bz reversal to near zero; (3) For extreme conditions in the solar
A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics
Mocz, Philip; Springel, Volker; Vogelsberger, Mark; Marinacci, Federico; Hernquist, Lars
2016-01-01
We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a moving mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the moving mesh code Arepo. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this co...
Data assimilation for magnetohydrodynamics systems
Mendoza, O. Barrero; de Moor, B.; Bernstein, D. S.
2006-05-01
Prediction of solar storms has become a very important issue due to the fact that they can affect dramatically the telecommunication and electrical power systems at the earth. As a result, a lot of research is being done in this direction, space weather forecast. Magnetohydrodynamics systems are being studied in order to analyse the space plasma dynamics, and techniques which have been broadly used in the prediction of earth environmental variables like the Kalman filter (KF), the ensemble Kalman filter (EnKF), the extended Kalman filter (EKF), etc., are being studied and adapted to this new framework. The assimilation of a wide range of space environment data into first-principles-based global numerical models will improve our understanding of the physics of the geospace environment and the forecasting of its behaviour. Therefore, the aim of this paper is to study the performance of nonlinear observers in magnetohydrodynamics systems, namely, the EnKF.The EnKF is based on a Monte Carlo simulation approach for propagation of process and measurement errors. In this paper, the EnKF for a nonlinear two-dimensional magnetohydrodynamic (2D-MHD) system is considered. For its implementation, two software packages are merged, namely, the Versatile Advection Code (VAC) written in Fortran and Matlab of Mathworks. The 2D-MHD is simulated with the VAC code while the EnKF is computed in Matlab. In order to study the performance of the EnKF in MHD systems, different number of measurement points as well as ensemble members are set.
Plasma Relaxation in Hall Magnetohydrodynamics
Shivamoggi, B K
2011-01-01
Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "potential vorticity" lines in 2D hydrodynamics.
Fundamental fluid mechanics and magnetohydrodynamics
Hosking, Roger J
2016-01-01
This book is primarily intended to enable postgraduate research students to enhance their understanding and expertise in Fluid Mechanics and Magnetohydrodynamics (MHD), subjects no longer treated in isolation. The exercises throughout the book often serve to provide additional and quite significant knowledge or to develop selected mathematical skills, and may also fill in certain details or enhance readers’ understanding of essential concepts. A previous background or some preliminary reading in either of the two core subjects would be advantageous, and prior knowledge of multivariate calculus and differential equations is expected.
Magnetohydrodynamic mechanism for pedestal formation.
Guazzotto, L; Betti, R
2011-09-16
Time-dependent two-dimensional magnetohydrodynamic simulations are carried out for tokamak plasmas with edge poloidal flow. Differently from conventional equilibrium theory, a density pedestal all around the edge is obtained when the poloidal velocity exceeds the poloidal sound speed. The outboard pedestal is induced by the transonic discontinuity, the inboard one by mass redistribution. The density pedestal follows the formation of a highly sheared flow at the transonic surface. These results may be relevant to the L-H transition and pedestal formation in high performance tokamak plasmas.
DISCO: A 3D Moving-Mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks
Duffell, Paul C
2016-01-01
This work presents the publicly available moving-mesh magnetohydrodynamics code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach number. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer timesteps than a static grid. Magnetohydrodynamics is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport scheme which is compatible with the mesh motion. DISCO is tested against a wide variety of problems, which are designed to test its stability, accuracy and scalability. In addition, several magnetohydrodynamics tests are performed which demonstrate the accuracy and stability of the new constrained transport approach, including two tests of the magneto-rotational instability (MRI); one testing the linear growth rate and the other following the instability...
DEFF Research Database (Denmark)
Albinus, Lars
2016-01-01
Nietzsches og Foucaults fremstilling af vestens asketiske ideal i religion, videnskab og filosofi......Nietzsches og Foucaults fremstilling af vestens asketiske ideal i religion, videnskab og filosofi...
DEFF Research Database (Denmark)
Albinus, Lars
2016-01-01
Nietzsches og Foucaults fremstilling af vestens asketiske ideal i religion, videnskab og filosofi......Nietzsches og Foucaults fremstilling af vestens asketiske ideal i religion, videnskab og filosofi...
The J–S model versus a non-ideal MHD theory
Energy Technology Data Exchange (ETDEWEB)
Franchi, Franca, E-mail: franca.franchi@unibo.it; Lazzari, Barbara, E-mail: barbara.lazzari@unibo.it; Nibbi, Roberta, E-mail: roberta.nibbi@unibo.it
2015-07-17
A new non-ideal electromagnetic interpretation of the J–S type viscoelastic model for polymeric fluids is given and a generalized resisto-elastic magnetohydrodynamic scenario for collisionless plasmas is proposed. The influence of the new theory on the incompressible transverse Alfvén waves is thoroughly investigated. - Highlights: • A non-ideal electromagnetic interpretation of the J–S type viscoelasticity is shown. • A generalized resisto-elastic magneto-hydrodynamic scenario for collision-less plasmas is proposed. • The shear-type magnetic waves are investigated.
Rotational stabilization of q < 1 modes
Energy Technology Data Exchange (ETDEWEB)
Waelbroeck, F.L.; Aydemir, A.Y. [Univ. of Texas, Austin, TX (United States)
1996-12-31
Analyses of high performance discharges with central safety factor below unity have shown that the ideal Magnetohydrodynamic stability threshold for the n=1 kink mode is often violated with impunity. For TFTR (Tokamak Fusion Test Reactor) supershots, the experimental observations can be explained by diamagnetic stabilization of the reconnecting model provided that the fluid free energy is suitably reduced by trapped particle effects. For the broader profiles typical of other high confinement regimes, however, diamagnetic effects cannot account for the experimental results. Furthermore, there is evidence that the Mercier stability condition can also be violated in some cases. Here, we show that toroidal rotation of the plasma can stabilize the kink mode even in the presence of resistivity in configurations that would otherwise be ideally unstable. Two effects can be distinguished. The first effect consists in a reduction of the ideal driving energy. This can be understood in view of the fact that, to a good approximation, the internal kink is a rigid body displacement combining a tilt of the plasma inside the q = 1 surface with a translation along the tilt axis. In the presence of rotation, this displacement must be accompanied by a precessional motion so as to conserve angular momentum. The kinetic energy of the precessional motion must be extracted from the energy driving the displacement. The second effect of rotation is to resolve the Alfven singularity. This is a consequence of the pressure perturbation caused by the equilibrium variation of the entropy within the flux surfaces. It results in the stabilization of resistive as well as weak ideal instabilities, including Mercier modes. For rotationally stabilized equilibria, it also implies the presence of a neutrally stable mode with frequency of the order of the growth rate of the internal kink.
Magnetohydrodynamic waves in fusion and astrophysical plasmas.
Goedbloed, J. P.
Macroscopic plasma dynamics in both controlled thermonuclear confinement machines and in the atmospheres of X-ray emitting stars is described by the equations of magnetohydrodynamics. This provides a vast area of overlapping research activities which is presently actively pursued. In this lecture the author concentrates on some important differences in the dynamics of the two confined plasma systems related to the very different geometries that are encountered and, thus, the role of the different boundary conditions that have to be posed. As a result, the basic MHD waves in a tokamak are quite different from those found in a solar magnetic flux tube. The result is that, whereas the three well-known MHD waves can be traced stepwise in the curved geometry of a tokamak, their separate existence is eliminated right from the start in a line-tied coronal loop because line-tying in general conflicts with the phase relationships between the vector components of the three velocity fields. The consequences are far-reaching, viz. completely different resonant frequencies and continuous spectra, absence of rational magnetic surfaces, and irrelevance of local marginal stability theory for coronal magnetic loops.
Nonexistence of self-similar singularities in ideal viscoelastic flows
Directory of Open Access Journals (Sweden)
Anthony Suen
2012-06-01
Full Text Available We prove the nonexistence of finite time self-similar singularities in an ideal viscoelastic flow in R^3. We exclude the occurrence of Leray-type self-similar singularities under suitable integrability conditions on velocity and deformation tensor. We also prove the nonexistence of asymptotically self-similar singularities in our system. The present work extends the results obtained by Chae in the case of magnetohydrodynamics (MHD.
Kinetic approach to Kaluza's magnetohydrodynamics
Sandoval-Villalbazo, A.; Garcia-Colin, L. S.
2011-11-01
Ten years ago we presented a formalism by means of which the basic tenets of relativistic magnetohydrodynamics were derived using Kaluza's ideas about unifying fields in terms of the corresponding space time curvature for a given metric. In this work we present an attempt to obtain the thermodynamic properties of a charged fluid using using Boltzmann's equation for a dilute system adapted to kaluza's formalism. The main results that we obtain are analytical expressions for the main currents and corresponding forces, within the formalism of linear irreversible thermodynamics. We also indicate how transport coefficients can be calculated. Other relevant results are also mentioned. A. Sandoval-Villalbazo and L.S. Garcia-Colin; Phys. of Plasmas 7, 4823 (2000).
Vortex disruption by magnetohydrodynamic feedback
Mak, Julian; Hughes, D W
2016-01-01
In an electrically conducting fluid, vortices stretch out a weak, large-scale magnetic field to form strong current sheets on their edges. Associated with these current sheets are magnetic stresses, which are subsequently released through reconnection, leading to vortex disruption, and possibly even destruction. This disruption phenomenon is investigated here in the context of two-dimensional, homogeneous, incompressible magnetohydrodynamics. We derive a simple order of magnitude estimate for the magnetic stresses --- and thus the degree of disruption --- that depends on the strength of the background magnetic field (measured by the parameter $M$, a ratio between the Alfv\\'en speed and a typical flow speed) and on the magnetic diffusivity (measured by the magnetic Reynolds number $\\mbox{Rm}$). The resulting estimate suggests that significant disruption occurs when $M^{2}\\mbox{Rm} = O(1)$. To test our prediction, we analyse direct numerical simulations of vortices generated by the breakup of unstable shear flo...
Shell Models of Magnetohydrodynamic Turbulence
Plunian, Franck; Frick, Peter
2012-01-01
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accu...
Method for manufacturing magnetohydrodynamic electrodes
Killpatrick, Don H.; Thresh, Henry R.
1982-01-01
A method of manufacturing electrodes for use in a magnetohydrodynamic (MHD) generator comprising the steps of preparing a billet having a core 10 of a first metal, a tubular sleeve 12 of a second metal, and an outer sheath 14, 16, 18 of an extrusile metal; evacuating the space between the parts of the assembled billet; extruding the billet; and removing the outer jacket 14. The extruded bar may be made into electrodes by cutting and bending to the shape required for an MDH channel frame. The method forms a bond between the first metal of the core 10 and the second metal of the sleeve 12 strong enough to withstand a hot and corrosive environment.
Scale locality of magnetohydrodynamic turbulence.
Aluie, Hussein; Eyink, Gregory L
2010-02-26
We investigate the scale locality of cascades of conserved invariants at high kinetic and magnetic Reynold's numbers in the "inertial-inductive range" of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross helicity-or, equivalently, fluxes of Elsässer energies-are dominated by the contributions of local triads. Flux of magnetic helicity may be dominated by nonlocal triads. The magnetic stretching term may also be dominated by nonlocal triads, but we prove that it can convert energy only between velocity and magnetic modes at comparable scales. We explain the disagreement with numerical studies that have claimed conversion nonlocally between disparate scales. We present supporting data from a 1024{3} simulation of forced MHD turbulence.
Micromachined magnetohydrodynamic actuators and sensors
Lee, Abraham P.; Lemoff, Asuncion V.
2000-01-01
A magnetohydrodynamic (MHD) micropump and microsensor which utilizes micromachining to integrate the electrodes with microchannels and includes a magnet for producing magnetic fields perpendicular to both the electrical current direction and the fluid flow direction. The magnet can also be micromachined and integrated with the micropump using existing technology. The MHD micropump, for example, can generate continuous, reversible flow, with readily controllable flow rates. The flow can be reversed by either reversing the electrical current flow or reversing the magnetic field. By mismatching the electrodes, a swirling vortex flow can be generated for potential mixing applications. No moving parts are necessary and the dead volume is minimal. The micropumps can be placed at any position in a fluidic circuit and a combination of micropumps can generate fluidic plugs and valves.
Magnetohydrodynamic turbulence: Observation and experiment
Energy Technology Data Exchange (ETDEWEB)
Brown, M. R.; Schaffner, D. A.; Weck, P. J. [Department of Physics and Astronomy, Swarthmore College, 500 College Avenue, Swarthmore, Pennsylvania 19081 (United States)
2015-05-15
We provide a tutorial on the paradigms and tools of magnetohydrodynamic (MHD) turbulence. The principal paradigm is that of a turbulent cascade from large scales to small, resulting in power law behavior for the frequency power spectrum for magnetic fluctuations E{sub B}(f). We will describe five useful statistical tools for MHD turbulence in the time domain: the temporal autocorrelation function, the frequency power spectrum, the probability distribution function of temporal increments, the temporal structure function, and the permutation entropy. Each of these tools will be illustrated with an example taken from MHD fluctuations in the solar wind. A single dataset from the Wind satellite will be used to illustrate all five temporal statistical tools.
Spectrum of weak magnetohydrodynamic turbulence.
Boldyrev, Stanislav; Perez, Jean Carlos
2009-11-27
Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or nonbalanced, in that the energies of Alfvén waves moving in opposite directions along the guide magnetic field are unequal. Based on high-resolution numerical simulations it is proposed that such turbulence spontaneously generates a condensate of the residual energy E(v) - E(b) at small field-parallel wave numbers. As a result, the energy spectra of Alfvén waves are generally not scale invariant in an inertial interval of limited extent. In the limit of an infinite Reynolds number, the universality is asymptotically restored at large wave numbers, and both spectra attain the scaling E(k) proportional to k(perpendicular)(-2). The generation of a condensate is apparently related to the breakdown of mirror symmetry in nonbalanced turbulence.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Introduction to Magneto-Hydrodynamics
Pelletier, Guy
Magneto-Hydrodynamics (hereafter MHD) describes plasmas on large scales and more generally electrically conducting fluids. This description does not discriminate between the various fluids that constitute the medium. In laboratory, it allows to globally describe a plasma machine, for instance a toroidal nuclear fusion reactor like a Tokamak. In astrophysics it plays an essential role in the description of cosmic objects and their environments, as well as the media, such as the interstellar or the intergalactic medium. A set of phenomena are specific to MHD description. Some of them will be presented in this lecture such as the tension effect, confinement, magnetic diffusivity, magnetic field freezing, Alfvén waves, magneto-sonic waves, reconnection. A celebrated phenomenon of MHD will not be introduced in this brief lecture, namely the dynamo effect.
Chapman, I T; Scannell, R; Cooper, W A; Graves, J P; Hastie, R J; Naylor, G; Zocco, A
2010-12-17
Thomson scattering measurements with subcentimeter spatial resolution have been made during a sawtooth crash in a Mega Ampere Spherical Tokamak fusion plasma. The unparalleled resolution of the temperature profile has shed new light on the mechanisms that underlie the sawtooth. As magnetic reconnection occurs, the temperature gradient at the island boundary increases. The increased local temperature gradient is sufficient to make the helical core unstable to ideal magnetohydrodynamic instabilities, thought to be responsible for the rapidity of the collapse.
Institute of Scientific and Technical Information of China (English)
LUO Zhen-dong; MAO Yun-kui; ZHU Jiang
2007-01-01
The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented.And the existence and error estimates of its solution are derived. Through this method,the combination among the mixed finite element spaces does not demand the discrete Babu(s)ka-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.
Marginal Stability Boundaries for Infinite-n Ballooning Modes in a Quasi-axisymmetric Stellarator
Energy Technology Data Exchange (ETDEWEB)
S.R. Hudson; C.C. Hegna
2003-09-15
A method for computing the ideal-MHD stability boundaries in three-dimensional equilibria is employed. Following Hegna and Nakajima [Phys. Plasmas 5 (May 1998) 1336], a two-dimensional family of equilibria are constructed by perturbing the pressure and rotational-transform profiles in the vicinity of a flux surface for a given stellarator equilibrium. The perturbations are constrained to preserve the magnetohydrodynamic equilibrium condition. For each perturbed equilibrium, the infinite-n ballooning stability is calculated. Marginal stability diagrams are thus constructed that are analogous to (s; a) diagrams for axisymmetric configurations. A quasi-axisymmetric stellarator is considered. Calculations of stability boundaries generally show regions of instability can occur for either sign of the average magnetic shear. Additionally, regions of second-stability are present.
Directory of Open Access Journals (Sweden)
Domingues M. O.
2013-12-01
Full Text Available We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via Harten’s cell average multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge–Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution.
High-beta turbulence in two-dimensional magnetohydrodynamics
Fyfe, D.; Montgomery, D.
1975-01-01
Incompressible turbulent flows were investigated in the framework of ideal magnetohydrodynamics. Equilibrium canonical distributions are determined in a phase whose coordinates are the real and imaginary parts of the Fourier coefficients for the field variables. The magnetic field and fluid velocity have variable x and y components, and all field quantities are independent of z. Three constants of the motion are found which survive the truncation in Fourier space and permit the construction of canonical distributions with three independent temperatures. Spectral densities are calculated. One of the more novel physical effects is the appearance of macroscopic structures involving long wavelength, self-generated, magnetic fields ("magnetic islands"). In the presence of finite dissipation, energy cascades to higher wave numbers can be accompanied by vector potential cascades to lower wave numbers, in much the same way that in the fluid dynamic case, energy cascades to lower wave numbers accompany entropy cascades to higher wave numbers.
Linearized analysis of one-dimensional magnetohydrodynamic flows
Gundersen, Roy M
1964-01-01
Magnetohydrodynamics is concerned with the motion of electrically conducting fluids in the presence of electric or magnetic fields. Un fortunately, the subject has a rather poorly developed experimental basis and because of the difficulties inherent in carrying out controlled laboratory experiments, the theoretical developments, in large measure, have been concerned with finding solutions to rather idealized problems. This lack of experimental basis need not become, however, a multi megohm impedance in the line of progress in the development of a satisfactory scientific theory. While it is true that ultimately a scientific theory must agree with and, in actuality, predict physical phenomena with a reasonable degree of accuracy, such a theory must be sanctioned by its mathematical validity and consistency. Physical phenomena may be expressed precisely and quite comprehensively through the use of differential equations, and the equations formulated by LUNDQUIST and discussed by FRIEDRICHS belong to a class ...
WOMBAT: A Scalable and High-performance Astrophysical Magnetohydrodynamics Code
Mendygral, P. J.; Radcliffe, N.; Kandalla, K.; Porter, D.; O’Neill, B. J.; Nolting, C.; Edmon, P.; Donnert, J. M. F.; Jones, T. W.
2017-02-01
We present a new code for astrophysical magnetohydrodynamics specifically designed and optimized for high performance and scaling on modern and future supercomputers. We describe a novel hybrid OpenMP/MPI programming model that emerged from a collaboration between Cray, Inc. and the University of Minnesota. This design utilizes MPI-RMA optimized for thread scaling, which allows the code to run extremely efficiently at very high thread counts ideal for the latest generation of multi-core and many-core architectures. Such performance characteristics are needed in the era of “exascale” computing. We describe and demonstrate our high-performance design in detail with the intent that it may be used as a model for other, future astrophysical codes intended for applications demanding exceptional performance.
Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence
Grete, Philipp; Schmidt, Wolfram; Schleicher, Dominik R G; Federrath, Christoph
2015-01-01
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pre...
Magnetohydrodynamic disc winds and line width distributions - II
Chajet, L. S.; Hall, P. B.
2017-02-01
We study AGN emission line profiles combining an improved version of the accretion disc-wind model of Murray & Chiang with the magnetohydrodynamic (MHD) model of Emmering et al. Here, we extend our previous work to consider central objects with different masses and/or luminosities. We have compared the dispersions in our model C IV line-width distributions to observational upper limit on that dispersion, considering both smooth and clumpy torus models. Following Fine et al., we transform that scatter in the profile line-widths into a constraint on the torus geometry and show how the half-opening angle of the obscuring structure depends on the mass of the central object and the accretion rate. We find that the results depend only mildly on the dimensionless angular momentum, one of the two integrals of motion that characterize the dynamics of the self-similar ideal MHD outflows.
The high beta tokamak-extended pulse magnetohydrodynamic mode control research program
Energy Technology Data Exchange (ETDEWEB)
Maurer, D A; Bialek, J; Byrne, P J; De Bono, B; Levesque, J P; Li, B Q; Mauel, M E; Navratil, G A; Pedersen, T S; Rath, N; Shiraki, D [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY (United States)
2011-07-15
The high beta tokamak-extended pulse (HBT-EP) magnetohydrodynamic (MHD) mode control research program is studying ITER relevant internal modular feedback control coil configurations and their impact on kink mode rigidity, advanced digital control algorithms and the effects of plasma rotation and three-dimensional magnetic fields on MHD mode stability. A new segmented adjustable conducting wall has been installed on the HBT-EP and is made up of 20 independent, movable, wall shell segments instrumented with three distinct sets of 40 saddle coils, totaling 120 in-vessel modular feedback control coils. Each internal coil set has been designed with varying toroidal angular coil coverage of 5, 10 and 15{sup 0}, spanning the toroidal angle range of an ITER port plug based internal coil to test resistive wall mode (RWM) interaction and multimode MHD plasma response to such highly localized control fields. In addition, we have implemented 336 new poloidal and radial magnetic sensors to quantify the applied three-dimensional fields of our control coils along with the observed plasma response. This paper describes the design and implementation of the new control shell incorporating these control and sensor coils on the HBT-EP, and the research program plan on the upgraded HBT-EP to understand how best to optimize the use of modular feedback coils to control instability growth near the ideal wall stabilization limit, answer critical questions about the role of plasma rotation in active control of the RWM and the ferritic resistive wall mode, and to improve the performance of MHD control systems used in fusion experiments and future burning plasma systems.
Directory of Open Access Journals (Sweden)
Ameer Jaber
2008-01-01
Full Text Available Problem Statement: Graded commutative ring with unity over an abelian group were introduced by many authors such as T. Y. Lam and C. T. C. Wall, and almost prime ideals over commutative rings with unity were introduced by S.M. Batwadeker and P.K. Sharma, and this forced us to try to extend the theory of almost and n-almost prime ideals to the graded case. Approach: We develop the theory of almost and n-almost prime ideals to the graded case. Results: We extended some basic results about almost and n-almost prime ideals to the graded case, and then we gave a relationship between n-almost graded prime ideals and weakly graded prime ideals. Conclusion: The extended results about almost and n-almost graded prime ideals allow us to classify further properties about almost graded prime ideals. 2000 AMS Mathematics Subject Classification: 13 A 02.
Clark, Timothy B P
2011-01-01
In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial ideals are lattice-linear and thus their minimal resolution can be constructed as a poset resolution. We then use this result to give a description of the minimal free resolution of a larger class of rigid monomial ideals by using $\\mathcal{L}(n)$, the lattice of all lcm-lattices of monomial ideals with $n$ generators. By fixing a stratum in $\\mathcal{L}(n)$ where all ideals have the same total Betti numbers we show that rigidity is a property which is upward closed in $\\mathcal{L}(n)$. Furthermore, the minimal resolution of all rigid ideals contained in a fixed stratum is shown to be isomorphic to the constructed minimal resolution.
Broken Ergodicity in Two-Dimensional Homogeneous Magnetohydrodynamic Turbulence
Shebalin, John V.
2010-01-01
Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence.The se features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo.Recently, the origin of broken ergodicity in 3-D MHD turbulence that is manifest in the lowest wavenumbers was explained. Here, a detailed description of the origins of broken ergodicity in 2-D MHD turbulence is presented. It will be seen that broken ergodicity in ideal 2-D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions.T he origins of broken ergodicity in ideal 2-D homogeneous MHD turbulence are found through an eigen analysis of the covariance matrices of the modal probability density functions.It will also be shown that when the lowest wavenumber magnetic field becomes quasi-stationary, the higher wavenumber modes can propagate as Alfven waves on these almost static large-scale magnetic structures
Magnetohydrodynamics turbulence: An astronomical perspective
Indian Academy of Sciences (India)
S Sridhar
2011-07-01
Early work on magnetohydrodynamic (MHD) turbulence in the 1960s due, independently, to Iroshnikov and Kraichnan (IK) considered isotropic inertial-range spectra. Whereas laboratory experiments were not in a position to measure the spectral index, they showed that the turbulence was strongly anisotropic. Theoretical horizons correspondingly expanded in the 1980s, to accommodate both the isotropy of the IK theory and the anisotropy suggested by the experiments. Since the discovery of pulsars in 1967, many years of work on interstellar scintillation suggested that small-scale interstellar turbulence must have a hydromagnetic origin; but the IK spectrum was too ﬂat and the ideas on anisotropic spectra too qualitative to explain the observations. In response, new theories of balanced MHD turbulence were proposed in the 1990s, which argued that the IK theory was incorrect, and made quantitative predictions of anisotropic inertial-range spectra; these theories have since found applications in many areas of astrophysics. Spacecraft measurements of solar-wind turbulence show that there is more power in Alfvén waves that travel away from the Sun than towards it. Theories of imbalanced MHD turbulence have now been proposed to address interplanetary turbulence. This very active area of research continues to be driven by astronomy.
Magnetohydrodynamic (MHD) driven droplet mixer
Lee, Abraham P.; Lemoff, Asuncion V.; Miles, Robin R.
2004-05-11
A magnetohydrodynamic fluidic system mixes a first substance and a second substance. A first substrate section includes a first flow channel and a first plurality of pairs of spaced electrodes operatively connected to the first flow channel. A second substrate section includes a second flow channel and a second plurality of pairs of spaced electrodes operatively connected to the second flow channel. A third substrate section includes a third flow channel and a third plurality of pairs of spaced electrodes operatively connected to the third flow channel. A magnetic section and a control section are operatively connected to the spaced electrodes. The first substrate section, the second substrate section, the third substrate section, the first plurality of pairs of spaced electrodes, the second plurality of pairs of spaced electrodes, the third plurality of pairs of spaced electrodes, the magnetic section, and the control section are operated to move the first substance through the first flow channel, the second substance through the second flow channel, and both the first substance and the second substance into the third flow channel where they are mixed.
Magnetohydrodynamic Propulsion for the Classroom
Font, Gabriel I.; Dudley, Scott C.
2004-10-01
The cinema industry can sometimes prove to be an ally when searching for material with which to motivate students to learn physics. Consider, for example, the electromagnetic force on a current in the presence of a magnetic field. This phenomenon is at the heart of magnetohydrodynamic (MHD) propulsion systems. A submarine employing this type of propulsion was immortalized in the movie Hunt for Red October. While mentioning this to students certainly gets their attention, it often elicits comments that it is only fiction and not physically possible. Imagine their surprise when a working system is demonstrated! It is neither difficult nor expensive to construct a working system that can be demonstrated in the front of a classroom.2 In addition, all aspects of the engineering hurdles that must be surmounted and myths concerning this "silent propulsion" system are borne out in a simple apparatus. This paper details how to construct an inexpensive MHD propulsion boat that can be demonstrated for students in the classroom.
Buoyancy-driven Magnetohydrodynamic Waves
Hague, A.; Erdélyi, R.
2016-09-01
Turbulent motions close to the visible solar surface may generate low-frequency internal gravity waves (IGWs) that propagate through the lower solar atmosphere. Magnetic activity is ubiquitous throughout the solar atmosphere, so it is expected that the behavior of IGWs is to be affected. In this article we investigate the role of an equilibrium magnetic field on propagating and standing buoyancy oscillations in a gravitationally stratified medium. We assume that this background magnetic field is parallel to the direction of gravitational stratification. It is known that when the equilibrium magnetic field is weak and the background is isothermal, the frequencies of standing IGWs are sensitive to the presence of magnetism. Here, we generalize this result to the case of a slowly varying temperature. To do this, we make use of the Boussinesq approximation. A comparison between the hydrodynamic and magnetohydrodynamic cases allows us to deduce the effects due to a magnetic field. It is shown that the frequency of IGWs may depart significantly from the Brunt-Väisälä frequency, even for a weak magnetic field. The mathematical techniques applied here give a clearer picture of the wave mode identification, which has previously been misinterpreted. An observational test is urged to validate the theoretical findings.
Magnetohydrodynamic Models of Molecular Tornadoes
Au, Kelvin; Fiege, Jason D.
2017-07-01
Recent observations near the Galactic Center (GC) have found several molecular filaments displaying striking helically wound morphology that are collectively known as molecular tornadoes. We investigate the equilibrium structure of these molecular tornadoes by formulating a magnetohydrodynamic model of a rotating, helically magnetized filament. A special analytical solution is derived where centrifugal forces balance exactly with toroidal magnetic stress. From the physics of torsional Alfvén waves we derive a constraint that links the toroidal flux-to-mass ratio and the pitch angle of the helical field to the rotation laws, which we find to be an important component in describing the molecular tornado structure. The models are compared to the Ostriker solution for isothermal, nonmagnetic, nonrotating filaments. We find that neither the analytic model nor the Alfvén wave model suffer from the unphysical density inversions noted by other authors. A Monte Carlo exploration of our parameter space is constrained by observational measurements of the Pigtail Molecular Cloud, the Double Helix Nebula, and the GC Molecular Tornado. Observable properties such as the velocity dispersion, filament radius, linear mass, and surface pressure can be used to derive three dimensionless constraints for our dimensionless models of these three objects. A virial analysis of these constrained models is studied for these three molecular tornadoes. We find that self-gravity is relatively unimportant, whereas magnetic fields and external pressure play a dominant role in the confinement and equilibrium radial structure of these objects.
Smoothed particle hydrodynamics and magnetohydrodynamics
Price, Daniel J.
2012-02-01
This paper presents an overview and introduction to smoothed particle hydrodynamics and magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several 'urban myths' regarding SPH, in particular the idea that one can simply increase the 'neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the NDSPMHD SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.
NDSPMHD Smoothed Particle Magnetohydrodynamics Code
Price, Daniel J.
2011-01-01
This paper presents an overview and introduction to Smoothed Particle Hydrodynamics and Magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several 'urban myths' regarding SPH, in particular the idea that one can simply increase the 'neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the NDSPMHD SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.
Magnetohydrodynamics of Chiral Relativistic Fluids
Boyarsky, Alexey; Ruchayskiy, Oleg
2015-01-01
We study the dynamics of a plasma of charged relativistic fermions at very high temperature $T\\gg m$, where $m$ is the fermion mass, coupled to the electromagnetic field. In particular, we derive a magneto-hydrodynamical description of the evolution of such a plasma. We show that, as compared to conventional MHD for a plasma of non-relativistic particles, the hydrodynamical description of the relativistic plasma involves new degrees of freedom described by a pseudo-scalar field originating in a local asymmetry in the densities of left-handed and right-handed fermions. This field can be interpreted as an effective axion field. Taking into account the chiral anomaly we present dynamical equations for the evolution of this field, as well as of other fields appearing in the MHD description of the plasma. Due to its non-linear coupling to helical magnetic fields, the axion field significantly affects the dynamics of a magnetized plasma and can give rise to a novel type of inverse cascade.
Center for Extended Magnetohydrodynamic Modeling Cooperative Agreement
Energy Technology Data Exchange (ETDEWEB)
Carl R. Sovinec
2008-02-15
The Center for Extended Magnetohydrodynamic Modeling (CEMM) is developing computer simulation models for predicting the behavior of magnetically confined plasmas. Over the first phase of support from the Department of Energy’s Scientific Discovery through Advanced Computing (SciDAC) initiative, the focus has been on macroscopic dynamics that alter the confinement properties of magnetic field configurations. The ultimate objective is to provide computational capabilities to predict plasma behavior—not unlike computational weather prediction—to optimize performance and to increase the reliability of magnetic confinement for fusion energy. Numerical modeling aids theoretical research by solving complicated mathematical models of plasma behavior including strong nonlinear effects and the influences of geometrical shaping of actual experiments. The numerical modeling itself remains an area of active research, due to challenges associated with simulating multiple temporal and spatial scales. The research summarized in this report spans computational and physical topics associated with state of the art simulation of magnetized plasmas. The tasks performed for this grant are categorized according to whether they are primarily computational, algorithmic, or application-oriented in nature. All involve the development and use of the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion (NIMROD) code, which is described at http://nimrodteam.org. With respect to computation, we have tested and refined methods for solving the large algebraic systems of equations that result from our numerical approximations of the physical model. Collaboration with the Terascale Optimal PDE Solvers (TOPS) SciDAC center led us to the SuperLU_DIST software library [http://crd.lbl.gov/~xiaoye/SuperLU/] for solving large sparse matrices using direct methods on parallel computers. Switching to this solver library boosted NIMROD’s performance by a factor of five in typical large
On magnetohydrodynamic gauge field theory
Webb, G. M.; Anco, S. C.
2017-06-01
Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963 Can. J. Phys. 41 2241-51). It is shown how the polarization vector {P} in Calkin’s approach naturally arises from the Lagrange multiplier constraint equation for Faraday’s equation for the magnetic induction {B} , or alternatively from the magnetic vector potential form of Faraday’s equation. Gauss’s equation, (divergence of {B} is zero) is incorporated in the variational principle by means of a Lagrange multiplier constraint. Noether’s theorem coupled with the gauge symmetries is used to derive the conservation laws for (a) magnetic helicity, (b) cross helicity, (c) fluid helicity for non-magnetized fluids, and (d) a class of conservation laws associated with curl and divergence equations which applies to Faraday’s equation and Gauss’s equation. The magnetic helicity conservation law is due to a gauge symmetry in MHD and not due to a fluid relabelling symmetry. The analysis is carried out for the general case of a non-barotropic gas in which the gas pressure and internal energy density depend on both the entropy S and the gas density ρ. The cross helicity and fluid helicity conservation laws in the non-barotropic case are nonlocal conservation laws that reduce to local conservation laws for the case of a barotropic gas. The connections between gauge symmetries, Clebsch potentials and Casimirs are developed. It is shown that the gauge symmetry functionals in the work of Henyey (1982 Phys. Rev. A 26 480-3) satisfy the Casimir determining equations.
Electron magnetohydrodynamics: dynamics and turbulence.
Lyutikov, Maxim
2013-11-01
We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron magnetohydrodynamics (EMHD). We argue that there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. On the other hand, the relaxation principle, the long term evolution of a weakly dissipative system towards Taylor-Beltrami state, remains valid in EMHD. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact nonlinear solutions; (ii) collinear whistlers do not interact (including counterpropagating); (iii) waves with the same value of the wave vector k(1)=k(2) do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfvén turbulence can not be transferred to the EMHD turbulence. We derive the Hamiltonian formulation of EMHD, and using Bogoliubov transformation reduce it to the canonical form; we calculate the matrix elements for the three-wave interaction of whistlers. We solve numerically the kinetic equation and show that, generally, the EMHD cascade develops within a broad range of angles, while transiently it may show anisotropic, nearly two-dimensional structures. Development of a cascade depends on the forcing (nonuniversal) and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade [proportionality]k(-2). The cascade remains weak (not critically balanced). The cascade is UV local, while the infrared locality is weakly (logarithmically) violated.
From the Einstein-Szilard Patent to Modern Magnetohydrodynamics.
Povh, I. L.; Barinberg, A. D.
1979-01-01
Examines present-day and future prospects of the applications of modern magnetohydrodynamics in a number of countries. Explains how the electromagnetic pump, which was invented by Einstein and Leo Szilard, led to the development of applied magnetohydrodynamics. (HM)
Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence
Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor
2010-01-01
We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.
Eigenanalysis of Ideal Hall MHD Turbulence
Fu, T.; Shebalin, J. V.
2011-12-01
Ideal, incompressible, homogeneous, Hall magnetohydrodynamic (HMHD) turbulence may be investigated through a Fourier spectral method. In three-dimensional periodic geometry, the independent Fourier coefficients represent a canonical ensemble described by a Gaussian probability density. The canonical ensemble is based on the conservation of three invariants: total energy, generalized helicity, and magnetic helicity. Generalized helicity in HMHD takes the place of cross helicity in MHD. The invariants determine the modal probability density giving the spectral structure and equilibrium statistics of ideal HMHD, which are compared to known MHD results. New results in absolute equilibrium ensemble theory are derived using a novel approach that involves finding the eigenvalues of a Hermitian covariance matrix for each modal probability density. The associated eigenvectors transform the original phase space variables into eigenvariables through a special unitary transformation. These are the normal modes which facilitate the analysis of ideal HMHD non-linear dynamics. The eigenanalysis predicts that the low wavenumber modes with very small eigenvalues may have mean values that are large compared to their standard deviations, contrary to the ideal ensemble prediction of zero mean values. (Expectation values may also be relatively large at the highest wave numbers, but the addition of even small levels of dissipation removes any relevance this may have for real-world turbulence.) This behavior is non-ergodic over very long times for a numerical simulation and is termed 'broken ergodicity'. For fixed values of the ideal invariants, the effect is seen to be enhanced with increased numerical grid size. Broken ergodicity at low wave number modes gives rise to large-scale, quasi-stationary, coherent structure. Physically, this corresponds to plasma relaxation to force-free states. For real HMHD turbulence with dissipation, broken ergodicity and coherent structure are still
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Magnetohydrodynamically generated velocities in confined plasma
Morales, Jorge A.; Bos, Wouter J. T.; Schneider, Kai; Montgomery, David C.
2015-04-01
We investigate by numerical simulation the rotational flows in a toroid confining a conducting magnetofluid in which a current is driven by the application of externally supported electric and magnetic fields. The computation involves no microscopic instabilities and is purely magnetohydrodynamic (MHD). We show how the properties and intensity of the rotations are regulated by dimensionless numbers (Lundquist and viscous Lundquist) that contain the resistivity and viscosity of the magnetofluid. At the magnetohydrodynamic level (uniform mass density and incompressible magnetofluids), rotational flows appear in toroidal, driven MHD. The evolution of these flows with the transport coefficients, geometry, and safety factor are described.
Generalized magnetofluid connections in relativistic magnetohydrodynamics.
Asenjo, Felipe A; Comisso, Luca
2015-03-20
The concept of magnetic connections is extended to nonideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall, and current-inertia effects, we derive a new covariant connection equation showing the existence of generalized magnetofluid connections that are preserved during the dissipationless plasma dynamics. These connections are intimately linked to a general antisymmetric tensor that unifies the electromagnetic and fluid fields, allowing the extension of the magnetic connection notion to a much broader concept.
Effects of seed magnetic fields on magnetohydrodynamic implosion structure and dynamics
Mostert, W.
2014-12-01
The effects of various seed magnetic fields on the dynamics of cylindrical and spherical implosions in ideal magnetohydrodynamics are investigated. Here, we present a fundamental investigation of this problem utilizing cylindrical and spherical Riemann problems under three seed field configurations to initialize the implosions. The resulting flows are simulated numerically, revealing rich flow structures, including multiple families of magnetohydrodynamic shocks and rarefactions that interact non-linearly. We fully characterize these flow structures, examine their axi- and spherisymmetry-breaking behaviour, and provide data on asymmetry evolution for different field strengths and driving pressures for each seed field configuration. We find that out of the configurations investigated, a seed field for which the implosion centre is a saddle point in at least one plane exhibits the least degree of asymmetry during implosion.
STABLE AND UNSTABLE IDEAL PLANE FLOWS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.
Efficient magnetohydrodynamic simulations on graphics processing units with CUDA
Wong, Hon-Cheng; Wong, Un-Hong; Feng, Xueshang; Tang, Zesheng
2011-10-01
Magnetohydrodynamic (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution methods for solving the ideal MHD equations are computationally expensive and Beowulf clusters or even supercomputers are often used to run the codes that implemented these methods. With the advent of the Compute Unified Device Architecture (CUDA), modern graphics processing units (GPUs) provide an alternative approach to parallel computing for scientific simulations. In this paper we present, to the best of the author's knowledge, the first implementation of MHD simulations entirely on GPUs with CUDA, named GPU-MHD, to accelerate the simulation process. GPU-MHD supports both single and double precision computations. A series of numerical tests have been performed to validate the correctness of our code. Accuracy evaluation by comparing single and double precision computation results is also given. Performance measurements of both single and double precision are conducted on both the NVIDIA GeForce GTX 295 (GT200 architecture) and GTX 480 (Fermi architecture) graphics cards. These measurements show that our GPU-based implementation achieves between one and two orders of magnitude of improvement depending on the graphics card used, the problem size, and the precision when comparing to the original serial CPU MHD implementation. In addition, we extend GPU-MHD to support the visualization of the simulation results and thus the whole MHD simulation and visualization process can be performed entirely on GPUs.
Nonlinear Alfv\\'en waves in extended magnetohydrodynamics
Abdelhamid, Hamdi M
2015-01-01
Large-amplitude Alfv\\'en waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfv\\'en wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfv\\'en waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \\small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat differ...
Energy Technology Data Exchange (ETDEWEB)
Haverkort, J.W. [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam (Netherlands); Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Blank, H.J. de [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Huysmans, G.T.A. [ITER Organization, Route de Vinon sur Verdon, 13115 Saint Paul Lez Durance (France); Pratt, J. [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Koren, B., E-mail: b.koren@tue.nl [Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)
2016-07-01
Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.
Institute of Scientific and Technical Information of China (English)
Zhi De YU
2003-01-01
In the paper, we study a class of standard ideals which are more general than the m-primarystandard ideals discussed in [2]. We will prove an important equality concerning I-weak sequences; thusa generalization of the equality of [2] is established.
V. Ruitinga (Volker)
2011-01-01
textabstractJohn Rawls presents his work on social justice as Ideal Theory. By taking an idealized scenario, he is able to consider the compatibility of different concepts relating to social justice without being hampered by all the complexities of society and its actors; an approach to social theor
Dynamic grid adaptation for computational magnetohydrodynamics
Keppens, R.; Nool, M.; Zegeling, P. A.; Goedbloed, J. P.; Bubak, M.; Williams, R.; Afsarmanesh, H.; Hertzberger, B.
2000-01-01
In many plasma physical and astrophysical problems, both linear and nonlinear effects can lead to global dynamics that induce, or occur simultaneously with, local phenomena. For example, a magnetically confined plasma column can potentially posses global magnetohydrodynamic (MHD) eigenmodes with an
Using high performance Fortran for magnetohydrodynamic simulations
Keppens, R.; Toth, G.
2000-01-01
Two scientific application programs, the Versatile Advection Code (VAC) and the HEating by Resonant Absorption (HERA) code are adapted to parallel computer platforms. Both programs can solve the time-dependent nonlinear partial differential equations of magnetohydrodynamics (MHD) with different nume
On the critical ideals of graphs
Corrales, Hugo
2012-01-01
The critical group of a connected graph G is a finite abelian group isomorphic to the sandpile group of G. In this paper we introduce some determinantal ideals of the generalized Laplacian matrix of G, that we have called critical ideals. Critical ideals of a graph generalize the critical group and they have the advantage that allow to separate the arithmetic information from the algebraic and combinatorial information of the graph contained in the critical group. The main results of this article concern to the determination of some minimal generator sets and the reduced Grobner basis for the critical ideals of the complete graphs, the cycles and the paths. Also, we establish a bound between the number of critical ideals that are trivial and the stability and clique numbers of the graph. Finally, we develop some combinatorial expressions for the minors of the generalized Laplacian matrix.
Helical mode interactions and spectral transfer processes in magnetohydrodynamic turbulence
Linkmann, Moritz F; McKay, Mairi E; Jäger, Julia
2015-01-01
Spectral transfer processes in magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of the interacting modes is derived. As expected from the inverse cascade of magnetic helicity in 3D MHD turbulence, mode interactions with like helicities lead to transfer of energy and magnetic helicity to smaller wavenumbers. However, some interactions of modes with unlike helicities also contribute to an inverse energy transfer. As such, an inverse energy cascade for nonhelical magnetic fields is shown to be possible. Fu...
Computational algorithms for multiphase magnetohydrodynamics and applications to accelerator targets
Directory of Open Access Journals (Sweden)
R.V. Samulyak
2010-01-01
Full Text Available An interface-tracking numerical algorithm for the simulation of magnetohydrodynamic multiphase/free surface flows in the low-magnetic-Reynolds-number approximation of (Samulyak R., Du J., Glimm J., Xu Z., J. Comp. Phys., 2007, 226, 1532 is described. The algorithm has been implemented in multi-physics code FronTier and used for the simulation of MHD processes in liquids and weakly ionized plasmas. In this paper, numerical simulations of a liquid mercury jet entering strong and nonuniform magnetic field and interacting with a powerful proton pulse have been performed and compared with experiments. Such a mercury jet is a prototype of the proposed Muon Collider/Neutrino Factory, a future particle accelerator. Simulations demonstrate the elliptic distortion of the mercury jet as it enters the magnetic solenoid at a small angle to the magnetic axis, jet-surface instabilities (filamentation induced by the interaction with proton pulses, and the stabilizing effect of the magnetic field.
Large scale instabilities in two-dimensional magnetohydrodynamics
Boffetta; Celani; Prandi
2000-04-01
The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state describing a motionless fluid and a layered magnetic field, becomes unstable with respect to large scale perturbations. The exact expressions for eddy-viscosity and eddy-resistivity are derived in the nearby of the critical point where the instability sets in. In this marginally unstable case the nonlinear phase of perturbation growth obeys to a Cahn-Hilliard-like dynamics characterized by coalescence of magnetic islands leading to a final new equilibrium state. High resolution numerical simulations confirm quantitatively the predictions of multiscale analysis.
Formation of relativistic jets. Magnetohydrodynamics and synchrotron radiation
Energy Technology Data Exchange (ETDEWEB)
Porth, Oliver Joachim Georg
2011-11-09
In this thesis, the formation of relativistic jets is investigated by means of special relativistic magnetohydrodynamic simulations and synchrotron radiative transfer. Our results show that the magnetohydrodynamic jet self-collimation paradigm can also be applied to the relativistic case. In the first part, jets launched from rotating hot accretion disk coronae are explored, leading to well collimated, but only mildly relativistic flows. Beyond the light-cylinder, the electric charge separation force balances the classical trans-field Lorentz force almost entirely, resulting in a decreased efficiency of acceleration and collimation in comparison to non-relativistic disk winds. In the second part, we examine Poynting dominated flows of various electric current distributions. By following the outflow for over 3000 Schwarzschild radii, highly relativistic jets of Lorentz factor Γ>or similar 8 and half-opening angles below 1 are obtained, providing dynamical models for the parsec scale jets of active galactic nuclei. Applying the magnetohydrodynamic structure of the quasi-stationary simulation models, we solve the relativistically beamed synchrotron radiation transport. This yields synthetic radiation maps and polarization patterns that can be used to confront high resolution radio and (sub-) mm observations of nearby active galactic nuclei. Relativistic motion together with the helical magnetic fields of the jet formation site imprint a clear signature on the observed polarization and Faraday rotation. In particular, asymmetries in the polarization direction across the jet can disclose the handedness of the magnetic helix and thus the spin direction of the central engine. Finally, we show first results from fully three-dimensional, high resolution adaptive mesh refinement simulations of jet formation from a rotating magnetosphere and examine the jet stability. Relativistic field-line rotation leads to an electric charge separation force that opposes the magnetic
Griffin, Garrett R; Kim, Jennifer C
2013-01-01
The concept of the ideal female eyebrow has changed over time. Modern studies examining youthful brow aesthetics are reviewed. An analysis of ideal female brow characteristics as depicted in the Western print media between 1945 and 2011 was performed. This analysis provided objective evidence that the ideal youthful brow peak has migrated laterally over time to lie at the lateral canthus. There has been a nonstatistically significant trend toward lower and flatter brows. These findings are discussed in relation to current concepts of female brow aging, with repercussions regarding endoscopic brow lift and aesthetic forehead surgery.
The Idealized Cultural Encounter
DEFF Research Database (Denmark)
Christiansen, Lene Bull
). This paper proposes to study cultural encounters which are organised around ideals of cultural difference as a positive social and political force. The Danish People to People NGO Mellemfolkeligt Samvirke (MS) is build around ideals of equality, co-operation, mutuality and solidarity between people...... framework for an investigation into MS’ organisation of what I have termed ‘the idealized cultural encounter’, while also questioning the ways in which ‘culture’ is envisioned in contexts where ‘encounter’ is seen as a positive and desirable force....
The Idealized Cultural Encounter
DEFF Research Database (Denmark)
Christiansen, Lene Bull
). This paper proposes to study cultural encounters which are organised around ideals of cultural difference as a positive social and political force. The Danish People to People NGO Mellemfolkeligt Samvirke (MS) is build around ideals of equality, co-operation, mutuality and solidarity between people...... framework for an investigation into MS’ organisation of what I have termed ‘the idealized cultural encounter’, while also questioning the ways in which ‘culture’ is envisioned in contexts where ‘encounter’ is seen as a positive and desirable force....
Helicity and its role in the varieties of magnetohydrodynamic turbulence
Montgomery, David C.; Bates, Jason W.
Magnetic helicity has appeared as an important but slippery quantity in the theory of magnetohydrodynamic (MHD) turbulence in two contexts: (1) as a slowly-decaying ideal invariant that can control to some extent the formation of a "relaxed" MHD state—one far from thermal equilibrium—in laboratory confinement devices such as the toroidal pinch; and (2) as a potentially inversely-cascadable global quantity in driven, homogeneous MHD turbulence. In the former case, the origin of helicity is straightforwardly clear: electric current is forced to flow along a dc magnetic field, generating poloidal magnetic flux and causing the magnetic field lines to kink up, helically. In the latter, helicity's origins and physical interpretation are more obscure, sometimes having to do with mechanically driven helical motions which supposedly generate magnetic helicity that, however, no longer has any obvious "linked flux" interpretation. In both cases, its usefulness and even its definition sometimes depend sensitively on boundary conditions in a way that, say, those for energy do not. We will examine what the utility of the concept of magnetic helicity has so far been shown to be in discussing turbulent MHD, and comment on some of the ways it differs from other global ideal invariants that have been discussed, such as kinetic energy in 2D Navier-Stokes flows, and mean-square magnetic vector potential in 2D MHD. Attention will be devoted to the evidence for variational principles such as "maximal helicity," or "minimum energy," conjectured to predict various relaxation processes and late-time laminar states in evolving MHD situations. What is believed to be an important distinction between applications of the principles to decaying and driven situations will be stressed. Our discussion will be confined to the cases of small but non-zero transport coefficients, and will not deal with any possible role of helicity in ideal MHD.
Local conservative regularizations of compressible magnetohydrodynamic and neutral flows
Krishnaswami, Govind S.; Sachdev, Sonakshi; Thyagaraja, A.
2016-02-01
Ideal systems like magnetohydrodynamics (MHD) and Euler flow may develop singularities in vorticity ( w =∇×v ). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper, we propose a minimal, local, conservative, nonlinear, dispersive regularization of compressible flow and ideal MHD, in analogy with the KdV regularization of the 1D kinematic wave equation. This work extends and significantly generalizes earlier work on incompressible Euler and ideal MHD. It involves a micro-scale cutoff length λ which is a function of density, unlike in the incompressible case. In MHD, it can be taken to be of order the electron collisionless skin depth c/ωpe. Our regularization preserves the symmetries of the original systems and, with appropriate boundary conditions, leads to associated conservation laws. Energy and enstrophy are subject to a priori bounds determined by initial data in contrast to the unregularized systems. A Hamiltonian and Poisson bracket formulation is developed and applied to generalize the constitutive relation to bound higher moments of vorticity. A "swirl" velocity field is identified, and shown to transport w/ρ and B/ρ, generalizing the Kelvin-Helmholtz and Alfvén theorems. The steady regularized equations are used to model a rotating vortex, MHD pinch, and a plane vortex sheet. The proposed regularization could facilitate numerical simulations of fluid/MHD equations and provide a consistent statistical mechanics of vortices/current filaments in 3D, without blowup of enstrophy. Implications for detailed analyses of fluid and plasma dynamic systems arising from our work are briefly discussed.
A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics
Mocz, Philip; Pakmor, Rüdiger; Springel, Volker; Vogelsberger, Mark; Marinacci, Federico; Hernquist, Lars
2016-11-01
We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a moving mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the moving mesh code AREPO. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a moving mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.
Ideal relaxation of the Hopf fibration
Smiet, Christopher Berg; Candelaresi, Simon; Bouwmeester, Dirk
2017-07-01
Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.
Ideals in intimate relationships.
Fletcher, G J; Simpson, J A; Thomas, G; Giles, L
1999-01-01
This research examined lay relationship and partner ideals in romantic relationships from both a social-cognitive and an evolutionary perspective. Studies 1 and 2 revealed that the qualities of an ideal partner were represented by 3 factors (partner warmth-trustworthiness, vitality-attractiveness, and status-resources), whereas the qualities of an ideal relationship were represented by 2 factors (relationship intimacy-loyalty and passion). A confirmatory factor analysis in Study 3 replicated these factor structures but found considerable overlap across the partner and relationship dimensions. Studies 4 and 5 produced convergent and discriminant validity evidence for all 5 factors. Study 6 indicated that the higher the consistency between the ideals and related assessments of the current partner and relationship, the more positively the current relationship was evaluated.
National Research Council Canada - National Science Library
Jacques Arnaud; Laurent Chusseau; Fabrice Philippe
2013-01-01
We show that the thermodynamics of ideal gases may be derived solely from the Democritean concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent...
DEFF Research Database (Denmark)
Thomsen, Line Hassall
ITV. En unik adgang til redaktioner, redaktionsmøder og journalisters daglige arbejdsgang giver et nyt indblik i journalistisk praksis i dag. Afhandlingen udfolder et spændingsfelt mellem journalisternes professionsidealer og de produktionsvilkår, de er underlagt. Denne forskel mellem ideal og...... realitet udforskes og analyseres som en konstant spænding mellem nye udfordringer og gamle, journalistiske idealer....
DEFF Research Database (Denmark)
Thomsen, Line Hassall
ITV. En unik adgang til redaktioner, redaktionsmøder og journalisters daglige arbejdsgang giver et nyt indblik i journalistisk praksis i dag. Afhandlingen udfolder et spændingsfelt mellem journalisternes professionsidealer og de produktionsvilkår, de er underlagt. Denne forskel mellem ideal og...... realitet udforskes og analyseres som en konstant spænding mellem nye udfordringer og gamle, journalistiske idealer....
Diffusive Magnetohydrodynamic Instabilities beyond the Chandrasekhar Theorem
Rüdiger, Günther; Schultz, Manfred; Stefani, Frank; Mond, Michael
2015-10-01
We consider the stability of axially unbounded cylindrical flows that contain a toroidal magnetic background field with the same radial profile as their azimuthal velocity. For ideal fluids, Chandrasekhar had shown the stability of this configuration if the Alfvén velocity of the field equals the velocity of the background flow, i.e., if the magnetic Mach number {Mm}=1. We demonstrate that magnetized Taylor-Couette flows with such profiles become unstable against non-axisymmetric perturbations if at least one of the diffusivities is finite. We also find that for small magnetic Prandtl numbers {Pm} the lines of marginal instability scale with the Reynolds number and the Hartmann number. In the limit {Pm}\\to 0 the lines of marginal instability completely lie below the line for {Mm}=1 and for {Pm}\\to ∞ they completely lie above this line. For any finite value of {Pm}, however, the lines of marginal instability cross the line {Mm}=1, which separates slow from fast rotation. The minimum values of the field strength and the rotation rate that are needed for the instability (slightly) grow if the rotation law becomes flat. In this case, the electric current of the background field becomes so strong that the current-driven Tayler instability (which also exists without rotation) appears in the bifurcation map at low Hartmann numbers.
Developmental Idealism in China.
Thornton, Arland; Xie, Yu
2016-10-01
This paper examines the intersection of developmental idealism with China. It discusses how developmental idealism has been widely disseminated within China and has had enormous effects on public policy and programs, on social institutions, and on the lives of individuals and their families. This dissemination of developmental idealism to China began in the 19(th) century, when China met with several military defeats that led many in the country to question the place of China in the world. By the beginning of the 20(th) century, substantial numbers of Chinese had reacted to the country's defeats by exploring developmental idealism as a route to independence, international respect, and prosperity. Then, with important but brief aberrations, the country began to implement many of the elements of developmental idealism, a movement that became especially important following the assumption of power by the Communist Party of China in 1949. This movement has played a substantial role in politics, in the economy, and in family life. The beliefs and values of developmental idealism have also been directly disseminated to the grassroots in China, where substantial majorities of Chinese citizens have assimilated them. These ideas are both known and endorsed by very large numbers in China today.
Institute of Scientific and Technical Information of China (English)
高庆弟; 张锦华; 曲洪鹏
2001-01-01
For a reversed magnetic shear plasma formed by early neutral beam injection into the HL-2A tokamak, magnetohydrodynamics instability analysis against ideal low-n modes and resistive interchange modes is carried out.Low-n modes located in the low shear region around the shear reversal point are driven unstable by a large pressure gradient, and they are of the characteristics of infernal modes. High pressure in the central negative shearregion drives resistive interchange modes with the unstable window extending to r /a ≈ 0.2, but not covering thelow shear region around the shear reversal point.
Two Types of Magnetohydrodynamic Sheath Jets
Kaburaki, Osamu
2009-01-01
Recent observations of astrophysical jets emanating from various galactic nuclei strongly suggest that a double layered structure, or a spine-sheath structure, is likely to be their common feature. We propose that such a sheath jet structure can be formed magnetohydrodynamically within a valley of the magnetic pressures, which is formed between the peaks due to the poloidal and toroidal components, with the centrifugal force acting on the rotating sheath plasma is balanced by the hoop stress of the toroidal field. The poloidal field concentrated near the polar axis is maintained by a converging plasma flow toward the jet region, and the toroidal field is developed outside the jet cone owing to the poloidal current circulating through the jet. Under such situations, the set of magnetohydrodynamic (MHD) equations allows two main types of solutions, at least, in the region far from the footpoint. The first type solution describes the jets of marginally bound nature. This type is realized when the jet temperature...
Magnetohydrodynamics on Heterogeneous architectures: a performance comparison
Pang, Bijia; Perrone, Michael
2010-01-01
We present magneto-hydrodynamic simulation results for heterogeneous systems. Heterogeneous architectures combine high floating point performance many-core units hosted in conventional server nodes. Examples include Graphics Processing Units (GPU's) and Cell. They have potentially large gains in performance, at modest power and monetary cost. We implemented a magneto-hydrodynamic (MHD) simulation code on a variety of heterogeneous and multi-core architectures --- multi-core x86, Cell, Nvidia and ATI GPU --- in different languages, FORTRAN, C, Cell, CUDA and OpenCL. We present initial performance results for these systems. To our knowledge, this is the widest comparison of heterogeneous systems for MHD simulations. We review the different challenges faced in each architecture, and potential bottlenecks. We conclude that substantial gains in performance over traditional systems are possible, and in particular that is possible to extract a greater percentage of peak theoretical performance from some systems when...
Efficient Acceleration of Relativistic Magnetohydrodynamic Jets
Toma, Kenji
2013-01-01
Relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts are widely considered to be magnetohydrodynamically driven by black hole accretion systems, although conversion mechanism from Poynting into particle kinetic energy flux is still open. Recent detailed numerical and analytical studies of global structures of steady, axisymmetric magnetohydrodynamic (MHD) flows with specific boundary conditions have not reproduced as rapid an energy conversion as required by observations. In order to find more suitable boundary conditions, we focus on the flow along a poloidal magnetic field line just inside the external boundary, without treating transfield force balance in detail. We find some examples of the poloidal field structure and corresponding external pressure profile for an efficient and rapid energy conversion as required by observations, and that the rapid acceleration requires a rapid decrease of the external pressure above the accretion disk. We also clarify the differences ...
Directory of Open Access Journals (Sweden)
Muhammad H. Al-Malack
2016-07-01
Full Text Available Fuel oil flyash (FFA produced in power and water desalination plants firing crude oils in the Kingdom of Saudi Arabia is being disposed in landfills, which increases the burden on the environment, therefore, FFA utilization must be encouraged. In the current research, the effect of adding FFA on the engineering properties of two indigenous soils, namely sand and marl, was investigated. FFA was added at concentrations of 5%, 10% and 15% to both soils with and without the addition of Portland cement. Mixtures of the stabilized soils were thoroughly evaluated using compaction, California Bearing Ratio (CBR, unconfined compressive strength (USC and durability tests. Results of these tests indicated that stabilized sand mixtures could not attain the ACI strength requirements. However, marl was found to satisfy the ACI strength requirement when only 5% of FFA was added together with 5% of cement. When the FFA was increased to 10% and 15%, the mixture’s strength was found to decrease to values below the ACI requirements. Results of the Toxicity Characteristics Leaching Procedure (TCLP, which was performed on samples that passed the ACI requirements, indicated that FFA must be cautiously used in soil stabilization.
Capacitor discharges, magnetohydrodynamics, X-rays, ultrasonics
Früngel, Frank B A
1965-01-01
High Speed Pulse Technology, Volume 1: Capacitor Discharges - Magnetohydrodynamics - X-Rays - Ultrasonics deals with the theoretical and engineering problems that arise in the capacitor discharge technique.This book discusses the characteristics of dielectric material, symmetrical switch tubes with mercury filling, and compensation conductor forms. The transformed discharge for highest current peaks, ignition transformer for internal combustion engines, and X-ray irradiation of subjects in mechanical motion are also elaborated. This text likewise covers the transformed capacitor discharge in w
Relabeling symmetries in hydrodynamics and magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Padhye, N.; Morrison, P.J.
1996-04-01
Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics relabeling results in Ertel`s theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eulerian variables are used to construct the Casimir invariants of the Hamiltonian formalism.
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
Socrates: Platonic Political Ideal
Directory of Open Access Journals (Sweden)
Christopher P. Long
2012-08-01
Full Text Available This essay articulates the differences and suggests the similarities between the practices of Socratic political speaking and those of Platonic political writing. The essay delineates Socratic speaking and Platonic writing as both erotically oriented toward ideals capable of transforming the lives of individuals and their relationships with one another. Besides it shows that in the Protagoras the practices of Socratic political speaking are concerned less with Protagoras than with the individual young man, Hippocrates. In the Phaedo, this ideal of a Socrates is amplified in such a way that Platonic writing itself emerges as capable of doing with readers what Socratic speaking did with those he encountered. Socrates is the Platonic political ideal. The result is a picture of the transformative political power of Socratic speaking and Platonic writing both.
Directory of Open Access Journals (Sweden)
Laurent Chusseau
2013-02-01
Full Text Available We show that the thermodynamics of ideal gases may be derived solely from the Democritean concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion, aside from the law of energy conservation. Only a single corpuscle in contact with a heat bath submitted to a z and t-invariant force is considered. Most of the end results are known but the method appears to be novel. The mathematics being elementary, the present paper should facilitate the understanding of the ideal gas law and of classical thermodynamics even though not-usually-taught concepts are being introduced.
The Jet in the Galactic Center: An Ideal Laboratory for Magnetohydrodynamics and General Relativity
Falcke, Heino; Bower, Geoffrey C; Gammie, Charles F; Moscibrodzka, Monika; Maitra, Dipankar
2010-01-01
In this paper we review and discuss some of the intriguing properties of the Galactic Center supermassive black hole candidate Sgr A*. Of all possible black hole sources, the event horizon of Sgr A*, subtends the largest angular scale on the sky. It is therefore a prime candidate to study and image plasma processes in strong gravity and it even allows imaging of the shadow cast by the event horizon. Recent mm-wave VLBI and radio timing observations as well as numerical GRMHD simulations now have provided several breakthroughs that put Sgr A* back into the focus. Firstly, VLBI observations have now measured the intrinsic size of Sgr A* at multiple frequencies, where the highest frequency measurements have approached the scale of the black hole shadow. Moreover, measurements of the radio variability show a clear time lag between 22 GHz and 43 GHz. The combination of size and timing measurements, allows one to actually measure the flow speed and direction of magnetized plasma at some tens of Schwarzschild radii....
Golovin, Sergey V
2010-01-01
Equations of magneto-gasdynamics in the natural curvilinear system of coordinates where trajectories and magnetic lines play a role of coordinate curves are reduced to the nonlinear vector wave equation coupled with the incompressibility condition in the form of the generalized Cauchy integral. The symmetry group of obtained equation, equivalence transformation, and group classification with respect to the constitutive equation are calculated. New exact solutions with functional arbitrariness describing non-stationary incompressible flows with constant total pressure are given by explicit formulae. The corresponding magnetic surfaces have the shape of deformed nested cylinders, tori, or knotted tubes.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
Del Zanna, L; Landi, S; Bugli, M; Bucciantini, N
2016-01-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retriev...
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Inghirami, Gabriele; Beraudo, Andrea; Moghaddam, Mohsen Haddadi; Becattini, Francesco; Bleicher, Marcus
2016-01-01
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magnetohydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant $3\\!+\\!1$ formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the Quark-Gluon Plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic-flow of the final hadrons. However, s...
Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Lingam, Manasvi, E-mail: mlingam@princeton.edu [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States); Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States); Miloshevich, George, E-mail: gmilosh@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States); Morrison, Philip J., E-mail: morrison@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States)
2016-07-15
Highlights: • Common Hamiltonian structure of the extended MHD models presented. • The generalized helicities of extended MHD shown to be topological invariants analogous to fluid/magnetic helicity. • Generalized helicities can be studied through powerful topological and knot-theoretic methods such as the Jones polynomial. • Each extended MHD model shown to possess two Lie-dragged 2-forms, which are interpreted as the generalized vorticity fluxes. - Abstract: The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie-dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, which is widely utilized in Chern–Simons theory. The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Inghirami, Gabriele; Del Zanna, Luca; Beraudo, Andrea; Moghaddam, Mohsen Haddadi; Becattini, Francesco; Bleicher, Marcus
2016-12-01
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant 3+1 formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark-gluon plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result.
Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence.
Eyink, Gregory; Vishniac, Ethan; Lalescu, Cristian; Aluie, Hussein; Kanov, Kalin; Bürger, Kai; Burns, Randal; Meneveau, Charles; Szalay, Alexander
2013-05-23
The idea of 'frozen-in' magnetic field lines for ideal plasmas is useful to explain diverse astrophysical phenomena, for example the shedding of excess angular momentum from protostars by twisting of field lines frozen into the interstellar medium. Frozen-in field lines, however, preclude the rapid changes in magnetic topology observed at high conductivities, as in solar flares. Microphysical plasma processes are a proposed explanation of the observed high rates, but it is an open question whether such processes can rapidly reconnect astrophysical flux structures much greater in extent than several thousand ion gyroradii. An alternative explanation is that turbulent Richardson advection brings field lines implosively together from distances far apart to separations of the order of gyroradii. Here we report an analysis of a simulation of magnetohydrodynamic turbulence at high conductivity that exhibits Richardson dispersion. This effect of advection in rough velocity fields, which appear non-differentiable in space, leads to line motions that are completely indeterministic or 'spontaneously stochastic', as predicted in analytical studies. The turbulent breakdown of standard flux freezing at scales greater than the ion gyroradius can explain fast reconnection of very large-scale flux structures, both observed (solar flares and coronal mass ejections) and predicted (the inner heliosheath, accretion disks, γ-ray bursts and so on). For laminar plasma flows with smooth velocity fields or for low turbulence intensity, stochastic flux freezing reduces to the usual frozen-in condition.
Resistive magnetohydrodynamic reconnection: Resolving long-term, chaotic dynamics
Energy Technology Data Exchange (ETDEWEB)
Keppens, R.; Restante, A. L.; Lapenta, G. [Centre for mathematical Plasma-Astrophysics, Department of Mathematics, KU Leuven (Belgium); Porth, O. [Department of Applied Mathematics, The University of Leeds, Leeds LS2 9JT (United Kingdom); Galsgaard, K.; Frederiksen, J. T. [The Niels Bohr Institute, University of Copenhagen, København K (Denmark); Parnell, C. [School of Mathematics and Statistics, University of St. Andrews, Fife (United Kingdom)
2013-09-15
In this paper, we address the long-term evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (grid-adaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shock-capturing, conservative, grid-adaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco-)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shock-capturing, high order finite differences, and particle in cell-like methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.
Numerical magneto-hydrodynamics for relativistic nuclear collisions
Energy Technology Data Exchange (ETDEWEB)
Inghirami, Gabriele [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe-Universitaet, Institute for Theoretical Physics, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Forschungszentrum Juelich, John von Neumann Institute for Computing, Juelich (Germany); Del Zanna, Luca [Universita di Firenze, Dipartimento di Fisica e Astronomia, Firenze (Italy); INAF - Osservatorio Astrofisico di Arcetri, Firenze (Italy); INFN - Sezione di Firenze, Firenze (Italy); Beraudo, Andrea [INFN - Sezione di Torino, Torino (Italy); Moghaddam, Mohsen Haddadi [INFN - Sezione di Torino, Torino (Italy); Hakim Sabzevari University, Department of Physics, P. O. Box 397, Sabzevar (Iran, Islamic Republic of); Becattini, Francesco [Universita di Firenze, Dipartimento di Fisica e Astronomia, Firenze (Italy); INFN - Sezione di Firenze, Firenze (Italy); Bleicher, Marcus [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe-Universitaet, Institute for Theoretical Physics, Frankfurt am Main (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Forschungszentrum Juelich, John von Neumann Institute for Computing, Juelich (Germany)
2016-12-15
We present an improved version of the ECHO-QGP numerical code, which self-consistently includes for the first time the effects of electromagnetic fields within the framework of relativistic magneto-hydrodynamics (RMHD). We discuss results of its application in relativistic heavy-ion collisions in the limit of infinite electrical conductivity of the plasma. After reviewing the relevant covariant 3 + 1 formalisms, we illustrate the implementation of the evolution equations in the code and show the results of several tests aimed at assessing the accuracy and robustness of the implementation. After providing some estimates of the magnetic fields arising in non-central high-energy nuclear collisions, we perform full RMHD simulations of the evolution of the quark-gluon plasma in the presence of electromagnetic fields and discuss the results. In our ideal RMHD setup we find that the magnetic field developing in non-central collisions does not significantly modify the elliptic flow of the final hadrons. However, since there are uncertainties in the description of the pre-equilibrium phase and also in the properties of the medium, a more extensive survey of the possible initial conditions as well as the inclusion of dissipative effects are indeed necessary to validate this preliminary result. (orig.)
Certain variants of multipermutohedron ideals
Indian Academy of Sciences (India)
AJAY KUMAR; CHANCHAL KUMAR
2016-10-01
Multipermutohedron ideals have rich combinatorial properties. An explicit combinatorial formula for the multigraded Betti numbers of a multipermutohedron ideal and their Alexander duals are known. Also, the dimension of the Artinian quotient of an Alexander dual of a multipermutohedron ideal is the number of generalized parking functions. In this paper, monomial ideals which are certain variants of multipermutohedron ideals are studied. Multigraded Betti numbers of these variant monomial ideals and their Alexander duals are obtained. Further, many interesting combinatorial properties of multipermutohedron ideals are extended to these variant monomial ideals.
Energy Technology Data Exchange (ETDEWEB)
Eshraghi, H [Iran University of Science and Technology (IUST), School of Physics, Institute for Studies in Theoretical Physics and Mathematics, Tehran (Iran, Islamic Republic of); Gibbon, J D [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom)
2008-08-29
After a review of some of the recent works by Holm and Gibbon on quaternions and their application to Lagrangian flows, particularly the incompressible Euler equations and the equations of ideal MHD, this paper investigates the compressible and relativistic Euler equations using these methods.
DEFF Research Database (Denmark)
Lund, Rebecca
This thesis explores how notions of what constitutes good academic work and the valuable academic are changing shaped by capitalism and neoliberalism. Taking the standpoint of junior female scholars the thesis explores how the “ideal academic” is constructed and how gendered social relations...
Explosive Magnetic Reconnection in Double-current Sheet Systems: Ideal versus Resistive Tearing Mode
Baty, Hubert
2017-03-01
Magnetic reconnection associated with the tearing instability occurring in double-current sheet systems is investigated within the framework of resistive magnetohydrodynamics (MHD) in a two-dimensional Cartesian geometry. A special emphasis on the existence of fast and explosive phases is taken. First, we extend the recent theory on the ideal tearing mode of a single-current sheet to a double-current layer configuration. A linear stability analysis shows that, in long and thin systems with (length to shear layer thickness) aspect ratios scaling as {S}L9/29 (S L being the Lundquist number based on the length scale L), tearing modes can develop on a fast Alfvénic timescale in the asymptotic limit {S}L\\to ∞ . The linear results are confirmed by means of compressible resistive MHD simulations at relatively high S L values (up to 3× {10}6) for different current sheet separations. Moreover, the nonlinear evolution of the ideal double tearing mode (IDTM) exhibits a richer dynamical behavior than its single-tearing counterpart, as a nonlinear explosive growth violently ends up with a disruption when the two current layers interact trough the merging of plasmoids. The final outcome of the system is a relaxation toward a new state, free of magnetic field reversal. The IDTM dynamics is also compared to the resistive double tearing mode dynamics, which develops in similar systems with smaller aspect ratios, ≳ 2π , and exhibits an explosive secondary reconnection, following an initial slow resistive growth phase. Finally, our results are used to discuss the flaring activity in astrophysical magnetically dominated plasmas, with a particular emphasis on pulsar systems.
On the structure and statistical theory of turbulence of extended magnetohydrodynamics
Miloshevich, George; Morrison, Philip J
2016-01-01
Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range - this is s...
Plasma stability theory including the resistive wall effects
Pustovitov, V. D.
2015-12-01
> Plasma stabilization due to a nearby conducting wall can provide access to better performance in some scenarios in tokamaks. This was proved by experiments with an essential gain in and demonstrated as a long-lasting effect at sufficiently fast plasma rotation in the DIII-D tokamak (see, for example, Strait et al., Nucl. Fusion, vol. 43, 2003, pp. 430-440). The rotational stabilization is the central topic of this review, though eventually the mode rotation gains significance. The analysis is based on the first-principle equations describing the energy balance with dissipation in the resistive wall. The method emphasizes derivation of the dispersion relations for the modes which are faster than the conventional resistive wall modes, but slower than the ideal magnetohydrodynamics modes. Both the standard thin wall and ideal-wall approximations are not valid in this range. Here, these are replaced by an approach incorporating the skin effect in the wall. This new element in the stability theory makes the energy sink a nonlinear function of the complex growth rate. An important consequence is that a mode rotating above a critical level can provide a damping effect sufficient for instability suppression. Estimates are given and applications are discussed.
Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows
Markakis, Charalampos; Uryū, Kōji; Gourgoulhon, Eric; Nicolas, Jean-Philippe; Andersson, Nils; Pouri, Athina; Witzany, Vojtěch
2017-09-01
Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. In this framework, Ertel's potential vorticity theorem for baroclinic fluids arises as a special case of a conservation law valid for any Hamiltonian system. Moreover, conserved circulation laws, such as those of Kelvin, Alfvén and Bekenstein-Oron, emerge simply as special cases of the Poincaré-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (nonisentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.
A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics
Mignone, A.; Ugliano, M.; Bodo, G.
2009-03-01
We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.
Directory of Open Access Journals (Sweden)
Nada S. Abdelwahab
2017-05-01
Full Text Available The present work concerns with the development of stability indicating the RP-HPLC method for simultaneous determination of guaifenesin (GUF and pseudoephedrine hydrochloride (PSH in the presence of guaifenesin related substance (Guaiacol. GUC, and in the presence of syrup excepients with minimum sample pre-treatment. In the developed RP-HPLC method efficient chromatographic separation was achieved for GUF, PSH, GUC and syrup excepients using ODS column as a stationary phase and methanol: water (50:50, v/v, pH = 4 with orthophosphoric acid as a mobile phase with a flow rate of 1 mL min−1 and UV detection at 210 nm. The chromatographic run time was approximately 10 min. Calibration curves were drawn relating the integrated area under peak to the corresponding concentrations of PSH, GUF and GUC in the range of 1–8, 1–20, 0.4–8 μg mL−1, respectively. The developed method has been validated and met the requirements delineated by ICH guidelines with respect to linearity, accuracy, precision, specificity and robustness. The validated method was successfully applied for determination of the studied drugs in triaminic chest congestion® syrup; moreover its results were statistically compared with those obtained by the official method and no significant difference was found between them.
Holcomb, C. T.; Ferron, J. R.; Luce, T. C.; Petrie, T. W.; Politzer, P. A.; Challis, C.; DeBoo, J. C.; Doyle, E. J.; Greenfield, C. M.; Groebner, R. J.; Groth, M.; Hyatt, A. W.; Jackson, G. L.; Kessel, C.; La Haye, R. J.; Makowski, M. A.; McKee, G. R.; Murakami, M.; Osborne, T. H.; Park, J.-M.; Prater, R.; Porter, G. D.; Reimerdes, H.; Rhodes, T. L.; Shafer, M. W.; Snyder, P. B.; Turnbull, A. D.; West, W. P.
2009-05-01
Recent studies on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] have elucidated key aspects of the dependence of stability, confinement, and density control on the plasma magnetic configuration, leading to the demonstration of nearly noninductive operation for >1 s with pressure 30% above the ideal no-wall stability limit. Achieving fully noninductive tokamak operation requires high pressure, good confinement, and density control through divertor pumping. Plasma geometry affects all of these. Ideal magnetohydrodynamics modeling of external kink stability suggests that it may be optimized by adjusting the shape parameter known as squareness (ζ). Optimizing kink stability leads to an increase in the maximum stable pressure. Experiments confirm that stability varies strongly with ζ, in agreement with the modeling. Optimization of kink stability via ζ is concurrent with an increase in the H-mode edge pressure pedestal stability. Global energy confinement is optimized at the lowest ζ tested, with increased pedestal pressure and lower core transport. Adjusting the magnetic divertor balance about a double-null configuration optimizes density control for improved noninductive auxiliary current drive. The best density control is obtained with a slight imbalance toward the divertor opposite the ion grad(B) drift direction, consistent with modeling of these effects. These optimizations have been combined to achieve noninductive current fractions near unity for over 1 s with normalized pressure of 3.565%, and a normalized confinement factor of H98(y ,2)≈1.5.
Nonlinear {omega}*-stabilization of the m = 1 mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Rogers, B. [Univ. of Maryland, College Park, MD (United States). Inst. for Plasma Research; Zakharov, L. [Princeton Univ., NJ (United States). Plasma Physics Lab.
1995-08-01
Earlier studies of sawtooth oscillations in Tokamak Fusion Test Reactor supershots (Levinton et al, Phys. Rev. Lett. 72, 2895 (1994); Zakharov, et al, Plasma Phys. and Contr. Nucl. Fus. Res., Proc. 15th Int. Conf., Seville 1994, Vienna) have found an apparent contradiction between conventional linear theory and experiment: even in sawtooth-free discharges, the theory typically predicts instability due to a nearly ideal m = 1 mode. Here, the nonlinear evolution of such mode is analyzed using numerical simulations of a two-fluid magnetohydrodynamic (MHD) model. We find the mode saturates nonlinearly at a small amplitude provided the ion and electron drift-frequencies {omega}*{sub i,e} are somewhat above the linear stability threshold of the collisionless m = 1 reconnecting mode. The comparison of the simulation results to m = 1 mode activity in TFTR suggests additional, stabilizing effects outside the present model are also important.
MHD simulation studies of z-pinch shear flow stabilization
Paraschiv, I.; Bauer, B. S.; Sotnikov, V. I.; Makhin, V.; Siemon, R. E.
2003-10-01
The development of the m=0 instability in a z-pinch in the presence of sheared plasma flows is investigated with the aid of a two-dimensional magnetohydrodynamic (MHD) simulation code (MHRDR). The linear growth rates are compared to the results obtained by solving the ideal MHD linearized equations [1] and to the results obtained using a 3D hybrid simulation code [2]. The instability development is followed into the nonlinear regime where its growth and saturation are examined. [1] V.I. Sotnikov, I. Paraschiv, V. Makhin, B.S. Bauer, J.-N. Leboeuf, and J.M. Dawson, "Linear analysis of sheared flow stabilization of global magnetohydrodynamic instabilities based on the Hall fluid mode", Phys. Plasmas 9, 913 (2002). [2] V.I. Sotnikov, V. Makhin, B.S. Bauer, P. Hellinger, P. Travnicek, V. Fiala, J.-N. Leboeuf, "Hybrid Simulations of Current-Carrying Instabilities in Z-pinch Plasmas with Sheared Axial Flow", AIP Conference Proceedings, Volume 651, Dense Z-Pinches: 5th International Conference on Dense Z-Pinches, edited by J. Davis et al., page 396, June 2002.
Thermoelectric magnetohydrodynamic stirring of liquid metals.
Jaworski, M A; Gray, T K; Antonelli, M; Kim, J J; Lau, C Y; Lee, M B; Neumann, M J; Xu, W; Ruzic, D N
2010-03-01
The direct observation of a thermoelectric magnetohydrodynamic (TEMHD) flow has been achieved and is reported here. The origin of the flow is identified based on a series of qualitative tests and corresponds, quantitatively, with a swirling flow TEMHD model. A theory for determining the dominant driver of a free-surface flow, TEMHD or thermocapillary (TC), is found to be consistent with the experimental results. The use of the analytical form for an open geometry develops a new dimensionless parameter describing the ratio of TEMHD to TC generated flows.
Intrinsic rotation of toroidally confined magnetohydrodynamics.
Morales, Jorge A; Bos, Wouter J T; Schneider, Kai; Montgomery, David C
2012-10-26
The spatiotemporal self-organization of viscoresistive magnetohydrodynamics in a toroidal geometry is studied. Curl-free toroidal magnetic and electric fields are imposed. It is observed in our simulations that a flow is generated, which evolves from dominantly poloidal to toroidal when the Lundquist numbers are increased. It is shown that this toroidal organization of the flow is consistent with the tendency of the velocity field to align with the magnetic field. Up-down asymmetry of the geometry causes the generation of a nonzero toroidal angular momentum.
Decaying magnetohydrodynamics: effects of initial conditions
Basu
2000-02-01
We study the effects of homogenous and isotropic initial conditions on decaying magnetohydrodynamics (MHD). We show that for an initial distribution of velocity and magnetic-field fluctuations, appropriately defined structure functions decay as a power law in time. We also show that for a suitable choice of initial cross correlations between velocity and magnetic fields even-order structure functions acquire anomalous scaling in time where as scaling exponents of the odd-order structure functions remain unchanged. We discuss our results in the context of fully developed MHD turbulence.
DECAY ESTIMATES FOR ISENTROPIC COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAIN
Institute of Scientific and Technical Information of China (English)
Mohamed Ahmed Abdallah; Jiang Fei; Tan Zhong
2012-01-01
In this paper,under the hypothesis that (o) is upper bounded,we construct a Lyapunov functional for the multidimensional isentropic compressible magnetohydrodynamic equations and show that the weak solutions decay exponentially to the equilibrium state in L2 norm.Our result verifies that the method of Daoyuan Fang,Ruizhao Zi and Ting Zhang [1] can be adapted to magnetohydrodynamic equations.
Delivering ideal employee experiences.
Weiss, Marjorie D; Tyink, Steve; Kubiak, Curt
2009-05-01
Employee-centric strategies have moved from employee satisfaction and brand awareness to employee "affinity" or "attachment." In today's marketplace, occupational health nurses understand that differentiation (i.e., the perception of uniqueness) is the direct result of superior employee interactions, which lead to better employee care, enduring employee relationships, loyal employees, and satisfied employers. What drives employees to occupational health nurse attachment? The answer is a passion for rising above the competition to create ideal employee experiences.
Socrates: Platonic Political Ideal
Directory of Open Access Journals (Sweden)
Christopher P. Long
2012-01-01
Full Text Available El ensayo articula diferencias y sugiere similitudes entre las prácticas del diálogo político de Sócrates y aquellas de la escritura política de Platón. Propone, además, que tanto el diálogo socrático como la escritura platónica se orientan eróticamente hacia ideales capaces de transformar las vidas de los individuos y sus relaciones. Demuestra que en el Protágoras las prácticas del diálogo socrático se ocupan menos de Protágoras que del joven Hipócrates. En el Fedón, este ideal de Sócrates se amplía de tal manera que la misma escritura platónica aparece como capaz de hacer con los lectores lo que el diálogo de Sócrates hacía con sus interlocutores. Sócrates es el ideal político platónico. El resultado es una visión del poder de transformación política tanto del diálogo socrático como de la escritura platónica.
Double-duct liquid metal magnetohydrodynamic engine
Haaland, Carsten M.
1995-01-01
An internal combustion, liquid metal (LM) magnetohydrodynamic (MHD) engine and an alternating current (AC) magnetohydrodynamic generator, are used in combination to provide useful AC electric energy output. The engine design has-four pistons and a double duct configuration, with each duct containing sodium potassium liquid metal confined between free pistons located at either end of the duct. The liquid metal is forced to flow back and forth in the duct by the movement of the pistons, which are alternatively driven by an internal combustion process. In the MHD generator, the two LM-MHD ducts pass in close proximity through a Hartmann duct with output transformer. AC power is produced by operating the engine with the liquid metal in the two generator ducts always flowing in counter directions. The amount of liquid metal maintained in the ducts may be varied. This provides a variable stroke length for the pistons. The engine/generator provides variable AC power at variable frequencies that correspond to the power demands of the vehicular propulsion. Also the engine should maintain nearly constant efficiency throughout the range of power usage. Automobiles and trucks could be powered by the invention, with no transmission or power converter devices being required.
The Calculus of Variations and the Ideal MHD Energy Principle
Schnack, Dalton D.
In Lecture 22, we showed that the ideal MHD force operator is self-adjoint and suggested that this allowed a formulation in which the stability of a system could be determined without solving a differential equation. Going further requires a little background in the calculus of variations. In the lecture we begin this discussion,1 and formulate the ideal MHD energy principle.
Directory of Open Access Journals (Sweden)
Kenneth D. Magill
2001-01-01
Full Text Available We determine, up to isomorphism, all those topological nearrings n whose additive groups are the n-dimensional Euclidean groups, n>1, and which contain n one-dimensional linear subspaces {Ji}i=1n which are also right ideals of the nearring satisfying several additional properties. Specifically, for each w∈n, we require that there exist wi∈Ji, 1≤i≤n, such that w=w1+w2+⋯+wn and multiplication on the left of w yields the same result as multiplication by the same element on the left of wn. That is, vw=vwn for each v∈n.
Capturing medical students' idealism.
Smith, Janice K; Weaver, Donna B
2006-01-01
Students' idealism and desire to work with underserved populations decline as they progress from preclinical training through clerkships and residency. With an increasingly diverse population and increasing health disparities, academic health centers need to incorporate changes in their curricula to train socially responsible and idealistic physicians. International electives can provide valuable learning experiences to help achieve these goals. Sixty-six preclinical medical students at the University of Texas Medical Branch participated in an international elective from 1997 to 2005. After 1 week of didactics, they spent 3 weeks as part of a multidisciplinary medical team in rural Nicaragua. Postelective questionnaires were administered. From students' responses, we identified common learning themes and grouped them under the categories of attitudes, awareness, and skills. Limitations included a self-selection bias, lack of a control group, and limited follow-up. After the elective, students had an increased interest in volunteerism, humanitarian efforts, and working with underserved populations both in the United States and abroad, as well as more compassion toward the underserved. Students also reported a heightened awareness of social determinants of health and public health, and a broadened global perspective, as well as increased self-awareness. Our findings illustrate that a well-structured, mentored experience in international health can have a positive impact on preclinical students' attitudes, including their compassion, volunteerism, and interest in serving under-served populations, all measures of idealism.
Capturing Medical Students’ Idealism
Smith, Janice K.; Weaver, Donna B.
2006-01-01
PURPOSE Students’ idealism and desire to work with underserved populations decline as they progress from preclinical training through clerkships and residency. With an increasingly diverse population and increasing health disparities, academic health centers need to incorporate changes in their curricula to train socially responsible and idealistic physicians. International electives can provide valuable learning experiences to help achieve these goals. METHODS Sixty-six preclinical medical students at the University of Texas Medical Branch participated in an international elective from 1997 to 2005. After 1 week of didactics, they spent 3 weeks as part of a multidisciplinary medical team in rural Nicaragua. Postelective questionnaires were administered. From students’ responses, we identified common learning themes and grouped them under the categories of attitudes, awareness, and skills. Limitations included a self-selection bias, lack of a control group, and limited follow-up. RESULTS After the elective, students had an increased interest in volunteerism, humanitarian efforts, and working with underserved populations both in the United States and abroad, as well as more compassion toward the underserved. Students also reported a heightened awareness of social determinants of health and public health, and a broadened global perspective, as well as increased self-awareness. CONCLUSIONS Our findings illustrate that a well-structured, mentored experience in international health can have a positive impact on preclinical students’ attitudes, including their compassion, volunteerism, and interest in serving under-served populations, all measures of idealism. PMID:17003160
Disk magnetohydrodynamic power conversion system for NERVA reactor
Energy Technology Data Exchange (ETDEWEB)
Jackson, W.D. (HMJ Corporation. 10400 Connecticut Ave., Kensington, Maryland 20895 (United States)); Bernard, F.E. (Westinghouse Corp., P.O. Box 355, Pittsburgh, Pennsylvania 15230 (United States)); Holman, R.R. (HMJ Corporation, 10400 Connecticut Ave., Kensington, Maryland 20895 (United States)); Maxwell, C.D. (STD Research Corp., P.O. Box C, Arcadia, California 91006 (United States)); Seikel, G.R. (SeiTec, Inc., P.O. Box 81264, Cleveland, Ohio 44181 (United States))
1993-01-15
The combination of a magnetohydrodynamic (MHD) generator of the disk type with a NERVA reactor yields an advanced power system particularly suited to space applications with the capability of producing up to gigawatt pulses and multi-megawatt continuous operation. Several unique features result from the combination of this type of reactor and a disk MHD generator in which hydrogen serves as the plasma working fluid. Cesium seedings is utilized under conditions which enable the generator to operate stably in the non-equilibrium electrical conduction mode. In common with all practical MHD generators, the disk output is DC and voltages in the range 20--100 kV are attainable. This leads to a simplification of the power conditioning system and a major reduction in specific mass. Taken together with the high performance capabilities of the NERVA reactor, the result is an attractively low overall system specific mass. Further, the use of non-equilibrium ionization enables system specific enthalpy extractions in excess of 40% to be attained. This paper reports the results of a study to establish the basis for the design of a cesium seeded hydrogen MHD disk generator. Generator performance results are presented in terms of a stability factor which is related to cesium seeded hydrogen plasma behavior. It is shown that application of the results already obtained with cesium seeded noble gases (argon and helium) to the case of hydrogen as the working fluid in a disk MHD generator enables a high performance power system to be defined.
Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
Del Zanna, L.; Papini, E.; Landi, S.; Bugli, M.; Bucciantini, N.
2016-08-01
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula; hence, its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two-dimensional numerical simulations, the linear phase and the subsequent non-linear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics (MHD), as appropriate in situations where the Alfvén velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S-1/3 are considered, the so-called ideal tearing regime is retrieved, with modes growing independently of S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfvén velocity. In the fully non-linear stage, we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfvén speed from the X-point, and a fast reconnection rate at the predicted value {R}˜ (ln S)^{-1}.
An explicit scheme for ohmic dissipation with smoothed particle magneto-hydrodynamics
Tsukamoto, Yusuke; Inutsuka, Shu-ichiro
2013-01-01
In this paper, we present an explicit scheme for Ohmic dissipation with smoothed particle magneto-hydrodynamics (SPMHD). We propose a SPH discretization of Ohmic dissipation and solve Ohmic dissipation part of induction equation with the supertime-stepping method (STS) which allows us to take a longer time-step than Courant-Friedrich-Levy stability condition. Our scheme is second-order accurate in space and first-order accurate in time. Our numerical experiments show that optimal choice of the parameters of STS for Ohmic dissipation of SPMHD is {\
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
Zenitani, Seiji; Hesse, Michael; Klimas, Alex
2010-01-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten-Lan-van Leer method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfv enic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond-chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet-Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Shear instabilities in shallow-water magnetohydrodynamics
Mak, Julian; Hughes, D W
2016-01-01
Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as H{\\o}iland's growth rate bound and Howard's semi-circle theorem, are extended to this shallow-water system for quite general profiles. Two specific piecewise-constant velocity profiles, the vortex sheet and the rectangular jet, are studied analytically and asymptotically; it is found that the magnetic field and stratification (as measured by the Froude number) are generally both stabilising, but weak instabilities can be found at arbitrarily large Froude number. Numerical solutions are computed for corresponding smooth velocity profiles, the hyperbolic-tangent shear layer and the Bickley jet, for a uniform background field. A generalisation of the long-wave asymptotic analysis of Drazin & Howard (1962) is employed in order to understand the instability characteristics for both ...
Generalized global symmetries and dissipative magnetohydrodynamics
Grozdanov, Sašo; Iqbal, Nabil
2016-01-01
The conserved magnetic flux of U(1) electrodynamics coupled to matter in four dimensions is associated with a generalized global symmetry. We study the realization of such a symmetry at finite temperature and develop the hydrodynamic theory describing fluctuations of a conserved 2-form current around thermal equilibrium. This can be thought of as a systematic derivation of relativistic magnetohydrodynamics, constrained only by symmetries and effective field theory. We construct the entropy current and show that at first order in derivatives, there are six dissipative transport coefficients. We present a universal definition of resistivity in a theory of dynamical electromagnetism and derive a direct Kubo formula for the resistivity in terms of correlation functions of the electric field operator. We also study fluctuations and collective modes, deriving novel expressions for the dissipative widths of magnetosonic and Alfven modes. Finally, we demonstrate that a non-trivial truncation of the theory can be perf...
Classes of hydrodynamic and magnetohydrodynamic turbulent decay
Brandenburg, Axel
2016-01-01
We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, and not by the initial conditions, as is widely assumed. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wavenumber k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k^4). All of our self-similar solutions have an intrinsic subinertial range close to k^4$.
Aharonov–Bohm effects in magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Yahalom, Asher, E-mail: asya@ariel.ac.il [Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH (United Kingdom); Ariel University, Ariel 40700 (Israel)
2013-10-30
It is shown that an Aharonov–Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables (Kats, 2004; Yahalom and Lynden-Bell, 2008; Yahalom, 2010) [1,10,12]. If a MHD flow has a non-trivial topology some of the functions appearing in the MHD Lagrangian are non-single-valued. These functions have properties similar to the phases in the AB celebrated effect (Aharonov and Bohm, 1959; van Oudenaarden et al., 1998) [2,3]. While the manifestation of the quantum AB effect is in interference fringe patterns (Tonomura et al., 1982) [4], the manifestation of the MHD Aharonov–Bohm effects are through new dynamical conservation laws.
Action principles for extended magnetohydrodynamic models
Energy Technology Data Exchange (ETDEWEB)
Keramidas Charidakos, I.; Lingam, M.; Morrison, P. J.; White, R. L. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712 (United States); Wurm, A. [Department of Physical and Biological Sciences, Western New England University, Springfield, Massachusetts 01119 (United States)
2014-09-15
The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.
Magnetohydrodynamic Origin of Jets from Accretion Disks
Lovelace, R V E; Koldoba, A V
1999-01-01
A review is made of recent magnetohydrodynamic (MHD) theory and simulations of origin of jets from accretion disks. Many compact astrophysical objects emit powerful, highly-collimated, oppositely directed jets. Included are the extra galactic radio jets of active galaxies and quasars, and old compact stars in binaries, and emission line jets in young stellar objects. It is widely thought that these different jets arise from rotating, conducting accretion disks threaded by an ordered magnetic field. The twisting of the magnetic field by the rotation of the disk drives the jets by magnetically extracting matter, angular momentum, and energy from the accretion disk. Two main regimes have been discussed theoretically, hydromagnetic winds which have a significant mass flux, and Poynting flux jets where the mass flux is negligible. Over the past several years, exciting new developments on models of jets have come from progress in MHD simulations which now allow the study of the origin - the acceleration and collima...
Extended inertial range phenomenology of magnetohydrodynamic turbulence
Matthaeus, William H.; Zhou, YE
1989-01-01
A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan (1965). The role of Alfven wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22-1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented 'golden rules' for relating the spectral transfer time scale to the Alfven and eddy-turnover time scales.
Resistive Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection
Zenitani, Seiji; Klimas, Alex
2010-01-01
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten--Lan--van Leer (HLL) method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfv\\'{e}nic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond--chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet--Parker-type reconnection slowly evolves. Under a current-dependent resistivity, plasmoids are repeatedly formed in an elongated current sheet. It is concluded that the resistivity model is of critical importance for RRMHD modeling of relativistic magnetic reconnection.
Anomalous magnetohydrodynamics in the extreme relativistic domain
Giovannini, Massimo
2016-01-01
The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In particular we explore the situation where the conventional vector currents are complemented by the axial-vector currents arising either from the pseudo Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite fermionic density effects. After expanding the generally covariant equations in inverse powers of the conductivity, the relativistic analog of the magnetic diffusivity equation is derived in the presence of vortical and magnetic currents. While the anomalous contributions are generally suppressed by the diffusivity, they are shown to disappear in the perfectly conducting limit. When the flow is irrotational, boost-invariant and with vanishing four-acceleration the corresponding evolution equations are explicitly integrated so that the various physic...
Computer simulation of a magnetohydrodynamic dynamo. II
Kageyama, Akira; Sato, Tetsuya; Complexity Simulation Group
1995-05-01
A computer simulation of a magnetohydrodynamic dynamo in a rapidly rotating spherical shell is performed. Extensive parameter runs are carried out changing electrical resistivity. When resistivity is sufficiently small, total magnetic energy can grow more than ten times larger than total kinetic energy of convection motion which is driven by an unlimited external energy source. When resistivity is relatively large and magnetic energy is comparable or smaller than kinetic energy, the convection motion maintains its well-organized structure. However, when resistivity is small and magnetic energy becomes larger than kinetic energy, the well-organized convection motion is highly irregular. The magnetic field is organized in two ways. One is the concentration of component parallel to the rotation axis and the other is the concentration of perpendicular component. The parallel component tends to be confined inside anticyclonic columnar convection cells, while the perpendicular component is confined outside convection cells.
Exploring Astrophysical Magnetohydrodynamics in the Laboratory
Manuel, Mario
2014-10-01
Plasma evolution in many astrophysical systems is dominated by magnetohydrodynamics. Specifically of interest to this talk are collimated outflows from accretion systems. Away from the central object, the Euler equations can represent the plasma dynamics well and may be scaled to a laboratory system. We have performed experiments to investigate the effects of a background magnetic field on an otherwise hydrodynamically collimated plasma. Laser-irradiated, cone targets produce hydrodynamically collimated plasma jets and a pulse-powered solenoid provides a constant background magnetic field. The application of this field is shown to completely disrupt the original flow and a new magnetically-collimated, hollow envelope is produced. Results from these experiments and potential implications for their astrophysical analogs will be discussed.
Rarefaction wave in relativistic steady magnetohydrodynamic flows
Energy Technology Data Exchange (ETDEWEB)
Sapountzis, Konstantinos, E-mail: ksapountzis@phys.uoa.gr; Vlahakis, Nektarios, E-mail: vlahakis@phys.uoa.gr [Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece)
2014-07-15
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.
Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
Verma, Mahendra K.
2017-08-01
In this review we summarise the current status of the quasi-static magnetohydrodynamic turbulence. The energy spectrum is steeper than Kolmogorov’s k -5/3 spectrum due to the decrease of the kinetic energy flux with wavenumber k as a result of Joule dissipation. The spectral index decreases with the increase of interaction parameter. The flow is quasi two-dimensional with strong {{\\mathbf{U}}\\bot} at small k and weak {{U}\\parallel} at large k, where {{\\mathbf{U}}\\bot} and {{U}\\parallel} are the perpendicular and parallel components of velocity relative to the external magnetic field. For small k, the energy flux of {{\\mathbf{U}}\\bot} is negative, but for large k, the energy flux of {{U}\\parallel} is positive. Pressure mediates the energy transfer from {{\\mathbf{U}}\\bot} to {{U}\\parallel} .
Magnetohydrodynamic Modeling of the Jovian Magnetosphere
Walker, Raymond
2005-01-01
Under this grant we have undertaken a series of magnetohydrodynamic (MHD) simulation and data analysis studies to help better understand the configuration and dynamics of Jupiter's magnetosphere. We approached our studies of Jupiter's magnetosphere in two ways. First we carried out a number of studies using our existing MHD code. We carried out simulation studies of Jupiter s magnetospheric boundaries and their dependence on solar wind parameters, we studied the current systems which give the Jovian magnetosphere its unique configuration and we modeled the dynamics of Jupiter s magnetosphere following a northward turning of the interplanetary magnetic field (IMF). Second we worked to develop a new simulation code for studies of outer planet magnetospheres.
Lattice kinetic simulation of nonisothermal magnetohydrodynamics.
Chatterjee, Dipankar; Amiroudine, Sakir
2010-06-01
In this paper, a lattice kinetic algorithm is presented to simulate nonisothermal magnetohydrodynamics in the low-Mach number incompressible limit. The flow and thermal fields are described by two separate distribution functions through respective scalar kinetic equations and the magnetic field is governed by a vector distribution function through a vector kinetic equation. The distribution functions are only coupled via the macroscopic density, momentum, magnetic field, and temperature computed at the lattice points. The novelty of the work is the computation of the thermal field in conjunction with the hydromagnetic fields in the lattice Boltzmann framework. A 9-bit two-dimensional (2D) lattice scheme is used for the numerical computation of the hydrodynamic and thermal fields, whereas the magnetic field is simulated in a 5-bit 2D lattice. Simulation of Hartmann flow in a channel provides excellent agreement with corresponding analytical results.
Integrable version of Burgers equation in magnetohydrodynamics.
Olesen, P
2003-07-01
It is pointed out that for the case of (compressible) magnetohydrodynamics (MHD) with the fields v(y)(y,t) and Bx(y,t), one can have equations of the Burgers type which are integrable. We discuss the solutions. It turns out that the propagation of the nonlinear effects is governed by the initial velocity (as in Burgers case) as well as by the initial Alfvén velocity. Many results previously obtained for the Burgers equation can be transferred to the MHD case. We also discuss equipartition v(y)=+/-Bx. It is shown that an initial localized small scale magnetic field will end up in fields moving to the left and the right, thus transporting energy from smaller to larger distances.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Energy Technology Data Exchange (ETDEWEB)
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
A Multidimensional Code For Isothermal Magnetohydrodynamic Flows
Kim, J; Jones, T W; Hong, S S; Kim, Jongsoo; Ryu, Dongsu
1999-01-01
We present a multi-dimensional numerical code to solve isothermal magnetohydrodynamic (IMHD) equations for use in modeling astrophysical flows. First, we have built a one-dimensional code which is based on an explicit finite-difference method on an Eulerian grid, called the total variation diminishing (TVD) scheme. Recipes for building the one-dimensional IMHD code, including the normalized right and left eigenvectors of the IMHD Jacobian matrix, are presented. Then, we have extended the one-dimensional code to a multi-dimensional IMHD code through a Strang-type dimensional splitting. In the multi-dimensional code, an explicit cleaning step has been included to eliminate non-zero $\
IDEAL trial: economic analysis
Directory of Open Access Journals (Sweden)
Simona de Portu
2008-01-01
Full Text Available Introduction: the IDEAL (“High-dose atorvastatin vs usual-dose simvastatin for secondary prevention after myocardial infarction” study was carried out to compare intensive lowering of low-density lipoprotein (LDL-cholesterol using the highest recommended dose of atorvastatin 80 mg with simvastatin 20 mg. Aim: our aim was to investigate the economic consequence of high dose of atorvastatin vs usual-dose of simvastatin in reducing major coronary events in patients with a history of acute myocardial infarction (AMI. Methods: the analysis is based on clinical outcome data from the IDEAL study. We conducted a cost-effectiveness analysis, comparing high dose of atorvastatin (80 mg/die versus usual-dose of simvastatin (20 mg/die in the perspective of the Italian National Health Service. We identified and quantified medical costs: drug costs according to the Italian National Therapeutic Formulary and hospitalizations were quantified based on the Italian National Health Service tariffs (2008. Effects were measured in terms of morbidity reduction (frequency of hospitalizations. We considered an observation period of 4.8 years. The costs borne after the first 12 months were discounted using an annual rate of 3%. We conducted one and multi-way sensitivity analyses on unit cost and effectiveness. Results: the cost of atorvastatin therapy over the 4.8 years period amounted to approximately 2.4 millions euro per 1,000 patients. The total cost of atorvastatin high dose was about 3.9 millions euro, the incremental cost per patient free from event is 31.176,03 euro. Discussion: this evaluation found that atorvastatin therapy is cost-effective. Results were sensitive to either clinical or economic variables.
Structures in magnetohydrodynamic turbulence: detection and scaling.
Uritsky, V M; Pouquet, A; Rosenberg, D; Mininni, P D; Donovan, E F
2010-11-01
We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stem from numerical simulations of decaying three-dimensional magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536³ points and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X -point configuration embedded in three dimensions, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic-field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with magnetohydrodynamics. We suggest that this range can be governed by turbulence dynamics as opposed to criticality and propose an interpretation of intermittency in terms of propagation of local instabilities.
Adams, Colin S; Hsu, Scott C
2014-01-01
We present time-resolved observations of Rayleigh-Taylor-instability growth at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time ($\\sim 10$ $\\mu$s) is consistent with the estimated linear Rayleigh-Taylor growth rate calculated using experimentally inferred values of density ($\\sim 10^{14}$ cm$^{-3}$) and acceleration ($10^9$ m/s$^2$). The observed instability wavelengths ($\\gtrsim 1$ cm) are consistent with stabilization of short wavelengths by a magnetic field of the experimentally measured magnitude ($\\sim 15$ G) and direction. Comparisons of data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization.
Multi-fluid problems in magnetohydrodynamics with applications to astrophysical processes
Greenfield, Eric John
2016-01-01
I begin this study by presenting an overview of the theory of magnetohydrodynamics and the necessary conditions to justify the fluid treatment of a plasma. Upon establishing the fluid description of a plasma we move on to a discussion of magnetohydrodynamics in both the ideal and Hall regimes. This framework is then extended to include multiple plasmas in order to consider two problems of interest in the field of theoretical space physics. The first is a study on the evolution of a partially ionized plasma, a topic with many applications in space physics. A multi-fluid approach is necessary in this case to account for the motions of an ion fluid, electron fluid and neutral atom fluid; all of which are coupled to one another by collisions and/or electromagnetic forces. The results of this study have direct application towards an open question concerning the cascade of Kolmogorov-like turbulence in the interstellar plasma which we will discuss below. The second application of multi-fluid magnetohydrodynamics that we consider in this thesis concerns the amplification of magnetic field upstream of a collisionless, parallel shock. The relevant fluids here are the ions and electrons comprising the interstellar plasma and the galactic cosmic ray ions. Previous works predict that the streaming of cosmic rays lead to an instability resulting in significant amplification of the interstellar magnetic field at supernova blastwaves. This prediction is routinely invoked to explain the acceleration of galactic cosmic rays up to energies of 1015 eV. I will examine this phenomenon in detail using the multi-fluid framework outlined below. The purpose of this work is to first confirm the existence of an instability using a purely fluid approach with no additional approximations. If confirmed, I will determine the necessary conditions for it to operate.
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)
Monomial ideals, computations and applications
Gimenez, Philippe; Sáenz-de-Cabezón, Eduardo
2013-01-01
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the devel...
Time dependent two phase flows in Magnetohydrodynamics: A ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT Subscription or Fee Access. Time dependent two phase flows in Magnetohydrodynamics: A Greens function approach. BK Jha, HM Jibril ...
Viscosity and Vorticity in Reduced Magneto-Hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Joseph, Ilon [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-08-12
Magneto-hydrodynamics (MHD) critically relies on viscous forces in order for an accurate determination of the electric eld. For each charged particle species, the Braginskii viscous tensor for a magnetized plasma has the decomposition into matrices with special symmetries.
Rossmanith, James A
2013-01-01
The modification of the celebrated Yee scheme from Maxwell equations to magnetohydrodynamics is often referred to as the constrained transport approach. Constrained transport can be viewed as a sort of predictor-corrector method for updating the magnetic field, where a magnetic field value is first predicted by a method that does not preserve the divergence-free condition on the magnetic field, followed by a correction step that aims to control these divergence errors. This strategy has been successfully used in conjunction with a variety of shock-capturing methods including WENO, central, and wave propagation schemes. In this work we show how to extend the basic CT framework to the discontinuous Galerkin finite element method on both 2D and 3D Cartesian grids. We first review the entropy-stability theory for semi-discrete DG discretizations of ideal MHD, which rigorously establishes the need for a magnetic field that satisfies the following conditions: (1) the divergence of the magnetic field is zero on each...
Dislocations in magnetohydrodynamic waves in a stellar atmosphere.
López Ariste, A; Collados, M; Khomenko, E
2013-08-23
We describe the presence of wave front dislocations in magnetohydrodynamic waves in stratified stellar atmospheres. Scalar dislocations such as edges and vortices can appear in Alfvén waves, as well as in general magnetoacoustic waves. We detect those dislocations in observations of magnetohydrodynamic waves in sunspots in the solar chromosphere. Through the measured charge of all the dislocations observed, we can give for the first time estimates of the modal contribution in the waves propagating along magnetic fields in solar sunspots.
An AC magnetohydrodynamic micropump: towards a true integrated microfluidic system
Energy Technology Data Exchange (ETDEWEB)
Lee, A P; Lemoff, A V; McConaghy, C F; Miles, R R
1999-03-01
An AC Magnetohydrodynamic (MHD) micropump has been demonstrated in which the Lorentz force is used to propel an electrolytic solution along a microchannel etched in silicon. This micropump has no moving parts, produces a continuous (not pulsatile) flow, and is compatible with solutions containing biological specimens. micropump, using the Lorentz force as the pumping mechanism for biological analysis. The AC Magnetohydrodynamic (MHD) micropump investigated produces a continuous flow and allows for complex microchannel design.
Dislocations in magnetohydrodynamic waves in a stellar atmosphere
Ariste, A López; Khomenko, E
2013-01-01
We describe the presence of wavefront dislocations in magnetohydrodynamic waves in stratified stellar atmospheres. Scalar dislocations such as edges and vortices can appear in Alfv\\'en waves, as well as in general magneto-acoustic waves. We detect those dislocations in observations of magnetohydrodynamic waves in sunspots in the solar chromosphere. Through the measured charge of all the dislocations observed, we can give for the first time estimates of the modal contribution in the waves propagating along magnetic fields in solar sunspots.
Attractors of magnetohydrodynamic flows in an Alfvenic state
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Sanz, Javier [Departamento de Analisis Matematico, Universidad de Valladolid, Valladolid (Spain)
1999-08-13
We present a simplified form of the magnetohydrodynamic system which describes the evolution of a plasma where the small-scale velocity and magnetic field are aligned in the form of Alfven waves, such as happens in several turbulent situations. Bounds on the dimension of the global attractor are found, and are shown to be an improvement of the standard ones for the full magnetohydrodynamic equations. (author)
Webb, G M; McKenzie, J F; Hu, Q; Zank, G P
2013-01-01
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabelling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler Poincar\\'e variational approach is also used to derive conservation laws associated with fluid relabelling symmetries using Noether's second theorem.
Arnaud, Jacques; Philippe, Fabrice
2011-01-01
The air density on earth decays as a function of altitude $z$ approximately according to an $\\exp(-w\\,z/\\theta)$-law, where $w$ denotes the weight of a nitrogen molecule and $\\theta=\\kB T$ where $k_B$ is a constant and $T$ is the thermodynamic temperature. To derive this law one usually invokes the Boltzmann factor, itself derived from statistical considerations. We show that this (barometric) law may be derived solely from the democritian concept of corpuscles moving in vacuum. We employ a principle of simplicity, namely that this law is \\emph{independent} of the law of corpuscle motion. This view-point puts aside restrictive assumptions that are source of confusion. Similar observations apply to the ideal-gas law. In the absence of gravity, when a cylinder terminated by a piston, containing a single corpuscle and with height $h$ has temperature $\\theta$, the average force that the corpuscle exerts on the piston is: $\\ave{F}=\\theta/h$. This law is valid at any temperature, except at very low temperatures whe...
The ideal physician entrepreneur.
Bottles, K
2000-01-01
How does the sometimes elusive and high-stakes world of venture capital really work? How can physician executives with innovative ideas or new technologies approach venture capitalists to help them raise capital to form a start-up company? These important questions are explored in this new column on the physician as entrepreneur. The ideal physician executive is described as: (1) an expert in an area that Wall Street perceives as hot; (2) a public speaker who can enthusiastically communicate scientific and business plans to a variety of audiences; (3) a team leader who is willing to share equity in the company with other employees; (4) a recruiter and a motivator; (5) an implementer who can achieve milestones quickly that allow the company to go public as soon as possible; and (6) a realist who does not resent the terms of the typical deal. The lucrative world of the venture capitalists is foreign territory for physician executives and requires a great idea, charisma, risk-taking, connections, patience, and perseverance to navigate it successfully.
Surface Wave Propagation in non--ideal plasmas
Pandey, B P
2015-01-01
The properties of surface waves in a partially ionized, compressible magnetized plasma slab are investigated in this work. The waves are affected by the nonideal magnetohydrodynamic effects which causes finite drift of the magnetic field in the medium. When the magnetic field drift is ignored, the characteristics of the wave propagation in a partially ionized plasma fluid is similar to the fully ionized ideal MHD except now the propagation properties depend on the fractional ionization as well as on the compressibility of the medium. The phase velocity of the sausage and kink waves increases marginally (by a few percent) due to the compressibility of the medium in both ideal as well as Hall diffusion dominated regimes. However, unlike ideal regime, only waves below certain cut off frequency can propagate in the medium in Hall dominated regime. This cut off for a thin slab has a weak dependence on the plasma beta whereas for thick slab no such dependence exists. More importantly, since the cut off is introduce...
Non-ideal MHD turbulent decay in molecular clouds
Downes, T P
2009-01-01
It is well known that non-ideal magnetohydrodynamic effects are important in the dynamics of molecular clouds: both ambipolar diffusion and possibly the Hall effect have been identified as significant. We present the results of a suite of simulations with a resolution of 512-cubed of turbulent decay in molecular clouds incorporating a simplified form of both ambipolar diffusion and the Hall effect simultaneously. The initial velocity field in the turbulence is varied from being super-Alfv\\'enic and hypersonic, through to trans-Alfv\\'enic but still supersonic. We find that ambipolar diffusion increases the rate of decay of the turbulence increasing the decay from $t^{-1.25}$ to $t^{-1.4}$. The Hall effect has virtually no impact in this regard. The power spectra of density, velocity and the magnetic field are all affected by the non-ideal terms, being steepened significantly when compared with ideal MHD turbulence with exponents. The density power spectra components change from about 1.4 to about 2.1 for the i...
The Small-Scale Dynamo and Non-Ideal MHD in Primordial Star Formation
Schober, Jennifer; Federrath, Christoph; Glover, Simon; Klessen, Ralf; Banerjee, Robi
2012-01-01
We study the amplification of magnetic fields during the formation of primordial halos. The turbulence generated by gravitational infall motions during the formation of the first stars and galaxies can amplify magnetic fields very efficiently and on short timescales up to dynamically significant values. Using the Kazantsev theory, which describes the so-called small-scale dynamo - a magnetohydrodynamical process converting kinetic energy from turbulence into magnetic energy - we can then calculate the growth rate of the small-scale magnetic field. Our calculations are based on a detailed chemical network and we include non-ideal magnetohydrodynamical effects such as ambipolar diffusion and Ohmic dissipation. We follow the evolution of the magnetic field up to larger scales until saturation occurs on the Jeans scale. Assuming a weak magnetic seed field generated by the Biermann battery process, both Burgers and Kolmogorov turbulence lead to saturation within a rather small density range. Such fields are likely...
Popov, M.
Erwin Schrodinger suggested that " Scientific knowledge forms part of the idealistic background of human life", which exalted man from a nude and savage state to true humanity [Science and Humanism, Cambridge, 1961, p9]. Modern space sciences an space exploration are a brilliant demonstration of the validity of Schrodinger's thesis on Idealism. Moreover, Schrodingers thesis could be considered also as a basic principle for the New Educational Space Philosophical Project "TIMAEUS"."TIMAEUS" is not only an attempt to to start a new dialogue between Science, the Humanities and Religion; but also it is an origin of the cultural innovations of our so strange of globilisation. TIMAEUS, thus, can reveal Idealism as something more fundamental , more refined, more developed than is now accepted by the scientific community and the piblic. TIMAEUS has a significant cultural agenda, connected with the high orbital performance of the synthetic arts, combining a knowledge of the truly spiritual as well as the universal. In particular, classical ballet as a synthetic art can be a new and powerful perfector and re-creator of the real human, real idealistic, real complex culture in orbit. As is well known, Carlo Blasis, the most important dance theorist of the 19t h .century, made probably the first attempts to use the scientific ideas of Leonardo da Vinci and Isaac Newton for the understanding of the gravitational nature of balance and allegro in ballet. In particular Blasis's idea of the limited use of the legs in classical dance realised by the gifted pupils of Enrico Cecchetti - M.Fokine, A.Pavlova and V.Nijinsky, with thinkable purity and elegance of style. V.Nijinsky in his remarkable animation of the dance of two dimensional creatures of a Euclidean flat world (L'Apres Midi d'un Faune,1912) discovered that true classical dance has some gravitational limits. For example, Nijinsky's Faunes and Nymphs mut use running on the heels (In accordance with "Partitura" 1916); they
Roslyn, J J
1993-04-01
I started out asking the question can we achieve our goals and are our goals realistic in the 1990s? I believe that we can achieve anything that we set our minds to. Our goals of providing quality care to our patients, performing research, teaching the next generation, and having an impact on our local environment are worth pursuing. However, the rules have changed and the status quo is simply not good enough. If we are to survive, we must be prepared for the future. You have the ability to change and the power to control the future. You are the future. Seize the opportunity and get involved. Become knowledgeable about health care economics, become involved with the political process, and position yourselves so that you can be a part of the solution to our health care system's woes. Don't allow the moment to pass. Don't be afraid of the realities of today, and don't forget your ideals and principles. Confront today's challenges with the same determination that academic surgeons through the years have confronted the unknown mysteries of disease. Let me conclude by trying to synthesize my remarks in five generic recommendations: 1. We need to go forward in the research area by developing multidisciplinary programs that involve basic science. These programs can be used to highlight our clinical areas and expertise. In this manner, both areas will be benefitted. 2. We need to educate the public and the government about the virtues of research and the importance of maintaining academic surgery.(ABSTRACT TRUNCATED AT 250 WORDS)
Isichenko, M B
1994-01-01
The long-time relaxation of ideal two dimensional magnetohydrodynamic turbulence subject to the conservation of two infinite families of constants of motion---the magnetic and the "cross" topology invariants--is examined. The analysis of the Gibbs ensemble, where all integrals of motion are respected, predicts the initial state to evolve into an equilibrium, stable coherent structure (the most probable state) and decaying Gaussian turbulence (fluctuations) with a vanishing, but always positive temperature. The non-dissipative turbulence decay is accompanied by decrease in both the amplitude and the length scale of the fluctuations, so that the fluctuation energy remains finite. The coherent structure represents a set of singular magnetic islands with plasma flow whose magnetic topology is identical to that of the initial state, while the energy and the cross topology invariants are shared between the coherent structure and the Gaussian turbulence. These conservation laws suggest the variational principle of i...
Mostert, W.
2017-01-27
We present numerical simulations of ideal magnetohydrodynamics showing suppression of the Richtmyer-Meshkov instability in spherical implosions in the presence of an octahedrally symmetric magnetic field. This field configuration is of interest owing to its high degree of spherical symmetry in comparison with previously considered dihedrally symmetric fields. The simulations indicate that the octahedral field suppresses the instability comparably to the other previously considered candidate fields for light-heavy interface accelerations while retaining a highly symmetric underlying flow even at high field strengths. With this field, there is a reduction in the root-mean-square perturbation amplitude of up to approximately 50% at representative time under the strongest field tested while maintaining a homogeneous suppression pattern compared to the other candidate fields.
Mostert, W.
2015-10-06
The effects of seed magnetic fields on the Richtmyer-Meshkov instability driven by converging cylindrical and spherical implosions in ideal magnetohydrodynamics are investigated. Two different seed field configurations at various strengths are applied over a cylindrical or spherical density interface which has a single-dominant-mode perturbation. The shocks that excite the instability are generated with appropriate Riemann problems in a numerical formulation and the effect of the seed field on the growth rate and symmetry of the perturbations on the density interface is examined. We find reduced perturbation growth for both field configurations and all tested strengths. The extent of growth suppression increases with seed field strength but varies with the angle of the field to interface. The seed field configuration does not significantly affect extent of suppression of the instability, allowing it to be chosen to minimize its effect on implosion distortion. However, stronger seed fields are required in three dimensions to suppress the instability effectively.
GRHydro: A new open source general-relativistic magnetohydrodynamics code for the Einstein Toolkit
Moesta, Philipp; Faber, Joshua A; Haas, Roland; Noble, Scott C; Bode, Tanja; Loeffler, Frank; Ott, Christian D; Reisswig, Christian; Schnetter, Erik
2013-01-01
We present the new general-relativistic magnetohydrodynamics (GRMHD) capabilities of the Einstein Toolkit, an open-source community-driven numerical relativity and computational relativistic astrophysics code. The GRMHD extension of the Toolkit builds upon previous releases and implements the evolution of relativistic magnetised fluids in the ideal MHD limit in fully dynamical spacetimes using the same shock-capturing techniques previously applied to hydrodynamical evolution. In order to maintain the divergence-free character of the magnetic field, the code implements both hyperbolic divergence cleaning and constrained transport schemes. We present test results for a number of MHD tests in Minkowski and curved spacetimes. Minkowski tests include aligned and oblique planar shocks, cylindrical explosions, magnetic rotors, Alfv\\'en waves and advected loops, as well as a set of tests designed to study the response of the divergence cleaning scheme to numerically generated monopoles. We study the code's performanc...
General-Relativistic Resistive Magnetohydrodynamics in three dimensions: formulation and tests
Dionysopoulou, Kyriaki; Palenzuela, Carlos; Rezzolla, Luciano; Giacomazzo, Bruno
2013-01-01
We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of Implicit-Explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for small electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing physical setups in all ranges of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe testbed for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that als...
Kawazura, Yohei; Morrison, Philip J
2016-01-01
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to [Comisso \\textit{et al.}, Phys. Rev. Lett. {\\bf 113}, 045001 (2014)] for the electron--positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked con...
A Dynamical Systems Approach to a Bianchi Type I Viscous Magnetohydrodynamic Model
Kohli, Ikjyot Singh
2013-01-01
We use the expansion-normalized variables approach to study the dynamics of a non-tilted Bianchi Type I cosmological model with both a pure, homogeneous source-free magnetic field and viscous fluid with both bulk and shear viscous effects, employing the ideal magnetohydrodynamic approximation. The dynamical system is then studied in detail through a fixed-point analysis which determines the local sink and source behaviour in combination with standard dynamical system theory and numerical experiments that give a very good indication of the asymptotic behaviour of the system. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.
Magnetohydrodynamic DiscWinds and LineWidth Distributions.II
Chajet, L S
2016-01-01
We study AGN emission line profiles combining an improved version of the accretion disc-wind model of Murray & Chiang with the magneto-hydrodynamic model of Emmering et al. (1992). Here we extend our previous work to consider central objects with different masses and/or luminosities. We have compared the dispersions in our model C IV linewidth distributions to observational upper limit on that dispersion, considering both smooth and clumpy torus models. Following Fine et al., we transform that scatter in the profile line-widths into a constraint on the torus geometry and show how the half-opening angle of the obscuring structure depends on the mass of the central object and the accretion rate. We find that the results depend only mildly on the dimensionless angular momentum, one of the two integrals of motion that characterise the dynamics of the self-similar ideal MHD outflows
Zaliznyak, Yu A; Goedbloed, J P; Zaliznyak, Yu.
2003-01-01
We present a numerical study of an idealized magnetohydrodynamic (MHD) configuration consisting of a planar wake flow embedded into a three-dimensional (3D) sheared magnetic field. Our simulations investigate the possibility for in-situ development of large-scale compressive disturbances at cospatial current sheet -- velocity shear regions in the heliosphere. Using a linear MHD solver, we first systematically chart the destabilized wavenumbers, corresponding growth rates, and physical parameter ranges for dominant 3D sinuous-type instabilities in an equilibrium wake--current sheet system. Wakes bounded by sufficiently supersonic (Mach number $M_s > 2.6$) flow streams are found to support dominant fully 3D sinuous instabilities when the plasma beta is of order unity. Fully nonlinear, compressible 2.5D and 3D MHD simulations show the self-consistent formation of shock fronts of fast magnetosonic type. They carry density perturbations far away from the wake's center. Shock formation conditions are identified in ...
A computational magnetohydrodynamic model of a gasdynamic fusion space propulsion system
Ohlandt, Chad J. R.
This work advances the gasdynamic mirror (GDM) fusion space propulsion system concept by testing the potential of an advanced aneutronic fusion fuel combination of proton-11boron and evaluating GDMs operating at less than breakeven being driven with nuclear electric reactors. Finding neither option to be a panacea, the author moves forward in developing an ideal 3-D magnetohydrodynamic (MHD) computational model for simulating concept GDMs. The challenges identified and remediated include Alfven wave-speeds a few percent the speed of light with characteristic lengths on the order of a centimeter, the extreme aspect ratio of GDM systems, massive background magnetic fields, and traveling waves along the length of the GDM. Due to the remaining physical challenges of modeling the GDM system, including a slow systemic relaxation time and localized radiation losses, the computational requirements of the full 3-D MHD model remains too computationally demanding, which suggests a future approach involving a hybrid of 1-D and 3-D models.
Vlasov fluid stability of a 2-D plasma with a linear magnetic field null
Energy Technology Data Exchange (ETDEWEB)
Kim, J.S.
1984-01-01
Vlasov fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov fluid dispersion functional by using set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null.
Vlasov Fluid stability of a 2-D plasma with a linear magnetic field null
Energy Technology Data Exchange (ETDEWEB)
Kim, J.S.
1984-01-01
Vlasov Fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov Fluid dispersion functional by using a set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null.
Numerical magnetohydrodynamics in astrophysics algorithm and tests for one-dimensional flow
Ryu, D; Dongsu Ryu
1994-01-01
We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a nonlinear Riemann solver for ideal MHD, which includes rarefactions as well as shocks and produces exact solutions for two-dimensional magnetic field structures as well as for the three-dimensional ones. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (\\ie ~one-dimensional flows) are presented. These include those for which the field structure is two-dimensional ({\\it i.e.}, those flows often called ``1 + 1/2 dimensional'') as well as those for which the magnetic field plane rotates ({\\it i.e.,}, those flows often called ``1 + 1/2 + 1/2 dimensional''). Results indicate that the code can re...
An Ideal Integrating Bolometer Project
National Aeronautics and Space Administration — An ideal integrating bolometer can achieve breakthrough sensitivity in IR photon detection by removing practical barriers to extreme thermal isolation of the...
-Fuzzy Ideals in Ordered Semigroups
Directory of Open Access Journals (Sweden)
Asghar Khan
2009-01-01
Full Text Available We introduce the concept of 𝒩-fuzzy left (right ideals in ordered semigroups and characterize ordered semigroups in terms of 𝒩-fuzzy left (right ideals. We characterize left regular (right regular and left simple (right simple ordered semigroups in terms of 𝒩-fuzzy left (𝒩-fuzzy right ideals. The semilattice of left (right simple semigroups in terms of 𝒩-fuzzy left (right ideals is discussed.
Institute of Scientific and Technical Information of China (English)
CHEN Huan Yin; LI Fu An
2002-01-01
In this paper, we investigate ideals of regular rings and give several characterizations for an ideal to satisfy the comparability. In addition, it is shown that, if Ⅰ is a minimal two-sided ideal of a regular ring R, then Ⅰ satisfies the comparability if and only if Ⅰ is separative. Furthermore, we prove that, for ideals with stable range one, Roth's problem has an affirmative solution. These extend the corresponding results on unit-regularity and one-sided unit-regularity.
An Ideal Integrating Bolometer Project
National Aeronautics and Space Administration — An ideal integrating bolometer can achieve breakthrough sensitivity in IR photon detection by removing practical barriers to extreme thermal isolation of the...
Edge Ideals of Weighted Graphs
Paulsen, Chelsey
2012-01-01
We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of "weighted vertex covers". We use these, for instance, to say when these ideals are m-unmixed. We explicitly describe which weighted cycles and trees are unmixed and which ones are Cohen-Macaulay, and we prove that all weighted complete graphs are Cohen-Macaulay.
Researching Acquisition Sequences: Idealization and De-Idealization in SLA
Ellis, Rod
2015-01-01
Idealization plays a fundamental role in scientific inquiry. This article examines the case for maintaining the claim that the second language acquisition (SLA) of grammatical structures such as negation manifests identifiable stages of acquisition. It proposes that, while research has demonstrated the need for de-idealization, there is no need to…
Linear wave propagation in relativistic magnetohydrodynamics
Keppens, R
2008-01-01
The properties of linear Alfv\\'en, slow, and fast magnetoacoustic waves for uniform plasmas in relativistic magnetohydrodynamics (MHD) are discussed, augmenting the well-known expressions for their phase speeds with knowledge on the group speed. A 3+1 formalism is purposely adopted to make direct comparison with the Newtonian MHD limits easier and to stress the graphical representation of their anisotropic linear wave properties using the phase and group speed diagrams. By drawing these for both the fluid rest frame and for a laboratory Lorentzian frame which sees the plasma move with a three-velocity having an arbitrary orientation with respect to the magnetic field, a graphical view of the relativistic aberration effects is obtained for all three MHD wave families. Moreover, it is confirmed that the classical Huygens construction relates the phase and group speed diagram in the usual way, even for the lab frame viewpoint. Since the group speed diagrams correspond to exact solutions for initial conditions co...
COUNTER-ROTATION IN RELATIVISTIC MAGNETOHYDRODYNAMIC JETS
Energy Technology Data Exchange (ETDEWEB)
Cayatte, V.; Sauty, C. [Laboratoire Univers et Théories, Observatoire de Paris, UMR 8102 du CNRS, Université Paris Diderot, F-92190 Meudon (France); Vlahakis, N.; Tsinganos, K. [Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece); Matsakos, T. [Department of Astronomy and Astrophysics, The University of Chicago, Chicago, IL 60637 (United States); Lima, J. J. G., E-mail: veronique.cayatte@obspm.fr [Centro de Astrofísica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal)
2014-06-10
Young stellar object observations suggest that some jets rotate in the opposite direction with respect to their disk. In a recent study, Sauty et al. showed that this does not contradict the magnetocentrifugal mechanism that is believed to launch such outflows. Motion signatures that are transverse to the jet axis, in two opposite directions, have recently been measured in M87. One possible interpretation of this motion is that of counter-rotating knots. Here, we extend our previous analytical derivation of counter-rotation to relativistic jets, demonstrating that counter-rotation can indeed take place under rather general conditions. We show that both the magnetic field and a non-negligible enthalpy are necessary at the origin of counter-rotating outflows, and that the effect is associated with a transfer of energy flux from the matter to the electromagnetic field. This can be realized in three cases: if a decreasing enthalpy causes an increase of the Poynting flux, if the flow decelerates, or if strong gradients of the magnetic field are present. An illustration of the involved mechanism is given by an example of a relativistic magnetohydrodynamic jet simulation.
Fast magnetohydrodynamic density waves in spiral galaxies
Lou, Yu-Qing; Han, J. L.; Fan, Zuhui
1999-09-01
The newly observed large-scale structures of a southern grand-design spiral galaxy NGC 2997 in total and polarized radio-continuum emission together with their overall correlations with the known optical spiral structure are physically interpreted in terms of fast magnetohydrodynamic (MHD) density waves in contrast to slow MHD density waves in NGC 6946. The global spiral pattern of such fast MHD density waves extends from the very centre, where the disc rotates almost rigidly within ~0.5arcmin, all the way to the outer disc with a more or less flat rotation curve. To strengthen the case, several known features of spiral galaxies M51 and IC 342 are referred to and their pattern identifications discussed. It is emphasized that the nature of a magnetized spiral galaxy would be much better appreciated by examining large-scale structures in optical, atomic hydrogen Hi, total and polarized radio-continuum and infrared emission together. As various star-formation processes occur concurrently and/or sequentially in spiral arms of high gas concentration, relatively broad and fuzzy Hi arms, roughly coincident with optical arms in the inner disc, are expected to extend from the extremities of fading optical arms further into the outer gas disc. We predict that the south-east `magnetic arm', apparently isolated from any optical features, in total and polarized radio-continuum intensity maps of NGC 2997 should be associated with an Hi gas arm yet to be detected in 21-cm line emission.
NIMROD Resistive Magnetohydrodynamic Simulations of Spheromak Physics
Energy Technology Data Exchange (ETDEWEB)
Hooper, E B; Cohen, B I; McLean, H S; Wood, R D; Romero-Talamas, C A; Sovinec, C R
2007-12-11
The physics of spheromak plasmas is addressed by time-dependent, three-dimensional, resistive magneto-hydrodynamic simulations with the NIMROD code. Included in some detail are the formation of a spheromak driven electrostatically by a coaxial plasma gun with a flux-conserver geometry and power systems that accurately model the Sustained Spheromak Physics Experiment (SSPX) (R. D. Wood, et al., Nucl. Fusion 45, 1582 (2005)). The controlled decay of the spheromak plasma over several milliseconds is also modeled as the programmable current and voltage relax, resulting in simulations of entire experimental pulses. Reconnection phenomena and the effects of current profile evolution on the growth of symmetry-breaking toroidal modes are diagnosed; these in turn affect the quality of magnetic surfaces and the energy confinement. The sensitivity of the simulation results address variations in both physical and numerical parameters, including spatial resolution. There are significant points of agreement between the simulations and the observed experimental behavior, e.g., in the evolution of the magnetics and the sensitivity of the energy confinement to the presence of symmetry-breaking magnetic fluctuations.
Ambipolar diffusion in smoothed particle magnetohydrodynamics
Wurster, James; Ayliffe, Ben A
2014-01-01
In partially ionised plasmas, the magnetic field can become decoupled from the neutral gas and diffuse through it in a process known as ambipolar diffusion. Although ambipolar diffusion has been implemented in several grid codes, we here provide an implementation in smoothed particle magnetohydrodynamics (SPMHD). We use the strong coupling approximation in which the ion density is negligible, allowing a single fluid approach. The equations are derived to conserve energy, and to provide a positive definite contribution to the entropy. We test the implementation in both a simple 1D SPMHD code and the fully 3D code PHANTOM. The wave damping test yields agreement within 0.03-2 per cent of the analytical result, depending on the value of the collisional coupling constant. The oblique C-shocks test yields results that typically agree within 4 per cent of the semi-analytical result. Our algorithm is therefore suitable for exploring the effect ambipolar diffusion has on physical processes, such as the formation of st...
Magnetohydrodynamic Waves in an Asymmetric Magnetic Slab
Allcock, Matthew; Erdélyi, Robert
2017-02-01
Analytical models of solar atmospheric magnetic structures have been crucial for our understanding of magnetohydrodynamic (MHD) wave behaviour and in the development of the field of solar magneto-seismology. Here, an analytical approach is used to derive the dispersion relation for MHD waves in a magnetic slab of homogeneous plasma enclosed on its two sides by non-magnetic, semi-infinite plasma with different densities and temperatures. This generalises the classic magnetic slab model, which is symmetric about the slab. The dispersion relation, unlike that governing a symmetric slab, cannot be decoupled into the well-known sausage and kink modes, i.e. the modes have mixed properties. The eigenmodes of an asymmetric magnetic slab are better labelled as quasi-sausage and quasi-kink modes. Given that the solar atmosphere is highly inhomogeneous, this has implications for MHD mode identification in a range of solar structures. A parametric analysis of how the mode properties (in particular the phase speed, eigenfrequencies, and amplitudes) vary in terms of the introduced asymmetry is conducted. In particular, avoided crossings occur between quasi-sausage and quasi-kink surface modes, allowing modes to adopt different properties for different parameters in the external region.
Lack of universality in decaying magnetohydrodynamic turbulence.
Lee, E; Brachet, M E; Pouquet, A; Mininni, P D; Rosenberg, D
2010-01-01
Using computations of three-dimensional magnetohydrodynamic (MHD) turbulence with a Taylor-Green flow, whose inherent time-independent symmetries are implemented numerically, and in the absence of either a forcing function or an imposed uniform magnetic field, we show that three different inertial ranges for the energy spectrum may emerge for three different initial magnetic fields, the selecting parameter being the ratio of nonlinear eddy to Alfvén time. Equivalent computational grids range from 128(3) to 2048(3) points with a unit magnetic Prandtl number and a Taylor Reynolds number of up to 1500 at the peak of dissipation. We also show a convergence of our results with Reynolds number. Our study is consistent with previous findings of a variety of energy spectra in MHD turbulence by studies performed in the presence of both a forcing term with a given correlation time and a strong, uniform magnetic field. However, in contrast to the previous studies, here the ratio of characteristic time scales can only be ascribed to the intrinsic nonlinear dynamics of the paradigmatic flows under study.
Imbalanced Relativistic Force-Free Magnetohydrodynamic Turbulence
Cho, Jungyeon
2013-01-01
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfv\\'enic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., \\$b_+^2/b_-^2 \\propto (\\epsilon_+/\\epsilon_-)^n \\$ with n>2). These result...
Structures in magnetohydrodynamic turbulence: detection and scaling
Uritsky, Vadim M; Rosenberg, Duane; Mininni, Pablo D; Donovan, Eric
2010-01-01
We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stems from numerical simulations of decaying three-dimensional (3D) magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536^3 points, and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X-point configuration embedded in 3D, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8,000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two...
A Magnetohydrodynamic Boost for Relativistic Jets
Mizuno, Yosuke; Hardee, Philip; Hartmann, Dieter H.; Nishikawa, Ken-Ichi; Zhang, Bing
2007-01-01
We performed relativistic magnetohydrodynamic simulations of the hydrodynamic boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006) using the RAISHIN code. Simulation results show that the presence of a magnetic field changes the properties of the shock interface between the tenuous, overpressured jet (V^z j) flowing tangentially to a dense external medium. We find that magnetic fields can lead to more efficient acceleration of the jet, in comparison to the pure-hydrodynamic case. A "poloidal" magnetic field (B^z), tangent to the interface and parallel to the jet flow, produces both a stronger outward moving shock and a stronger inward moving rarefaction wave. This leads to a large velocity component normal to the interface in addition to acceleration tangent to the interface, and the jet is thus accelerated to larger Lorentz factors than those obtained in the pure-hydrodynamic case. Likewise, a strong "toroidal" magnetic field (B^y), tangent to the interface but perpendicular to the jet flow, also leads to stronger acceleration tangent to the shock interface relative to the pure-hydrodynamic case. Thus. the presence and relative orientation of a magnetic field in relativistic jets can significant modify the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).
Anodic stripping voltammetry enhancement by redox magnetohydrodynamics.
Clark, Emily A; Fritsch, Ingrid
2004-04-15
The effect of an external magnetic field on linear scan anodic stripping voltammetry (ASV) in solutions of 10(-6)-10(-7) M concentrations of lead, cadmium, and copper at mercury films on glassy carbon electrodes has been investigated. A high concentration of Hg(2+) was added to the analyte solution to induce a large cathodic current during the deposition step. Therefore, a large Lorentz force from the net flux of charge through the magnetic field resulted in convection due to magnetohydrodynamics. The faster delivery of analytes to the mercury film electrode during deposition caused an increase in the anodic stripping peaks. The effect of varying Hg(2+) concentrations (0-60 mM) and magnetic field strengths (0-1.77 T) on the enhancement of the stripping peaks was investigated. Enhancements as large as 129% for peak currents and 167% for peak areas were observed. An enhancement of approximately 100% was observed when 60 mM Fe(3+) replaced high concentrations of Hg(2+). This method of convection exhibits promise for small-volume ASV analysis with possible improved limits of detection and decreased preconcentration times.
Finite dissipation and intermittency in magnetohydrodynamics.
Mininni, P D; Pouquet, A
2009-08-01
We present an analysis of data stemming from numerical simulations of decaying magnetohydrodynamic (MHD) turbulence up to grid resolution of 1536(3) points and up to Taylor Reynolds number of approximately 1200 . The initial conditions are such that the initial velocity and magnetic fields are helical and in equipartition, while their correlation is negligible. Analyzing the data at the peak of dissipation, we show that the dissipation in MHD seems to asymptote to a constant as the Reynolds number increases, thereby strengthening the possibility of fast reconnection events in the solar environment for very large Reynolds numbers. Furthermore, intermittency of MHD flows, as determined by the spectrum of anomalous exponents of structure functions of the velocity and the magnetic field, is stronger than that of fluids, confirming earlier results; however, we also find that there is a measurable difference between the exponents of the velocity and those of the magnetic field, reminiscent of recent solar wind observations. Finally, we discuss the spectral scaling laws that arise in this flow.
A New Perspective on Classical Ideal Gases
Directory of Open Access Journals (Sweden)
Fabrice Philippe
2013-08-01
Full Text Available The ideal-gas barometric and pressure laws are derived from the Democritian concept of independent corpuscles moving in vacuum, plus a principle of simplicity, namely that these laws are independent of the kinetic part of the Hamiltonian. A single corpuscle in contact with a heat bath in a cylinder and submitted to a constant force (weight is considered. The paper importantly supplements a previously published paper: First, the stability of ideal gases is established. Second, we show that when walls separate the cylinder into parts and are later removed, the entropy is unaffected. We obtain full agreement with Landsberg’s and others’ (1994 classical thermodynamic result for the entropy of a column of gas submitted to gravity.
Fusion rings and fusion ideals
DEFF Research Database (Denmark)
Andersen, Troels Bak
by the so-called fusion ideals. The fusion rings of Wess-Zumino-Witten models have been widely studied and are well understood in terms of precise combinatorial descriptions and explicit generating sets of the fusion ideals. They also appear in another, more general, setting via tilting modules for quantum...
Directory of Open Access Journals (Sweden)
Kharatti Lal
2015-12-01
Full Text Available This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R is isomorphic to the lattice of fuzzy normal subgroup of G (respectively fuzzy ideals of R.In Yuan Boond Wu wangrning investigated the relationship between the fuzzy ideals and the fuzzy congruences on a distributive lattice and obtained that the lattice of fuzzy ideals is isomorphic to the lattice of fuzzy congruences on a generalized Boolean algebra. Fuzzy group theory can be used to describe, symmetries and permutation in nature and mathematics. The fuzzy group is one of the oldest branches of abstract algebra. For example group can be used is classify to all of the forms chemical crystal can take. Group can be used to count the number of non-equivalent objects and permutation or symmetries. For example, the number of different is switching functions of n, variable when permutation of the input are allowed. Beside crystallography and combinatory group have application of quantum mechanics.
Ambipolar diffusion in low-mass star formation. I. General comparison with the ideal MHD case
Masson, Jacques; Hennebelle, Patrick; Vaytet, Neil; Commerçon, Benoit
2015-01-01
In this paper, we provide a more accurate description of the evolution of the magnetic flux redistribution during prestellar core collapse by including resistive terms in the magnetohydrodynamics (MHD) equations. We focus more particularly on the impact of ambipolar diffusion. We use the adaptive mesh refinement code RAMSES to carry out such calculations. The resistivities required to calculate the ambipolar diffusion terms were computed using a reduced chemical network of charged, neutral and grain species. The inclusion of ambipolar diffusion leads to the formation of a magnetic diffusion barrier in the vicinity of the core, preventing accumulation of magnetic flux in and around the core and amplification of the field above 0.1G. The mass and radius of the first Larson core remain similar between ideal and non-ideal MHD models. This diffusion plateau has crucial consequences on magnetic braking processes, allowing the formation of disk structures. Magnetically supported outflows launched in ideal MHD models...
Directory of Open Access Journals (Sweden)
Syahira Mansur
Full Text Available The magnetohydrodynamic (MHD stagnation point flow of a nanofluid over a permeable stretching/shrinking sheet is studied. Numerical results are obtained using boundary value problem solver bvp4c in MATLAB for several values of parameters. The numerical results show that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. For the stable solution, the skin friction is higher in the presence of magnetic field and increases when the suction effect is increased. It is also found that increasing the Brownian motion parameter and the thermophoresis parameter reduces the heat transfer rate at the surface.
Mansur, Syahira; Ishak, Anuar; Pop, Ioan
2015-01-01
The magnetohydrodynamic (MHD) stagnation point flow of a nanofluid over a permeable stretching/shrinking sheet is studied. Numerical results are obtained using boundary value problem solver bvp4c in MATLAB for several values of parameters. The numerical results show that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. For the stable solution, the skin friction is higher in the presence of magnetic field and increases when the suction effect is increased. It is also found that increasing the Brownian motion parameter and the thermophoresis parameter reduces the heat transfer rate at the surface.
DISCO: A 3D Moving-mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks
Duffell, Paul C.
2016-09-01
This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide variety of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.
Mansur, Syahira; Ishak, Anuar; Pop, Ioan
2015-01-01
The magnetohydrodynamic (MHD) stagnation point flow of a nanofluid over a permeable stretching/shrinking sheet is studied. Numerical results are obtained using boundary value problem solver bvp4c in MATLAB for several values of parameters. The numerical results show that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. For the stable solution, the skin friction is higher in the presence of magnetic field and increases when the suction effect is increased. It is also found that increasing the Brownian motion parameter and the thermophoresis parameter reduces the heat transfer rate at the surface. PMID:25760733
Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades
Aluie, Hussein
2017-02-01
We formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales ℓ. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatially-averaged at an arbitrary scale of resolution. The microscopic equations for the ‘bare’ velocity and magnetic fields are ‘renormalized’ by coarse-graining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. Particular attention is given to the effects of these subscale terms on the balances of the quadratic invariants of ideal incompressible MHD—energy, cross-helicity and magnetic helicity. At large coarse-graining length-scales, the direct dissipation of the invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological flux-linkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarse-graining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress and subscale EMF, we derive rigorous upper bounds on the effective dissipation they produce in terms of scaling exponents of the velocity and magnetic fields. These bounds provide exact constraints on phenomenological theories of MHD turbulence in order to allow the nonlinear cascade of energy and cross-helicity. On the other hand, we prove a very strong version of the Woltjer-Taylor conjecture
Performance Analyses of IDEAL Algorithm on Highly Skewed Grid System
Directory of Open Access Journals (Sweden)
Dongliang Sun
2014-03-01
Full Text Available IDEAL is an efficient segregated algorithm for the fluid flow and heat transfer problems. This algorithm has now been extended to the 3D nonorthogonal curvilinear coordinates. Highly skewed grids in the nonorthogonal curvilinear coordinates can decrease the convergence rate and deteriorate the calculating stability. In this study, the feasibility of the IDEAL algorithm on highly skewed grid system is analyzed by investigating the lid-driven flow in the inclined cavity. It can be concluded that the IDEAL algorithm is more robust and more efficient than the traditional SIMPLER algorithm, especially for the highly skewed and fine grid system. For example, at θ = 5° and grid number = 70 × 70 × 70, the convergence rate of the IDEAL algorithm is 6.3 times faster than that of the SIMPLER algorithm, and the IDEAL algorithm can converge almost at any time step multiple.
Magnetic moment nonconservation in magnetohydrodynamic turbulence models.
Dalena, S; Greco, A; Rappazzo, A F; Mace, R L; Matthaeus, W H
2012-07-01
The fundamental assumptions of the adiabatic theory do not apply in the presence of sharp field gradients or in the presence of well-developed magnetohydrodynamic turbulence. For this reason, in such conditions the magnetic moment μ is no longer expected to be constant. This can influence particle acceleration and have considerable implications in many astrophysical problems. Starting with the resonant interaction between ions and a single parallel propagating electromagnetic wave, we derive expressions for the magnetic moment trapping width Δμ (defined as the half peak-to-peak difference in the particle magnetic moments) and the bounce frequency ω(b). We perform test-particle simulations to investigate magnetic moment behavior when resonance overlapping occurs and during the interaction of a ring-beam particle distribution with a broadband slab spectrum. We find that the changes of magnetic moment and changes of pitch angle are related when the level of magnetic fluctuations is low, δB/B(0) = (10(-3),10(-2)), where B(0) is the constant and uniform background magnetic field. Stochasticity arises for intermediate fluctuation values and its effect on pitch angle is the isotropization of the distribution function f(α). This is a transient regime during which magnetic moment distribution f(μ) exhibits a characteristic one-sided long tail and starts to be influenced by the onset of spatial parallel diffusion, i.e., the variance grows linearly in time as in normal diffusion. With strong fluctuations f(α) becomes completely isotropic, spatial diffusion sets in, and the f(μ) behavior is closely related to the sampling of the varying magnetic field associated with that spatial diffusion.
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2008-09-01
Full Text Available This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003, most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable
Hamiltonian description of the ideal fluid
Energy Technology Data Exchange (ETDEWEB)
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.
Nijm, Grace M; Swiryn, Steven; Larson, Andrew C; Sahakian, Alan V
2008-07-01
The magnetohydrodynamic effect generates voltages related to blood flow, which are superimposed on the electrocardiogram (ECG) used for gating during cardiac magnetic resonance imaging (MRI). A method is presented for extracting the magnetohydrodynamic signal from the ECG. The extracted magnetohydrodynamic blood flow potential may be physiologically meaningful due to its relationship to blood flow. Removal of the magnetohydrodynamic voltages from the ECG can potentially lead to improved gating and diagnostically useful ECGs.
Alexander Duals of Multipermutohedron Ideals
Indian Academy of Sciences (India)
Ajay Kumar; Chanchal Kumar
2014-02-01
An Alexander dual of a multipermutohedron ideal has many combinatorial properties. The standard monomials of an Artinian quotient of such a dual correspond bijectively to some -parking functions, and many interesting properties of these Artinian quotients are obtained by Postnikov and Shapiro (Trans. Am. Math. Soc. 356 (2004) 3109–3142). Using the multigraded Hilbert series of an Artinian quotient of an Alexander dual of multipermutohedron ideals, we obtained a simple proof of Steck determinant formula for enumeration of -parking functions. A combinatorial formula for all the multigraded Betti numbers of an Alexander dual of multipermutohedron ideals are also obtained.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Generalization of the one-dimensional ideal plasma flow with spherical waves
Energy Technology Data Exchange (ETDEWEB)
Golovin, Sergey V [Queen' s University, Kingston, Ontario K7 L 3N6 (Canada)
2006-06-09
We give a description of the ideal plasma flow, which is governed by an exact partially invariant solution of the magnetohydrodynamics equations. The solution generalizes known one-dimensional flow with spherical waves. The generalization consists in addition of the special tangent vector components of the velocity and the magnetic field at any plasma particle. In the special case of zeroth tangential component the solution coincides with the classical one-dimensional one. This paper describes a three-dimensional picture of the plasma flow, governed by the obtained solution.
Spaces of Ideal Convergent Sequences
Directory of Open Access Journals (Sweden)
M. Mursaleen
2014-01-01
Full Text Available In the present paper, we introduce some sequence spaces using ideal convergence and Musielak-Orlicz function ℳ=Mk. We also examine some topological properties of the resulting sequence spaces.
Ideal AFROC and FROC observers.
Khurd, Parmeshwar; Liu, Bin; Gindi, Gene
2010-02-01
Detection of multiple lesions in images is a medically important task and free-response receiver operating characteristic (FROC) analyses and its variants, such as alternative FROC (AFROC) analyses, are commonly used to quantify performance in such tasks. However, ideal observers that optimize FROC or AFROC performance metrics have not yet been formulated in the general case. If available, such ideal observers may turn out to be valuable for imaging system optimization and in the design of computer aided diagnosis techniques for lesion detection in medical images. In this paper, we derive ideal AFROC and FROC observers. They are ideal in that they maximize, amongst all decision strategies, the area, or any partial area, under the associated AFROC or FROC curve. Calculation of observer performance for these ideal observers is computationally quite complex. We can reduce this complexity by considering forms of these observers that use false positive reports derived from signal-absent images only. We also consider a Bayes risk analysis for the multiple-signal detection task with an appropriate definition of costs. A general decision strategy that minimizes Bayes risk is derived. With particular cost constraints, this general decision strategy reduces to the decision strategy associated with the ideal AFROC or FROC observer.
Magneto-hydrodynamics Simulation in Astrophysics
Pang, Bijia
2011-08-01
Magnetohydrodynamics (MHD) studies the dynamics of an electrically conducting fluid under the influence of a magnetic field. Many astrophysical phenomena are related to MHD, and computer simulations are used to model these dynamics. In this thesis, we conduct MHD simulations of non-radiative black hole accretion as well as fast magnetic reconnection. By performing large scale three dimensional parallel MHD simulations on supercomputers and using a deformed-mesh algorithm, we were able to conduct very high dynamical range simulations of black hole accretion of Sgr A* at the Galactic Center. We find a generic set of solutions, and make specific predictions for currently feasible observations of rotation measure (RM). The magnetized accretion flow is subsonic and lacks outward convection flux, making the accretion rate very small and having a density slope of around -1. There is no tendency for the flows to become rotationally supported, and the slow time variability of th! e RM is a key quantitative signature of this accretion flow. We also provide a constructive numerical example of fast magnetic reconnection in a three-dimensional periodic box. Reconnection is initiated by a strong, localized perturbation to the field lines and the solution is intrinsically three-dimensional. Approximately 30% of the magnetic energy is released in an event which lasts about one Alfvén time, but only after a delay during which the field lines evolve into a critical configuration. In the co-moving frame of the reconnection regions, reconnection occurs through an X-like point, analogous to the Petschek reconnection. The dynamics appear to be driven by global flows rather than local processes. In addition to issues pertaining to physics, we present results on the acceleration of MHD simulations using heterogeneous computing systems te{shan2006heterogeneous}. We have implemented the MHD code on a variety of heterogeneous and multi-core architectures (multi-core x86, Cell, Nvidia and
Generalizing Tanisaki's ideal via ideals of truncated symmetric functions
Mbirika, Aba
2010-01-01
We define a family of ideals I_h in the polynomial ring Z[x_1,x_2,...,x_n] that are parametrized by Hessenberg functions h (equivalently Dyck paths or ample partitions). The ideals I_h generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define I_h, we use polynomials in a subset of the variables {x_1,...,x_n} that are symmetric under the corresponding permutation subgroup. We call these polynomials truncated symmetric functions and show combinatorial identities relating different kinds of truncated symmetric polynomials. We then prove several key properties of I_h, including that if h > h' in the natural partial order on Dyck paths then I_h \\subset I_{h'}, and explicitly construct a Grobner basis for I_h. We define a second family of ideals J_h for which some of the claims are easier to see, and then prove that I_h = J_h. Using earlier work of the first author, the current manuscript proves t...
Webb, G. M.; Dasgupta, B.; McKenzie, J. F.; Hu, Q.; Zank, G. P.
2014-03-01
In this paper advected invariants and conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics are obtained using Lie dragging techniques. There are different classes of invariants that are advected or Lie dragged with the flow. Simple examples are the advection of the entropy S (a 0-form), and the conservation of magnetic flux (an invariant 2-form advected with the flow). The magnetic flux conservation law is equivalent to Faraday's equation. The gauge condition for the magnetic helicity to be advected with the flow is determined. Different variants of the helicity in ideal fluid dynamics and MHD including: fluid helicity, cross helicity and magnetic helicity are investigated. The fluid helicity conservation law and the cross-helicity conservation law in MHD are derived for the case of a barotropic gas. If the magnetic field lies in the constant entropy surface, then the gas pressure can depend on both the entropy and the density. In these cases the conservation laws are local conservation laws. For non-barotropic gases, we obtain nonlocal conservation laws for fluid helicity and cross helicity by using Clebsch variables. These nonlocal conservation laws are the main new results of the paper. Ertel's theorem and potential vorticity, the Hollman invariant, and the Godbillon-Vey invariant for special flows for which the magnetic helicity is zero are also discussed.
On the structure and statistical theory of turbulence of extended magnetohydrodynamics
Miloshevich, George; Lingam, Manasvi; Morrison, Philip J.
2017-01-01
Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville’s theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range—this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.
Effect of the Plasma Pressure on Magnetohydrodynamic Kink Instability in a Cylindrical Geometry
Institute of Scientific and Technical Information of China (English)
DAI Yujie; LIU Jinyuan; WANG Xuehui
2009-01-01
A semi-analytical method is introduced to study kink instability in cylindrical plasma with line-tied boundary conditions. The method is based on an expansion for magne-tohydrodynamics (MHD) equations in one-dimensional (1D) radial eigenvalue problems by using Fourier transforms. The MHD equations then become an ordinary differential equation. This method is applicable to both ideal and non-ideal MHD problem. The effect of plasma pressure (P0) on kink instability is studied in a cylindrical geometry. Complex discrete spectra are pre-sented. Two-dimensional (2D) eigenfunctions with the line-tied boundary conditions are obtained. The growth rate and radial eigenfunctions are different in the two cases of P0 = 0 and P0 ≠ 0, which indicate that the effect of plasma pressure can not be ignored if it is large enough. This method allows us to understand the role of individual radial eigenfunctions, and is also compu-tationally efficient compared to direct solutions of the MHD equations by the finite difference method.
The role of pressure flattening in calculating tearing mode stability
Ham, C. J.; Connor, J. W.; Cowley, S. C.; Hastie, R. J.; Hender, T. C.; Liu, Y. Q.
2013-12-01
Calculations of tearing mode stability in tokamaks split conveniently into one in an external region, where marginally stable ideal magnetohydrodynamics (MHD) is applicable, and one in a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter Δ‧. Axisymmetric pressure and current perturbations localized around the rational surface significantly alter Δ‧. Equations governing the changes in the external solution and Δ‧ are derived for arbitrary perturbations in axisymmetric toroidal geometry. These equations can be used in two ways: (i) the Δ‧ can be calculated for a physically occurring perturbation to the pressure or current; (ii) alternatively we can use these equations to calculate Δ‧ for profiles with a pressure gradient at the rational surface in terms of the value when the perturbation removes this gradient. It is the second application we focus on here since resistive magnetohydrodynamics (MHD) codes do not contain the appropriate layer physics and therefore cannot predict stability for realistic hot plasma directly. They can, however, be used to calculate Δ‧. Existing methods (Ham et al 2012 Plasma Phys. Control. Fusion 54 025009) for extracting Δ‧ from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface and favourable average curvature because of the Glasser stabilizing effect (Glasser et al 1975 Phys. Fluids 18 875). To overcome this difficulty we introduce a specific artificial pressure flattening function that allows the earlier approach to be used. The technique is first tested numerically in cylindrical geometry with an artificial favourable curvature. Its application to toroidal geometry is then demonstrated using the toroidal tokamak tearing mode stability code T7 (Fitzpatrick et al 1993 Nucl. Fusion 33 1533) which employs an approximate analytic equilibrium. The prospects for applying this
Non-ideal memristors for a non-ideal world
Gale, Ella
2016-01-01
Memristors have pinched hysteresis loops in the $V-I$ plane. Ideal memristors are everywhere non-linear, cross at zero and are rotationally symmetric. In this paper we extend memristor theory to produce different types of non-ideality and find that: including a background current (such as an ionic current) moves the crossing point away from zero; including a degradation resistance (that increases with experimental time) leads to an asymmetry; modelling a low resistance filament in parallel describes triangular $V-I$ curves with a straight-line low resistance state. A novel measurement of hysteresis asymmetry was introduced based on hysteresis and it was found that which lobe was bigger depended on the size of the breaking current relative to the memristance. The hysteresis varied differently with each type of non-ideality, suggesting that measurements of several device I-V curves and calculation of these parameters could give an indication of the underlying mechanism.
Decay rates of the magnetohydrodynamic model for quantum plasmas
Pu, Xueke; Xu, Xiuli
2017-02-01
In this paper, we consider the quantum magnetohydrodynamic model for quantum plasmas. We prove the optimal decay rates for the solution to the constant state in the whole space in the Lp-norm with 2≤ p≤ 6 and its first derivatives in L2-norm. The proof is based on the optimal decay of the linearized equation and nonlinear energy estimates.
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
Keppens, R.; Meliani, Z.; van Marle, A. J.; Delmont, P.; Vlasis, A.; van der Holst, B.
2012-01-01
Relativistic hydro and magnetohydrodynamics provide continuum fluid descriptions for gas and plasma dynamics throughout the visible universe. We present an overview of state-of-the-art modeling in special relativistic regimes, targeting strong shock-dominated flows with speeds approaching the speed
A high current density DC magnetohydrodynamic (MHD) micropump
Homsy, Alexandra; Koster, Sander; Eijkel, Jan C.T.; Berg, van den Albert; Lucklum, F.; Verpoorte, E.; Rooij, de Nico F.
2005-01-01
This paper describes the working principle of a DC magnetohydrodynamic (MHD) micropump that can be operated at high DC current densities (J) in 75-µm-deep microfluidic channels without introducing gas bubbles into the pumping channel. The main design feature for current generation is a micromachined
A high current density DC magnetohydrodynamic (MHD) micropump
Homsy, A; Koster, Sander; Eijkel, JCT; van den Berg, A; Lucklum, F; Verpoorte, E; de Rooij, NF
2005-01-01
This paper describes the working principle of a DC magnetohydrodynamic (MHD) micropump that can be operated at high DC current densities (J) in 75-mu m-deep microfluidic channels without introducing gas bubbles into the pumping channel. The main design feature for current generation is a micromachin
Parallel magnetohydrodynamics on the Cray T3D
Meijer, P. M.; Poedts, S.; Goedbloed, J. P.
1996-01-01
The equations of magnetohydrodynamics (MHD) are discussed in the framework of parallel computing. Both linear and nonlinear MHD models are addressed. Special attention is given to the parallellisation of the kernels of the existing sequential MHD codes. These kernels involve matrix-vector multiplica
Fast magnetic and turbulent-wave dynamos in electron magnetohydrodynamics
Lakhin, V. P.; Moiseev, S. S.; Schep, T. J.
2000-01-01
The influence of inertia on the spontaneous amplification of large-scale perturbations by electron magnetohydrodynamic (EMHD) turbulence is studied in a 2 1/2 -dimensional(2 1/2 -D) model. It is shown that electron inertia results in the modification of ct-like effects, which are due to the helicity
Instability of the magnetohydrodynamics system at vanishing Reynolds number
Bouya, Ismaël
2013-12-01
The aim of this note is to study the dynamo properties of the magnetohydrodynamics system at vanishing R m . Improving the analysis in Gérard-Varet (SIAM J Math Anal 37(3):815-840, 2006), we shall establish a generic Lyapunov instability result.
On the continua in two-dimensional nonadiabatic magnetohydrodynamic spectra
De Ploey, A.; Van der Linden, R. A. M.; Belien, A. J. C.
2000-01-01
The equations for the continuous subspectra of the linear magnetohydrodynamic (MHD) normal modes spectrum of two-dimensional (2D) plasmas are derived in general curvilinear coordinates, taking nonadiabatic effects in the energy equation into account. Previously published derivations of continuous sp
THE FORMATION OF SHOCK WAVES OF THE EQUATIONS OF MAGNETOHYDRODYNAMICS
Institute of Scientific and Technical Information of China (English)
董黎明; 史一蓬
2001-01-01
The property of fluid field of one- dimensional magnetohydrodynamics (MHD)transverse flow after the appearance of singularity is discussed. By the method of iteration,the strong discontinuity (shock wave) and entropy solution are constructed and the estimations on the singularity of the solution near the point of blow- up are obtained.
Directory of Open Access Journals (Sweden)
Grzegorz Dymek
2015-01-01
set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.
Acceleration and Collimation of Relativistic Magnetohydrodynamic Disk Winds
Porth, Oliver; Fendt, Christian
2010-02-01
We perform axisymmetric relativistic magnetohydrodynamic simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. Newtonian gravity is added to the relativistic treatment in order to establish the physical boundary condition of an underlying accretion disk in centrifugal and pressure equilibrium. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Substantial effort has been made to implement a current-free, numerical outflow boundary condition in order to avoid artificial collimation present in the standard outflow conditions. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100 × 200 inner disk radii. The simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Two options for the initial field geometries are applied—an hourglass-shaped potential magnetic field and a split monopole field. Most of our parameter runs evolve into a steady state solution which can be further analyzed concerning the physical mechanism at work. In general, we obtain collimated beams of mildly relativistic speed with Lorentz factors up to 6 and mass-weighted half-opening angles of 3-7 deg. The split-monopole initial setup usually results in less collimated outflows. The light surface of the outflow magnetosphere tends to align vertically—implying three relativistically distinct regimes in the flow—an inner subrelativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface—similar to the spine-sheath structure
Nonlinear magnetohydrodynamics of edge localized mode precursors
Energy Technology Data Exchange (ETDEWEB)
Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)
2015-02-15
A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.
Acceleration of Particles in Imbalanced Magnetohydrodynamic Turbulence
Teaca, Bogdan; Jenko, Frank; Schlickeiser, Reinhard
2014-01-01
The present work investigates the acceleration of test particles in balanced and imbalanced Alfv\\'{e}nic turbulence, relevant to the solar-wind problem. These turbulent states, obtained numerically by prescribing the injection rates for the ideal invariants, are evolved dynamically with the particles. While the energy spectrum for balanced and imbalanced states is known, the impact made on particle heating is a matter of debate, with different considerations giving different results. By performing direct numerical simulations, resonant and non-resonant particle accelerations are automatically considered and the correct turbulent phases are taken into account. For imbalanced turbulence, it is found that the acceleration rate of charged particles is reduced and the heating rate diminished. This behaviour is independent of the particle gyroradius, although particles that have a stronger adiabatic motion (smaller gyroradius) tend to experience a larger heating.
Energy Technology Data Exchange (ETDEWEB)
Sovinec, C.R.
1995-12-31
Numerical computation is used to investigate resistive magnetohydrodynamic (MHD) fluctuations in the reversed-field pinch (RFP) and in tokamak-like configurations driven solely by direct current (DC) helicity injection. A Lundquist number (S) scan of RFP turbulence without plasma pressure produces the weak scaling of S{sup -0.18} for the root-mean-square magnetic fluctuation level for 2.5x10{sup 3}{le}S{le}4x10{sup 4}. The temporal behavior of fluctuations and the reversal parameter becomes more regular as S is increased, acquiring a {open_quotes}sawtooth{close_quotes} shape at the largest value of S. Simulations with plasma pressure and anisotropic thermal conduction demonstrate energy transport resulting from parallel heat fluctuations. To investigate means of improving RFP energy confinement, three forms of current profile modification are tested. Radio frequency (RF) current drive is modeled with an auxiliary electron force, and linear stability calculations are used.
Energy Technology Data Exchange (ETDEWEB)
Sovinec, Carl R. [Univ. of Wisconsin, Madison, WI (United States)
1995-11-01
Numerical computation is used to investigate resistive magnetohydrodynamic (MHD) fluctuations in the reversed-field pinch (RFP) and in tokamak-like configurations driven solely by direct current (DC) helicity injection. A Lundquist number (S) scan of RFP turbulence without plasma pressure produces the weak scaling of S^{-0.18} for the root-mean-square magnetic fluctuation level for 2.5x10^{3}≤S≤4x10^{4}. The temporal behavior of fluctuations and the reversal parameter becomes more regular as S is increased, acquiring a "sawtooth" shape at the largest value of S. Simulations with plasma pressure and anisotropic thermal conduction demonstrate energy transport resulting from parallel heat fluctuations. To investigate means of improving RFP energy confinement, three forms of current profile modification are tested. Radio frequency (RF) current drive is modeled with an auxiliary electron force, and linear stability calculations are used.
Energy Technology Data Exchange (ETDEWEB)
Held, E.D. [Univ. of Wisconsin, Madison, WI (United States). Center for Plasma Theory and Computation; Leboeuf, J.N.; Carreras, B.A. [Oak Ridge National Lab., TN (United States). Fusion Energy Div.
1998-07-01
The linear and nonlinear stability of a nonmonotonic q profile is examined using a reduced set of magnetohydrodynamic (MHD) equations with an equilibrium, sheared toroidal flow. The reversed shear profile is shown to be unstable to a rich variety of resistive MHD modes including pressure-driven instabilities and tearing instabilities possessing a tearing/interchange character at low Lundquist number, S, and taking on a double/triple tearing structure at high S. Linear calculations show that the destabilizing effect of toroidal velocity shear on tearing modes is enhanced at finite pressure seen previously for tearing modes at high S. Nonlinear calculations show the generation of a large, m = 1, n = 0, Reynolds-stress-driven poloidal flow in the absence of significant flow damping. Calculations in which the poloidal flow was heavily damped show that sub-Alfvenic, sheared toroidal flows have a minimal effect on weakly-coupled, localized instabilities.
Kinet, Maxime; Knaepen, Bernard; Molokov, Sergei
2009-10-01
This Letter presents a numerical study of a magnetohydrodynamic flow in a square duct with electrically conducting walls subject to a uniform, transverse magnetic field. Two regimes of instability and transition of Hunt's jets at the walls parallel to the magnetic field have been identified. The first one occurs for relatively low values of the Reynolds number Re and is associated with weak, periodic, counterrotating vortices discovered previously in linear stability studies. The second is a new regime taking place for higher values of Re. It is associated with trains of small-scale vortices enveloped into larger structures, and involves partial detachment of jets from parallel walls. Once this regime sets in, the kinetic energy of perturbations increases by 2 orders of magnitude.
Bhatia, Tanayveer Singh
2016-01-01
The emergence of turbulence in shear flows is a well-investigated field. Yet, one of major issues is the apparent contradiction between linear stability analysis quoting a flow to be stable and results from experiments and simulations proving it to be otherwise. There is some success, in particular in astrophysical systems, based on Magneto-Rotational Instability (MRI). However, MRI requires the system to be weakly magnetized, which is not a feature of general magnetohydrodynamic (MHD) flows. Nevertheless, linear perturbations of such flows are nonnormal in nature which argues for an origin of nonlinearity therein. The idea is, nonnormal perturbations could produce huge transient energy growth (TEG), which may lead to non-linearity and further turbulence. However, so far, nonnormal effects in shear flows have not been explored much in the presence of magnetic fields. Here, we consider the perturbed visco-resistive incompressible MHD shear flows with rotation in general. Basically we consider the magnetized ve...
Dynamo onset as a first-order transition: lessons from a shell model for magnetohydrodynamics.
Sahoo, Ganapati; Mitra, Dhrubaditya; Pandit, Rahul
2010-03-01
We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number PrM and the magnetic Reynolds number ReM. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (PrM-1,ReM) plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.
Andreussi, T.; Morrison, P. J.; Pegoraro, F.
2016-10-01
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is absent.
Idealism and materialism in perception.
Rose, David; Brown, Dora
2015-01-01
Koenderink (2014, Perception, 43, 1-6) has said most Perception readers are deluded, because they believe an 'All Seeing Eye' observes an objective reality. We trace the source of Koenderink's assertion to his metaphysical idealism, and point to two major weaknesses in his position-namely, its dualism and foundationalism. We counter with arguments from modern philosophy of science for the existence of an objective material reality, contrast Koenderink's enactivism to his idealism, and point to ways in which phenomenology and cognitive science are complementary and not mutually exclusive.
De Luca, R.; Faella, O.
2017-01-01
The kinematics of a free-kick is studied. As in projectile motion, the free-kick is ideal since we assume that a point-like ball moves in the absence of air resistance. We have experienced the fortunate conjuncture of a classical mechanics lecture taught right before an important football game. These types of sports events might trigger a great deal of attention from the classroom. The idealized problem is devised in such a way that students are eager to come to the end of the whole story.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
Magnetohydrodynamic instabilities in rotating and precessing sheared flows: an asymptotic analysis.
Salhi, A; Lehner, T; Cambon, C
2010-07-01
Linear magnetohydrodynamic instabilities are studied analytically in the case of unbounded inviscid and electrically conducting flows that are submitted to both rotation and precession with shear in an external magnetic field. For given rotation and precession the possible configurations of the shear and of the magnetic field and their interplay are imposed by the "admissibility" condition (i.e., the base flow must be a solution of the magnetohydrodynamic Euler equations): we show that an "admissible" basic magnetic field must align with the basic absolute vorticity. For these flows with elliptical streamlines due to precession we undertake an analytical stability analysis for the corresponding Floquet system, by using an asymptotic expansion into the small parameter ε (ratio of precession to rotation frequencies) by a method first developed in the magnetoelliptical instabilities study by Lebovitz and Zweibel [Astrophys. J. 609, 301 (2004)]10.1086/420972. The present stability analysis is performed into a suitable frame that is obtained by a systematic change of variables guided by symmetry and the existence of invariants of motion. The obtained Floquet system depends on three parameters: ε , η (ratio of the cyclotron frequency to the rotation frequency) and χ=cos α, with α being a characteristic angle which, for circular streamlines, ε=0, identifies with the angle between the wave vector and the axis of the solid body rotation. We look at the various (centrifugal or precessional) resonant couplings between the three present modes: hydrodynamical (inertial), magnetic (Alfvén), and mixed (magnetoinertial) modes by computing analytically to leading order in ε the instabilities by estimating their threshold, growth rate, and maximum growth rate and their bandwidths as functions of ε, η, and χ. We show that the subharmonic "magnetic" mode appears only for η>square root of 5/2 and at large η (>1) the maximal growth rate of both the "hydrodynamic" and
Fitzpatrick, Richard
2016-05-01
The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes in tokamak plasmas is calculated using an improved, neoclassical, four-field, drift-magnetohydrodynamical model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing or stabilizing provided that ηi≡d ln Ti/d ln ne does not exceed some threshold value. In certain ranges of ηi, the polarization current is found to have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.
"Ideally" unstable current sheets and the triggering of fast magnetic reconnection
Tenerani, Anna; Pucci, Fulvia; Landi, Simone; Rappazzo, Antonio Franco
2016-01-01
Magnetic reconnection is thought to be the dynamical mechanism underlying many explosive phenomena observed both in space and in the laboratory, though the question of how fast magnetic reconnection is triggered in such high Lundquist ($S$) number plasmas has remained elusive. It has been well established that reconnection can develop over timescales faster than those predicted traditionally once kinetic scales are reached. It has also been shown that, within the framework of resistive Magnetohydrodynamics (MHD), fast reconnection is achieved for thin enough sheets via the onset of the so-called plasmoid instability. The latter was discovered in studies specifically devoted to the Sweet-Parker current sheet, either as an initial condition or an apparent transient state developing in nonlinear studies. On the other hand, a fast tearing instability can grow on an ideal, i.e., $S$-independent, timescale (dubbed "ideal" tearing) within current sheets whose aspect ratio scales with the macroscopic Lundquist number...
DEFF Research Database (Denmark)
Fléron, René
2016-01-01
solution is likewise challenging. The conceiving, designing, implementation and operation phases in the CDIO education aims to bring the student through a scenario simulating real life engineering. A satellite mission constitutes an ideal case for a CDIO project. Designing, building, launching...
Daisley, R. E.
1973-01-01
Presents some organized ideas in thermodynamics which are suitable for use with high school (GCE A level or ONC) students. Emphases are placed upon macroscopic observations and intimate connection of the modern definition of temperature with the concept of ideal gas. (CC)
Characteristics of an Ideal Colleague.
Nielsen, Linda
1979-01-01
A stratified random sample of male and female faculty members from two universities was surveyed regarding traits of the ideal colleague. The results were analyzed according to the respondent's sex, tenure status, private or state university position, and academic discipline. Also diagnosed was the masculine or feminine value of each trait. (JMD)
Chemical Laws, Idealization and Approximation
Tobin, Emma
2013-01-01
This paper examines the notion of laws in chemistry. Vihalemm ("Found Chem" 5(1):7-22, 2003) argues that the laws of chemistry are fundamentally the same as the laws of physics they are all "ceteris paribus" laws which are true "in ideal conditions". In contrast, Scerri (2000) contends that the laws of chemistry are…
DEFF Research Database (Denmark)
Mehlsen, Camilla
2010-01-01
Salget af hudblegecremer er eksploderet. Hvorfor drømmer så mange om at få lys hud? Hvorfor vil børn hellere lege med hvide dukker end brune? Svaret er, at hvid er et globalt ideal. Interview med Dorthe Staunæs og Les Back....
Optimal forager against ideal free distributed prey.
Garay, József; Cressman, Ross; Xu, Fei; Varga, Zoltan; Cabello, Tomás
2015-07-01
The introduced dispersal-foraging game is a combination of prey habitat selection between two patch types and optimal-foraging approaches. Prey's patch preference and forager behavior determine the prey's survival rate. The forager's energy gain depends on local prey density in both types of exhaustible patches and on leaving time. We introduce two game-solution concepts. The static solution combines the ideal free distribution of the prey with optimal-foraging theory. The dynamical solution is given by a game dynamics describing the behavioral changes of prey and forager. We show (1) that each stable equilibrium dynamical solution is always a static solution, but not conversely; (2) that at an equilibrium dynamical solution, the forager can stabilize prey mixed patch use strategy in cases where ideal free distribution theory predicts that prey will use only one patch type; and (3) that when the equilibrium dynamical solution is unstable at fixed prey density, stable behavior cycles occur where neither forager nor prey keep a fixed behavior.
The Platonic Ideal of Stalactite Growth
Short, Martin; Toomey, Rickard
2005-03-01
The chemical mechanisms underlying the growth of cave formations such as stalactites are well-known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites. A linear stability analysis shows is used to explain the instability of this state to the formation of centimeter-scale ripples, as commonly seen on a wide range of speleothem surfaces.
Ideal MHD beta-limits of poloidally asymmetric equilibria
Energy Technology Data Exchange (ETDEWEB)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in ..beta../sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is ..beta../sub critical/ approx. = 6.5%.
Resistive relativistic magnetohydrodynamics from a charged multi-fluids perspective
Andersson, N
2012-01-01
We consider general relativistic magnetohydrodynamics from a charged multifluids point-of-view, taking a variational approach as our starting point. We develop the case of two charged components in detail, accounting for a phenomenological resistivity, providing specific examples for pair plasmas and proton-electron systems. We discuss both cold, low velocity, plasmas and hot systems where we account for a dynamical entropy component. The results for the cold case (which accord with recent work in the literature) provide a complete model for resistive relativistic magnetohydrodynamics, clarifying the assumptions that lead to various models that have been used in astrophysical applications. The analysis of the hot case is (as far as we are aware) novel, accounting for the relaxation times that are required to ensure causality and demonstrating the explicit coupling between fluxes of heat and charge.
Anomalous k⊥(-8/3) spectrum in electron magnetohydrodynamic turbulence.
Meyrand, Romain; Galtier, Sébastien
2013-12-27
Electron magnetohydrodynamic turbulence is investigated under the presence of a relatively strong external magnetic field b0e∥ and through three-dimensional direct numerical simulations. Our study reveals the emergence of a k⊥(-8/3) scaling for the magnetic energy spectrum at scales k∥(D)≤k⊥≤k⊥(D), where k∥(D) and k⊥(D) are, respectively, the typical largest dissipative scales along and transverse to the b0 direction. Unlike standard magnetohydrodynamic, this turbulence regime is characterized by filaments of electric currents parallel to b0. The anomalous scaling is in agreement with a heuristic model in which the transfer in the parallel direction is negligible. Implications for solar wind turbulence are discussed.
Smoothed Particle Magnetohydrodynamics: A State of the Union
Lewis, Benjamin T; Tricco, Terrence S
2016-01-01
Obtaining a stable magnetohydrodynamical (MHD) formalism in SPH - i.e. smoothed particle magnetohydrodynamics (SPMHD) - has proven remarkably difficult. To implement MHD requires two steps: a modification to the momentum equation and an induction equation, and both present challenges. We first provide an overview of how SPMHD is implemented, and then discuss how this implementation fails and the limitation of various corrective methods - with particular reference to the effects of particle disorder. Although there are many problems for which, with careful choice of corrective measures, good results can be obtained, we then show that, at the very limits of the state of the art, the ability to perform stable MHD calculations in SPH is curtailed by numerical issues.
Intermittency in Hall-magnetohydrodynamics with a strong guide field
Imazio, P Rodriguez; Dmitruk, P; Mininni, P D
2013-01-01
We present a detailed study of intermittency in the velocity and magnetic field fluctuations of compressible Hall-magnetohydrodynamic turbulence with an external guide field. To solve the equations numerically, a reduced model valid when a strong guide field is present is used. Different values for the ion skin depth are considered in the simulations. The resulting data is analyzed computing field increments in several directions perpendicular to the guide field, and building structure functions and probability density functions. In the magnetohydrodynamic limit we recover the usual results with the magnetic field being more intermittent than the velocity field. In the presence of the Hall effect, field fluctuations at scales smaller than the ion skin depth show a substantial decrease in the level of intermittency, with close to monofractal scaling.
Lattice kinetic simulations in three-dimensional magnetohydrodynamics.
Breyiannis, G; Valougeorgis, D
2004-06-01
A lattice kinetic algorithm to simulate three-dimensional (3D) incompressible magnetohydrodynamics is presented. The fluid is monitored by a distribution function, which obeys a scalar kinetic equation, subject to an external force due to the imposed magnetic field. Following the work of J. Comput. Phys. 179, 95 (2002)], the magnetic field is represented by a different three-component vector distribution function, which obeys a corresponding vector kinetic equation. Discretization of the 3D phase space is based on a 19-bit scheme for the hydrodynamic part and on a 7-bit scheme for the magnetic part. Numerical results for magnetohydrodynamic (MHD) flow in a rectangular duct with insulating and conducting walls provide excellent agreement with corresponding analytical solutions. The scheme maintains in all cases tested the MHD constraint inverted Delta.B=0 within machine round-off error.
Strong Ideal Convergence in Probabilistic Metric Spaces
Indian Academy of Sciences (India)
Celaleddin Şençimen; Serpil Pehlivan
2009-06-01
In the present paper we introduce the concepts of strongly ideal convergent sequence and strong ideal Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong ideal limit points and the strong ideal cluster points of a sequence in this space and investigate some properties of these concepts.
Ueckerdt, Torsten
2010-01-01
We consider the problem of generating all ideals of a poset. It is a long standing open problem, whether or not the ideals of any poset can be generated in constant amortized time, CAT for short. We refine the tree traversal, a method introduced by Pruesse and Ruskey in 1993, to obtain a CAT-generator for two large classes of posets: posets of interval dimension at most two and so called locally planar posets. This includes all posets for which a CAT-generator was known before. Posets of interval dimension at most two generalize both, interval orders and 2-dimensional posets. Locally planar posets generalize for example posets with a planar cover graph. We apply our results to CAT-generate all $c$-orientations of a planar graph. As a special case this is a CAT-generator for many combinatorial objects like domino and lozenge tilings, planar spanning trees, planar bipartite perfect matchings, Schnyder woods, and others.
Arnaud, Jacques; Philippe, Fabrice
2011-01-01
When a cylinder terminated by a piston, containing $N$ corpuscles, and with height $h$ is raised at temperature $\\theta$, the force that the corpuscles exerts on the piston is, to within constant factors: $F=N\\,\\theta/h$. This law, called the "ideal gas law", is valid at any temperature (except at very low temperatures when quantum effects are significant) and for any collection of corpuscles, in a space of arbitrary dimensions. It is usually derived under the assumption that the temperature is proportional to the corpuscle's kinetic energy. We show that this law rests only upon the democritian concept of corpuscles moving in vacuum, postulating that it is independent of the law of motion. This view-point puts aside restrictive assumptions that are sources of confusion. The present paper should accordingly facilitate the understanding of the physical meaning of the ideal gas law. The mathematics is elementary.
Smoothness in Binomial Edge Ideals
Directory of Open Access Journals (Sweden)
Hamid Damadi
2016-06-01
Full Text Available In this paper we study some geometric properties of the algebraic set associated to the binomial edge ideal of a graph. We study the singularity and smoothness of the algebraic set associated to the binomial edge ideal of a graph. Some of these algebraic sets are irreducible and some of them are reducible. If every irreducible component of the algebraic set is smooth we call the graph an edge smooth graph, otherwise it is called an edge singular graph. We show that complete graphs are edge smooth and introduce two conditions such that the graph G is edge singular if and only if it satisfies these conditions. Then, it is shown that cycles and most of trees are edge singular. In addition, it is proved that complete bipartite graphs are edge smooth.
Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests
2008-01-01
Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly-curved, dynamical spacetime. Such systems include coalescing compact binaries containing neutron stars or white dwarfs, disks around merging black holes, core collapse supernovae, collapsars, and gamma-ray burst sources. To model these phenomena, all of which involve general relativity, radiation (photon and/or neutrino), and magnetohydrodynamics, w...
Energy Technology Data Exchange (ETDEWEB)
Brett, Walter
2014-07-21
In the presented work the Kelvin-Helmholtz-Instability in magnetohydrodynamic flows is analyzed with the methods of Multiple Scales. The concerned fluids are incompressible or have a varying density perpendicular to the vortex sheet, which is taken into account using a Boussinesq-Approximation and constant Brunt-Vaeisaelae-Frequencies. The Multiple Scale Analysis leads to nonlinear evolution equations for the amplitude of the perturbations. Special solutions to these equations are presented and the effects of the magnetic fields are discussed.
Forward and inverse problems in fundamental and applied magnetohydrodynamics
2012-01-01
This Minireview summarizes the recent efforts to solve forward and inverse problems as they occur in different branches of fundamental and applied magnetohydrodynamics. As for the forward problem, the main focus is on the numerical treatment of induction processes, including self-excitation of magnetic fields in non-spherical domains and/or under the influence of non-homogeneous material parameters. As an important application of the developed numerical schemes, the functioning of the von-K\\'...
Experimental Magnetohydrodynamic Energy Extraction from a Pulsed Detonation
2015-03-01
specific heat capacity, that would result in a 24% loss in energy for ionization. Second, the water and aqueous NaCl were added prior to detonation . This...Experimental Magnetohydrodynamic Energy Extraction from a Pulsed Detonation THESIS Kaz I. Teope, Captain, USAF AFIT-ENY-MS-15-M-224 DEPARTMENT OF THE... DETONATION THESIS Presented to the Faculty Department of Aeronautics and Astronautics Graduate School of Engineering and Management Air Force
Magnetic reversals in a simple model of magnetohydrodynamics.
Benzi, Roberto; Pinton, Jean-François
2010-07-09
We study a simple magnetohydrodynamical approach in which hydrodynamics and MHD turbulence are coupled in a shell model, with given dynamo constraints in the large scales. We consider the case of a low Prandtl number fluid for which the inertial range of the velocity field is much wider than that of the magnetic field. Random reversals of the magnetic field are observed and it shown that the magnetic field has a nontrivial evolution--linked to the nature of the hydrodynamics turbulence.
A new lattice Boltzmann model for incompressible magnetohydrodynamics
Institute of Scientific and Technical Information of China (English)
Chen Xing-Wang; Shi Bao-Chang
2005-01-01
Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical error.
Regularity of large solutions for the compressible magnetohydrodynamic equations
Directory of Open Access Journals (Sweden)
Qin Yuming
2011-01-01
Full Text Available Abstract In this paper, we consider the initial-boundary value problem of one-dimensional compressible magnetohydrodynamics flows. The existence and continuous dependence of global solutions in H 1 have been established in Chen and Wang (Z Angew Math Phys 54, 608-632, 2003. We will obtain the regularity of global solutions under certain assumptions on the initial data by deriving some new a priori estimates.
Slip Magnetohydrodynamic Viscous Flow over a Permeable Shrinking Sheet
Institute of Scientific and Technical Information of China (English)
FANG Tie-Gang; ZHANG Ji; YAO Shan-shan
2010-01-01
@@ The magnetohydrodynamic(MHD)flow under slip conditions over a shrinMng sheet js solved analytically.The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes equations.Interesting solution behavior is observed with muiriple solution branches for certain parameter domain.The effects of the mass transfer,slip,andmagnetic parameters are discussed.
Magnetohydrodynamic channel flows with weak transverse magnetic fields.
Rothmayer, A P
2014-07-28
Magnetohydrodynamic flow of an incompressible fluid through a plane channel with slowly varying walls and a magnetic field applied transverse to the channel is investigated in the high Reynolds number limit. It is found that the magnetic field can first influence the hydrodynamic flow when the Hartmann number reaches a sufficiently large value. The magnetic field is found to suppress the steady and unsteady viscous flow near the channel walls unless the wall shapes become large.
Named Entity Recognition for IDEAL
Du, Qianzhou; Zhang, Xuan
2015-01-01
This project explored how to apply Named Entity Recognition to large Twitter and web page datasets to extract useful entities such as people, organization, location, and date. In addition, this NER utility has been scaled to the MapReduce framework on the Hadoop cluster. A schema and software allow this to be integrated with IDEAL. The term “Named Entity”, which was first introduced by Grishman and Sundheim, is widely used in Natural Language Processing (NLP). The researchers were focusing...
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
Ferraro, N. M.; Jardin, S. C.
2009-11-01
M3D- C1 is an implicit, high-order finite element code for the solution of the time-dependent nonlinear two-fluid magnetohydrodynamic equations [S.C. Jardin, J. Breslau, N. Ferraro, A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions, J. Comp. Phys. 226 (2) (2007) 2146-2174]. This code has now been extended to allow computations in toroidal geometry. Improvements to the spatial integration and time-stepping algorithms are discussed. Steady-states of a resistive two-fluid model, self-consistently including flows, anisotropic viscosity (including gyroviscosity) and heat flux, are calculated for diverted plasmas in geometries typical of the National Spherical Torus Experiment (NSTX) [M. Ono et al., Exploration of spherical torus physics in the NSTX device, Nucl. Fusion 40 (3Y) (2000) 557-561]. These states are found by time-integrating the dynamical equations until the steady-state is reached, and are therefore stationary or statistically steady on both magnetohydrodynamic and transport time-scales. Resistively driven cross-surface flows are found to be in close agreement with Pfirsch-Schlüter theory. Poloidally varying toroidal flows are in agreement with comparable calculations [A.Y. Aydemir, Shear flows at the tokamak edge and their interaction with edge-localized modes, Phys. Plasmas 14]. New effects on core toroidal rotation due to gyroviscosity and a local particle source are observed.
The fate of idealism in modern medicine.
Manson, Aaron
1994-01-01
William Osler's description of the ideal physician remains the dominant character-ideal for modern physicians. He believed that the personality traits that resulted from a belief in ascetic Protestantism, what has been called the Puritan temper, were essential in the practice of medicine. However, this idealism has been weakened by modern psychological theories which view idealism as an illness. In a culture oriented to health, rather than virtue, as an ultimate ideal, physicians can help develop a science of limits.
Cunningham, Andrew J.; Frank, Adam; Varnière, Peggy; Mitran, Sorin; Jones, Thomas W.
2009-06-01
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh-refinement code for ideal magnetohydrodynamics. The code provides several high-resolution shock-capturing schemes which are constructed to maintain conserved quantities of the flow in a finite-volume sense. Divergence-free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptive grids is achieved using prolongation and restriction operators which preserve the divergence and curl of the magnetic field across collocated grids of different resolutions. The robustness and correctness of the code is demonstrated by comparing the numerical solution of various tests with analytical solutions or previously published numerical solutions obtained by other codes.
Nonlinear magnetohydrodynamics in the Dag confinement configuration
Strauss, H. R.
2004-03-01
The Dag magnetic fusion confinement configuration is a spheromak-like toroidal device. It consists of central vertical current channel, and an outer toroidal chamber with a toroidal current. It has a special magnetic topology. Whether this has consequences for plasma confinement is a motive for this study. A restricted class of computations, using the Multi-level 3D code [Park et al., Phys. Plasmas 6, 1796 (1999)], indicate stability for β<15%. For higher β, the simulations exhibit turbulent magnetic behavior similar to spheromaks and reverse field pinches. A reverse field pinch-like variant should be capable of a less turbulent start up and higher β than the spheromak-like Dag.
Remarks on rotating shallow-water magnetohydrodynamics
Directory of Open Access Journals (Sweden)
V. Zeitlin
2013-10-01
Full Text Available We show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion of the baroclinic effects. A quasi-geostrophic version of the model, both in barotropic and in baroclinic cases, is derived in the limit of strong rotation. The basic properties of the model(s are sketched, including the stabilizing role of magnetic fields in the baroclinic version.
On Fuzzy Ideals of BL-Algebras
Directory of Open Access Journals (Sweden)
Biao Long Meng
2014-01-01
Full Text Available In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω0=1 and |Im(ω|=2. We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.
On Fuzzy Ideals of BL-Algebras
Xin, Xiao Long
2014-01-01
In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω(0) = 1 and |Im(ω)| = 2. We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true. PMID:24892085
Fuzzy Ideals and Fuzzy Distributive Lattices%Fuzzy Ideals and Fuzzy Distributive Lattices*
Institute of Scientific and Technical Information of China (English)
S.H.Dhanani; Y. S. Pawar
2011-01-01
Our main objective is to study properties of a fuzzy ideals (fuzzy dual ideals). A study of special types of fuzzy ideals (fuzzy dual ideals) is also furnished. Some properties of a fuzzy ideals (fuzzy dual ideals) are furnished. Properties of a fuzzy lattice homomorphism are discussed. Fuzzy ideal lattice of a fuzzy lattice is defined and discussed. Some results in fuzzy distributive lattice are proved.
Energy Technology Data Exchange (ETDEWEB)
Adams, Colin Stuart [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
2015-01-15
The Rayleigh-Taylor instability causes mixing in plasmas throughout the universe, from micron-scale plasmas in inertial confinement fusion implosions to parsec-scale supernova remnants. The evolution of this interchange instability in a plasma is influenced by the presence of viscosity and magnetic fields, both of which have the potential to stabilize short-wavelength modes. Very few experimental observations of Rayleigh-Taylor growth in plasmas with stabilizing mechanisms are reported in the literature, and those that are reported are in sub-millimeter scale plasmas that are difficult to diagnose. Experimental observations in well-characterized plasmas are important for validation of computational models used to make design predictions for inertial confinement fusion efforts. This dissertation presents observations of instability growth during the interaction between a high Mach-number, initially un-magnetized plasma jet and a stagnated, magnetized plasma. A multi-frame fast camera captures Rayleigh-Taylor-instability growth while interferometry, spectroscopy, photodiode, and magnetic probe diagnostics are employed to estimate plasma parameters in the vicinity of the collision. As the instability grows, an evolution to longer mode wavelength is observed. Comparisons of experimental data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization. These data provide the opportunity to benchmark computational models used in astrophysics and fusion research.
Energy Technology Data Exchange (ETDEWEB)
Adams, Colin Stuart [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States); Univ. of Washington, Seattle, WA (United States)
2015-01-15
The Rayleigh-Taylor instability causes mixing in plasmas throughout the universe, from micron-scale plasmas in inertial confinement fusion implosions to parsec-scale supernova remnants. The evolution of this interchange instability in a plasma is influenced by the presence of viscosity and magnetic fields, both of which have the potential to stabilize short-wavelength modes. Very few experimental observations of Rayleigh-Taylor growth in plasmas with stabilizing mechanisms are reported in the literature, and those that are reported are in sub-millimeter scale plasmas that are difficult to diagnose. Experimental observations in well-characterized plasmas are important for validation of computational models used to make design predictions for inertial confinement fusion efforts. This dissertation presents observations of instability growth during the interaction between a high Mach-number, initially un-magnetized plasma jet and a stagnated, magnetized plasma. A multi-frame fast camera captures Rayleigh-Taylor-instability growth while interferometry, spectroscopy, photodiode, and magnetic probe diagnostics are employed to estimate plasma parameters in the vicinity of the collision. As the instability grows, an evolution to longer mode wavelength is observed. Comparisons of experimental data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization. These data provide the opportunity to benchmark computational models used in astrophysics and fusion research.
Magnetohydrodynamic-based Laboratories on a Chip for Analysis of Biomolecules Project
National Aeronautics and Space Administration — A laboratory-on-a-chip design based on magnetohydrodynamic (MHD) microfluidics and integrated microelectrochemical detection is proposed. The proposed device is...
General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests
Dionysopoulou, Kyriaki; Alic, Daniela; Palenzuela, Carlos; Rezzolla, Luciano; Giacomazzo, Bruno
2013-08-01
We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe tested for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the ℓ=1 mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.
Magnetohydrodynamics with Embedded Particle-in-Cell Simulation of Mercury's Magnetosphere
Chen, Y.; Toth, G.; Jia, X.; Gombosi, T. I.; Markidis, S.
2015-12-01
Mercury's magnetosphere is much more dynamic than other planetary magnetospheres because of Mercury's weak intrinsic magnetic field and its proximity to the Sun. Magnetic reconnection and Kelvin-Helmholtz phenomena occur in Mercury's magnetopause and magnetotail at higher frequencies than in other planetary magnetosphere. For instance, chains of flux transfer events (FTEs) on the magnetopause, have been frequentlyobserved by the the MErcury Surface, Space ENvironment, GEochemistry and Ranging (MESSENGER) spacecraft (Slavin et al., 2012). Because ion Larmor radius is comparable to typical spatial scales in Mercury's magnetosphere, finite Larmor radius effects need to be accounted for. In addition, it is important to take in account non-ideal dissipation mechanisms to accurately describe magnetic reconnection. A kinetic approach allows us to model these phenomena accurately. However, kinetic global simulations, even for small-size magnetospheres like Mercury's, are currently unfeasible because of the high computational cost. In this work, we carry out global simulations of Mercury's magnetosphere with the recently developed MHD-EPIC model, which is a two-way coupling of the extended magnetohydrodynamic (XMHD) code BATS-R-US with the implicit Particle-in-Cell (PIC) model iPIC3D. The PIC model can cover the regions where kinetic effects are most important, such as reconnection sites. The BATS-R-US code, on the other hand, can efficiently handle the rest of the computational domain where the MHD or Hall MHD description is sufficient. We will present our preliminary results and comparison with MESSENGER observations.
Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure
Energy Technology Data Exchange (ETDEWEB)
Hagstrom, George I.; Hameiri, Eliezer [Courant Institute of Mathematical Sciences, New York, New York 10012 (United States)
2014-02-15
Hall-magnetohydrodynamics (HMHD) is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar traveling wave solutions and we find solutions with discontinuities in the hydrodynamic variables, which arise due to the presence of real characteristics in Hall-MHD. We introduce a small viscosity into the equations and use the method of matched asymptotic expansions to show that solutions with a discontinuity satisfying the Rankine-Hugoniot conditions and also an entropy condition have continuous shock structures. The lowest order inner equations reduce to the compressible Navier-Stokes equations, plus an equation which implies the constancy of the magnetic field inside the shock structure. We are able to show that the current is discontinuous across the shock, even as the magnetic field is continuous, and that the lowest order outer equations, which are the equations for traveling waves in inviscid Hall-MHD, are exactly integrable. We show that the inner and outer solutions match, which allows us to construct a family of uniformly valid continuous composite solutions that become discontinuous when the diffusivity vanishes.
Kawazura, Yohei; Miloshevich, George; Morrison, Philip J.
2017-02-01
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to Comisso et al., Phys. Rev. Lett. 113, 045001 (2014) for the electron-positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked contrast to nonrelativistic Hall MHD that does satisfy the frozen-in condition. We also find the violation of the frozen-in condition is accompanied by freezing-in of an alternative flux determined by a generalized vector potential. Finally, we derive a more general 3 + 1 Poisson bracket for nonrelativistic extended MHD, one that does not assume smallness of the electron ion mass ratio.
Scaling and anisotropy in magnetohydrodynamic turbulence in a strong mean magnetic field.
Grappin, Roland; Müller, Wolf-Christian
2010-08-01
We present an analysis of the anisotropic spectral energy distribution in incompressible magnetohydrodynamic turbulence permeated by a strong mean magnetic field. The turbulent flow is generated by high-resolution pseudospectral direct numerical simulations with large-scale isotropic forcing. Examining the radial energy distribution for various angles θ with respect to B0 reveals a specific structure which remains hidden when not taking axial symmetry with respect to B0 into account. For each direction, starting at the forced large scales, the spectrum first exhibits an amplitude drop around a wave number k0 which marks the start of a scaling range and goes on up to a dissipative wave number k(d)(θ). The three-dimensional spectrum for k≥k0 is described by a single θ-independent functional form F(k/k(d)), with the scaling law being the same in every direction. The previous properties still hold when increasing the mean field from B0=5 up to B0=10b(rms), as well as when passing from resistive to ideal flows. We conjecture that at fixed B0 the direction-independent scaling regime is reached when increasing the Reynolds number above a threshold which raises with increasing B0. Below that threshold critically balanced turbulence is expected.
Compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas
Energy Technology Data Exchange (ETDEWEB)
Panwar, Anuraj; Rizvi, H.; Ryu, C. M. [Department of Physics, POSTECH, Hyoja-Dong San 31, KyungBuk, Pohang 790-784 (Korea, Republic of)
2013-08-15
Generation of compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas is investigated. Dispersive effect caused by non-ideal electron inertia currents perpendicular to the ambient magnetic field can balance the nonlinear steepening of waves leading to the formation of a soliton. The reductive perturbation method is used to obtain a Korteweg–de Vries (KdV) equation describing the evolution of the solitary wave. The height of a soliton is proportional to the soliton speed “U” and inversely proportional to plasma “β” (ratio of plasma thermal pressure to pressure of the confining magnetic field) and the width of soliton is proportional to the electron inertial length. KdV equation is used to study the nonlinear evolution of modulationally unstable compressional Alfvénic wavepackets via the nonlinear Schrödinger equation. The characteristics of rogue wave influenced by plasma “β” and the electron inertial length are described.
Webb, Gary M; McKenzie, James F; Hu, Qiang; Zank, Gary P
2013-01-01
In this paper we discuss conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics associated with advected invariants. The invariants in some cases, can be related to fluid relabelling symmetries associated with the Lagrangian map. There are different classes of invariants that are advected or Lie dragged with the flow. Simple examples are the advection of the entropy S (a 0-form), and the conservation of magnetic flux (an invariant 2-form advected with the flow). The magnetic flux conservation law is equivalent to Faraday's equation. We discuss the gauge condition required for the magnetic helicity to be advected with the flow. The conditions for the cross helicity to be an invariant are discussed. We discuss the different variants of helicity in fluid dynamics and in MHD, including: fluid helicity, cross helicity and magnetic helicity. The fluid helicity conservation law and the cross helcity conservation law in MHD are derived for the case of a barotropic gas. If the magnetic field lies in th...
Approximate Harten-Lax-van Leer Riemann solvers for relativistic magnetohydrodynamics
Mignone, Andrea; Bodo, G.; Ugliano, M.
2012-11-01
We review a particular class of approximate Riemann solvers in the context of the equations of ideal relativistic magnetohydrodynamics. Commonly prefixed as Harten-Lax-van Leer (HLL), this family of solvers approaches the solution of the Riemann problem by providing suitable guesses to the outermots characteristic speeds, without any prior knowledge of the solution. By requiring consistency with the integral form of the conservation law, a simplified set of jump conditions with a reduced number of characteristic waves may be obtained. The degree of approximation crucially depends on the wave pattern used in prepresnting the Riemann fan arising from the initial discontinuity breakup. In the original HLL scheme, the solution is approximated by collapsing the full characteristic structure into a single average state enclosed by two outermost fast mangnetosonic speeds. On the other hand, HLLC and HLLD improves the accuracy of the solution by restoring the tangential and Alfvén modes therefore leading to a representation of the Riemann fan in terms of 3 and 5 waves, respectively.
Multispectral Emission of the Sun during the First Whole Sun Month: Magnetohydrodynamic Simulations
Lionello, Roberto; Linker, Jon A.; Mikic, Zoran
2008-01-01
We demonstrate that a three-dimensional magnetohydrodynamic (MHD) simulation of the corona can model its global plasma density and temperature structure with sufficient accuracy to reproduce many of the multispectral properties of the corona observed in extreme ultraviolet (EW) and X-ray emission. The key ingredient to this new type of global MHD model is the inclusion of energy transport processes (coronal heating, anisotropic thermal conduction, and radiative losses) in the energy equation. The calculation of these processes has previously been confined to one-dimensional loop models, idealized two-dimensional computations, and three-dimensional active region models. We refer to this as the thermodynamic MHD model, and we apply it to the time period of Carrington rotation 1913 (1996 August 22 to September 18). The form of the coronal heating term strongly affects the plasma density and temperature of the solutions. We perform our calculation for three different empirical heating models: (1) a heating function exponentially decreasing in radius; (2) the model of Schrijver et al.; and (3) a model reproducing the heating properties of the quiet Sun and active regions. We produce synthetic emission images from the density and temperature calculated with these three heating functions and quantitatively compare them with observations from E W Imaging Telescope on the Solar and Heliospheric Observatory and the soft X-ray telescope on Yohkoh. Although none of the heating models provide a perfect match, heating models 2 and 3 provide a reasonable match to the observations.
Hall-magnetohydrodynamic surface waves in solar wind flow-structures
Miteva, Rossitsa; Zhelyazkov, Ivan; Erdélyi, Robert
2004-02-01
This paper investigates the parallel propagation of agnetohydrodynamic (MHD) surface waves travelling along an ideal steady plasma slab surrounded by a steady plasma environment in the framework of Hall magnetohydrodynamics. The magnitudes of the ambient magnetic field, plasma density and flow velocity inside and outside the slab are different. Two possible directions of the relative flow velocity (in a frame of reference co-moving with the ambient flow) have been studied. In contrast to the conventional MHD surface waves which are usually assumed to be pure surface or pseudo-surface waves, the Hall-MHD approach makes it necessary to treat the normal MHD slab's modes as generalized surface waves. The latter have to be considered as a superposition of two partial waves, one of which is a pure/pseudo-surface-wave whereas the other constitutive wave is a leaky one. From the two kinds of surface-wave modes that can propagate, notably sausage and kink ones, the dispersion behaviour of the kink mode turns out to be more complicated than that of the sausage mode. In general, the flow increases the waves' phase velocities comparing with their magnitudes in a static Hall-MHD plasma slab. The applicability of the results to real solar wind flow-structures is briefly discussed. EHPRG Award Lecture.
Fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras
Institute of Scientific and Technical Information of China (English)
PENG Jia-yin
2008-01-01
The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are intro duced,several appropriate examples are provided,and their some properties are investigated.The relations among fuzzy ideal,fuzzy H-ideal,fuzzy dot ideal and fuzzy dot H-ideals in BCH algebras are discussed,several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals (fuzzy dot H-ideals) are studied. The relations between a fuzzy dot ideal (fuzzy dot H-ideal) in BCH-algebras and a fuzzy dot ideal (fuzzy dot H-ideal) in the product algebra of BCH-algebras are given.
Ideal 3D asymmetric concentrator
Energy Technology Data Exchange (ETDEWEB)
Garcia-Botella, Angel [Departamento Fisica Aplicada a los Recursos Naturales, Universidad Politecnica de Madrid, E.T.S.I. de Montes, Ciudad Universitaria s/n, 28040 Madrid (Spain); Fernandez-Balbuena, Antonio Alvarez; Vazquez, Daniel; Bernabeu, Eusebio [Departamento de Optica, Universidad Complutense de Madrid, Fac. CC. Fisicas, Ciudad Universitaria s/n, 28040 Madrid (Spain)
2009-01-15
Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used for producing reflective and refractive optical devices, including reverse engineering techniques. In this paper we apply photometric field theory and elliptic ray bundles method to study 3D asymmetric - without rotational or translational symmetry - concentrators, which can be useful components for nontracking solar applications. We study the one-sheet hyperbolic concentrator and we demonstrate its behaviour as ideal 3D asymmetric concentrator. (author)
Measuring explosive non-ideality
Energy Technology Data Exchange (ETDEWEB)
Souers, P C
1999-02-17
The sonic reaction zone length may be measured by four methods: (1) size effect, (2) detonation front curvature, (3) crystal interface velocity and (4) in-situ gauges. The amount of data decreases exponentially from (1) to (4) with there being almost no gauge data for prompt detonation at steady state. The ease and clarity of obtaining the reaction zone length increases from (1) to (4). The method of getting the reaction zone length,
Imagining the ideal dairy farm.
Cardoso, Clarissa S; Hötzel, Maria José; Weary, Daniel M; Robbins, Jesse A; von Keyserlingk, Marina A G
2016-02-01
Practices in agriculture can have negative effects on the environment, rural communities, food safety, and animal welfare. Although disagreements are possible about specific issues and potential solutions, it is widely recognized that public input is needed in the development of socially sustainable agriculture systems. The aim of this study was to assess the views of people not affiliated with the dairy industry on what they perceived to be the ideal dairy farm and their associated reasons. Through an online survey, participants were invited to respond to the following open-ended question: "What do you consider to be an ideal dairy farm and why are these characteristics important to you?" Although participants referenced social, economic, and ecological aspects of dairy farming, animal welfare was the primary issue raised. Concern was expressed directly about the quality of life for the animals, and the indirect effect of animal welfare on milk quality. Thus participants appeared to hold an ethic for dairy farming that included concern for the animal, as well as economic, social, and environmental aspects of the dairy system.
Walendziak, Andrzej
2015-01-01
The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050
Comparability for ideals of regular rings
Institute of Scientific and Technical Information of China (English)
CHEN Huanyin
2005-01-01
In this paper we investigate necessary and sufficient conditions under which the ideals possess comparability structure. For regular rings, we prove that every square matrix over ideals satisfying general comparability admits a diagonal reduction by quasi invertible matrices.
Changing Masculinity Ideals in a Danish Context
DEFF Research Database (Denmark)
Bloksgaard, Lotte; Christensen, Ann-Dorte
, indicating that Danish masculinity ideals may be under change. Also several Nordic studies emphasize that traditional masculinity ideals are challenged by new, more ‘modern’ masculinity ideals related to fatherhood, child care and gender equality. The first part of the paper develops an analytical model...... of the paper is an empirical analysis of different masculinity ideals in contemporary Danish society (the emotional man, the ideal masculine worker, and the involved father). The analysis indicates that dominant masculinity ideals in Denmark are relatively oriented towards families and towards gender equality....... However, at the micro level the picture get more blurred, and consensus about dominating masculinity ideals (related to gender equality) are characterized by complexity and ambiguity: In practice ambiguous masculinity ideals has been located that both support gender equality (for example involved...
Leprovost, Nicolas; Kim, Eun-Jin
2009-08-01
We investigate three-dimensional magnetohydrodynamics turbulence in the presence of velocity and magnetic shear (i.e., with both a large-scale shear flow and a nonuniform magnetic field). By assuming a turbulence driven by an external forcing with both helical and nonhelical spectra, we investigate the combined effect of these two shears on turbulence intensity and turbulent transport represented by turbulent diffusivities (turbulent viscosity, alpha and beta effect) in Reynolds-averaged equations. We show that turbulent transport (turbulent viscosity and diffusivity) is quenched by a strong flow shear and a strong magnetic field. For a weak flow shear, we further show that the magnetic shear increases the turbulence intensity while decreasing the turbulent transport. In the presence of a strong flow shear, the effect of the magnetic shear is found to oppose the effect of flow shear (which reduces turbulence due to shear stabilization) by enhancing turbulence and transport, thereby weakening the strong quenching by flow shear stabilization. In the case of a strong magnetic field (compared to flow shear), magnetic shear increases turbulence intensity and quenches turbulent transport.
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
Valutazione economica dello studio IDEAL
Directory of Open Access Journals (Sweden)
Enrica Menditto
2007-10-01
Full Text Available Introduction: the IDEAL (“High-dose atorvastatin vs usual-dose simvastatin for secondary prevention after myocardial infarction” study was carried out to compare intensive lowering of low-density lipoprotein (LDL-cholesterol using the highest recommended dose of atorvastatin 80 mg with simvastatin 40 mg. Aim: our aim was to investigate the economic consequence of high dose of atorvastatin vs usual-dose of simvastatin in reducing major coronary events in patients with a history of acute myocardial infarction (AMI. Methods: the analysis is based on clinical outcome data from the IDEAL study. We conducted a cost-effectiveness analysis, comparing high dose of atorvastatin (80 mg/die versus usual-dose of simvastatin (20 mg/die in the perspective of the Italian National Health Service. We identified and quantified medical costs: drug costs according to the Italian National Therapeutic Formulary and hospitalizations were quantified based on the Italian National Health Service tariffs (2006. Effects were measured in terms of mortality and morbidity reduction (number of deaths, life years gained and frequency of hospitalizations. We considered an observation period of 4.8 years. The costs borne after the first 12 months were discounted using an annual rate of 3%. We conducted one and multi-way sensitivity analyses on unit cost and effectiveness. We also conducted a threshold analysis. Results: the cost of simvastatin or atorvastatin therapy over the 4.8 years period amounted to approximately 2.3 millions euro and 2.6 millions euro per 1,000 patients respectively. Atorvastatin was more efficacious compared to simvastatin and the overall cost of care per 1,000 patients over 4.8 years of follow-up was estimated at 4.3 millions euro in the simvastatin and 4,18 millions euro in the atorvastatin group, resulting into a cost saving of 121,518 euro that is 2.8% of total costs occurred in the simvastatin group. Discussion: this study is the first economic
On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence
Directory of Open Access Journals (Sweden)
Jean Carlos Perez
2012-10-01
Full Text Available The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048^{3} mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state magnetohydrodynamics turbulence to date. We study both the balanced case, where the energies associated with Alfvén modes propagating in opposite directions along the guide field, E^{+}(k_{⊥} and E^{-}(k_{⊥}, are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent -3/2 as the Reynolds number is increased, which is consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, with E^{+}>E^{-}, the simulations show that E^{-}∝k_{⊥}^{-3/2} for all Reynolds numbers considered, while E^{+} has a slightly steeper spectrum at small Re. As the Reynolds number increases, E^{+} flattens. Since E^{±} are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as E^{+}∝E^{-}∝k_{⊥}^{-3/2}. Questions regarding the universality of the spectrum and the value of the “Kolmogorov constant” are discussed.
√z-Ideals and√z°-Ideals in C(X)
Institute of Scientific and Technical Information of China (English)
F. AZARPANAH; R. MOHAMADIAN
2007-01-01
It is well known that every prime ideal minimal over a z-ideal is also a z-ideal. The converseis also well known in C(X). Thus whenever I is an ideal in C(X), then √I is a z-ideal if and only ifI is, in which case √I= I. We show the same fact for z°-ideals and then it turns out that the sum ofa primary ideal and a z-ideal (z°-ideal) in C(X) which are not in a chain is a prime z-ideal (z°-ideal).We also show that every decomposable z-ideal (z°-ideal) in C(X) is the intersection of a finite numberof prime z-ideals (z°-ideal). Some counter-examples in general rings and some characterizations for thelargest (smallest) z-ideal and z°-ideal contained in (containing) an ideal are given.
On T-Fuzzy Ideals in Nearrings
Directory of Open Access Journals (Sweden)
Muhammad Akram
2007-01-01
Full Text Available We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.