A Numerical Approach to Solving the Hall MHD Equations Including Diamagnetic Drift (Preprint)
2008-02-19
Article 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER FA9300-06-D-0002 0003 A Numerical Approach to Solving the Hall MHD...Loverich and U. Shumlak. Nonlinear full two-fluid study of m=0 sausage instabilities in an axisymmetric z pinch. Physics of Plasmas, (13), 2006. [19
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
MHD Equations with Regularity in One Direction
Zujin Zhang
2014-01-01
Full Text Available We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, ∂3u∈Lp0, T;LqR3, with 2/p + 3/q = γ ∈ [1,3/2, 3/γ ≤ q ≤ 1/(γ - 1, then the solution is in fact smooth. This improves previous results greatly.
Equations of state for self-excited MHD generator studies
Rogers, F.J.; Ross, M.; Haggin, G.L.; Wong, L.K.
1980-02-26
We have constructed a state-of-the-art equation of state (EOS) for argon covering the temperature density range attainable by currently proposed self-excited MHD generators. The EOS for conditions in the flow channel was obtained primarily by a non-ideal plasma code (ACTEX) that is based on a many body activity expansion. For conditions in the driver chamber the EOS was primarily obtained from a fluid code (HDFP) that calculates the fluid properties from perturbation theory based on the insulator interatomic pair potential but including electronic excitations. The results are in agreement with several sets of experimental data in the 0.6 - 91 GPa pressure range.
Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow
Dimitrov, Z D; Hristov, T S; Mishonov, T M
2011-01-01
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space.
Asymmetric and Moving-Frame Approaches to MHD Equations
Bin Tao CAO
2012-01-01
The magnetohydrodynamic (MHD) equations of incompressible viscous fluids with finite electrical conductivity describe the motion of viscous electrically conducting fluids in a magnetic field.In this paper,we find eight families of solutions of these equations by Xu's asymmetric and moving frame methods.A family of singular solutions may reflect basic characteristics of vortices.The other solutions are globally analytic with respect to the spacial variables.Our solutions may help engineers to develop more effective algorithms to find physical numeric solutions to practical models.
Fierros Palacios, Angel [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico)
2001-02-01
In this work the complete set of differential field equations which describes the dynamic state of a continuos conducting media which flow in presence of a perturbed magnetic field is obtained. Then, the thermic equation of state, the wave equation and the conservation law of energy for the Alfven MHD waves are obtained. [Spanish] Es este trabajo se obtiene el conjunto completo de ecuaciones diferenciales de campo que describen el estado dinamico de un medio continuo conductor que se mueve en presencia de un campo magnetico externo perturbado. Asi, se obtiene la ecuacion termica de estado, la ecuacion de onda y la ley de la conservacion de la energia para las ondas de Alfven de la MHD.
A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS
FENG Xueshang; WEI Fengsi; ZHONG Dingkun
2003-01-01
In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.
Li, Xujing; Zheng, Weiying
2016-10-01
A new parallel code based on discontinuous Galerkin (DG) method for hyperbolic conservation laws on three dimensional unstructured meshes is developed recently. This code can be used for simulations of MHD equations, which are very important in magnetic confined plasma research. The main challenges in MHD simulations in fusion include the complex geometry of the configurations, such as plasma in tokamaks, the possibly discontinuous solutions and large scale computing. Our new developed code is based on three dimensional unstructured meshes, i.e. tetrahedron. This makes the code flexible to arbitrary geometries. Second order polynomials are used on each element and HWENO type limiter are applied. The accuracy tests show that our scheme reaches the desired three order accuracy and the nonlinear shock test demonstrate that our code can capture the sharp shock transitions. Moreover, One of the advantages of DG compared with the classical finite element methods is that the matrices solved are localized on each element, making it easy for parallelization. Several simulations including the kink instabilities in toroidal geometry will be present here. Chinese National Magnetic Confinement Fusion Science Program 2015GB110003.
Variational Integration for Ideal MHD with Built-in Advection Equations
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Burby, J. W. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2014-08-05
Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
A stochastic approach to uncertainty in the equations of MHD kinematics
Phillips, Edward G., E-mail: egphillips@math.umd.edu [Applied Mathematics & Statistics, and Scientific Computation Program, University of Maryland, College Park, MD (United States); Elman, Howard C., E-mail: elman@cs.umd.edu [Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD (United States)
2015-03-01
The magnetohydrodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system, this may introduce some epistemic uncertainty into the model. If the velocity of a physical system is not known with certainty, the magnetic field obtained from the model may not be reflective of the magnetic field seen in experiments. Additionally, uncertainty in physical parameters such as the magnetic resistivity may affect the reliability of predictions obtained from this model. By modeling the velocity and the resistivity as random variables in the MHD kinematics model, we seek to quantify the effects of uncertainty in these fields on the induced magnetic field. We develop stochastic expressions for these quantities and investigate their impact within a finite element discretization of the kinematics equations. We obtain mean and variance data through Monte Carlo simulation for several test problems. Toward this end, we develop and test an efficient block preconditioner for the linear systems arising from the discretized equations.
Golovin, Sergey V., E-mail: sergey@hydro.nsc.r [Lavrentyev Institute of Hydrodynamics SB RAS, 630090 Novosibirsk (Russian Federation); Department of Mechanics and Mathematics, Novosibirsk State University, 630090 Novosibirsk (Russian Federation)
2011-01-17
Equations of magnetohydrodynamics (MHD) in the natural curvilinear system of coordinates where trajectories and magnetic lines play a role of coordinate curves are reduced to the non-linear vector wave equation coupled with the incompressibility condition in the form of the generalized Cauchy integral. The symmetry group of obtained equation, equivalence transformation, and group classification with respect to the constitutive equation are calculated. New exact solutions with functional arbitrariness describing non-stationary incompressible flows with constant total pressure are given by explicit formulae. The corresponding magnetic surfaces have the shape of deformed nested cylinders, tori, or knotted tubes.
Boričić Zoran
2009-01-01
Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
Zhai, Xiaoping; Yin, Zhaoyang
2017-02-01
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (2012) [2], and (2013) [3] to a lower regularity index about the initial velocity. The key to that improvement is a new a priori estimate for an elliptic equation with nonconstant coefficients in Besov spaces which have the same degree as L2 in R3. Finally, we also generalize our well-posedness result to the inhomogeneous incompressible MHD equations.
Full Boltzmann equations for leptogenesis including scattering
Hahn-Woernle, F; Wong, Y Y Y
2009-01-01
We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukawa couplings by means of the full Boltzmann equations. We find that in our full Boltzmann treatment the final lepton asymmetry can be suppressed by as much as a factor of 1.5 in the weak wash-out regime (K1), the full Boltzmann treatment and the integrated approach give nearly identical final lepton asymmetries (within 10 % of each other at K>3). Finally, we show that the opposing effects of quantum statistics on decays/i...
Energy Equality and Uniqueness of Weak Solutions to MHD Equations in L∞(O,T;Ln(Ω))
Yan YONG; Quan Sen JIU
2009-01-01
In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L∞(O,T; Ln(Ω)). We prove that if the velocity u belongs to the critical space L∞(O,T; Ln(Ω)), the energy equality holds. On the basis of the energy equality, we further prove that the weak solution to the MHD equations is unique.
Furuya, Atsushi [Kyushu Univ., Interdisciplinary Graduate School of Engineering Sciences, Kasuga, Fukuoka (Japan); Yagi, Masatoshi; Itoh, Sanae-I. [Kyushu Univ., Research Institute for Applied Mechanics, Kasuga, Fukuoka (Japan)
2003-02-01
The linear neoclassical tearing mode is investigated using the four-field reduced neoclassical MHD equations, in which the fluctuating ion parallel flow and ion neoclassical viscosity are taken into account. The dependences of the neoclassical tearing mode on collisionality, diamagnetic drift and q profile are investigated. These results are compared with the results from the conventional three-field model. It is shown that the linear neoclassical tearing mode is stabilized by the ion neoclassical viscosity in the banana regime even if {delta}' > 0. (author)
Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces
Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.
2017-02-01
This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in {R^d}, where d = 2, 3, with initial data {B_0in H^s(R^d)} and {u_0in H^{s-1+ɛ}(R^d)} for {s > d/2} and any {0 < ɛ < 1}. The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to taking {ɛ=0} is explained by the failure of solutions of the heat equation with initial data {u_0in H^{s-1}} to satisfy {uin L^1(0,T; H^{s+1})}; we provide an explicit example of this phenomenon.
Local 4/5-law and energy dissipation anomaly in turbulence of incompressible MHD Equations
Guo, Shanshan; Tan, Zhong
2016-12-01
In this paper, we establish the longitudinal and transverse local energy balance equation of distributional solutions of the incompressible three-dimensional MHD equations. In particular, we find that the functions D_L^ɛ (u,B) and D_T^ɛ (u,B) appeared in the energy balance, all converging to the defect distribution (in the sense of distributions) D(u,B) which has been defined in Gao et al. (Acta Math Sci 33:865-871, 2013). Furthermore, we give a simpler form of defect distribution term, which is similar to the relation in turbulence theory, called the "4 / 3-law." As a corollary, we give the analogous "4 / 5-law" holds in the local sense.
Proceedings of the workshop on nonlinear MHD and extended MHD
NONE
1998-12-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
A spatial discretization of the MHD equations based on the finite volume - spectral method
Miyoshi, Takahiro [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA{sub {phi}}, is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
Optimal decay rates of classical solutions for the full compressible MHD equations
Gao, Jincheng; Tao, Qiang; Yao, Zheng-an
2016-04-01
In this paper, we are concerned with optimal decay rates for higher-order spatial derivatives of classical solutions to the full compressible MHD equations in three-dimensional whole space. If the initial perturbation is small in {H^3}-norm and bounded in {L^q(qin [1, 6/5 ))}-norm, we apply the Fourier splitting method by Schonbek (Arch Ration Mech Anal 88:209-222, 1985) to establish optimal decay rates for the second-order spatial derivatives of solutions and the third-order spatial derivatives of magnetic field in {L^2}-norm. These results improve the work of Pu and Guo (Z Angew Math Phys 64:519-538, 2013).
A discontinuous Galerkin method for solving the fluid and MHD equations in astrophysical simulations
Mocz, Philip; Sijacki, Debora; Hernquist, Lars
2013-01-01
A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite volume (FV) approach. We demonstrate that the DG technique offers distinct advantages over FV formulations on both static and moving meshes. The DG method is also easily generalized to higher than second-order accuracy without requiring the use of extended stencils to estimate derivatives (thereby making the scheme highly parallelizable). We implement the technique in the AREPO code for solving the fluid and the magnetohydrodynamic (MHD) equations. By examining various test problems, we show that our new formulation provides improved accuracy over FV approaches of the same order, and reduces post-shock oscillations and artificial diffusion of angular momentum. In addition, the DG method makes it possible to represent magnetic fields in a locally divergence-free way, improving th...
A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero magnetic diffusivity
Gala, Sadek; Ragusa, Maria Alessandra
2016-06-01
In this work, we show that a smooth solution of the 3D MHD equations with zero magnetic diffusivity in the whole space ℝ3 breaks down if and only if a certain norm of the magnetic field blows up at the same time.
Hanasoge, S M; Gizon, L
2010-01-01
Perfectly matched layers are a very efficient and accurate way to absorb waves in media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. However, the technique as applied to the Magneto-hydrodynamic (MHD) equations requires the use of a sponge, which, despite placing the perfectly matched status in question, is still highly efficient at absorbing outgoing waves. We study solutions of the equations in the backdrop of models of linearized wave propagation in the Sun. We test the numerical stability of the schemes by integrating the equations over a large number of wave periods.
An FCT finite element scheme for ideal MHD equations in 1D and 2D
Basting, Melanie; Kuzmin, Dmitri
2017-06-01
This paper presents an implicit finite element (FE) scheme for solving the equations of ideal magnetohydrodynamics in 1D and 2D. The continuous Galerkin approximation is constrained using a flux-corrected transport (FCT) algorithm. The underlying low-order scheme is constructed using a Rusanov-type artificial viscosity operator based on scalar dissipation proportional to the fast wave speed. The accuracy of the low-order solution can be improved using a shock detector which makes it possible to prelimit the added viscosity in a monotonicity-preserving iterative manner. At the FCT correction step, the changes of conserved quantities are limited in a way which guarantees positivity preservation for the density and thermal pressure. Divergence-free magnetic fields are extracted using projections of the FCT predictor into staggered finite element spaces forming exact sequences. In the 2D case, the magnetic field is projected into the space of Raviart-Thomas finite elements. Numerical studies for standard test problems are performed to verify the ability of the proposed algorithms to enforce relevant constraints in applications to ideal MHD flows.
Si, Xin; Ye, Xia
2016-10-01
This paper concerns an initial-boundary value problem of the inhomogeneous incompressible MHD equations in a smooth bounded domain. The viscosity and resistivity coefficients are density-dependent. The global well-posedness of strong solutions is established, provided the initial norms of velocity and magnetic field are suitably small in some sense, or the lower bound of the transport coefficients are large enough. More importantly, there is not any smallness condition on the density and its gradient.
3D MHD VDE and disruptions simulations of tokamaks plasmas including some ITER scenarios
Paccagnella, R.; Strauss, H. R.; Breslau, J.
2009-03-01
Tokamaks vertical displacement events (VDEs) and disruptions simulations in toroidal geometry by means of a single fluid visco-resistive magneto-hydro-dynamic (MHD) model are presented in this paper. The plasma model is completed with the presence of a 2D wall with finite resistivity which allows the study of the relatively slowly growing magnetic perturbation, the resistive wall mode (RWM), which is, in this paper, the main drive of the disruption evolution. Amplitudes and asymmetries of the halo currents pattern at the wall are also calculated and comparisons with tokamak experimental databases and predictions for ITER are given.
Kawasaki, Akira; Kubota, Kenichi; Funaki, Ikkoh; Okuno, Yoshihiro
2016-09-01
Steady-state and self-field magnetoplasmadynamic (MPD) thruster, which utilizes high-intensity direct-current (DC) discharge, is one of the prospective candidates of future high-power electric propulsion devices. In order to accurately assess the thrust performance and the electrode temperature, input electric power and wall heat flux must correctly be evaluated where electrostatic sheaths formed in close proximity of the electrodes affect these quantities. Conventional model simulates only plasma flows occurring in MPD thrusters with the absence of electrostatic sheath consideration. Therefore, this study extends the conventional model to a coupled magnetohydrodynamic (MHD) and thermal model by incorporating the phenomena relevant to the electrostatic sheaths. The sheaths are implemented as boundary condition of the MHD model on the walls. This model simulated the operation of the 100-kW-class thruster at discharge current ranging from 6 to 10 kA with argon propellant. The extended model reproduced the discharge voltages and wall heat load which are consistent with past experimental results. In addition, the simulation results indicated that cathode sheath voltages account for approximately 5-7 V subject to approximately 20 V of discharge voltages applied between the electrodes. This work was supported by JSPS KAKENHI Grant Numbers 26289328 and 15J10821.
Hoelzl, M.; Huijsmans, G. T. A.; Merkel, P.; Atanasiu, C.; Lackner, K.; Nardon, E.; Aleynikova, K.; Liu, F.; Strumberger, E.; McAdams, R.; Chapman, I.; Fil, A.
2014-11-01
The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.
Heat transfer including radiation and slag particles evolution in MHD channel-I
Im, K H; Ahluwalia, R K
1980-01-01
Accurate estimates of convective and radiative heat transfer in the magnetohydrodynamic channel are provided. Calculations performed for a base load-size channel indicate that heat transfer by gas radiation almost equals that by convection for smooth walls, and amounts to 70% as much as the convective heat transfer for rough walls. Carbon dioxide, water vapor, and potassium atoms are the principal participating gases. The evolution of slag particles by homogeneous nucleation and condensation is also investigated. The particle-size spectrum so computed is later utilized to analyze the radiation enhancement by slag particles in the MHD diffuser. The impact of the slag particle spectrum on the selection of a workable and design of an efficient seed collection system is discussed.
Linearizing neutrino evolution equations including neutrino-antineutrino pairing correlations
Väänänen, D
2013-01-01
We linearize the neutrino mean-field evolution equations describing the neutrino propagation in a background of matter and of neutrinos, using techniques from many-body microscopic approaches. The procedure leads to an eigenvalue equation that allows to identify instabilities in the evolution, associated with a change of the curvature of the neutrino energy-density surface. Our result includes all contributions from the neutrino Hamiltonian and is generalizable to linearize the equations of motion at an arbitrary point of the evolution. We then consider the extended equations that comprise the normal mean field as well as the abnormal mean field that is associated with neutrino-antineutrino pairing correlations. We first re-derive the extended neutrino Hamiltonian and show that such a Hamiltonian can be diagonalized by introducing a generalized Bogoliubov transformation with quasi-particle operators that mix neutrinos and antineutrinos. We give the eigenvalue equations that determine the energies of the quasi...
Frutos-Alfaro, Francisco
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a code that can be used as a seed for a MHD code for numerical applications. As an example, we present part of output of our programs for Cartesian coordinates and how to do the discretization.
MHD Instabilities Occurring Near/AT the Transport Barrier, Including Loss of Confinement in H-Modes
L. L. Lao
1999-09-01
In configurations with transport barriers the improved edge and core confinement leads to large pressure gradient and large edge bootstrap current density which often drive magnetohydrodynamic (MHD) instabilities terminating the discharge or reducing the discharge performance. The edge and the core transport barriers deteriorate or are completely lost. In this presentation, recent experimental and theoretical developments concerning MHD instabilities occurring near/at the edge and the core transport barriers are summarized emphasizing the dominant instabilities and the comparison with theory.
Frutos-Alfaro, Francisco; Carboni-Mendez, Rodrigo
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a c...
BLOW-UP CRITERION OF SMOOTH SOLUTIONS TO THE MHD EQUATIONS IN BESOV SPACES
YUAN Baoquan
2005-01-01
In this paper we discuss the logarithmic Sobolev inequalities in Besov spaces,and show their applications to the blow-up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.
Generalization of the Lorentz-Dirac equation to include spin
Barut, A. O.; Unal, Nuri
1989-11-01
For the classical point electron with Zitterbewegung (hence spin) we derive, after regularization, the radiation reaction force and covariant equations for the dynamical variables (xμ, πμ, vμ, and Sμν), which reduce to the Lorentz-Dirac equation in the spinless limit.
Caffarelli, Luis; Nirenberg, Louis
2011-01-01
The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.
Effective equations for isotropic quantum cosmology including matter
Bojowald, Martin; Skirzewski, Aureliano
2007-01-01
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties associated with the full quantum equations can be avoided in this way. Here, effective equations for Wheeler-DeWitt and loop quantizations of spatially flat, isotropic cosmological models sourced by a massive or interacting scalar are derived and studied. The resulting systems are remarkably different from that given for a free, massless scalar. This has implications for the coherence of evolving states and the realization of a bounce in loop quantum cosmology.
Westerhof, E.; de Blank, H. J.; Pratt, J.
2016-03-01
Two dimensional reduced MHD simulations of neoclassical tearing mode growth and suppression by ECCD are performed. The perturbation of the bootstrap current density and the EC drive current density perturbation are assumed to be functions of the perturbed flux surfaces. In the case of ECCD, this implies that the applied power is flux surface averaged to obtain the EC driven current density distribution. The results are consistent with predictions from the generalized Rutherford equation using common expressions for Δ \\text{bs}\\prime and Δ \\text{ECCD}\\prime . These expressions are commonly perceived to describe only the effect on the tearing mode growth of the helical component of the respective current perturbation acting through the modification of Ohm’s law. Our results show that they describe in addition the effect of the poloidally averaged current density perturbation which acts through modification of the tearing mode stability index. Except for modulated ECCD, the largest contribution to the mode growth comes from this poloidally averaged current density perturbation.
Very High Order $\\PNM$ Schemes on Unstructured Meshes for the Resistive Relativistic MHD Equations
Dumbser, Michael
2009-01-01
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The nonlinear system under consideration is purely hyperbolic and contains a source term, the one for the evolution of the electric field, that becomes stiff for low values of the resistivity. For the spatial discretization we propose to use high order $\\PNM$ schemes as introduced in \\cite{Dumbser2008} for hyperbolic conservation laws and a high order accurate unsplit time discretization is achieved using the element-local space-time discontinuous Galerkin approach proposed in \\cite{DumbserEnauxToro} for one-dimensional balance laws with stiff source terms. The divergence free character of the magnetic field is accounted for through the divergence cleaning procedure of Dedner et al. \\cite{Dedneretal}. To validate our high order method we first solve some numerical test c...
Dynamic hysteresis modeling including skin effect using diffusion equation model
Hamada, Souad; Louai, Fatima Zohra; Nait-Said, Nasreddine; Benabou, Abdelkader
2016-07-01
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Dynamic hysteresis modeling including skin effect using diffusion equation model
Hamada, Souad, E-mail: souadhamada@yahoo.fr [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Louai, Fatima Zohra, E-mail: fz_louai@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Nait-Said, Nasreddine, E-mail: n_naitsaid@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Benabou, Abdelkader, E-mail: Abdelkader.Benabou@univ-lille1.fr [L2EP, Université de Lille1, 59655 Villeneuve d’Ascq (France)
2016-07-15
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
On 2-D Boussinesq equations for MHD convection with stratification effects
Bian, Dongfen; Gui, Guilong
2016-08-01
This paper is concerned with the two-dimensional magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. The first progress on this topic was made independently by Chae and Hou-Li [8,26] where the Boussinesq system with partial constant viscosity is obtained. Recently, Wang-Zhang [45] considered the temperature-dependent viscosity and thermal diffusivity, and Li-Xu [16] generalized the Wang-Zhang's result to the inviscid case with temperature-dependent thermal diffusivity. In this paper, we include the stratification and magnetic effects and consider the full system, in the framework of low regularity. We prove that, without any smallness assumption on the initial data, the full system is globally well-posed. Moreover, by applying the uniformly bounded generalized Oseen operator, time decay estimate of the solution is obtained.
Hoelzl, M; Merkel, P; Atanasiu, C; Lackner, K; Nardon, E; Aleynikova, K; Liu, F; Strumberger, E; McAdams, R; Chapman, I; Fil, A
2014-01-01
The dynamics of large scale plasma instabilities can strongly be influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realist...
Finite Larmor radius influence on MHD solitary waves
E. Mjølhus
2009-04-01
Full Text Available MHD solitons are studied in a model where the usual Hall-MHD model is extended to include the finite Larmor radius (FLR corrections to the pressure tensor. The resulting 4-dimensional set of differential equations is treated numerically. In this extended model, the point at infinity can be of several types. Necessary for the existence of localized solutions is that it is either a saddle-saddle, a saddle-center, or, possibly, a focus-focus. In cases of saddle-center, numerical solutions for localized travelling structures have been obtained, and compared with corresponding results from the Hall-MHD model.
Khan, Sabeel M.; Hammad, M.; Sunny, D. A.
2017-08-01
In this article, the influence of thermal relaxation time and chemical reaction is studied on the MHD upper-convected viscoelastic fluid with internal structure using the Cattaneo-Christov heat flux equation for the first time in the literature. The flow-governing equations are formulated and are converted into their respective ordinary differential equations (ODEs) with the application of similarity functions. The resulting system of coupled nonlinear ODEs is solved along with the prescribed conditions at boundary using a finite-difference code in MATLAB. Influence of chemical reaction, thermal relaxation time and internal material parameter on the macroscopic and micropolar velocities as well as on the temperature and concentration profiles is examined along with other physical parameters ( e.g., magnetic parameter, Eckert number, Prandtl number and fluid relaxation time). The accuracy of the obtained numerical solution is shown by comparing the physical parameters of interest with particular cases of existing results in the literature.
Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations
Kallesøe, Bjarne Skovmose
2007-01-01
This paper extends Hodges-Dowell's partial differential equations of blade motion, by including the effects from gravity, pitch action and varying rotor speed. New equations describing the pitch action and rotor speeds are also derived. The physical interpretation of the individual terms...... in the equations is discussed. The partial differential equations of motion are approximated by ordinary differential equations of motion using an assumed mode method. The ordinary differential equations are used to simulate a sudden pitch change of a rotating blade. This work is a part of a project on pitch blade...
MHD Flows in Compact Astrophysical Objects Accretion, Winds and Jets
Beskin, Vasily S
2010-01-01
Accretion flows, winds and jets of compact astrophysical objects and stars are generally described within the framework of hydrodynamical and magnetohydrodynamical (MHD) flows. Analytical analysis of the problem provides profound physical insights, which are essential for interpreting and understanding the results of numerical simulations. Providing such a physical understanding of MHD Flows in Compact Astrophysical Objects is the main goal of this book, which is an updated translation of a successful Russian graduate textbook. The book provides the first detailed introduction into the method of the Grad-Shafranov equation, describing analytically the very broad class of hydrodynamical and MHD flows. It starts with the classical examples of hydrodynamical accretion onto relativistic and nonrelativistic objects. The force-free limit of the Grad-Shafranov equation allows us to analyze in detail the physics of the magnetospheres of radio pulsars and black holes, including the Blandford-Znajek process of energy e...
Greenshields, Christopher J
2007-01-01
Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.0-12.0 (while conventional Navier-Stokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the Navier-Stokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to t...
Boričić Zoran
2005-01-01
Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.
Shumaker, D E; Woodward, C S
2005-05-03
In this paper, the authors investigate performance of a fully implicit formulation and solution method of a diffusion-reaction system modeling radiation diffusion with material energy transfer and a fusion fuel source. In certain parameter regimes this system can lead to a rapid conversion of potential energy into material energy. Accuracy in time integration is essential for a good solution since a major fraction of the fuel can be depleted in a very short time. Such systems arise in a number of application areas including evolution of a star and inertial confinement fusion. Previous work has addressed implicit solution of radiation diffusion problems. Recently Shadid and coauthors have looked at implicit and semi-implicit solution of reaction-diffusion systems. In general they have found that fully implicit is the most accurate method for difficult coupled nonlinear equations. In previous work, they have demonstrated that a method of lines approach coupled with a BDF time integrator and a Newton-Krylov nonlinear solver could efficiently and accurately solve a large-scale, implicit radiation diffusion problem. In this paper, they extend that work to include an additional heating term in the material energy equation and an equation to model the evolution of the reactive fuel density. This system now consists of three coupled equations for radiation energy, material energy, and fuel density. The radiation energy equation includes diffusion and energy exchange with material energy. The material energy equation includes reaction heating and exchange with radiation energy, and the fuel density equation includes its depletion due to the fuel consumption.
Toward 3D MHD modeling of neoclassical tearing mode suppression by ECCD
Westerhof E.
2012-09-01
Full Text Available We propose a framework to extend the magnetohydrodynamic (MHD equations to include electron cyclotron current drive (ECCD and discuss previous models proposed by Giruzzi et al. [2] and by Hegna and Callen [3]. To model neoclassical tearing mode (NTM instabilities and study the growth of magnetic islands as NTMs evolve, we employ the nonlinear reduced-MHD simulation JOREK. We present tearing-mode growth-rate calculations from JOREK simulations.
Including inputs and control within equation-free architectures for complex systems
Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan
2016-11-01
The increasing ubiquity of complex systems that require control is a challenge for existing methodologies in characterization and controller design when the system is high-dimensional, nonlinear, and without physics-based governing equations. We review standard model reduction techniques such as Proper Orthogonal Decomposition (POD) with Galerkin projection and Balanced POD (BPOD). Further, we discuss the link between these equation-based methods and recently developed equation-free methods such as the Dynamic Mode Decomposition and Koopman operator theory. These data-driven methods can mitigate the challenge of not having a well-characterized set of governing equations. We illustrate that this equation-free approach that is being applied to measurement data from complex systems can be extended to include inputs and control. Three specific research examples are presented that extend current equation-free architectures toward the characterization and control of complex systems. These examples motivate a potentially revolutionary shift in the characterization of complex systems and subsequent design of objective-based controllers for data-driven models.
An MHD model of the earth's magnetosphere
Wu, C. C.
1985-01-01
It is pointed out that the earth's magnetosphere arises from the interaction of the solar wind with the earth's geomagnetic field. A global magnetohydrodynamics (MHD) model of the earth's magnetosphere has drawn much attention in recent years. In this model, MHD equations are used to describe the solar wind interaction with the magnetosphere. In the present paper, some numerical aspects of the model are considered. Attention is given to the ideal MHD equations, an equation of state for the plasma, the model as an initial- and boundary-value problem, the shock capturing technique, computational requirements and techniques for global MHD modeling, a three-dimensional mesh system employed in the global MHD model, and some computational results.
Characteristics of laminar MHD fluid hammer in pipe
Huang, Z.Y.; Liu, Y.J., E-mail: yajun@scut.edu.cn
2016-01-01
As gradually wide applications of MHD fluid, transportation as well as control with pumps and valves is unavoidable, which induces MHD fluid hammer. The paper attempts to combine MHD effect and fluid hammer effect and to investigate the characteristics of laminar MHD fluid hammer. A non-dimensional fluid hammer model, based on Navier–Stocks equations, coupling with Lorentz force is numerically solved in a reservoir–pipe–valve system with uniform external magnetic field. The MHD effect is represented by the interaction number which associates with the conductivity of the MHD fluid as well as the external magnetic field and can be interpreted as the ratio of Lorentz force to Joukowsky force. The transient numerical results of pressure head, average velocity, wall shear stress, velocity profiles and shear stress profiles are provided. The additional MHD effect hinders fluid motion, weakens wave front and homogenizes velocity profiles, contributing to obvious attenuation of oscillation, strengthened line packing and weakened Richardson annular effect. Studying the characteristics of MHD laminar fluid hammer theoretically supplements the gap of knowledge of rapid-transient MHD flow and technically provides beneficial information for MHD pipeline system designers to better devise MHD systems. - Highlights: • Characteristics of laminar MHD fluid hammer are discussed by simulation. • MHD effect has significant influence on attenuation of wave. • MHD effect strengthens line packing. • MHD effect inhibits Richardson annular effect.
Critical Dynamics : The Expansion of the Master Equation Including a Critical Point
Dekker, H.
1980-01-01
In this thesis it is shown how to solve the master equation for a Markov process including a critical point by means of successive approximations in terms of a small parameter. A critical point occurs if, by adjusting an externally controlled quantity, the system shows a transition from normal monos
The CHEASE code for toroidal MHD equilibria
Luetjens, H. [Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique; Bondeson, A. [Chalmers Univ. of Technology, Goeteborg (Sweden). Inst. for Electromagnetic Field Theory and Plasma Physics; Sauter, O. [ITER-San Diego, La Jolla, CA (United States)
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function {Psi}. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs.
Cosmological AMR MHD with Enzo
Xu, Hao [Los Alamos National Laboratory; Li, Hui [Los Alamos National Laboratory; Li, Shengtai [Los Alamos National Laboratory
2009-01-01
In this work, we present EnzoMHD, the extension of the cosmological code Enzoto include magnetic fields. We use the hyperbolic solver of Li et al. (2008) for the computation of interface fluxes. We use constrained transport methods of Balsara & Spicer (1999) and Gardiner & Stone (2005) to advance the induction equation, the reconstruction technique of Balsara (2001) to extend the Adaptive Mesh Refinement of Berger & Colella (1989) already used in Enzo, though formulated in a slightly different way for ease of implementation. This combination of methods preserves the divergence of the magnetic field to machine precision. We use operator splitting to include gravity and cosmological expansion. We then present a series of cosmological and non cosmologjcal tests problems to demonstrate the quality of solution resulting from this combination of solvers.
Global MHD model of the earth's magnetosphere
Wu, C. C.
1983-01-01
A global MHD model of the earth's magnetosphere is defined. An introduction to numerical methods for solving the MHD equations is given with emphasis on the shock-capturing technique. Finally, results concerning the shape of the magnetosphere and the plasma flows inside the magnetosphere are presented.
Alfven Wave Tomography for Cold MHD Plasmas
I.Y. Dodin; N.J. Fisch
2001-09-07
Alfven waves propagation in slightly nonuniform cold plasmas is studied by means of ideal magnetohydrodynamics (MHD) nonlinear equations. The evolution of the MHD spectrum is shown to be governed by a matrix linear differential equation with constant coefficients determined by the spectrum of quasi-static plasma density perturbations. The Alfven waves are shown not to affect the plasma density inhomogeneities, as they scatter off of them. The application of the MHD spectrum evolution equation to the inverse scattering problem allows tomographic measurements of the plasma density profile by scanning the plasma volume with Alfven radiation.
Younsi Ramdane
2015-01-01
Full Text Available In the present paper, three-dimensional equations for coupled heat and mass conservation equations for wood are solved to study the transient heat and mass transfer during high thermal treatment of wood. The model is based on Luikov’s approach, including pressure. The model equations are solved numerically by the commercial package FEMLfor the temperature and moisture content histories under different treatment conditions. The simulation of the proposed conjugate problem allows the assessment of the effect of the heat and mass transfer within wood. A parametric study was also carried out to determine the effects of several parameters such as initial moisture content and the sample thickness on the temperature, pressure and moisture content distributions within the samples during heat treatment.
Lectures in magnetohydrodynamics. With an appendix on extended MHD
Schnack, Dalton D. [Wisconsin Univ., Madison, WI (United States). Dept. Physics
2009-07-01
This concise and self-contained primer is based on class-tested notes for an advanced graduate course in MHD. The broad areas chosen for presentation are the derivation and properties of the fundamental equations, equilibrium, waves and instabilities, self-organization, turbulence, and dynamos. The latter topics require the inclusion of the effects of resistivity and nonlinearity. Together, these span the range of MHD issues that have proven to be important for understanding magnetically confined plasmas as well as in some space and astrophysical applications. The combined length and style of the thirty-eight lectures are appropriate for complete presentation in a single semester. An extensive appendix on extended MHD is included as further reading. (orig.)
The mathematical theory of reduced MHD models for fusion plasmas
Guillard, Hervé
2015-01-01
The derivation of reduced MHD models for fusion plasma is here formulated as a special instance of the general theory of singular limit of hyperbolic system of PDEs with large operator. This formulation allows to use the general results of this theory and to prove rigorously that reduced MHD models are valid approximations of the full MHD equations. In particular, it is proven that the solutions of the full MHD system converge to the solutions of an appropriate reduced model.
Dreiner, H; Dreiner, Herbi; Pois, Heath
1995-01-01
We present the complete 2-loop renormalization group equations of the supersymmetric standard model. We thus explicitly include the full set of R -parity violating couplings, including \\kappa_iL_iH_2. We use these equations to do a first study of (a) gauge coupling unification, (b) bottom-tau unification, (c) the fixed point structure of the top quark Yukawa coupling, and (d) two-loop bounds from perturbative unification. We find significant shifts which can be larger than the effect from the top quark Yukawa coupling. The value of \\alpha_3(M_Z) can change by \\pm5\\%. The \\tan\\beta region for bottom-tau unification and for the top quark IR quasi fixed point structure is significantly increased. For heavy scalar fermion masses {\\cal{O}}(1\\tev) the limits on the \\Delta L\
Nonlinear helical MHD instability
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
Master equation with quantized atomic motion including dipole-dipole interactions
Damanet, François; Braun, Daniel; Martin, John
2016-05-01
We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and is relevant for experiments with ultracold trapped atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find analytical formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that the dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion. The effects predicted should be experimentally observable with Rydberg atoms. FD would like to thank the F.R.S.-FNRS for financial support. FD is a FRIA Grant holder of the Fonds de la Recherche Scientifique-FNRS.
MHD Energy Bypass Scramjet Engine
Mehta, Unmeel B.; Bogdanoff, David W.; Park, Chul; Arnold, Jim (Technical Monitor)
2001-01-01
Revolutionary rather than evolutionary changes in propulsion systems are most likely to decrease cost of space transportation and to provide a global range capability. Hypersonic air-breathing propulsion is a revolutionary propulsion system. The performance of scramjet engines can be improved by the AJAX energy management concept. A magneto-hydro-dynamics (MHD) generator controls the flow and extracts flow energy in the engine inlet and a MHD accelerator downstream of the combustor accelerates the nozzle flow. A progress report toward developing the MHD technology is presented herein. Recent theoretical efforts are reviewed and ongoing experimental efforts are discussed. The latter efforts also include an ongoing collaboration between NASA, the US Air Force Research Laboratory, US industry, and Russian scientific organizations. Two of the critical technologies, the ionization of the air and the MHD accelerator, are briefly discussed. Examples of limiting the combustor entrance Mach number to a low supersonic value with a MHD energy bypass scheme are presented, demonstrating an improvement in scramjet performance. The results for a simplified design of an aerospace plane show that the specific impulse of the MHD-bypass system is better than the non-MHD system and typical rocket over a narrow region of flight speeds and design parameters. Equilibrium ionization and non-equilibrium ionization are discussed. The thermodynamic condition of air at the entrance of the engine inlet determines the method of ionization. The required external power for non-equilibrium ionization is computed. There have been many experiments in which electrical power generation has successfully been achieved by magneto-hydrodynamic (MHD) means. However, relatively few experiments have been made to date for the reverse case of achieving gas acceleration by the MHD means. An experiment in a shock tunnel is described in which MHD acceleration is investigated experimentally. MHD has several
Modeling magnetized neutron stars using resistive MHD
Palenzuela, Carlos
2013-01-01
This work presents an implementation of the resistive MHD equations for a generic algebraic Ohm's law which includes the effects of finite resistivity within full General Relativity. The implementation naturally accounts for magnetic-field-induced anisotropies and, by adopting a phenomenological current, is able to accurately describe electromagnetic fields in the star and in its magnetosphere. We illustrate the application of this approach in interesting systems with astrophysical implications; the aligned rotator solution and the collapse of a magnetized rotating neutron star to a black hole.
Relativistic MHD with Adaptive Mesh Refinement
Anderson, M; Liebling, S L; Neilsen, D; Anderson, Matthew; Hirschmann, Eric; Liebling, Steven L.; Neilsen, David
2006-01-01
We solve the relativistic magnetohydrodynamics (MHD) equations using a finite difference Convex ENO method (CENO) in 3+1 dimensions within a distributed parallel adaptive mesh refinement (AMR) infrastructure. In flat space we examine a Balsara blast wave problem along with a spherical blast wave and a relativistic rotor test both with unigrid and AMR simulations. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. We also investigate the impact of hyperbolic divergence cleaning for the spherical blast wave and relativistic rotor. We include unigrid and mesh refinement parallel performance measurements for the spherical blast wave.
Kim, Sun Jung; Yoo, Il Young
2016-03-01
The purpose of this study was to explain the health promotion behavior of Chinese international students in Korea using a structural equation model including acculturation factors. A survey using self-administered questionnaires was employed. Data were collected from 272 Chinese students who have resided in Korea for longer than 6 months. The data were analyzed using structural equation modeling. The p value of final model is .31. The fitness parameters of the final model such as goodness of fit index, adjusted goodness of fit index, normed fit index, non-normed fit index, and comparative fit index were more than .95. Root mean square of residual and root mean square error of approximation also met the criteria. Self-esteem, perceived health status, acculturative stress and acculturation level had direct effects on health promotion behavior of the participants and the model explained 30.0% of variance. The Chinese students in Korea with higher self-esteem, perceived health status, acculturation level, and lower acculturative stress reported higher health promotion behavior. The findings can be applied to develop health promotion strategies for this population. Copyright © 2016. Published by Elsevier B.V.
Metzler, Adam M; Siegmann, William L; Collins, Michael D
2012-02-01
The parabolic equation method with a single-scattering correction allows for accurate modeling of range-dependent environments in elastic layered media. For problems with large contrasts, accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single-scattering problems. This approach generates several computational parameters, such as the number of interface slices, an iteration convergence parameter τ, and the number of iterations n for convergence. Using a narrow-angle approximation, the choices of n=1 and τ=2 give accurate solutions. Analogous results from the narrow-angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces. The approach is applied to a generic ocean waveguide that includes the generation of a Rayleigh interface wave. Results are presented in both frequency and time domains.
Stationary MHD equilibria describing azimuthal rotations in symmetric plasmas
da Silva, Sidney T.; Viana, Ricardo L.
2016-12-01
We consider the stationary magnetohydrodynamical (MHD) equilibrium equation for an axisymmetric plasma undergoing azimuthal rotations. The case of cylindrical symmetry is treated, and we present two semi-analytical solutions for the stationary MHD equilibrium equations, from which a number of physical properties of the magnetically confined plasma are derived.
Resistive MHD jet simulations with large resistivity
Cemeljic, Miljenko; Vlahakis, Nektarios; Tsinganos, Kanaris
2009-01-01
Axisymmetric resistive MHD simulations for radially self-similar initial conditions are performed, using the NIRVANA code. The magnetic diffusivity could occur in outflows above an accretion disk, being transferred from the underlying disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We introduce, in addition to the classical magnetic Reynolds number Rm, which measures the importance of resistive effects in the induction equation, a new number Rb, which measures the importance of the resistive effects in the energy equation. We find two distinct regimes of solutions in our simulations. One is the low-resistivity regime, in which results do not differ much from ideal-MHD solutions. In the high-resistivity regime, results seem to show some periodicity in time-evolution, and depart significantly from the ideal-MHD case. Whether this departure is caused by numerical or physical reasons is of considerable interest for nu...
Derivation of a viscous KP including surface tension, and related equations
Meur, Hervé Le
2015-01-01
The aim of this article is to derive surface wave models in the presence of surface tension and viscosity. Using the Navier-Stokes equations with a free surface, flat bottom and surface tension, we derive the viscous 2D Boussinesq system with a weak transverse variation. The assumed transverse variation is on a larger scale than along the main propagation direction. This Boussinesq system is only an intermediate result that enables us to derive the Kadomtsev-Petviashvili (KP) equation which is a 2D generalization of the KdV equation. In addition, we get the 1D KdV equation, and lastly the Boussinesq equation. All these equations are derived for non-vanishing initial conditions.
Gala, Sadek; Ragusa, Maria Alessandra
2016-04-01
In this paper, we establish a blow-up criterion of strong solutions to the 3D incompressible magnetohydrodynamics equations including two nonlinear extra terms: the Hall term (quadratic with respect to the magnetic field) and the ion-slip term (cubic with respect to the magnetic field). This is an improvement of the recent results given by Fan et al. (Z Angew Math Phys, 2015).
A global solution curve for a class of periodic problems, including the pendulum equation
Korman, Philip
2007-09-01
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for a class of periodically forced pendulum-like equations. Our results apply also to the first order equations. We also show that by choosing a forcing term, one can produce periodic solutions with any number of Fourier coefficients arbitrarily prescribed.
QCD Equation of State From a Chiral Hadronic Model Including Quark Degrees of Freedom
Rau, Philip; Schramm, Stefan; Stöcker, Horst
2013-01-01
This work presents an effective model for strongly interacting matter and the QCD equation of state (EoS). The model includes both hadron and quark degrees of freedom and takes into account the transition of chiral symmetry restoration as well as the deconfinement phase transition. At low temperatures $T$ and baryonic densities $\\rho_B$ a hadron resonance gas is described using a SU(3)-flavor sigma-omega model and a quark phase is introduced in analogy to PNJL models for higher $T$ and $\\rho_B$. In this way, the correct asymptotic degrees of freedom are used in a wide range of $T$ and $\\rho_B$. Here, results of this model concerning the chiral and deconfinement phase transitions and thermodynamic model properties are presented. Large hadron resonance multiplicities in the transition region emphasize the importance of heavy-mass resonance states in this region and their impact on the chiral transition behavior. The resulting phase diagram of QCD matter at small chemical potentials is in line with latest lattic...
Simulation of three-dimensional nonideal MHD flow at low magnetic Reynolds number
LU HaoYu; LEE ChunHian
2009-01-01
A numerical procedure based on a five-wave model associated with non-ideal,low magnetic Reynolds number magnetohydrodynamic(MHD)flows was developed.It is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations,in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of flow field.To validate the developed procedure,two different test cases were used which included MHD Rayleigh problem and MHD Hartmann problem.The simulations were performed under the assumption of low magnetic Reynolds number.The simulated results were found to be in good agreement with the closed form analytical solutions deduced in the present study,showing that the present algorithm could simulate engineering MHD flow at low magnetic Reynolds number effectively.In the end,a flow field between a pair of segmented electrodes in a three dimensional MHD channel was simulated using the present algorithm with and without including Hall effects.Without the introduction of Hall effects,no distortion was observed in the current and potential lines.By taking the Hall effects into account,the potential lines distorted and clustered at the upstream and downstream edges of the cathode and anode,respectively.
Dewar, R L; Mills, R; Hole, M J, E-mail: robert.dewar@anu.edu.a [Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)
2009-05-01
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics. To resolve the continuation problem we regularize the Newcomb equation, solve it in terms of Legendre functions of imaginary argument, and define the small weak solutions of the Newcomb equation as generalized functions in the manner of Lighthill, i.e. via a limiting sequence of analytic functions that connect smoothly across the singularity.
Dewar, R. L.; Mills, R.; Hole, M. J.
2009-05-01
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics. To resolve the continuation problem we regularize the Newcomb equation, solve it in terms of Legendre functions of imaginary argument, and define the small weak solutions of the Newcomb equation as generalized functions in the manner of Lighthill, i.e. via a limiting sequence of analytic functions that connect smoothly across the singularity.
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
He, Qingyun; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; Feng, Jingchao
2015-12-15
Highlights: • A 3D PISO-MHD was implemented on Kepler-class graphics processing units (GPUs) using CUDA technology. • A consistent and conservative scheme is used in the code which was validated by three basic benchmarks in a rectangular and round ducts. • Parallelized of CPU and GPU acceleration were compared relating to single core CPU in MHD problems and non-MHD problems. • Different preconditions for solving MHD solver were compared and the results showed that AMG method is better for calculations. - Abstract: The pressure-implicit with splitting of operators (PISO) magnetohydrodynamics MHD solver of the couple of Navier–Stokes equations and Maxwell equations was implemented on Kepler-class graphics processing units (GPUs) using the CUDA technology. The solver is developed on open source code OpenFOAM based on consistent and conservative scheme which is suitable for simulating MHD flow under strong magnetic field in fusion liquid metal blanket with structured or unstructured mesh. We verified the validity of the implementation on several standard cases including the benchmark I of Shercliff and Hunt's cases, benchmark II of fully developed circular pipe MHD flow cases and benchmark III of KIT experimental case. Computational performance of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms and meshes. The resulted showed that a GPU (GTX 770) can outperform a server-class 4-core, 8-thread CPU (Intel Core i7-4770k) by a factor of 2 at least.
Magnetohydrodynamic (MHD) channel corner seal
Spurrier, Francis R.
1980-01-01
A corner seal for an MHD duct includes a compressible portion which contacts the duct walls and an insulating portion which contacts the electrodes, sidewall bars and insulators. The compressible portion may be a pneumatic or hydraulic gasket or an open-cell foam rubber. The insulating portion is segmented into a plurality of pieces of the same thickness as the electrodes, insulators and sidewall bars and aligned therewith, the pieces aligned with the insulator being of a different size from the pieces aligned with the electrodes and sidewall bars to create a stepped configuration along the corners of the MHD channel.
The expansion of the Fokker-Planck equation including a critical point
Dekker, H.; Kampen, N.G. van
1980-01-01
The known expansion of the master equation for weak diffusion in an external potential applies to both the monostable and the bistable case, but fails at the critical point. This can be remedied by taking as zeroth order approximation a suitably defined set of eigenfunctions. The resulting expansion
Applications of a finite-volume algorithm for incompressible MHD problems
Vantieghem, S; Jackson, A
2016-01-01
We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of geometries. Our method implements a mixed Adams-Bashforth/Crank-Nicolson scheme for the nonlinear terms in the MHD equations and we prove that it is stable independent of the time step. To ensure that the solenoidal condition is met for the magnetic field, we use a method whereby a pseudo-pressure is introduced into the induction equation; since we are concerned with incompressible flows, the resulting Poisson equation for the pseudo-pressure is solved alongside the equivalent Poisson problem for the velocity field. We validate our code in a variety of geometries including periodic boxes, spheres, spherical shells, spheroids and ellipsoids; for the finite geometries we implement the so-called ferromagnetic or pseudo-vacuum boundary conditions appropriate for a surrounding medium w...
The complete set of Casimirs in Hall-MHD
Kawazura, Yohei; Hameiri, Eliezer
2012-03-01
A procedure to determine all Casimir constants of motion in MHDfootnotetextE. Hameiri, Phy. Plasmas, 11, 3423 (2004). is extended to Hall-MHD. We obtain differential equations for the variational derivatives of all Casimirs which must be satisfied for any dynamically accessible motion of Hall-MHD. In an extension of the more commonly considered model, we also include the electron fluid entropy. The most interesting case, usually true for axisymmetric configurations, is when both the electron and ion entropy functions form families of nested toroidal surfaces. The Casimirs are then three functions of each of the entropies, involving fluxes of certain vector fields and the number of particles contained in each torus. If any of the species loses its nested tori, the number of the associated Casimirs is much larger (but physically less relevant).
Ground-state solution for a class of biharmonic equations including critical exponent
Liu, Hongliang; Chen, Haibo
2015-12-01
In this paper, we study the following biharmonic equations Δ^2 u = λ{|u|^{2^{astast}(s)-2}u/|x|^s} + β a(x)|u|^{r-2}u,quad xin {{R}}^N. Under some suitable assumptions of {λ}, {β} and {a(x)}, the existence of ground-state solution and nonexistence of nontrivial solution are obtained by using variational methods. Moreover, the phenomenon of concentration of solutions is also explored.
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.
M. Schüssler
Full Text Available Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere ('convective collapse' are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10^{5} G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.
Key words. Solar physics · astrophysics and astronomy (photosphere and chromosphere; stellar interiors and dynamo theory; numerical simulation studies.
An equation of state for polymethylpentene (TPX) including multi-shock response
Aslam, Tariq D.; Gustavsen, Rick; Sanchez, Nathaniel; Bartram, Brian D.
2012-03-01
The equation of state (EOS) of polymethylpentene (TPX) is examined through both single shock Hugoniot data as well as more recent multi-shock compression and release experiments. Results from the recent multi-shock experiments on LANL's two-stage gas gun will be presented. A simple conservative Lagrangian numerical scheme utilizing total variation diminishing interpolation and an approximate Riemann solver will be presented as well as the methodology of calibration. It is shown that a simple Mie-Grüneisen EOS based on a Keane fitting form for the isentrope can replicate both the single shock and multi-shock experiments.
2006-09-01
Aerospace Applications, AIAA-Paper 96-2355, New Orleans, 1996 2. V.A.Bityurin, A.N.Bocharov, J.Lineberry, MHD Aerospace Applications, Invited Lecture ...Paper 2003- 4303, Orlando, FL 8. V.A.Bityurin, Prospective of MHD Interaction in Hypersonic and Propulsion Technologies, In: von Karman Series : Lectures ...Efforts in MHD AeoSpace Applications, In: von Karman Series : Lectures , Introduction of Magneto-Fluid Dynamics for AeroSpace Applications, von Karman
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...
MHD Turbulence and Magnetic Dynamos
Shebalin, John V
2014-01-01
Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much
Supernova equations of state including full nuclear ensemble with in-medium effects
Furusawa, Shun; Sumiyoshi, Kohsuke; Yamada, Shoichi; Suzuki, Hideyuki
2017-01-01
We construct new equations of state for baryons at sub-nuclear densities for the use in core-collapse supernova simulations. The abundance of various nuclei is obtained together with thermodynamic quantities. The formulation is an extension of the previous model, in which we adopted the relativistic mean field theory with the TM1 parameter set for nucleons, the quantum approach for d, t, h and α as well as the liquid drop model for the other nuclei under the nuclear statistical equilibrium. We reformulate the model of the light nuclei other than d, t, h and α based on the quasi-particle description. Furthermore, we modify the model so that the temperature dependences of surface and shell energies of heavy nuclei could be taken into account. The pasta phases for heavy nuclei and the Pauli- and self-energy shifts for d, t, h and α are taken into account in the same way as in the previous model. We find that nuclear composition is considerably affected by the modifications in this work, whereas thermodynamical quantities are not changed much. In particular, the washout of shell effect has a great impact on the mass distribution above T ∼ 1 MeV. This improvement may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.
Multi-fluid MHD study of the solar wind interaction with Pluto
Dong, C.; Ma, Y.; McComas, D. J.; Bhattacharjee, A.; Zirnstein, E.; Toth, G.; Luhmann, J. G.; Wang, L.
2016-12-01
The study of the solar wind interaction with Pluto's upper atmosphere has triggered a great of interest in recent years. The Solar Wind Around Pluto (SWAP) instrument onboard New Horizon (NH) spacecraft has provided a wealth of detailed and quantitative information about Pluto and its interaction with the tenuous solar wind out at 33 AU. The SWAP data reveals Pluto's unique interaction with the solar wind as a hybrid of comet-like and the Venus/Mars-like interactions. While SWAP data has provided many of the key results, a lot of details are still missing merely based on NH flyby observations. In order to further investigate the solar wind-Pluto interaction from a global point of view, we develop a 3-D multi-fluid MHD (MF-MHD) model. The MF-MHD model solves separate continuity, momentum and energy equations for each ion species. We adopt the 1-D modeled neutral atmosphere, which is based on NH observations, as the MF-MHD input. Photoionization, charge exchange and electron impact ionization are all included in the MF-MHD model. We will study the ion escape rate, and Pluto's magnetosphere and heavy ion tail structure. We will also do some data-model comparisons. This work has the potential to improve our understanding of present day Pluto's unique solar wind interaction and thus enhance the science returned from the NH mission.
Cascades and Spectra of Elastic Turbulence in 2D: Spinodal Decomposition & MHD
Fan, Xiang; Diamond, Patrick; Chacon, Luis
2016-10-01
We report on studies of turbulence in 2D spinodal decompositions of symmetric binary mixtures. This study emphasizes a comparison and contrast of the physics of spinodal turbulence with that of 2D MHD turbulence. The important similarities include basic equations, ideal quadratic conserved quantities, cascade directions and elastic waves. Turbulence in spinodal decomposition exhibits an elastic range when the Hinze scale is sufficiently larger than the dissipation scale, i.e. LH k (analogous to HkA ≡k in MHD) scales as k - 7 / 3. This suggests an inverse cascade of Hψ, corresponding to the case in MHD. However, we also show that, the kinetic energy spectrum scales as k-3, as in the direct enstrophy cascade range for a 2D fluid (not MHD!). The resolution of this dilemma is that capillarity acts only at blob boundaries. This is in contrast to B in MHD. Thus, as blob merger progresses, the packing fraction of interfaces decreases, thus explaining the outcome for the kinetic energy spectrum. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award Number DE-FG02-04ER54738.
Pollock, M. D.
The Wheeler-DeWitt equation for the wave function of the Universe Ψ can be derived for the heterotic superstring, after reduction of the effective action, including terms hat { R}4 quartic in the Riemann tensor, from ten dimensions to { D} = M+1 dimensions, where { D} Feynman path-integral formulation of Ψ.
Hodograph method in MHD orthogonal fluid flows
P. V. Nguyen
1992-01-01
Full Text Available Equations for steady plane MHD orthogonal flows of a viscous incompressible fluid of finite electrical conductivity are recast in the hodograph plane by using the Legendre transform function of the streamfunction. Three examples are studied to illustrate the developed theory. Solutions and geometries for these examples are determined.
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Open Boundary Conditions for Dissipative MHD
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
MHD Thin Film Flows of a Third Grade Fluid on a Vertical Belt with Slip Boundary Conditions
Taza Gul; Rehan Ali Shah; Saeed Islam; Muhammad Arif
2013-01-01
The problem of heat transfer analysis is considered in electrically conducting thin film flows with slip boundary conditions. The flow is assumed to be obeying the nonlinear rheological constitutive equation of a third grade fluid. We have solved the governing nonlinear equations of present problems using the traditional Adomian decomposition method (ADM). Particular attention is given to the combined effect of heat and MHD on the velocity field. The results include the profile of velocity, v...
Schnack, Dalton D.
In this lecture we will examine some simple examples of MHD equilibrium configurations. These will all be in cylindrical geometry. They form the basis for more complicated equilibrium states in toroidal geometry.
Towards a Realistic, Data-Driven Thermodynamic MHD Model of the Global Solar Corona
Downs, Cooper; van der Holst, Bart; Lugaz, Noé; Sokolov, Igor V; Gombosi, Tamas I
2009-01-01
In this work we describe our implementation of a thermodynamic energy equation into the global corona model of the Space Weather Modeling Framework (SWMF), and its development into the new Lower Corona (LC) model. This work includes the integration of the additional energy transport terms of coronal heating, electron heat conduction, and optically thin radiative cooling into the governing magnetohydrodynamic (MHD) energy equation. We examine two different boundary conditions using this model; one set in the upper transition region (the Radiative Energy Balance model), as well as a uniform chromospheric condition where the transition region can be modeled in its entirety. Via observation synthesis from model results and the subsequent comparison to full sun extreme ultraviolet (EUV) and soft X-Ray observations of Carrington Rotation (CR) 1913 centered on Aug 27, 1996, we demonstrate the need for these additional considerations when using global MHD models to describe the unique conditions in the low corona. Th...
Evolutionary Conditions in the Dissipative MHD System Revisited
Inoue, Tsuyoshi
2007-01-01
The evolutionary conditions for the dissipative continuous magnetohydrodynamic (MHD) shocks are studied. We modify Hada's approach in the stability analysis of the MHD shock waves. The matching conditions between perturbed shock structure and asymptotic wave modes shows that all types of the MHD shocks, including the intermediate shocks, are evolutionary and perturbed solutions are uniquely defined. We also adopt our formalism to the MHD shocks in the system with resistivity without viscosity, which is often used in numerical simulation, and show that all types of shocks that are found in the system satisfy the evolutionary condition and perturbed solutions are uniquely defined. These results suggest that the intermediate shocks may appear in reality.
Dynamics of nonlinear resonant slow MHD waves in twisted flux tubes
R. Erdélyi
2002-01-01
Full Text Available Nonlinear resonant magnetohydrodynamic (MHD waves are studied in weakly dissipative isotropic plasmas in cylindrical geometry. This geometry is suitable and is needed when one intends to study resonant MHD waves in magnetic flux tubes (e.g. for sunspots, coronal loops, solar plumes, solar wind, the magnetosphere, etc. The resonant behaviour of slow MHD waves is confined in a narrow dissipative layer. Using the method of simplified matched asymptotic expansions inside and outside of the narrow dissipative layer, we generalise the so-called connection formulae obtained in linear MHD for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These connection formulae for resonant MHD waves across the dissipative layer play a similar role as the well-known Rankine-Hugoniot relations connecting solutions at both sides of MHD shock waves. The key results are the nonlinear connection formulae found in dissipative cylindrical MHD which are an important extension of their counterparts obtained in linear ideal MHD (Sakurai et al., 1991, linear dissipative MHD (Goossens et al., 1995; Erdélyi, 1997 and in nonlinear dissipative MHD derived in slab geometry (Ruderman et al., 1997. These generalised connection formulae enable us to connect solutions obtained at both sides of the dissipative layer without solving the MHD equations in the dissipative layer possibly saving a considerable amount of CPU-time when solving the full nonlinear resonant MHD problem.
Alexakis, A.
2009-04-01
Most astrophysical and planetary systems e.g., solar convection and stellar winds, are in a turbulent state and coupled to magnetic fields. Understanding and quantifying the statistical properties of magneto-hydro-dynamic (MHD) turbulence is crucial to explain the involved physical processes. Although the phenomenological theory of hydro-dynamic (HD) turbulence has been verified up to small corrections, a similar statement cannot be made for MHD turbulence. Since the phenomenological description of Hydrodynamic turbulence by Kolmogorov in 1941 there have been many attempts to derive a similar description for turbulence in conducting fluids (i.e Magneto-Hydrodynamic turbulence). However such a description is going to be based inevitably on strong assumptions (typically borrowed from hydrodynamics) that do not however necessarily apply to the MHD case. In this talk I will discuss some of the properties and differences of the energy and helicity cascades in turbulent MHD and HD flows. The investigation is going to be based on the analysis of direct numerical simulations. The cascades in MHD turbulence appear to be a more non-local process (in scale space) than in Hydrodynamics. Some implications of these results to turbulent modeling will be discussed
Approximate Riemann solvers for the cosmic ray magnetohydrodynamical equations
Kudoh, Yuki; Hanawa, Tomoyuki
2016-11-01
We analyse the cosmic ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully conservation form, the CR energy equation is replaced with the CR `number' conservation, where the CR number density is defined as the three-fourths power of the CR energy density. The former contains an extra source term, while latter does not. An approximate Riemann solver is derived from the CR MHD equations in the fully conservation form. Based on the analysis, we propose a numerical scheme of which solutions satisfy the Rankine-Hugoniot relation at any shock. We demonstrate that it reproduces the Riemann solution derived by Pfrommer et al. for a 1D CR hydrodynamic shock tube problem. We compare the solution with those obtained by solving the CR energy equation. The latter solutions deviate from the Riemann solution seriously, when the CR pressure dominates over the gas pressure in the post-shocked gas. The former solutions converge to the Riemann solution and are of the second-order accuracy in space and time. Our numerical examples include an expansion of high-pressure sphere in a magnetized medium. Fast and slow shocks are sharply resolved in the example. We also discuss possible extension of the CR MHD equations to evaluate the average CR energy.
Lattice Boltzmann Large Eddy Simulation Model of MHD
Flint, Christopher
2016-01-01
The work of Ansumali \\textit{et al.}\\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single rel...
Relativistic MHD and excision: formulation and initial tests
Neilsen, David; Hirschmann, Eric W; Millward, R Steven [Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602 (United States)
2006-08-21
A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids and elliptic and hyperbolic divergence cleaning.
Relativistic MHD and black hole excision: Formulation and initial tests
Neilsen, D; Millward, R S; Hirschmann, Eric W; Neilsen, David
2006-01-01
A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids, and elliptic and hyperbolic divergence cleaning.
Safety and reliability in superconducting MHD magnets
Laverick, C.; Powell, J.; Hsieh, S.; Reich, M.; Botts, T.; Prodell, A.
1979-07-01
This compilation adapts studies on safety and reliability in fusion magnets to similar problems in superconducting MHD magnets. MHD base load magnet requirements have been identified from recent Francis Bitter National Laboratory reports and that of other contracts. Information relevant to this subject in recent base load magnet design reports for AVCO - Everett Research Laboratories and Magnetic Corporation of America is included together with some viewpoints from a BNL workshop on structural analysis needed for superconducting coils in magnetic fusion energy. A summary of design codes used in large bubble chamber magnet design is also included.
Cheng Jian-zheng; Zhang De-jun; Lan Cong-qing; Ye Chao-hui
2000-01-01
Based on the cell model, the general formula for the free energy of solids is derived analytically with the lowest order anharmonic modification and correlation effect taken into account. Combining a method of summing over lattice sites, the analytic equation of state for generalized Lennard-Jones solid is derived. The calculations show that the agreement between theory and computer simulation is quite good and is significantly improved as compared with the numerical results in literature. The comparison of different effects shows the theory including all neighbors but only considering the lowest anharmonic and correlation effects may be a good and convenient approximation for practical solids. The approximation can be easily extended to the quantum case and other generalized potentials.
Studying effect of MHD on thin films of a micropolar fluid
Abdel-Rahman, Gamal M., E-mail: gamalm60@yahoo.co [Department of Mathematics, Faculty of Science, Benha University, 13518 Benha (Egypt)
2009-11-15
This paper deals with the study of the effect of MHD on thin films of a micropolar fluid. These thin films are considered for three different geometries, namely: (i) flow down an inclined plane, (ii) flow on a moving belt and (iii) flow down a vertical cylinder. The transformed boundary layer governing equations of a micropolar fluid and the resulting system of coupled non-linear ordinary differential equations are solved numerically by using shooting method. Numerical results were presented for velocity and micro-rotation profiles within the boundary layer for different parameters of the problem including micropolar fluid parameters, magnetic field parameter, etc., which are also discussed numerically and illustrated graphically.
Principal characteristics of SFC type MHD generator
Kayukawa, Naoyuki; Oikawa, Shun-ichi; Aoki, Yoshiaki; Seidou, Tadashi; Okinaka, Noriyuki
1988-02-01
This paper describes the experimental and analytical results obtained for an MHD channel with a two dimensionally shaped magnetic field configuration called 'the SFC-type'. The power generating performance was examined under various load conditions and B-field intensities with a 2 MWt shock tunnel MHD facility. It is demonstrated that the power output performance and the enthalpy extraction scaling law of the conventional uniform B-field MHD generator (UFC-type) were significantly improved by the SFC-design of the spatial distribution of the magnetic field. The arcing processes were also examined by a high speed camera and the post-test observation of arc spot traces on electrodes. Further, the characteristic frequencies of each of the so-called micro and constricted arcs were clarified by spectral analyses. The critical current densities, which define the transient conditions of each from the diffuse-to micro arc, and from the micro-to constricted arc modes could be clearly obtained by the present spectral analysis method. We also investigated the three-dimensional behavior under strong magnetic field based on the coupled electrical and hydrodynamical equations for both of the middle scale SFC-and UFC-type generators. Finally, it is concluded from the above mentioned various aspects that the shaped 2-D magnetic field design will offer a most useful means for the realization of a compact, high efficiency and a long duration open-cycle MHD generator.
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
Local conservative regularizations of compressible MHD and neutral flows
Krishnaswami, Govind S; Thyagaraja, Anantanarayanan
2016-01-01
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper we propose a minimal, local, conservative, nonlinear, dispersive regularization of compressible flow and ideal MHD, in analogy with the KdV regularization of the 1D kinematic wave equation. This work extends and significantly generalizes earlier work on incompressible Euler and ideal MHD. It involves a micro-scale cutoff length lambda which is a function of density, unlike in the incompressible case. In MHD, it can be taken to be of order the electron collisionless skin depth c/omega_pe. Our regularization preserves the symmetries of the original systems, and with appropriate boundary conditions, leads to associated conservation laws. Energy and enstrophy are subject to a priori bounds determined by initial data in contrast to the unregularized systems. A Hamiltonian and Poisson bracket formulation is developed and applied ...
MHD squeezing flow between two infinite plates
Umar Khan
2014-03-01
Full Text Available Magneto hydrodynamic (MHD squeezing flow of a viscous fluid has been discussed. Conservation laws combined with similarity transformations have been used to formulate the flow mathematically that leads to a highly nonlinear ordinary differential equation. Analytical solution to the resulting differential equation is determined by employing Variation of Parameters Method (VPM. Runge–Kutta order-4 method is also used to solve the same problem for the sake of comparison. It is found that solution using VPM reduces the computational work yet maintains a very high level of accuracy. The influence of different parameters is also discussed and demonstrated graphically.
Pamadi, Bandu N.; Toniolo, Matthew D.; Tartabini, Paul V.; Roithmayr, Carlos M.; Albertson, Cindy W.; Karlgaard, Christopher D.
2016-01-01
The objective of this report is to develop and implement a physics based method for analysis and simulation of multi-body dynamics including launch vehicle stage separation. The constraint force equation (CFE) methodology discussed in this report provides such a framework for modeling constraint forces and moments acting at joints when the vehicles are still connected. Several stand-alone test cases involving various types of joints were developed to validate the CFE methodology. The results were compared with ADAMS(Registered Trademark) and Autolev, two different industry standard benchmark codes for multi-body dynamic analysis and simulations. However, these two codes are not designed for aerospace flight trajectory simulations. After this validation exercise, the CFE algorithm was implemented in Program to Optimize Simulated Trajectories II (POST2) to provide a capability to simulate end-to-end trajectories of launch vehicles including stage separation. The POST2/CFE methodology was applied to the STS-1 Space Shuttle solid rocket booster (SRB) separation and Hyper-X Research Vehicle (HXRV) separation from the Pegasus booster as a further test and validation for its application to launch vehicle stage separation problems. Finally, to demonstrate end-to-end simulation capability, POST2/CFE was applied to the ascent, orbit insertion, and booster return of a reusable two-stage-to-orbit (TSTO) vehicle concept. With these validation exercises, POST2/CFE software can be used for performing conceptual level end-to-end simulations, including launch vehicle stage separation, for problems similar to those discussed in this report.
Electron MHD: dynamics and turbulence
Lyutikov, Maxim
2013-01-01
(Abridged) We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron MHD (EMHD). We argue there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact non-linear solutions; (ii) co-linear whistlers do not interact (including counter-propagating); (iii) waves with the same value of the wave vector, $k_1=k_2$, do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero-mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfven turbulence cannot be transferred to the E...
Exact solutions for MHD flow of couple stress fluid with heat transfer
Najeeb Alam Khan
2016-01-01
Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.
MHD equilibrium and stability in heliotron plasmas
Ichiguchi, Katsuji [National Inst. for Fusion Science, Toki, Gifu (Japan)
1999-09-01
Recent topics in the theoretical magnetohydrodynamic (MHD) analysis in the heliotron configuration are overviewed. Particularly, properties of three-dimensional equilibria, stability boundary of the interchange mode, effects of the net toroidal current including the bootstrap current and the ballooning mode stability are focused. (author)
Io's Magnetospheric Interaction: An MHD Model with Day-Night Asymmetry
Kabin, K.; Combi, M. R.; Gombosi, T. I.; DeZeeuw, D. L.; Hansen, K. C.; Powell, K. G.
2001-01-01
In this paper we present the results of all improved three-dimensional MHD model for Io's interaction with Jupiter's magnetosphere. We have included the day-night asymmetry into the spatial distribution of our mass-loading, which allowed us to reproduce several smaller features or the Galileo December 1995 data set. The calculation is performed using our newly modified description of the pick-up processes that accounts for the effects of the corotational electric field existing in the Jovian magnetosphere. This change in the formulation of the source terms for the MHD equations resulted in significant improvements in the comparison with the Galileo measurements. We briefly discuss the limitations of our model and possible future improvements.
Algorithm and exploratory study of the Hall MHD Rayleigh-Taylor instability.
Gardiner, Thomas Anthony
2010-09-01
This report is concerned with the influence of the Hall term on the nonlinear evolution of the Rayleigh-Taylor (RT) instability. This begins with a review of the magnetohydrodynamic (MHD) equations including the Hall term and the wave modes which are present in the system on time scales short enough that the plasma can be approximated as being stationary. In this limit one obtains what are known as the electron MHD (EMHD) equations which support two characteristic wave modes known as the whistler and Hall drift modes. Each of these modes is considered in some detail in order to draw attention to their key features. This analysis also serves to provide a background for testing the numerical algorithms used in this work. The numerical methods are briefly described and the EMHD solver is then tested for the evolution of whistler and Hall drift modes. These methods are then applied to study the nonlinear evolution of the MHD RT instability with and without the Hall term for two different configurations. The influence of the Hall term on the mixing and bubble growth rate are analyzed.
High-Order Finite Difference GLM-MHD Schemes for Cell-Centered MHD
Mignone, A; Bodo, G
2010-01-01
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting...
A 3rd Order WENO GLM-MHD Scheme for Magnetic Reconnection
FENG Xueshang; ZHOU Yufen; HU Yanqi
2006-01-01
A new numerical scheme of 3rd order Weighted Essentially Non-Oscillatory (WENO)type for 2.5D mixed GLM-MHD in Cartesian coordinates is proposed. The MHD equations are modified by combining the arguments as by Dellar and Dedner et al to couple the divergence constraint with the evolution equations using a Generalized Lagrange Multiplier (GLM). Moreover, the magnetohydrodynamic part of the GLM-MHD system is still in conservation form. Meanwhile, this method is very easy to add to an existing code since the underlying MHD solver does not have to be modified. To show the validation and capacity of its application to MHD problem modelling,interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems are used to verify this new MHD code. The numerical tests for 2D Orszag and Tang's MHD vortex,interaction between a magnetosonic shock and a denser cloud and magnetic reconnection problems show that the third order WENO MHD solvers are robust and yield reliable results by the new mixed GLM or the mixed EGLM correction here even if it can not be shown that how the divergence errors are transported as well as damped as done for one dimensional ideal MHD by Dedner et al.
Global and Kinetic MHD Simulation by the Gpic-MHD Code
Hiroshi NAITOU; Yusuke YAMADA; Kenji KAJIWARA; Wei-li LEE; Shinji TOKUDA; Masatoshi YAGI
2011-01-01
In order to implement large-scale and high-beta tokamak simulation, a new algorithm of the electromagnetic gyrokinetic PIC （particle-in-cell） code was proposed and installed on the Gpic-MHD code [Gyrokinetic PIC code for magnetohydrodynamic （MHD） simulation]. In the new algorithm, the vorticity equation and the generalized Ohm＇s law along the magnetic field are derived from the basic equations of the gyrokinetic Vlasov, Poisson, and Ampere system and are used to describe the spatio-temporal evolution of the field quantities of the electrostatic potential φ and the longitudinal component of the vector potential Az. The basic algorithm is equivalent to solving the reduced-MHD-type equations with kinetic corrections, in which MHD physics related to Alfven modes are well described. The estimation of perturbed electron pressure from particle dynamics is dominant, while the effects of other moments are negligible. Another advantage of the algorithm is that the longitudinal induced electric field, ETz = -δAz/δt, is explicitly estimated by the generalized Ohm＇s law and used in the equations of motion. Furthermore, the particle velocities along the magnetic field are used （vz-formulation） instead of generalized momentums （pz-formulation）, hence there is no problem of ＇cancellation＇, which would otherwise appear when Az is estimated from the Ampere＇s law in the pz-formulation. The successful simulation of the collisionless internal kink mode by the new Gpic-MHD with realistic values of the large-scale and high-beta tokamaks revealed the usefulness of the new algorithm.
MHD discontinuities in solar flares: continuous transitions and plasma heating
Ledentsov, L S
2015-01-01
The boundary conditions for the ideal MHD equations on a plane dis- continuity surface are investigated. It is shown that, for a given mass flux through a discontinuity, its type depends only on the relation between inclina- tion angles of a magnetic field. Moreover, the conservation laws on a surface of discontinuity allow changing a discontinuity type with gradual (continu- ous) changes in the conditions of plasma flow. Then there are the so-called transition solutions that satisfy simultaneously two types of discontinuities. We obtain all transition solutions on the basis of the complete system of boundary conditions for the MHD equations. We also found the expression describing a jump of internal energy of the plasma flowing through the dis- continuity. Firstly, this allows constructing a generalized scheme of possible continuous transitions between MHD discontinuities. Secondly, it enables the examination of the dependence of plasma heating by plasma density and configuration of the magnetic field near t...
MHD Integrated Topping Cycle Project
1992-07-01
This seventeenth quarterly technical progress report of the MHD Integrated Topping Cycle Project presents the accomplishments during the period August 1, 1991 to October 31, 1991. Manufacturing of the prototypical combustor pressure shell has been completed including leak, proof, and assembly fit checking. Manufacturing of forty-five cooling panels was also completed including leak, proof, and flow testing. All precombustor internal components (combustion can baffle and swirl box) were received and checked, and integration of the components was initiated. A decision was made regarding the primary and backup designs for the 1A4 channel. The assembly of the channel related prototypical hardware continued. The cathode wall electrical wiring is now complete. The mechanical design of the diffuser has been completed.
Fully Parallel MHD Stability Analysis Tool
Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang
2015-11-01
Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Results of MARS parallelization and of the development of a new fix boundary equilibrium code adapted for MARS input will be reported. Work is supported by the U.S. DOE SBIR program.
Analogue Kerr-like geometries in a MHD inflow
Noda, Sousuke; Takahashi, Masaaki
2016-01-01
We present a model of the analogue black hole in magnetohydrodynamic (MHD) flow. For a two dimensional axisymmetric stationary trans-magnetosonic inflow with a sink, using the dispersion relation of the MHD waves, we introduce the effective geometries for magnetoacoustic waves propagating in the MHD flow. Investigating the properties of the effective potentials for magnetoacoustic rays, we find that the effective geometries can be classified into five types which include analogue spacetimes of the Kerr black hole, ultra spinning stars with ergoregions and spinning stars without ergoregions. We address the effects of the magnetic pressure and the magnetic tension on each magnetoacoustic geometries.
Louis, J.F.
1978-03-01
Research and development in open-cycle coal-fired MHD power generation is described. The scope and objectives of the MIT program are: (1) establish chemical, thermal, and electrical data to guide materials selection, develop improved detail designs, and support performance analyses of MHD electrode modules and insulator materials; (2) parametrically investigate selected electrode properties of critical design importance in chemical, thermal, and electrical environments simulating a coal-fired MHD generator; (3) develop combustion data pertinent to the design of MHD combustors; (4) establish techniques for the analysis and understanding of critical MHD phenomena which have an important bearing on MHD generator performance; such phenomena include inter-electrode breakdown, time-dependent behavior, effective plasma properties and plasma inhomogeneities; (5) establish the operating characteristics of an MHD disk generator; (6) continue work on computer techniques for modeling and for design and cost analysis of MHD components and the overall system; (7) integrate the engineering data and design criteria, as applicable, which are developed in the listed tasks into a model of the MHD channel; (8) participate in the US/USSR Cooperative Program in MHD Power Generation; and (9) participate in technical support of the DOE MHD Project Office. Progress in each of these areas is reported. (WHK)
A New MHD-assisted Stokes Inversion Technique
Riethmüller, T. L.; Solanki, S. K.; Barthol, P.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; van Noort, M.; Blanco Rodríguez, J.; Del Toro Iniesta, J. C.; Orozco Suárez, D.; Schmidt, W.; Martínez Pillet, V.; Knölker, M.
2017-03-01
We present a new method of Stokes inversion of spectropolarimetric data and evaluate it by taking the example of a Sunrise/IMaX observation. An archive of synthetic Stokes profiles is obtained by the spectral synthesis of state-of-the-art magnetohydrodynamics (MHD) simulations and a realistic degradation to the level of the observed data. The definition of a merit function allows the archive to be searched for the synthetic Stokes profiles that best match the observed profiles. In contrast to traditional Stokes inversion codes, which solve the Unno-Rachkovsky equations for the polarized radiative transfer numerically and fit the Stokes profiles iteratively, the new technique provides the full set of atmospheric parameters. This gives us the ability to start an MHD simulation that takes the inversion result as an initial condition. After a relaxation process of half an hour solar time we obtain physically consistent MHD data sets with a target similar to the observation. The new MHD simulation is used to repeat the method in a second iteration, which further improves the match between observation and simulation, resulting in a factor of 2.2 lower mean {χ }2 value. One advantage of the new technique is that it provides the physical parameters on a geometrical height scale. It constitutes a first step toward inversions that give results consistent with the MHD equations.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls
AKMEL De G; BAHI L.C
2013-01-01
We study the dynamics of a piecewise (in time) distributed optimal control problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time.The long-time behavior of solutions for an optimal distributed control problem associated with the Generalized MHD equations is studied.First,a quasi-optimal solution for the Generalized MHD equations is constructed; this quasi-optimal solution possesses the decay (in time) properties.Then,some preliminary estimates for the long-time behavior of all solutions of Generalized MHD equations are derived.Next,the existence of a solution of optimal control problem is proved also optimality system is derived.Finally,the long-time decay properties for the optimal solutions is established.
G. García Segura
2000-01-01
Full Text Available Se presenta un escenario auto consistente para explicar la morfolog a de las nebulosas planetarias. El escenario es consistente con la distribuci on Gal actica de los diferentes tipos morfol ogicos. Este trabajo resuelve, por medio de efectos MHD, algunas de las caracter sticas controversiales que aparecen en las nebulosas planetarias. Estas caracter sticas incluyen la presencia de ujos axisim etricos y colimados, con una cinem atica que aumenta linealmente con la distancia y la existencia de morfolog as asim etricas tales como las de las nebulosas con simetr a de punto.
Retallick, F.D.
1978-04-01
This document establishes criteria to be utilized for the design of a pilot-scale (150 to 300 MW thermal) open cycle, coal-fired MHD/steam plant. Criteria for this Engineering Test Facility (ETF) are presented relative to plant siting, plant engineering and operations, MHD-ETF testing, costing and scheduling.
MHD turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, that spectral properties of distributed chaos in MHD turbulence with zero mean magnetic field are similar to those of hydrodynamic turbulence. An exception is MHD spontaneous breaking of space translational symmetry, when the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ has $\\beta=4/7$.
General Description of Ideal Tokamak MHD Instability Ⅱ
石秉仁
2002-01-01
In this subsequent study on general description of ideal tokamak MHD instability,the part Ⅱ, by using a coordinate with rectified magnetic field lines, the eigenmode equationsdescribing the low-mode-number toroidal Alfven modes (TAE and EAE) are derived through afurther expansion of the shear Alfven equation of motion.
Local potential analysis of MHD instability
Sen, K. K.; Wilson, S. J.
1985-02-01
The use of the local potential method for studying instabilities of MHD fluids is examined. The mathematical method is similar to that developed by the authors for studying the time-dependent radiative transfer problem and the radiative stability of interstellar masers. The scheme is based on the universal evolution criterion proposed by Glansdorff and Prigogine (1964) as demonstrated by Hays (1965) for the heat equation and Schechter and Himmelblau (1965) for the Benard problem in hydrodynamics. The scheme for securing stability criteria is demonstrated for two particular cases.
Test-field method for mean-field coefficients with MHD background
Rheinhardt, M
2010-01-01
Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results: Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electr...
Tala-Tebue, E.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kofane, T. C.
2014-06-01
Using the Jacobi elliptic functions and the alternative ( G'/ G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.
Brasil, Carlos Alexandre
2011-01-01
The most general form for the generator of quantum dynamical semigroups is the one proposed by Lindblad, which can be used in several approaches involving quantum mechanics for open systems, from analysis of noise and dissipation to fundamental aspects of the quantum theory of measurement. When dealing with a system interacting with its environment, the trace of the environmental degrees of freedom using the traditional approach of exponentiation of the Hamiltonian terms, originates prohibitive and difficult calculations. This paper presents an alternative analytic method to derive, through superoperator algebra and Nakajima-Zwanzig thermodynamic projectors, a compact and fairly simple master equation describing the reduced system dynamics. As a simple example of the present approach, we analyze a two-level system in contact with an environment, which allows us to observe the decoherence intensification by the interaction.
Huthmacher, Klaus [Department of Physics and OPTIMAS Research Center, University of Kaiserslautern (Germany); Molberg, Andreas K. [Department of Chemistry and OPTIMAS Research Center, University of Kaiserslautern (Germany); Rethfeld, Bärbel [Department of Physics and OPTIMAS Research Center, University of Kaiserslautern (Germany); Gulley, Jeremy R., E-mail: jgulley@kennesaw.edu [Department of Physics, Kennesaw State University, Kennesaw, GA 30144 (United States)
2016-10-01
A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.
Huthmacher, Klaus; Molberg, Andreas K.; Rethfeld, Bärbel; Gulley, Jeremy R.
2016-10-01
A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron-phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron-electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron-electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.
Laser-powered MHD generators for space application
Jalufka, N. W.
1986-10-01
Magnetohydrodynamic (MHD) energy conversion systems of the pulsed laser-supported detonation (LSD) wave, plasma MHD, and liquid-metal MHD (LMMHD) types are assessed for their potential as space-based laser-to-electrical power converters. These systems offer several advantages as energy converters relative to the present chemical, nuclear, and solar devices, including high conversion efficiency, simple design, high-temperature operation, high power density, and high reliability. Of these systems, the Brayton cycle liquid-metal MHD system appears to be the most attractive. The LMMHD technology base is well established for terrestrial applications, particularly with regard to the generator, mixer, and other system components. However, further research is required to extend this technology base to space applications and to establish the technology required to couple the laser energy into the system most efficiently. Continued research on each of the three system types is recommended.
李莉; 刘悦; 许欣洋; 夏新念
2012-01-01
A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Linearized resistivity MHD equations with plasma viscosity are adopted to describe our model, and the equations are solved numerically as an initial value problem. Some of the results are used as benchmark tests for the code, and then a series of equilibrium current profiles are used to simulate the bootstrap current profiles in actual experiments with a bump on tail. Thus the effects of these kinds of profiles on MHD instabilities in tokamaks are revealed. From the analysis of the numerical results, it is found that more plasma can be confined when the center of the current bump is closer to the plasma surface, and a higher and narrower current bump has a better stabilizing effect on the MHD instabilities.
MHD Technology Transfer, Integration and Review Committee
1992-01-01
This fifth semi-annual status report of the MHD Technology Transfer, Integration, and Review Committee (TTIRC) summarizes activities of the TTIRC during the period April 1990 through September 1990. It includes summaries and minutes of committee meetings, progress summaries of ongoing Proof-of-Concept (POC) contracts, discussions pertaining to technical integration issues in the POC program, and planned activities for the next six months.
Varado, N.; Braud, I.; Ross, P. J.
2003-04-01
A new numerical method for solving the 1D Richard's equation has been proposed by P. Ross (Agronomy J., 2003, in press). The Kirchhoff transform or degree of saturation is used instead of the classical matrix potential. The solution can be used both for saturated or non saturated soils. Hydraulic properties are described using the Brooks and Corey model. The soil is discretized into layers. Their thickness can be larger than in classical matrix potential methods, due to the use of a time and space varying weighing procedure for the calculation of fluxes between layers. This allows the use of a non iterative procedure, ensuring a very fast numerical solution. Extensive tests showed that the new method was very accurate for bare soils. The next step was the addition of a root extraction module in order to account for plant transpiration. Two root water uptake modules with compensation mechanisms in case of water stress were chosen from the literature. They express the transpiration source term in the Richards equation as a linear function of a potential transpiration and take into account water stress and its effects on plant transpiration. These modules were proposed first by Lai and Katul (Adv. Water Resour., 2000) and Li et al. (J. Hydrol., 2001). The new version of the model has been tested in a systematic way with several soils characteristics, climate forcings, and evapotranspiration calculation. Like the tests without vegetation, the SiSPAT (Simple Soil Plant Atmosphere Transfer) model was considered as a reference after implementation of the same roots modules. The numerical solution was also tested using a soybean data set. The variations and the cumulative values like drainage, water content, real transpiration and real evapotranspiration were in a good agreement with the SiSPAT modelling, with a relative error of less than 3%. The error on soil evaporation remained important (about 20%) on low cumulative values (less than 20mm), i.e. when LAI was close to
Standing Slow MHD Waves in Radiatively Cooling Coronal Loops
Al-Ghafri, Khalil Salim
2015-01-01
The standing slow magneto-acoustic oscillations in cooling coronal loops are investigated. There are two damping mechanisms which are considered to generate the standing acoustic modes in coronal magnetic loops namely thermal conduction and radiation. The background temperature is assumed to change temporally due to optically thin radiation. In particular, the background plasma is assumed to be radiatively cooling. The effects of cooling on longitudinal slow MHD modes is analytically evaluated by choosing a simple form of radiative function that ensures the temperature evolution of the background plasma due to radiation coincides with the observed cooling profile of coronal loops. The assumption of low-beta plasma leads to neglect the magnetic field perturbation and eventually reduces the MHD equations to a 1D system modelling longitudinal MHD oscillations in a cooling coronal loop. The cooling is assumed to occur on a characteristic time scale much larger than the oscillation period that subsequently enables...
Course 1: Accretion and Ejection-Related MHD
Heyvaerts, Jean
This lecture is an introduction to MHD. Relevant equations, both in the classical and special-relativistic regimes are derived. The magnetic field evolution is considered both in the perfect-MHD limit and when weak resistivity is present, giving rise to reconnection flows. A short section gives a flavour of dynamo theory. Examples of simple stationnary flows and equilibria are then presented. Stationnary, axisymmetric, rotating perfect-MHD winds and jets are discussed in some more detail. Their asymptotic structure is described. The last sections deal with small motions about an equilibrium and stability. These issues are illustrated by a few classical examples. The last section discusses linear aspects of the magneto-rotationnal instability.
Louis, J.F.
1977-12-01
Research and development in open-cycle coal-fired MHD power generation at Massachusetts Institute of Technology (MIT) is summarized. Progress is reported on the following tasks: (1) Establish chemical, thermal, and electrical data to guide materials selection, develop improved detail designs, and support performance analyses of MHD electrode modules and insulator materials; (2) parametrically investigate selected electrode properties of critical design importance in chemical, thermal, and electrical environments simulating a coal-fired MHD generator; (3) develop combustion data pertinent to the design of MHD combustors; this work is intended to determine the combustion characteristics of selected coal feedstock in terms of devolatilization kinetics, char characteristics, and combustion gas chemistry; (4) establish techniques for the analysis and understanding of critical MHD phenomena which have an important bearing on MHD generator performance; such phenomena include inter-electrode breakdown, time-dependent behavior, effective plasma properties and plasma inhomogeneities; (5) establish the operating characteristics of an MHD disk generator; (6) continue work on computer techniques for modeling and for design and cost analysis of MHD components and the overall system; (7) integrate the engineering data and design criteria, as applicable, which are developed in the above-listed tasks into a model of the MHD channel; (8) participate in technical support of the DOE MHD Project Office.
Louis, J.F.
1977-08-01
Research progress in open-cycle coal-fired MHD power generation at Massachusetts Institute of Technology (MIT) is reported. The scope and objectives of the MIT program are to: (1) Establish chemical, thermal, and electrical data to guide materials selection, develop improved detail designs, and support performance analyses of MHD electrode modules and insulator materials; (2) establish basic mechanical properties to guide detail design and fabrication of high field strength superconducting magnets for MHD applications; (3) parametrically investigate selected electrode properties of critical design importance in chemical, thermal, and electrical environments simulating a coal-fired MHD generator; (4) develop combustion data pertinent to the design of MHD combustors; (5) establish techniques for the analysis and understanding of critical MHD phenomena which have an important bearing on MHD generator performance; such phenomena include inter-electrode breakdown, time-dependent behavior, effective plasma properties and plasma inhomogeneities; (6) establish the operating characteristics of an MHD disk generator; (7) continue work on computer techniques for modeling and for design and cost analysis of MHD components and the overall system; (8) integrate the engineering data and design criteria, as applicable, which are developed in the above-listed tasks into a model of the MHD channel; (9) Participate in technical support of the ERDA MHD Project Office; (10) participate in the US/USSR Cooperative Program in MHD Power Generation. (11) During the summer of 1976, a short-term task in U-25 electrode screening was temporarily added to the scope of the contract. This effort involved screening tests, in the MIT MHD simulation facility of electrode modules and configurations intended for tests in the Soviet U-25 generator.
HIDENEK: An implicit particle simulation of kinetic-MHD phenomena in three-dimensional plasmas
Tanaka, Motohiko
1993-05-01
An advanced 'kinetic-MHD' simulation method and its applications to plasma physics are given in this lecture. This method is quite stable for studying strong nonlinear, kinetic processes associated with large space-scale, low-frequency electromagnetic phenomena of plasmas. A full set of the Maxwell equations, and the Newton-Lorentz equations of motion for particle ions and guiding-center electrons are adopted. In order to retain only the low-frquency waves and instabilities, implicit particle-field equations are derived. The present implicit-particle method is proved to reproduce the MHD eigenmodes such as Alfven, magnetosonic and kinetic Alfven waves in a thermally near-equilibrium plasma. In the second part of the lecture, several physics applications are shown. These include not only the growth of the instabilities of beam ions against the background plasmas and helical link of the current, but they also demonstrate nonlinear results such as pitch-angle scattering of the ions. Recent progress in the simulation of the Kelvin-Helmholtz instability is also presented with a special emphasis on the mixing of the plasma particles.
MHD Equilibria and Triggers for Prominence Eruption
Fan, Yuhong
2015-01-01
Magneto-hydrodynamic (MHD) simulations of the emergence of twisted magnetic flux tubes from the solar interior into the corona are discussed to illustrate how twisted and sheared coronal magnetic structures (with free magnetic energy), capable of driving filament eruptions, can form in the corona in emerging active regions. Several basic mechanisms that can disrupt the quasi-equilibrium coronal structures and trigger the release of the stored free magnetic energy are discussed. These include both ideal processes such as the onset of the helical kink instability and the torus instability of a twisted coronal flux rope structure and the non-ideal process of the onset of fast magnetic reconnections in current sheets. Representative MHD simulations of the non-linear evolution involving these mechanisms are presented.
Cosmic ray transport in MHD turbulence
Yan, Huirong
2007-01-01
Numerical simulations shed light onto earlier not trackable problem of magnetohydrodynamic (MHD) turbulence. They allowed to test the predictions of different models and choose the correct ones. Inevitably, this progress calls for revisions in the picture of cosmic ray (CR) transport. It also shed light on the problems with the present day numerical modeling of CR. In this paper we focus on the analytical way of describing CR propagation and scattering, which should be used in synergy with the numerical studies. In particular, we use recently established scaling laws for MHD modes to obtain the transport properties for CRs. We include nonlinear effects arising from large scale trapping, to remove the 90 degree divergence. We determine how the efficiency of the scattering and CR mean free path depend on the characteristics of ionized media, e.g. plasma $\\beta$, Coulomb collisional mean free path. Implications for particle transport in interstellar medium and solar corona are discussed. We also examine the perp...
MHD Simulations of the Plasma Flow in the Magnetic Nozzle
Smith, T. E. R.; Keidar, M.; Sankaran, K.; olzin, K. A.
2013-01-01
The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the
Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry
Furukawa, M
2016-01-01
Simulated annealing (SA) is applied for three-dimensional (3D) equilibrium calculation of ideal, low-beta reduced MHD in cylindrical geometry. The SA is based on the theory of Hamiltonian mechanics. The dynamical equation of the original system, low-beta reduced MHD in this study, is modified so that the energy changes monotonically while preserving the Casimir invariants in the artificial dynamics. An equilibrium of the system is given by an extremum of the energy, therefore SA can be used as a method for calculating ideal MHD equilibrium. Previous studies demonstrated that the SA succeeds to lead to various MHD equilibria in two dimensional rectangular domain. In this paper, the theory is applied to 3D equilibrium of ideal, low-beta reduced MHD. An example of equilibrium with magnetic islands, obtained as a lower energy state, is shown. Several versions of the artificial dynamics are developed that can effect smoothing.
Mikel' son, Yu.Ya.; Yakovich, A.T.; Pavlov, S.I.
1978-01-01
Turbulent stresses are considered in an incompressible fluid due to MHD flow induced within an axisymmetric region by electromagnetic forces on the basis of the linearized equation of motion as well as on the basis of the stress tensor in terms of average velocities and turbulent viscosity. The turbulent viscosity is treated according to the Boussinesq hypothesis (constant turbulent viscosity), according to the generalized Karman hypothesis (turbulent viscosity a function of the derivatives of the velocity components with respect to the respective coordinates), or as the product of its coordinate functions. The results of numerical calculations indicate a close agreement between all these formulas for an average MHD flow and experimental data. Calculations including this additional turbulent force, appropriately related to the flow parameters, are applicable to the design of liquid-metal devices. 7 references, 3 figures.
Investigations on application of multigrid method to MHD equilibrium analysis
Ikuno, Soichiro [Faculty of Engineering Science, School of Engineering, Tokyo Univ. of Technology, Tokyo (Japan)
2000-06-01
The potentiality of application for Multi-grid method to MHD equilibrium analysis is investigated. The nonlinear eigenvalue problem often appears when the MHD equilibria are determined by solving the Grad-Shafranov equation numerically. After linearization of the equation, the problem is solved by use of the iterative method. Although the Red-Black SOR method or Gauss-Seidel method is often used for the solution of the linearized equation, it takes much CPU time to solve the problem. The Multi-grid method is compared with the SOR method for the Poisson Problem. The results of computations show that the CPU time required for the Multi-grid method is about 1000 times as small as that for the SOR method. (author)
Divergence-free MHD Simulations with the HERACLES Code
Vides J.
2013-12-01
Full Text Available Numerical simulations of the magnetohydrodynamics (MHD equations have played a significant role in plasma research over the years. The need of obtaining physical and stable solutions to these equations has led to the development of several schemes, all requiring to satisfy and preserve the divergence constraint of the magnetic field numerically. In this paper, we aim to show the importance of maintaining this constraint numerically. We investigate in particular the hyperbolic divergence cleaning technique applied to the ideal MHD equations on a collocated grid and compare it to the constrained transport technique that uses a staggered grid to maintain the property. The methods are implemented in the software HERACLES and several numerical tests are presented, where the robustness and accuracy of the different schemes can be directly compared.
The Modified Magnetohydrodynamical Equations
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.
Standing Slow MHD Waves in Radiatively Cooling Coronal Loops
K. S. Al-Ghafri
2015-06-01
The standing slow magneto-acoustic oscillations in cooling coronal loops are investigated. There are two damping mechanisms which are considered to generate the standing acoustic modes in coronal magnetic loops, namely, thermal conduction and radiation. The background temperature is assumed to change temporally due to optically thin radiation. In particular, the background plasma is assumed to be radiatively cooling. The effects of cooling on longitudinal slow MHD modes is analytically evaluated by choosing a simple form of radiative function, that ensures the temperature evolution of the background plasma due to radiation, coincides with the observed cooling profile of coronal loops. The assumption of low-beta plasma leads to neglecting the magnetic field perturbation and, eventually, reduces the MHD equations to a 1D system modelling longitudinal MHD oscillations in a cooling coronal loop. The cooling is assumed to occur on a characteristic time scale, much larger than the oscillation period that subsequently enables using the WKB theory to study the properties of standing wave. The governing equation describing the time-dependent amplitude of waves is obtained and solved analytically. The analytically derived solutions are numerically evaluated to give further insight into the evolution of the standing acoustic waves. We find that the plasma cooling gives rise to a decrease in the amplitude of oscillations. In spite of the reduction in damping rate caused by rising the cooling, the damping scenario of slow standing MHD waves strongly increases in hot coronal loops.
An advanced implicit solver for MHD
Udrea, Bogdan
A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel
Annular MHD Physics for Turbojet Energy Bypass
Schneider, Steven J.
2011-01-01
The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated assuming weakly ionized flows obtained from pulsed nanosecond discharges. The equations for a 1-D, axisymmetric MHD generator/accelerator are derived and numerically integrated to determine the generator/accelerator performance characteristics. The concept offers a shockless means of interacting with high speed inlet flows and potentially offers variable inlet geometry performance without the complexity of moving parts simply by varying the generator loading parameter. The cycle analysis conducted iteratively with a spike inlet and turbojet flying at M = 7 at 30 km altitude is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at an aggressive 2200 deg K. The annular MHD Hall generator/accelerator is L = 3 m in length with a B(sub r) = 5 Tesla magnetic field and a conductivity of sigma = 5 mho/m for the generator and sigma= 1.0 mho/m for the accelerator. The calculated isentropic efficiency for the generator is eta(sub sg) = 84 percent at an enthalpy extraction ratio, eta(sub Ng) = 0.63. The calculated isentropic efficiency for the accelerator is eta(sub sa) = 81 percent at an enthalpy addition ratio, eta(sub Na) = 0.62. An assessment of the ionization fraction necessary to achieve a conductivity of sigma = 1.0 mho/m is n(sub e)/n = 1.90 X 10(exp -6), and for sigma = 5.0 mho/m is n(sub e)/n = 9.52 X 10(exp -6).
Variational approach to low-frequency kinetic-MHD in the current coupling scheme
Burby, J W
2016-01-01
Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with an ensemble of hot particles, which is described by a kinetic equation. When the Vlasov description is adopted for the energetic particles, different Vlasov-MHD models have been shown to lack an exact energy balance, which was recently recovered by the introduction of non-inertial force terms in the kinetic equation. These force terms arise from fundamental approaches based on Hamiltonian and variational methods. In this work we apply Hamilton's variational principle to formulate new current-coupling kinetic-MHD models in the low-frequency approximation (i.e. large Larmor frequency limit). More particularly, we formulate current-coupling hybrid schemes, in which energetic particle dynamics are expressed in either guiding-center or gyrocenter coordinates.
Variational approach to low-frequency kinetic-MHD in the current-coupling scheme
Tronci, Cesare; Burby, Joshua
2016-10-01
Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with an ensemble of hot particles, which is described by a kinetic equation. When the Vlasov description is adopted for the energetic particles, different Vlasov-MHD models have been shown to lack an exact energy balance, unless non-inertial force terms are inserted in the kinetic equation. These force terms arise from fundamental approaches based on Hamiltonian and variational methods. In this work we apply Hamilton's variational principle to formulate new current-coupling kinetic-MHD models in the low-frequency approximation (i.e. large Larmor frequency limit). More particularly, we formulate current-coupling hybrid schemes, in which energetic particle dynamics are expressed in either guiding-center or gyrocenter coordinates. Financial support by the Leverhulme Trust Research Project Grant No. 2014-112 is greatly acknowledged.
Three-dimensional fluid and electrodynamic modeling for MHD DCW channels
Liu, B. L.; Lineberry, J. T.; Schmidt, H. J.
1983-01-01
A three dimensional, numerical solution for modeling diagonal conducting wall (DCW) magnetohydrodynamic (MHD) generators is developed and discussed. Cross plane gasdynamic and electrodynamic profiles are computed considering coupled MHD flow and electrical phenomena. A turbulent transport model based on the mixing length theory is used to deal with wall roughness generated turbulence effects. The infinitely fine electrode segmentation formulation is applied to simplify the governing electrical equations. Calculations show the development of distorted temperature and velocity profiles under influence of magnetohydrodynamic interaction. Since both sidewall and electrode wall boundary losses are treated, the results furnish a realistic representation of MHD generator behavior.
Louis, J.F.
1977-10-01
Current research and development in open-cycle coal-fired MHD power generation at Massachusetts Institute of Technology is presented. Progress is reported on the following tasks: (1) Establish chemical, thermal, and electrical data to guide materials selection, develop improved detail designs, and support performance analyses of MHD electrode modules and insulator materials; (2) Parametrically investigate selected electrode properties of critical design importance in chemical, thermal, and electrical environments simulating a coal-fired MHD generator; (3) Develop combustion data pertinent to the design of MHD combustors; this work is intended to determine the combustion characteristics of selected coal feed stock in terms of devolatilization kinetics, char characteristics, and combustion gas chemistry; (4) Establish techniques for the analysis and understanding of critical MHD phenomena which have an important bearing on MHD generator performance; such phenomena include inter-electrode breakdown, time-dependent behavior, effective plasma properties and plasma inhomogeneities; (5) Establish the operating characteristics of an MHD disk generator; (6) Continue work on computer techniques for modeling and for design and cost analysis of MHD components and the overall system; (7) Integrate the engineering data and design criteria, as applicable, which are developed in the above-listed tasks into a model of the MHD channel.
Unified Description of Tokamak Ideal MHD Instabilities（I）
石秉仁
2002-01-01
By using a coordinate system associated with magnetic surfaces,a unified eigenmode equation for describing the tokamak ideal MHD instabilities is derived in the shear-Alfven approximation.Based on this equation having a general operator form,the eigen-mode equation governing the large-scale perturbation (such as the kink mode,the low-n ballooning mode and the Alfven mode) and small-scale perturbation(such as the high-n ballooning mode,the local mode) can be further deduced.In the first part of the present study,the small-scale perturbation is discussed in detail.
Unified Description of Tokamak Ideal MHD Instabilities (Ⅰ)
石秉仁
2002-01-01
By using a coordinate system associated with magnetic surfaces, a unified eigen mode equation for describing the tokamak ideal MHD instabilities is derived in the shear-Alfven approximation. Based on this equation having a general operator form, the eigen-mode equation governing the large-scale perturbation (such as the kink mode, the low-n ballooning mode and the Alfven mode) and small-scale perturbation (such as the high-n ballooning mode, the local mode)can be further deduced. In the first part of the present study, the small-scale perturbation is discussed in detail.
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
The MHD simulations of 3D magnetic reconnection near null point of magnetic configurations
Bulanov, S.V. [Institute of General Physics, Russian Academy of Sciences, Moscow (Russian Federation); Echkina, E.Yu; Inovenkov, I.N.; Pichushkin, V.V. [Moscow State University, Moscow (Russian Federation); Pegoraro, F. [Dipartimento di Fisica dell' Universit' a di Pisa and INFM (Italy)
2000-07-01
We investigate 3D plasma flow in the vicinities of critical points of magnetic configurations. The study is based on the analysis of exact self-similar solution of the MHD equations and 3D computer simulations. Both the analytical solution and 3D MHD simulations demonstrate appearance of singular distribution of the electric current density near the magnetic field separatrix surfaces of the form of the current and vortex sheets. (author)
TRIM: A finite-volume MHD algorithm for an unstructured adaptive mesh
Schnack, D.D.; Lottati, I.; Mikic, Z. [Science Applications International Corp., San Diego, CA (United States)] [and others
1995-07-01
The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.
Simulation of three-dimensional nonideal MHD flow at high magnetic Reynolds number
无
2010-01-01
A conservative TVD scheme is adopted to solve the equations governing the three-dimensional flow of a nonideal compressible conducting fluid in a magnetic field.The eight-wave equations for magnetohydrodynamics(MHD) are proved to be a non-strict hyperbolic system,therefore it is difficult to develop its eigenstructure.Powell developed a new set of equations which cannot be numerically simulated by conservative TVD scheme directly due to its non-conservative form.A conservative TVD scheme augmented with a new set of eigenvectors is proposed in the paper.To validate this scheme,1-D MHD shock tube,unsteady MHD Rayleigh problem and steady MHD Hartmann problem for different flow conditions are simulated.The simulated results are in good agreement with the existing analytical results.So this scheme can be used to effectively simulate high-conductivity fluids such as cosmic MHD problem and hypersonic MHD flow over a blunt body,etc.
GPSAP/V2 with applications to open-cycle MHD systems
Geyer, H. K.
1981-01-01
A preprocessor technique for performing lumped component system analysis is presented. By employing simple preprocessor statements, system configurations, constraints, and objective functions can easily be established and analyzed. Use is made of M.J.D. Powell's hybrid equation solver and his sequential quadratic programming method for solving constrained optimization problems. The use of recursive calling capability in both equation solver and optimizer makes possible a fast and efficient general methodology for decomposition and analysis of systems. By retaining the build-up Jacobians and Hessians of the constraints and objective functions, and effective means of reducing computing time is developed during parameter studies. Also presented is a collection of simple first-order models used in open-cycle MHD (OCMHD) applications. Examples of simple system configurations and their analysis are included.
Protostellar collapse and fragmentation using an MHD GADGET
Bürzle, Florian; Stasyszyn, Federico; Greif, Thomas; Dolag, Klaus; Klessen, Ralf S; Nielaba, Peter
2010-01-01
Although the influence of magnetic fields is regarded as vital in the star formation process, only a few magnetohydrodynamics (MHD) simulations have been performed on this subject within the smoothed particle hydrodynamics (SPH) method. This is largely due to the unsatisfactory treatment of non-vanishing divergence of the magnetic field. Recently smoothed particle magnetohydrodynamics (SPMHD) simulations based on Euler potentials have proven to be successful in treating MHD collapse and fragmentation problems, however these methods are known to have some intrinsical difficulties. We have performed SPMHD simulations based on a traditional approach evolving the magnetic field itself using the induction equation. To account for the numerical divergence, we have chosen an approach that subtracts the effects of numerical divergence from the force equation, and additionally we employ artificial magnetic dissipation as a regularization scheme. We apply this realization of SPMHD to a widely known setup, a variation o...
Ikhdair, Sameer M
2011-01-01
The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital angular momentum number l and dimensional space D. The relativistic/non-relativistic energy spectrum equation and the corresponding unnormalized radial wave functions, in terms of the Jacobi polynomials P_{n}^{({\\alpha},{\\beta})}(z), where {\\alpha}>-1, {\\beta}>-1 and z\\in[-1,+1] or the generalized hypergeometric functions _{2}F_{1}(a,b;c;z), are found. The Nikiforov-Uvarov (NU) method is used in the solution. The solutions of the Eckart, Rosen-Morse, Hulth\\'en and Woods-Saxon potential models can be easily obtained from these solutions. Our results are identical with those ones appearing in the literature. Finally, under the PT-symmetry, we can easily obtain the bound state solutions of the trigonometric Rosen-Morse potential.
Generalized reduced magnetohydrodynamic equations
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.
Problems in nonlinear resistive MHD
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Variable properties of MHD third order fluid with peristalsis
Latif, T.; Alvi, N.; Hussain, Q.; Asghar, S.
This article addresses the impact of temperature dependent variable properties on peristaltic flow of third order fluid in a symmetric channel. The MHD fluid and viscous dissipation effects are taken into account. Assumptions of long wavelength and low Reynolds number are employed to model the problem. The governing nonlinear coupled equations are solved using perturbation method. Approximate solutions are obtained for the stream function, temperature and pressure gradient. The results are graphically analyzed with respect to various pertinent parameters.
Buoyancy induced MHD transient mass transfer flow with thermal radiation
N. Ahmed
2016-09-01
Full Text Available The problem of a transient MHD free convective mass transfer flow past an infinite vertical porous plate in presence of thermal radiation is studied. The fluid is considered to be a gray, absorbing-emitting radiating but non-scattered medium. Analytical solutions of the equations governing the flow problem are obtained. The effects of mass transfer, suction, radiation and the applied magnetic field on the flow and transport characteristics are discussed through graphs.
The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models
Hesse, Michael; Birn, Joachim
2011-01-01
Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.
Model problem of MHD flow in a lithium blanket
Cherepanov, V.Y.
1978-01-01
A model problem is considered for a feasibility study concerning controlled MHD flow in the blanket of a Tokamak nuclear reactor. The fundamental equations for the steady flow of an incompressible viscous fluid in a uniform transverse magnetic field are solved in rectangular coordinates, in the zero-induction approximation and with negligible induced currents. A numerical solution obtained for a set of appropriate boundary constraints establishes the conditions under which no stagnation zones will be formed.
A new MHD-assisted Stokes inversion technique
Riethmüller, T L; Barthol, P; Gandorfer, A; Gizon, L; Hirzberger, J; van Noort, M; Rodríguez, J Blanco; Iniesta, J C Del Toro; Suárez, D Orozco; Schmidt, W; Pillet, V Martínez; Knölker, M
2016-01-01
We present a new method of Stokes inversion of spectropolarimetric data and evaluate it by taking the example of a SUNRISE/IMaX observation. An archive of synthetic Stokes profiles is obtained by the spectral synthesis of state-of-the-art magnetohydrodynamics (MHD) simulations and a realistic degradation to the level of the observed data. The definition of a merit function allows the archive to be searched for the synthetic Stokes profiles that match the observed profiles best. In contrast to traditional Stokes inversion codes, which solve the Unno-Rachkovsky equations for the polarized radiative transfer numerically and fit the Stokes profiles iteratively, the new technique provides the full set of atmospheric parameters. This gives us the ability to start an MHD simulation that takes the inversion result as initial condition. After a relaxation process of half an hour solar time we obtain physically consistent MHD data sets with a target similar to the observation. The new MHD simulation is used to repeat t...
MHD discontinuities in solar flares: continuous transitions and plasma heating
Ledentsov, Leonid; Somov, Boris
The conservation laws on a surface of discontinuity in the ideal magnetohydrodynamics (MHD) allow changing a discontinuity type with gradual (continuous) changes in conditions of plasma. Then there are the so-called transition solutions that satisfy simultaneously two types of discontinuities. We obtain all transition solutions on the basis of a complete system of boundary conditions for the MHD equations. We also found an expression describing a jump of internal energy of the plasma flowing through the discontinuity. It allows, firstly, to construct a generalized scheme of possible transitions between MHD discontinuities, and secondly, to examine the dependence of plasma heating by plasma density and configuration of the magnetic field near the surface of the discontinuity (i.e., by the type of the MHD discontinuity). The problem of the heating of "superhot" plasma (with the electron temperature is greater than 10 keV) in solar flares are discussed. It is shown that the best conditions for heating are carried out in the vicinity of the reconnecting current layer near the areas of reverse currents. Bibl.: B.V.Somov. Plasma Astrophysics, Part II: Reconnection and Flares, Second Edition. (New York: Springer SBM, 2013).
Magnetic stresses in ideal MHD plasmas
Jensen, V.O.
1995-01-01
and it is shown that the resulting magnetic forces on a finite volume element can be obtained by integrating the magnetic stresses over the surface of the element. The concept is used to rederive and discuss the equilibrium conditions for axisymmetric toroidal plasmas, including the virial theorem......The concept of magnetic stresses in ideal MHD plasma theory is reviewed and revisited with the aim of demonstrating its advantages as a basis for calculating and understanding plasma equilibria. Expressions are derived for the various stresses that transmit forces in a magnetized plasma...
罗振东; 朱江; 曾庆存; 谢正辉
2004-01-01
An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Applications of a finite-volume algorithm for incompressible MHD problems
Vantieghem, S.; Sheyko, A.; Jackson, A.
2016-02-01
We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of geometries. Our method implements a mixed Adams-Bashforth/Crank-Nicolson scheme for the nonlinear terms in the MHD equations and we prove that it is stable independent of the time step. To ensure that the solenoidal condition is met for the magnetic field, we use a method whereby a pseudo-pressure is introduced into the induction equation; since we are concerned with incompressible flows, the resulting Poisson equation for the pseudo-pressure is solved alongside the equivalent Poisson problem for the velocity field. We validate our code in a variety of geometries including periodic boxes, spheres, spherical shells, spheroids and ellipsoids; for the finite geometries we implement the so-called ferromagnetic or pseudo-vacuum boundary conditions appropriate for a surrounding medium with infinite magnetic permeability. This implies that the magnetic field must be purely perpendicular to the boundary. We present a number of comparisons against previous results and against analytical solutions, which verify the code's accuracy. This documents the code's reliability as a prelude to its use in more difficult problems. We finally present a new simple drifting solution for thermal convection in a spherical shell that successfully sustains a magnetic field of simple geometry. By dint of its rapid stabilization from the given initial conditions, we deem it suitable as a benchmark against which other self-consistent dynamo codes can be tested.
MHD Field Line Resonances and Global Modes in Three-Dimensional Magnetic Fields
C.Z. Cheng
2002-05-30
By assuming a general isotropic pressure distribution P = P (y,a), where y and a are three-dimensional scalar functions labeling the field lines with B = -y x -a, we have derived a set of MHD eigenmode equations for both global MHD modes and field line resonances (FLR). Past MHD theories are restricted to isotropic pressures with P = P (y only). The present formulation also allows the plasma mass density to vary along the field line. The linearized ideal-MHD equations are cast into a set of global differential equations from which the field line resonance equations of the shear Alfvin waves and slow magnetosonic modes are naturally obtained for general three-dimensional magnetic field geometries with flux surfaces. Several new terms associated with the partial derivative of P with respect to alpha are obtained. In the FLR equations, a new term is found in the shear Alfvin FLR equation due to the geodesic curvature and the pressure gradient in the poloidal flux surface. The coupling between the shear Alfvin waves and the magnetosonic waves is through the combined effects of geodesic magnetic field curvature and plasma pressure as previously derived. The properties of the FLR eigenfunctions at the resonance field lines are investigated, and the behavior of the FLR wave solutions near the FLR surface are derived. Numerical solutions of the FLR equations for three-dimensional magnetospheric fields in equilibrium with high plasma pressure will be presented in a future publication.
Huang, Z.; Toth, G.; Gombosi, T. I.; Jia, X.; Rubin, M.; Hansen, K. C.; Fougere, N.; Bieler, A. M.; Shou, Y.; Altwegg, K.; Combi, M. R.; Tenishev, V.
2015-12-01
The neutral and plasma environment is critical in understanding the interaction of comet Churyumov-Gerasimenko (CG), the target of the Rosetta mission, and the solar wind. To serve this need and support the Rosetta mission, we develop a 3-D four fluid model, which is based on BATS-R-US within the SWMF (Space Weather Modeling Framework) that solves the governing multi-fluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates different mass loading processes, including photo and electron impact ionization, charge exchange, dissociative ion-electron recombination, and collisional interactions between different fluids. We simulate the near nucleus plasma and neutral gas environment near perihelion with a realistic shape model of CG and compare our simulation results with Rosetta observations.
Ideal MHD(-Einstein) Solutions Obeying The Force-Free Condition
Chu, Yi-Zen
2016-01-01
We find two families of analytic solutions to the ideal magnetohydrodynamics (iMHD) equations, in a class of 4-dimensional (4D) curved spacetimes. The plasma current is null, and as a result, the stress-energy tensor of the plasma itself can be chosen to take a cosmological-constant-like form. Despite the presence of a plasma, the force-free condition - where the electromagnetic current is orthogonal to the Maxwell tensor - continues to be maintained. Moreover, a special case of one of these two families leads us to a fully self-consistent solution to the Einstein-iMHD equations: we obtain the Vaidya-(anti-)de Sitter metric sourced by the plasma and a null electromagnetic stress tensor. We also provide a Mathematica code that researchers may use to readily verify analytic solutions to these iMHD equations in any curved 4D geometry.
A New MHD Code with Adaptive Mesh Refinement and Parallelization for Astrophysics
Jiang, R L; Chen, P F
2012-01-01
A new code, named MAP, is written in Fortran language for magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for computing the MHD part, namely, modified Mac Cormack Scheme (MMC), Lax-Friedrichs scheme (LF) and weighted essentially non-oscillatory (WENO) scheme. All of them are second order, two-step, component-wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann solvers are also equipped. A high resolution can be achieved by the hierarchical block-structured AMR mesh. We use the extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced by the scheme in the magnetic induction equation. The numerical algorithms for the non-ideal terms, e.g., the resistivity and the thermal conduction, are also equipped in the MAP code. The details of the AMR and MPI algorithms are d...
Variational approach to low-frequency kinetic-MHD in the current coupling scheme
Burby, Joshua W.; Tronci, Cesare
2017-04-01
Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with an ensemble of hot particles, which obeys a kinetic equation. In this work we apply Hamilton’s variational principle to formulate new current-coupling kinetic-MHD models in the low-frequency approximation (i.e. large Larmor frequency limit). More particularly, we formulate current-coupling schemes, in which energetic particle dynamics are expressed in either guiding center or gyrocenter coordinates. When guiding center theory is used to model the hot particles, we show how energy conservation requires corrections to the standard magnetization term. On the other hand, charge and momentum conservation in gyrokinetic-MHD lead to extra terms in the usual definition of the hot current density as well as modifications to conventional gyrocenter dynamics. All these new features arise naturally from the underlying variational structure of the proposed models.
Technical support for open-cycle MHD program. Progress report, April-June 1978
Bomkamp, D H [ed.
1979-07-01
The support program for open-cycle MHD at Argonne National Laboratory is developing the analytical tools needed to investigate the performance of the major components in the combined cycle MHD/steam power system. The analytical effort is centered on the primary components of the system that are unique to MHD and also on the integration of these analytical representations into a model of the entire power producing system. The project activities currently include modeling of the combustor, MHD channel, slag separator and the high temperature air heater. In addition, these models are combined into a complete system model which is presently capable of carrying out optimizations of the entire system on either thermodynamic efficiency or cost of electrical power. Also, in support of other aspects of the open-cycle program, test plans are developed and facility and program reviews are provided upon request to support the needs and requirements of the DOE/MHD Division.
Formation and collimation of relativistic MHD jets - simulations and radio maps
Fendt, Christian; Sheikhnezami, Somayeh
2013-01-01
We present results of magnetohydrodynamic (MHD) simulations of jet formation and propagation, discussing a variety of astrophysical setups. In the first approach we consider simulations of relativistic MHD jet formation, considering jets launched from the surface of a Keplerian disk, demonstrating numerically - for the first time - the self-collimating ability of relativistic MHD jets. We obtain Lorentz factors up to about 10 while acquiring a high degree of collimation of about 1 degree. We then present synchrotron maps calculated from the intrinsic jet structure derived from the MHD jet formation simulation. We finally present (non-relativistic) MHD simulations of jet lauching, treating the transition between accretion and ejection. These setups include a physical magnetic diffusivity which is essential for loading the accretion material onto the outflow. We find relatively high mass fluxes in the outflow, of the order of 20-40 % of the accretion rate.
MHD control in burning plasmas MHD control in burning plasmas
Donné, Tony; Liang, Yunfeng
2012-07-01
Fusion physics focuses on the complex behaviour of hot plasmas confined by magnetic fields with the ultimate aim to develop a fusion power plant. In the future generation of tokamaks like ITER, the power generated by the fusion reactions substantially exceeds the external input power (Pfusion}/Pin >= 10). When this occurs one speaks of a burning plasma. Twenty per cent of the generated fusion power in a burning plasma is carried by the charged alpha particles, which transfer their energy to the ambient plasma in collisions, a process called thermalization. A new phenomenon in burning plasmas is that the alpha particles, which form a minority but carry a large fraction of the plasma kinetic energy, can collectively drive certain types of magneto-hydrodynamic (MHD) modes, while they can suppress other MHD modes. Both types of MHD modes can have desirable effects on the plasma, as well as be detrimental to the plasma. For example, the so-called sawtooth instability, on the one hand, is largely responsible for the transport of the thermalized alpha particles out of the core, but, on the other hand, may result in the loss of the energetic alphas before they have fully thermalized. A further undesirable effect of the sawtooth instability is that it may trigger other MHD modes such as neoclassical tearing modes (NTMs). These NTMs, in turn, are detrimental to the plasma confinement and in some cases may even lead to disruptive termination of the plasma. At the edge of the plasma, finally, so-called edge localized modes or ELMs occur, which result in extremely high transient heat and particle loads on the plasma-facing components of a reactor. In order to balance the desired and detrimental effects of these modes, active feedback control is required. An additional complication occurs in a burning plasma as the external heating power, which is nowadays generally used for plasma control, is small compared to the heating power of the alpha particles. The scientific challenge
Magnetic levitation and MHD propulsion
Tixador, P.
1994-04-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried out in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ...) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. Depuis quelques années nous assistons à un redémarrage de programmes concernant la lévitation et la propulsion supraconductrices. Différents systèmes supraconducteurs de lévitation et de propulsion seront décrits en examinant plus particulièrement l'aspect électromagnétique. Quelques programmes à travers le monde seront abordés. Les trains à sustentation magnétique pourraient constituer un nouveau mode de transport terrestre à vitesse élevée (500 km/h) pour le 21^e siècle. Les japonais n'ont cessé de s'intéresser à ce système avec bobine supraconductrice. Ils envisagent un stade préindustriel avec la construction d'une ligne de 43 km. En 1991 un programme américain pour une durée de six ans a été lancé pour évaluer les performances des systèmes à lévitation pour le transport aux Etats Unis. La MHD (Magnéto- Hydro-Dynamique) présente des avantages intéressants pour la propulsion navale et un regain d'intérêt apparaît à l'heure actuelle. Le japon se situe là encore à la pointe des d
罗振东; 朱江; 曾庆存; 谢正辉
2004-01-01
The mixed finite element (MFE) methods for a shallow water equation system consisting of water dynamics equations, silt transport equation, and the equation of bottom topography change were derived. A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established. The existence and convergence of MFE solution of the discrete current velocity, elevation of the bottom topography, thickness of fluid column, and mass rate of sediment is demonstrated.
A heuristic model for MRI turbulent stresses in Hall MHD
Lingam, M
2016-01-01
Although the Shakura-Sunyaev $\\alpha$ viscosity prescription has been highly successful in characterizing myriad astrophysical environments, it has proven to be partly inadequate in modelling turbulent stresses driven by the MRI. Hence, we adopt the approach employed by \\citet{GIO03}, but in the context of Hall magnetohydrodynamics (MHD), to study MRI turbulence. We utilize the exact evolution equations for the stresses, and the non-linear terms are closed through the invocation of dimensional analysis and physical considerations. We demonstrate that the inclusion of the Hall term leads to non-trivial results, including the modification of the Reynolds and Maxwell stresses, as well as the (asymptotic) non-equipartition between the kinetic and magnetic energies; the latter issue is also addressed via the analysis of non-linear waves. The asymptotic ratio of the kinetic and magnetic energies is shown to be \\emph{independent} of the choice of initial conditions, but it is governed by the \\emph{Hall parameter}. W...
Ferreira, J
2006-01-01
This is a doctorate level lecture on the physics of accretion discs driving magnetically self-confined jets, usually referred to in the literature as disc winds. I will first review the governing magnetohydrodynamic equations and then discuss their physical content. At that level, necessary conditions to drive jets from keplerian accretion discs can already be derived. These conditions are validated with self-similar calculations of accretion-ejection structures. In a second part, I will critically discuss the biases introduced when using self-similarity as well as some other questions such as: Are these systems really unstable? Can a standard accretion disc provide the conditions to launch jets in its innermost parts? What is the difference between X-winds and disc-winds? Finally, the magnetic interaction between a protostar and its circumstellar disc will be discussed with a focus on stellar spin down.
Turbulent MHD transport coefficients - An attempt at self-consistency
Chen, H.; Montgomery, D.
1987-01-01
In this paper, some multiple scale perturbation calculations of turbulent MHD transport coefficients begun in earlier papers are first completed. These generalize 'alpha effect' calculations by treating the velocity field and magnetic field on the same footing. Then the problem of rendering such calculations self-consistent is addressed, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg for the Navier-Stokes case. The method also borrows from Kraichnan's direct interaction approximation. The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous 'alpha effect' and 'beta effect' coefficients emerge as limiting cases. A treatment of the inertial range can also be given, consistent with a -5/3 energy spectrum power law. In the Navier-Stokes limit, a value of 1.72 is extracted for the Kolmogorov constant. Further applications to MHD are possible.
Turning the resistive MHD into a stochastic field theory
M. Materassi
2008-08-01
Full Text Available Classical systems stirred by random forces of given statistics may be described via a path integral formulation in which their degrees of freedom are stochastic variables themselves, undergoing a multiple-history probabilistic evolution. This framework seems to be easily applicable to resistive Magneto-Hydro-Dynamics (MHD. Indeed, MHD equations form a dynamic system of classical variables in which the terms representing the density, the pressure and the conductivity of the plasma are irregular functions of space and time when turbulence occurs. By treating those irregular terms as random stirring forces, it is possible to introduce a Stochastic Field Theory which should represent correctly the impulsive phenomena caused by the spece- and time-irregularity of plasma turbulence. This work is motivated by the recent observational evidences of the crucial role played by stochastic fluctuations in space plasmas.
Turning the resistive MHD into a stochastic field theory
Materassi, M.; Consolini, G.
2008-08-01
Classical systems stirred by random forces of given statistics may be described via a path integral formulation in which their degrees of freedom are stochastic variables themselves, undergoing a multiple-history probabilistic evolution. This framework seems to be easily applicable to resistive Magneto-Hydro-Dynamics (MHD). Indeed, MHD equations form a dynamic system of classical variables in which the terms representing the density, the pressure and the conductivity of the plasma are irregular functions of space and time when turbulence occurs. By treating those irregular terms as random stirring forces, it is possible to introduce a Stochastic Field Theory which should represent correctly the impulsive phenomena caused by the spece- and time-irregularity of plasma turbulence. This work is motivated by the recent observational evidences of the crucial role played by stochastic fluctuations in space plasmas.
Seismic Halos Around Active Regions: An MHD Theory
Hanasoge, Shravan M
2007-01-01
Comprehending the manner in which magnetic fields affect propagating waves is a first step toward the helioseismic construction of accurate models of active region sub-surface structure and dynamics. Here, we present a numerical method to compute the linear interaction of waves with magnetic fields embedded in a solar-like stratified background. The ideal Magneto-Hydrodynamic (MHD) equations are solved in a 3-dimensional box that straddles the solar photosphere, extending from 35 Mm within to 1.2 Mm into the atmosphere. One of the challenges in performing these simulations involves generating a Magneto-Hydro-Static (MHS) state wherein the stratification assumes horizontal inhomogeneity in addition to the strong vertical stratification associated with the near-surface layers. Keeping in mind that the aim of this effort is to understand and characterize linear MHD interactions, we discuss a means of computing statically consistent background states. Results from a simulation of waves interacting with a flux tub...
MHD rotation of electrically conducting media in crossed fields
Nikitin, N.V.
1978-01-01
A nonlinear scheme is developed for calculating the hydrodynamic characteristics of MHD flow in a cylindrical vessel of finite dimensions, in an electric field and a magnetic field crossing each other. The incompressible fluid is assumed to have a constant viscosity and electrical conductivity. The solution to the complete system of MHD equations is expanded in a series with respect to the magnetic Reynolds number, for a large hydrodynamic Reynolds number. And rather simple engineering formulas for calculating the velocity field and the pressure field are derived by the Karman-Pohlhausen method of integral relations. The results are compared with experimental data pertaining to a model helium-xenon discharge chamber with distribution of the Lorentz force causing the plasma to rotate as a quasi-solid. 15 references, 5 figures, 1 table.
Integral Constraints and MHD Stability
Jensen, T. H.
2003-10-01
Determining stability of a plasma in MHD equilibrium, energetically isolated by a conducting wall, requires an assumption on what governs the dynamics of the plasma. One example is the assumption that the plasma obeys ideal MHD, leading to the well known ``δ W" criteria [I. Bernstein, et al., Proc. Roy. Soc. London A244, 17 (1958)]. A radically different approach was used by Taylor [J.B. Taylor, Rev. Mod. Phys. 58, 741 (1986)] in assuming that the dynamics of the plasma is restricted only by the requirement that helicity, an integral constant associated with the plasma, is conserved. The relevancy of Taylor's assumption is supported by the agreement between resulting theoretical results and experimental observations. Another integral constraint involves the canonical angular momentum of the plasma particles. One consequence of using this constraint is that tokamak plasmas have no poloidal current in agreement with some current hole tokamak observations [T.H. Jensen, Phys. Lett. A 305, 183 (2002)].
Birzvalk, Yu.
1978-01-01
The shunting ratio and the local shunting ratio, pertaining to currents induced by a magnetic field in a flow channel, are properly defined and systematically reviewed on the basis of the Lagrange criterion. Their definition is based on the energy balance and related to dimensionless parameters characterizing an MHD flow, these parameters evolving from the Hartmann number and the hydrodynamic Reynolds number as well as the magnetic Reynolds number, and the Lundquist number. These shunting ratios, of current density in the core of a stream (uniform) or equivalent mean current density to the short-circuit (maximum) current density, are given here for a slot channel with nonconducting or conducting walls, for a conduction channel with heavy side rails, and for an MHD-flow around bodies. 5 references, 1 figure.
Operational analysis of open-cycle MHD
Lippert, T. E.; McCutchan, D. A.
1980-07-01
Open cycle magnetohydrodynamic (OCMHD) conceptual power plant designs are studied in the context of a utility system to form a better basis for understanding their design, design requirements, and market possibilities. Based on assumed or projected plant costs and performance characteristics, assumed economics and escalation factors, and one coal supply and delivery scenario, overall and regional OCMHD utility market possibilities are reviewed. Additionally, for one hypothetical utility system a generation expansion plan is developed that includes OCMHD as a baseload power generating station. The impact on generation system economics and operation of alternating selected MHD plant cost and performance characteristics is reviewed. Baseload plant availability is shown as an important plant design consideration, and a general methodology and data base is developed to assess the impact on design and cost of various reliability decisions. An overall plant availability goal is set and the required availabilities of various MHD high technology components are derived to meet the plant goal. The approach is then extended to projecting channel life goals for various plant design configurations and assumptions.
Hot self-similar relativistic MHD flows
Zakamska, Nadia L; Blandford, Roger D
2008-01-01
We consider axisymmetric relativistic jets with a toroidal magnetic field and an ultrarelativistic equation of state, with the goal of studying the lateral structure of jets whose pressure is matched to the pressure of the medium through which they propagate. We find all self-similar steady-state solutions of the relativistic MHD equations for this setup. One of the solutions is the case of a parabolic jet being accelerated by the pressure gradient as it propagates through a medium with pressure declining as p(z)\\propto z^{-2}. As the jet material expands due to internal pressure gradients, it runs into the ambient medium resulting in a pile-up of material along the jet boundary, while the magnetic field acts to produce a magnetic pinch along the axis of the jet. Such jets can be in a lateral pressure equilibrium only if their opening angle \\theta_j at distance z is smaller than about 1/\\gamma, where \\gamma is the characteristic bulk Lorentz-factor at this distance; otherwise, different parts of the jet canno...
Yasukazu Nakanishi; Iwao Fukui; Kazunori Kihara; Hitoshi Masuda; Satoru Kawakami; Mizuaki Sakura; Yasuhisa Fujii; Kazutaka Saito; Fumitaka Koga; Masaya Ito; Junji Yonese
2012-01-01
Anthropometric measurements,e.g.,body weight (BW),body mass index (BMI),as well as serum prostate-specific antigen (PSA) and percent-free PSA (％fPSA) have been shown to have positive correlations with total prostate volume (TPV).We developed an equation and nomegram for estimating TPV,incorporating these predictors in men with benign prostatic hyperplasia (BPH).A total of 1852 men,including 1113 at Tokyo Medical and Dental University (TMDU) Hospital as a training set and 739 at Cancer Institute Hospital (CIH) as a validation set,with PSA levels of up to 20 ng ml-1,who underwent extended prostate biopsy and were proved to have BPH,were enrolled in this study.We developed an equation for continuously coded TPV and a logistic regression-based nomngram for estimating a TPV greater than 40 ml.Predictive accuracy and performance characteristics were assessed using an area under the receiver operating characteristics curve (AUC) and calibration plots.The final linear regression model indicated age,PSA,％fPSA and BW as independent predictors of continuously coded TPV.For predictions in the training set,the multiple correlation coefficient was increased from 0.38 for PSA alone to 0.60 in the final model.We developed a novel nomogram incorporating age,PSA,％fPSA and BW for estimating TPV greater than 40 ml.External validation confirmed its predictive accuracy,with AUC value of 0.764.Calibration plots showed good agreement between predicted probability and observed proportion.In conclusion,TPV can be easily estimated using these four independent predictors.
Effects of MHD slow shocks propagating along magnetic flux tubes in a dipole magnetic field
N. V. Erkaev
2002-01-01
Full Text Available Variations of the plasma pressure in a magnetic flux tube can produce MHD waves evolving into shocks. In the case of a low plasma beta, plasma pressure pulses in the magnetic flux tube generate MHD slow shocks propagating along the tube. For converging magnetic field lines, such as in a dipole magnetic field, the cross section of the magnetic flux tube decreases enormously with increasing magnetic field strength. In such a case, the propagation of MHD waves along magnetic flux tubes is rather different from that in the case of uniform magnetic fields. In this paper, the propagation of MHD slow shocks is studied numerically using the ideal MHD equations in an approximation suitable for a thin magnetic flux tube with a low plasma beta. The results obtained in the numerical study show that the jumps in the plasma parameters at the MHD slow shock increase greatly while the shock is propagating in the narrowing magnetic flux tube. The results are applied to the case of the interaction between Jupiter and its satellite Io, the latter being considered as a source of plasma pressure pulses.
Relativistic particle transport in extragalactic jets: I. Coupling MHD and kinetic theory
Casse, F
2003-01-01
Multidimensional magneto-hydrodynamical (MHD) simulations coupled with stochastic differential equations (SDEs) adapted to test particle acceleration and transport in complex astrophysical flows are presented. The numerical scheme allows the investigation of shock acceleration, adiabatic and radiative losses as well as diffusive spatial transport in various diffusion regimes. The applicability of SDEs to astrophysics is first discussed in regards to the different regimes and the MHD code spatial resolution. The procedure is then applied to 2.5D MHD-SDE simulations of kilo-parsec scale extragalactic jets. The ability of SDE to reproduce analytical solutions of the diffusion-convection equation for electrons is tested through the incorporation of an increasing number of effects: shock acceleration, spatially dependent diffusion coefficients and synchrotron losses. The SDEs prove to be efficient in various shock configuration occurring in the inner jet during the development of the Kelvin-Helmholtz instability. ...
Galkowski, A. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad`s ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs.
System study of an MHD/gas turbine combined-cycle baseload power plant. HTGL report No. 134
Annen, K.D.
1981-08-01
The MHD/gas turbine combined-cycle system has been designed specifically for applications where the availability of cooling water is very limited. The base case systems which were studied consisted of an MHD plant with a gas turbine bottoming plant, and required no cooling water. The gas turbine plant uses only air as its working fluid and receives its energy input from the MHD exhaust gases by means of metal tube heat exchangers. In addition to the base case systems, vapor cycle variation systems were considered which included the addition of a vapor cycle bottoming plant to improve the thermal efficiency. These systems required a small amount of cooling water. The MHD/gas turbine systems were modeled with sufficient detail, using realistic component specifications and costs, so that the thermal and economic performance of the system could be accurately determined. Three cases of MHD/gas turbine systems were studied, with Case I being similar to an MHD/steam system so that a direct comparison of the performances could be made, with Case II being representative of a second generation MHD system, and with Case III considering oxygen enrichment for early commercial applications. The systems are nominally 800 MW/sub e/ to 1000 MW/sub e/ in size. The results show that the MHD/gas turbine system has very good thermal and economic performances while requiring either little or no cooling water. Compared to the MHD/steam system which has a cooling tower heat load of 720 MW, the Base Case I MHD/gas turbine system has a heat rate which is 13% higher and a cost of electricity which is only 7% higher while requiring no cooling water. Case II results show that an improved performance can be expected from second generation MHD/gas turbine systems. Case III results show that an oxygen enriched MHD/gas turbine system may be attractive for early commercial applications in dry regions of the country.
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
Damping of Linear Nonadiabatic MHD Waves in a Flowing Prominence Medium
Nagendra Kumar
2014-01-01
Full Text Available We study the effect of shear flow on the time damping of linear nonadiabatic magnetoacoustic waves in a solar prominence. We consider a homogeneous, isothermal, and unbounded medium permeated by a uniform magnetic field. The adiabaticity is removed by including the optically thin radiative losses, thermal conduction, and heating term in energy equation. We present a local theory of MHD waves to obtain a dispersion relation. The dispersion relation is solved numerically to study the time damping of these waves. It is found that flow influences the damping time and damping per period of both the slow and fast waves significantly. Damping time and damping per period of slow waves are very much higher than the damping time and damping per period of fast waves.
Design of helium-driven MHD disk generators with high performance
Matsubara, H.; Kabashima, S.; Yamasaki, H.; Shioda, S. (Tokyo Inst. of Tech. (JP). Dept. of Energy Sciences)
1990-01-01
A design method for helium-driven MHD disk generator channels including boundary-layer behavior is proposed. In this method, the main flow in the channels is one-dimensionally treated, taking account of the concept of effective cross-sectional area of the channels. This effective area is determined by solving two-dimensional boundary-layer equations. Using this method, the generator channels on various scales are numerically designed under the condition of fully ionized seed. Furthermore, the scale effects of the boundary layer on the area ratio, heat loss and adiabatic efficiency of the generators are examined. It is found from this study that a generator having a thermal input of more than 100 MW is required to achieve high enthalpy extraction with high adiabatic efficiency (more than 65%). (author).
Angular Momentum Transport by Acoustic Modes Generated in the Boundary Layer II: MHD Simulations
Belyaev, Mikhail A; Stone, James M
2013-01-01
We perform global unstratified 3D magnetohydrodynamic simulations of an astrophysical boundary layer (BL) -- an interface region between an accretion disk and a weakly magnetized accreting object such as a white dwarf -- with the goal of understanding the effects of magnetic field on the BL. We use cylindrical coordinates with an isothermal equation of state and investigate a number of initial field geometries including toroidal, vertical, and vertical with zero net flux. Our initial setup consists of a Keplerian disk attached to a non-rotating star. In a previous work, we found that in hydrodynamical simulations, sound waves excited by shear in the BL were able to efficiently transport angular momentum and drive mass accretion onto the star. Here we confirm that in MHD simulations, waves serve as an efficient means of angular momentum transport in the vicinity of the BL, despite the magnetorotational instability (MRI) operating in the disk. In particular, the angular momentum current due to waves is at times...
Design of a vertical annulus with MHD flow using entropy generation analysis
Mahian Omid
2013-01-01
Full Text Available Optimal design of a heat exchanger is one of the concerns of energy conversion engineers. In the present work, the mixed convection flow between two vertical concentric pipes with constant heat flux at the boundaries and MHD flow effects is considered. To determine the optimal design for such a heat exchanger, at first, the momentum and energy equations are simplified and solved analytically. Next, using entropy generation analysis and cost analysis, the operational costs due to entropy generation are estimated. It is concluded that with an increase in the Hartmann number, the energy costs increase. In addition, for two small deviations from the base radius ratio 2(=P including 9.1=P and 1.2=P , the changes in the energy cost are calculated. It is found that for 9.1=P the energy cost increases by 17.5% while for P = 2.1 the energy cost is reduced by 13.6 %.
Travelling Waves in Hall-MHD and the Ion-Acoustic Shock Structure
Hagstrom, George I
2013-01-01
Hall-MHD 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 travelling 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, an...
Characterization of the three-dimensional supersonic flow for the MHD generator
LU HaoYu; LEE ChunHian; DONG HaiTao
2009-01-01
A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy condi-tioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann ef-fects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy cur-rent was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the cor-ner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.
Characterization of the three-dimensional supersonic flow for the MHD generator
LEE; ChunHian
2009-01-01
A numerical procedure based on a five-wave MHD model associated with non-ideal,low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations,in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode,where the local adverse pressure gradient is large,and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases,and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction,all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section,which,in turn,induces the corner eddy current at the corner. A numerical parametric study was also performed,and the computed performance parameters for the MHD generator suggest that,in order to enhance the performance of MHD generator,the magnetic interaction parameter should be elevated.
MHD Driving of Relativistic Jets
Arieh Königl
2007-01-01
Full Text Available Paulatinamente se ha ido reconociendo que los campos magnéticos juegan un papel dominante en la producción y colimación de chorros astrofísicos. Demostramos aquí, usando soluciones semianalíticas exactas para las ecuaciones de MHD ideal en relatividad especial, que un disco de acreción altamente magnetizado (con un campo magnético principalmente poloidal o azimutal alrededor de un agujero negro es capaz de acelerar un flujo de protones y electrones a los factores de Lorentz y energías cinéticas asociadas a fuentes de destellos de rayos gama y nucleos activos de galaxias. También se discuten las contribuciones a la aceleración provenientes de efectos térmicos (por presión de radiación y pares electrón-positrón y de MHD no ideal. Notamos que la aceleración por MHD se caracteriza por ser extendida espacialmente, y esta propiedad se manifesta más claramente en flujos relativistas. Las indicaciones observacionales de que la aceleración de movimientos superlumínicos en chorros de radio ocurre sobre escalas mucho más grandes que las del agujero negro propiamente, apoyan la idea de que la producción de chorros es principalmente un fenómeno magnético. Presentamos resultados preliminares de un modelo global que puede utilizarse para probar esta interpretación.
A simplified MHD model of capillary Z-Pinch compared with experiments
Shapolov, A.A.; Kiss, M.; Kukhlevsky, S.V. [Institute of Physics, University of Pecs (Hungary)
2016-11-15
The most accurate models of the capillary Z-pinches used for excitation of soft X-ray lasers and photolithography XUV sources currently are based on the magnetohydrodynamics theory (MHD). The output of MHD-based models greatly depends on details in the mathematical description, such as initial and boundary conditions, approximations of plasma parameters, etc. Small experimental groups who develop soft X-ray/XUV sources often use the simplest Z-pinch models for analysis of their experimental results, despite of these models are inconsistent with the MHD equations. In the present study, keeping only the essential terms in the MHD equations, we obtained a simplified MHD model of cylindrically symmetric capillary Z-pinch. The model gives accurate results compared to experiments with argon plasmas, and provides simple analysis of temporal evolution of main plasma parameters. The results clarify the influence of viscosity, heat flux and approximations of plasma conductivity on the dynamics of capillary Z-pinch plasmas. The model can be useful for researchers, especially experimentalists, who develop the soft X-ray/XUV sources. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
MHD Thin Film Flows of a Third Grade Fluid on a Vertical Belt with Slip Boundary Conditions
Taza Gul
2013-01-01
Full Text Available The problem of heat transfer analysis is considered in electrically conducting thin film flows with slip boundary conditions. The flow is assumed to be obeying the nonlinear rheological constitutive equation of a third grade fluid. We have solved the governing nonlinear equations of present problems using the traditional Adomian decomposition method (ADM. Particular attention is given to the combined effect of heat and MHD on the velocity field. The results include the profile of velocity, volume flux, skin friction, average velocity, and the temperature distribution across the film. The effects of model parameters on velocity, skin friction and temperature variation have been studied. Optimal homotopy asymptotic method (OHAM is also used for comparison. The numerical results and absolute errors are derived in tables.
Muhammad Ramzan
Full Text Available The present exploration discusses the influence of Newtonian heating on the magnetohydrodynamic (MHD three dimensional couple stress nanofluid past a stretching surface. Viscous dissipation and Joule heating effects are also considered. Moreover, the nanofluid model includes the combined effects of thermophoresis and Brownian motion. Using an appropriate transformation, the governing non linear partial differential equations are converted into nonlinear ordinary differential equations. Series solutions using Homotopy Analysis method (HAM are computed. Plots are presented to portrait the arising parameters in the problem. It is seen that an increase in conjugate heating parameter results in considerable increase in the temperature profile of the stretching wall. Skin friction coefficient, local Nusselt and local Sherwood numbers tabulated and analyzed. Higher values of conjugate parameter, Thermophoresis parameter and Brownian motion parameter result in enhancement of temperature distribution.
MHD Turbulence, Turbulent Dynamo and Applications
Beresnyak, Andrey
2014-01-01
MHD Turbulence is common in many space physics and astrophysics environments. We first discuss the properties of incompressible MHD turbulence. A well-conductive fluid amplifies initial magnetic fields in a process called small-scale dynamo. Below equipartition scale for kinetic and magnetic energies the spectrum is steep (Kolmogorov -5/3) and is represented by critically balanced strong MHD turbulence. In this paper we report the basic reasoning behind universal nonlinear small-scale dynamo and the inertial range of MHD turbulence. We measured the efficiency of the small-scale dynamo $C_E=0.05$, Kolmogorov constant $C_K=4.2$ and anisotropy constant $C_A=0.63$ for MHD turbulence in high-resolution direct numerical simulations. We also discuss so-called imbalanced or cross-helical MHD turbulence which is relevant for in many objects, most prominently in the solar wind. We show that properties of incompressible MHD turbulence are similar to the properties of Alfv\\'enic part of MHD cascade in compressible turbul...
Sych, Robert
2015-01-01
The review addresses the spatial frequency morphology of sources of sunspot oscillations and waves, including their localization, size, oscillation periods, height localization with the mechanism of cut-off frequency that forms the observed emission variability. Dynamic of sunspot wave processes, provides the information about the structure of wave fronts and their time variations, investigates the oscillation frequency transformation depending on the wave energy is shown. The initializing solar flares caused by trigger agents like magnetoacoustic waves, accelerated particle beams, and shocks are discussed. Special attention is paid to the relation between the flare reconnection periodic initialization and the dynamics of sunspot slow magnetoacoustic waves. A short review of theoretical models of sunspot oscillations is provided.
Observational Tests of Recent MHD Turbulence Perspectives
Ghosh, Sanjoy
2001-06-01
This grant seeks to analyze the Heliospheric Missions data to test current theories on the angular dependence (with respect to mean magnetic field direction) of magnetohydrodynamic (MHD) turbulence in the solar wind. Solar wind turbulence may be composed of two or more dynamically independent components. Such components include magnetic pressure-balanced structures, velocity shears, quasi-2D turbulence, and slab (Alfven) waves. We use a method, developed during the first two years of this grant, for extracting the individual reduced spectra of up to three separate turbulence components from a single spacecraft time series. The method has been used on ISEE-3 data, Pioneer Venus Orbiter, Ulysses, and Voyager data samples. The correlation of fluctuations as a function of angle between flow direction and magnetic-field direction is the focus of study during the third year.
Intermittency in MHD turbulence and coronal nanoflares modelling
P. Veltri
2005-01-01
Full Text Available High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD. The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis.
Performance and flow characteristics of MHD seawater thruster
Doss, E.D.
1990-01-01
The main goal of the research is to investigate the effects of strong magnetic fields on the electrical and flow fields inside MHD thrusters. The results of this study is important in the assessment of the feasibility of MHD seawater propulsion for the Navy. To accomplish this goal a three-dimensional fluid flow computer model has been developed and applied to study the concept of MHD seawater propulsion. The effects of strong magnetic fields on the current and electric fields inside the MHD thruster and their interaction with the flow fields, particularly those in the boundary layers, have been investigated. The results of the three-dimensional computations indicate that the velocity profiles are flatter over the sidewalls of the thruster walls in comparison to the velocity profiles over the electrode walls. These nonuniformities in the flow fields give rise to nonuniform distribution of the skin friction along the walls of the thrusters, where higher values are predicted over the sidewalls relative to those over the electrode walls. Also, a parametric study has been performed using the three-dimensional MHD flow model to analyze the performance of continuous electrode seawater thrusters under different operating parameters. The effects of these parameters on the fluid flow characteristics, and on the thruster efficiency have been investigated. Those parameters include the magnetic field (10--20 T), thruster diameter, surface roughness, flow velocity, and the electric load factor. The results show also that the thruster performance improves with the strength of the magnetic field and thruster diameter, and the efficiency decreases with the flow velocity and surface roughness.
EVIDENCE OF ACTIVE MHD INSTABILITY IN EULAG-MHD SIMULATIONS OF SOLAR CONVECTION
Lawson, Nicolas; Strugarek, Antoine; Charbonneau, Paul, E-mail: nicolas.laws@gmail.ca, E-mail: strugarek@astro.umontreal.ca, E-mail: paulchar@astro.umontreal.ca [Département de Physique, Université de Montréal, C.P. 6128 Succ. Centre-ville, Montréal, Qc H3C 3J7 (Canada)
2015-11-10
We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD “millennium simulation” of Passos and Charbonneau. This simulation sustains a large-scale magnetic cycle characterized by solar-like polarity reversals taking place on a regular multidecadal cadence, and in which zonally oriented bands of strong magnetic fields accumulate below the convective layers, in response to turbulent pumping from above in successive magnetic half-cycles. Key aspects of this simulation include low numerical dissipation and a strongly sub-adiabatic fluid layer underlying the convectively unstable layers corresponding to the modeled solar convection zone. These properties are conducive to the growth and development of two-dimensional instabilities that are otherwise suppressed by stronger dissipation. We find evidence for the action of a non-axisymmetric magnetoshear instability operating in the upper portions of the stably stratified fluid layers. We also investigate the possibility that the Tayler instability may be contributing to the destabilization of the large-scale axisymmetric magnetic component at high latitudes. On the basis of our analyses, we propose a global dynamo scenario whereby the magnetic cycle is driven primarily by turbulent dynamo action in the convecting layers, but MHD instabilities accelerate the dissipation of the magnetic field pumped down into the overshoot and stable layers, thus perhaps significantly influencing the magnetic cycle period. Support for this scenario is found in the distinct global dynamo behaviors observed in an otherwise identical EULAG-MHD simulations, using a different degree of sub-adiabaticity in the stable fluid layers underlying the convection zone.
Feasibility of MHD submarine propulsion
Doss, E.D. (ed.) (Argonne National Lab., IL (United States)); Sikes, W.C. (ed.) (Newport News Shipbuilding and Dry Dock Co., VA (United States))
1992-09-01
This report describes the work performed during Phase 1 and Phase 2 of the collaborative research program established between Argonne National Laboratory (ANL) and Newport News Shipbuilding and Dry Dock Company (NNS). Phase I of the program focused on the development of computer models for Magnetohydrodynamic (MHD) propulsion. Phase 2 focused on the experimental validation of the thruster performance models and the identification, through testing, of any phenomena which may impact the attractiveness of this propulsion system for shipboard applications. The report discusses in detail the work performed in Phase 2 of the program. In Phase 2, a two Tesla test facility was designed, built, and operated. The facility test loop, its components, and their design are presented. The test matrix and its rationale are discussed. Representative experimental results of the test program are presented, and are compared to computer model predictions. In general, the results of the tests and their comparison with the predictions indicate that thephenomena affecting the performance of MHD seawater thrusters are well understood and can be accurately predicted with the developed thruster computer models.
Vinš, Václav; Planková, Barbora; Hrubý, Jan
2013-05-01
In this study, the Cahn-Hilliard density gradient theory (GT) is used for predicting the surface tension of various binary mixtures at relatively wide temperature ranges and for testing the application of the GT for predictions of homogeneous nucleation. The GT was combined with two physically based equations of state (EoS), namely the perturbed-chain (PC) statistical associating fluid theory (SAFT) and its modification for polar substances the perturbed-chain polar (PCP) SAFT. The GT applied to the planar phase interface was employed to predict the interfacial tension for various quadrupolar (CO2 and benzene) and dipolar (difluoromethane, i.e., R32; pentafluoroethane, i.e., R125; and 1,1,1,2-tetrafluoroethane, i.e., R134a) substances and for five binary mixtures including polar components ( n-decane + CO2, benzene + CO2, R32 + R125, R32 + R134a, R134a + R125). The PCP-SAFT EoS combined with the GT provides more accurate results for both the quadrupolar and dipolar substances than the original PC-SAFT EoS. Besides the planar phase interface, the GT was also applied to the spherical phase interface simulating a critical cluster occurring in homogeneous nucleation of droplets. Carbon dioxide was considered, because it has a relatively high quadrupole moment and because of its relevance to natural gas processing. Application of the PCP-SAFT EoS provides a significant improvement compared to the PC-SAFT EoS, and it is clearly superior to the classical cubic Peng-Robinson EoS, which is still used for modeling droplet nucleation.
Simulation of MHD collimation from differential rotation
Carey, Christopher
2005-10-01
Recent observations indicate that astrophysical outflows from active galactic nuclei are permeated with helical magnetic fields[1]. The most promising theory for the formation of the magnetic configurations in these magnetically driven jets is the coiling of an initial seed field by the differential rotation of the accretion disk surrounding the central object. We have begun simulations that are relevant to these Poynting jets using the NIMROD code[2]. To simulate dynamics on length scales that are significantly larger than the accretion disk, the non-relativistic MHD equations are evolved on a hemispherical logarithmic mesh. The accretion disk is treated as a condition on the lower boundary by applying a Keplerian velocity to the azimuthal component of the fluid velocity and a prescribed flux of mass through the boundary. The magnetic field configuration is initialized to a dipole like field. Formation of a jet outflow is observed later in time. The initial field is coiled up and collimated, driving a large current density on the axis of symmetry. Slipping of magnetic field lines due to non-ideal effects has been investigated. 1. Asada K. et. al., Pub. of the Astr. Soc. of Japan, 54, L39-L43, 2002 2. Sovinec C. et. al., J. Comp. Phys., 195, 355-386, 2004
Rigo, H. S.; Bercaw, R. W.; Burkhart, J. A.; Mroz, T. S.; Bents, D. J.; Hatch, A. M.
1981-01-01
A description and the design requirements for the 200 MWe (nominal) net output MHD Engineering Test Facility (ETF) Conceptual Design, are presented. Performance requirements for the plant are identified and process conditions are indicated at interface stations between the major systems comprising the plant. Also included are the description, functions, interfaces and requirements for each of these major systems. The lastest information (1980-1981) from the MHD technology program are integrated with elements of a conventional steam electric power generating plant.
MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method
S. Nadeem; Anwar Hussain
2009-01-01
The present paper investigates the magnetohydrodynamic (MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet. The governing equations are simplified by similarity transformations. The reduced problem is then solved by the homotopy analysis method. The pertinent parameters appearing in the problem are discussed graphically and presented in tables. It is found that the shrinking solutions exist in the presence of MHD. It is also observed from the tables that the solutions for f"(0) with different values of parameters are convergent.
Nanoflares and MHD turbulence in coronal loops: a hybrid shell model.
Nigro, Giuseppina; Malara, Francesco; Carbone, Vincenzo; Veltri, Pierluigi
2004-05-14
A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulence in coronal loops, is presented. The model is based on the use of the shell technique in the wave vector space applied to the set of reduced MHD equations. Numerical simulation showed that the energy injected is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions among these fluctuations give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. The statistical analysis performed on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics.
Technical support for open-cycle MHD program. Progress report, January-June 1979
Bomkamp, D. H. [ed.
1980-07-01
The support program for open-cycle MHD at the Argonne National Laboratory consists of developing the analytical tools needed for investigation of the performance of the major components in the combined-cycle MHD/steam power system. The analytical effort is centered on the primary components of the system that are unique to MHD and, also, on the integration of these analytical models into a model of the entire power-producing system. The present project activities include modeling of the combustor, generator, seed deposition, and formation and decomposition of NO. Parametric studies were performed to evaluate the performance of the U-25B generator and to support the design of the US U-25B generator. Refinements and improvements to the MHD systems code and executive program are described.
Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel
Jawad Raza
2016-01-01
Full Text Available A numerical investigation is made to determine the occurrence of the multiple solutions of MHD Casson fluid in a porous channel. Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. Numerical technique known as shooting method is used to investigate the existence of the multiple solutions for the variations of different parameters. Effects of physical parameters on velocity profile, temperature, concentration, and skin friction are presented in pictorial and tabulation representation.
Furusawa, S.; Togashi, H.; Nagakura, H.; Sumiyoshi, K.; Yamada, S.; Suzuki, H.; Takano, M.
2017-09-01
We have constructed a nuclear equation of state (EOS) that includes a full nuclear ensemble for use in core-collapse supernova simulations. It is based on the EOS for uniform nuclear matter that two of the authors derived recently, applying a variational method to realistic two- and three-body nuclear forces. We have extended the liquid drop model of heavy nuclei, utilizing the mass formula that accounts for the dependences of bulk, surface, Coulomb and shell energies on density and/or temperature. As for light nuclei, we employ a quantum-theoretical mass evaluation, which incorporates the Pauli- and self-energy shifts. In addition to realistic nuclear forces, the inclusion of in-medium effects on the full ensemble of nuclei makes the new EOS one of the most realistic EOSs, which covers a wide range of density, temperature and proton fraction that supernova simulations normally encounter. We make comparisons with the FYSS EOS, which is based on the same formulation for the nuclear ensemble but adopts the relativistic mean field theory with the TM1 parameter set for uniform nuclear matter. The new EOS is softer than the FYSS EOS around and above nuclear saturation densities. We find that neutron-rich nuclei with small mass numbers are more abundant in the new EOS than in the FYSS EOS because of the larger saturation densities and smaller symmetry energy of nuclei in the former. We apply the two EOSs to 1D supernova simulations and find that the new EOS gives lower electron fractions and higher temperatures in the collapse phase owing to the smaller symmetry energy. As a result, the inner core has smaller masses for the new EOS. It is more compact, on the other hand, due to the softness of the new EOS and bounces at higher densities. It turns out that the shock wave generated by core bounce is a bit stronger initially in the simulation with the new EOS. The ensuing outward propagations of the shock wave in the outer core are very similar in the two simulations, which
A three dimensional MHD model of the earth's magnetosphere
Wu, C. C.; Walker, R. J.; Dawson, J. M.
1981-01-01
The results of a global MHD calculation of the steady state solar wind interaction with a dipole magnetic field are presented. The computer code used, being much faster than previous codes, makes it possible to increase the number of grid points in the system by an order of magnitude. The resulting model qualitatively reproduces many of the observed features of the quiet time magnetosphere including the bow shock, magnetopause, and plasma sheet.
Fromang, S; Teyssier, R
2006-01-01
In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport. The algorithm is based on a previous work in which the MUSCL--Hancock scheme was used to evolve the induction equation. In this paper, we detail the extension of this scheme to the full MHD equations and discuss its properties. Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax-Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to two completely different astrophysical situations well studied in the past years: the growth of the magnetorotational instability in the shearing box and the collapse of magnetized cloud cores. We have implemented this new Godunov scheme to solve the ideal MHD equations in the AMR code RAMSES. It results in a powerful tool that can be applied to a grea...
Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.
2017-09-01
The Hamiltonian structure of ideal translationally symmetric extended MHD (XMHD) is obtained by employing a method of Hamiltonian reduction on the three-dimensional noncanonical Poisson bracket of XMHD. The existence of the continuous spatial translation symmetry allows the introduction of Clebsch-like forms for the magnetic and velocity fields. Upon employing the chain rule for functional derivatives, the 3D Poisson bracket is reduced to its symmetric counterpart. The sets of symmetric Hall, Inertial, and extended MHD Casimir invariants are identified, and used to obtain energy-Casimir variational principles for generalized XMHD equilibrium equations with arbitrary macroscopic flows. The obtained set of generalized equations is cast into Grad-Shafranov-Bernoulli (GSB) type, and special cases are investigated: static plasmas, equilibria with longitudinal flows only, and Hall MHD equilibria, where the electron inertia is neglected. The barotropic Hall MHD equilibrium equations are derived as a limiting case of the XMHD GSB system, and a numerically computed equilibrium configuration is presented that shows the separation of ion-flow from electro-magnetic surfaces.
On MHD waves, fire-hose and mirror instabilities in anisotropic plasmas
L.-N. Hau
2007-09-01
Full Text Available Temperature or pressure anisotropies are characteristic of space plasmas, standard magnetohydrodynamic (MHD model for describing large-scale plasma phenomena however usually assumes isotropic pressure. In this paper we examine the characteristics of MHD waves, fire-hose and mirror instabilities in anisotropic homogeneous magnetized plasmas. The model equations are a set of gyrotropic MHD equations closed by the generalized Chew-Goldberger-Low (CGL laws with two polytropic exponents representing various thermodynamic conditions. Both ions and electrons are allowed to have separate plasma beta, pressure anisotropy and energy equations. The properties of linear MHD waves and instability criteria are examined and numerical examples for the nonlinear evolutions of slow waves, fire-hose and mirror instabilities are shown. One significant result is that slow waves may develop not only mirror instability but also a new type of compressible fire-hose instability. Their corresponding nonlinear structures thus may exhibit anticorrelated density and magnetic field perturbations, a property used for identifying slow and mirror mode structures in the space plasma environment. The conditions for nonlinear saturation of both fire-hose and mirror instabilities are examined.
On the 2D behavior of 3D MHD with a strong guiding field
Alexakis, Alexandros
2011-01-01
The Magneto-hydrodynamic (MHD) equations in the presence of a guiding magnetic field are investigated by means of direct numerical simulations. The basis of the investigation consists of 9 runs forced at the small scales. The results demonstrate that for a large enough uniform magnetic field the large scale flow behaves as a two dimensional (non-MHD) fluid exhibiting an inverse cascade of energy in the direction perpendicular to the magnetic field, while the small scales behave like a three dimensional MHD-fluid cascading the energy forwards. The amplitude of the inverse cascade is sensitive to the magnetic field amplitude, the domain size, the forcing mechanism, and the forcing scale. All these dependencies are demonstrated by the varying parameters of simulations. Furthermore, in the case that the system is forced anisotropically in the small parallel scales an inverse cascade in the parallel direction is observed that is feeding the 2D modes.
On the measurements of numerical viscosity and resistivity in Eulerian MHD codes
Rembiasz, Tomasz; Cerdá-Durán, Pablo; Aloy, Miguel-Ángel; Müller, Ewald
2016-01-01
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven waves, and the tearing mode instability using the MHD code Aenus. By comparing the simu- lation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of tearing modes we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast-magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependance of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results we infer the numerical resolution (as a function of the spatial reconstruction ...
A mode filter for plasma waves in the Hall-MHD approximation
C. Vocks
Full Text Available A filter method is presented which allows a qualitative and quantitative identification of wave modes observed with plasma experiments on satellites. Hitherto existing mode filters are based on the MHD theory and thus they are restricted to low frequencies well below the ion cyclotron frequency. The present method is generalized to cover wave modes up to the characteristic ion frequencies. The spectral density matrix determined by the observations is decomposed using the eigenvectors of the linearized Hall-MHD equations. As the wave modes are dispersive in this formalism, a precise determination of the k->-vectors requires the use of multi-point measurements. Therefore the method is particularly relevant to multi-satellite missions. The method is tested using simulated plasma data. The Hall-MHD filter is able to identify the modes excited in the model plasma and to assign the correct energetic contributions. By comparison with the former method it is shown that the simple MHD filter leads to large errors if the frequency is not well below the ion cyclotron frequency. Further the range of validity of the linear theory is examined rising the simulated wave amplitudes.
Key words. Magnetospheric physics (MHD waves and instabilities; plasma waves and instabilities
Direct numerical simulations of helical dynamo action: MHD and beyond
D. O. Gómez
2004-01-01
Full Text Available Magnetohydrodynamic dynamo action is often invoked to explain the existence of magnetic fields in several astronomical objects. In this work, we present direct numerical simulations of MHD helical dynamos, to study the exponential growth and saturation of magnetic fields. Simulations are made within the framework of incompressible flows and using periodic boundary conditions. The statistical properties of the flow are studied, and it is found that its helicity displays strong spatial fluctuations. Regions with large kinetic helicity are also strongly concentrated in space, forming elongated structures. In dynamo simulations using these flows, we found that the growth rate and the saturation level of magnetic energy and magnetic helicity reach an asymptotic value as the Reynolds number is increased. Finally, extensions of the MHD theory to include kinetic effects relevant in astrophysical environments are discussed.
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D; Abdelhamid, H M; Morrison, P J
2016-01-01
A comprehensive study of a reduced version of Lust's equations, the extended magnetohydrodynamic (XMHD) model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality, is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way energy conservation along with four families of Casimir invariants are naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
Hamiltonian and action formalisms for two-dimensional gyroviscous MHD
Morrison, P J; Acevedo, R
2014-01-01
A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD) model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.
Extended MHD Modeling of Tearing-Driven Magnetic Relaxation
Sauppe, Joshua
2016-10-01
Driven plasma pinch configurations are characterized by the gradual accumulation and episodic release of free energy in discrete relaxation events. The hallmark of this relaxation in a reversed-field pinch (RFP) plasma is flattening of the parallel current density profile effected by a fluctuation-induced dynamo emf in Ohm's law. Nonlinear two-fluid modeling of macroscopic RFP dynamics has shown appreciable coupling of magnetic relaxation and the evolution of plasma flow. Accurate modeling of RFP dynamics requires the Hall effect in Ohm's law as well as first order ion finite Larmor radius (FLR) effects, represented by the Braginskii ion gyroviscous stress tensor. New results find that the Hall dynamo effect from / ne can counter the MHD effect from - in some of the relaxation events. The MHD effect dominates these events and relaxes the current profile toward the Taylor state, but the opposition of the two dynamos generates plasma flow in the direction of equilibrium current density, consistent with experimental measurements. Detailed experimental measurements of the MHD and Hall emf terms are compared to these extended MHD predictions. Tracking the evolution of magnetic energy, helicity, and hybrid helicity during relaxation identifies the most important contributions in single-fluid and two-fluid models. Magnetic helicity is well conserved relative to the magnetic energy during relaxation. The hybrid helicity is dominated by magnetic helicity in realistic low-beta pinch conditions and is also well conserved. Differences of less than 1 % between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution through ion FLR effects, which have not been included in contemporary relaxation theories. The kinetic energy driven by relaxation in the computations is dominated by velocity components perpendicular to the magnetic field, an effect that had not been predicted. Work performed at University of Wisconsin
MHD magnet technology development program summary, September 1982
1983-11-01
The program of MHD magnet technology development conducted for the US Department of Energy by the Massachusetts Institute of Technology during the past five years is summarized. The general strategy is explained, the various parts of the program are described and the results are discussed. Subjects covered include component analysis, research and development aimed at improving the technology base, preparation of reference designs for commercial-scale magnets with associated design evaluations, manufacturability studies and cost estimations, the detail design and procurement of MHD test facility magnets involving transfer of technology to industry, investigations of accessory subsystem characteristics and magnet-flow-train interfacing considerations and the establishment of tentative recommendations for design standards, quality assurance procedures and safety procedures. A systematic approach (framework) developed to aid in the selection of the most suitable commercial-scale magnet designs is presented and the program status as of September 1982 is reported. Recommendations are made for future work needed to complete the design evaluation and selection process and to provide a sound technological base for the detail design and construction of commercial-scale MHD magnets. 85 references.
MHD equilibria with diamagnetic effects
Tessarotto, M.; Zorat, R.; Johnson, J. L.; White, R. B.
1997-11-01
An outstanding issue in magnetic confinement is the establishment of MHD equilibria with enhanced flow shear profiles for which turbulence (and transport) may be locally effectively suppressed or at least substantially reduced with respect to standard weak turbulence models. Strong flows develop in the presence of equilibrium E× B-drifts produced by a strong radial electric field, as well as due to diamagnetic contributions produced by steep equilibrium radial profiles of number density, temperature and the flow velocity itself. In the framework of a kinetic description, this generally requires the construction of guiding-center variables correct to second order in the relevant expansion parameter. For this purpose, the Lagrangian approach developed recently by Tessarotto et al. [1] is adopted. In this paper the conditions of existence of such equilibria are analyzed and their basic physical properties are investigated in detail. 1 - M. Pozzo, M. Tessarotto and R. Zorat, in Theory of fusion Plasmas, E.Sindoni et al. eds. (Societá Italiana di Fisica, Editrice Compositori, Bologna, 1996), p.295.
MHD Jets in inhomogeneous media
S. O´Sullivan
2002-01-01
Full Text Available Presentamos simulaciones de la propagaci on de jets moleculares no-adiab aticos en un medio ambiente inhomog eneo. Los jets tienen condiciones descritos por un modelo de jet MHD en el cual la forma de las l neas magn eticas se prescribe cerca de la fuente. Per les de densidad ambiental fueron elegidos para representar la zona de transici on entre las regiones exteriores de una nube molecular y el medio interestelar. Escalamos las tasas de enfriamiento at omico y molecular a niveles apropriados para resolver todas las escalas espaciales apropriadas. Con la inclusi on de variabilidad de la fuente, las simulaciones reproducen varias caracter sticas observacionales de jets moleculares, entre ellas las cavidades moleculares. Adicionalmente, encontramos similitudes entre teor a y observaci on para la fracci on de ionizaci on a lo largo del jet. Encontramos que la extensi on lateral de las super cies de trabajo internas son sensibles al medio ambiente. Tambi en presentamos resultados preliminares para un m etodo de calcular mapas de emisi on en l neas usando solamente variables fundamentales de estado que parecen reproducir la emisi on lamentosa de Balmer en frentes de choque.
MHD Integrated Topping Cycle Project
1992-02-01
This fourteenth quarterly technical progress report of the MHD Integrated Topping Cycle Project presents the accomplishments during the period November 1, 1990 to January 31, 1991. Testing of the High Pressure Cooling Subsystem electrical isolator was completed. The PEEK material successfully passed the high temperature, high pressure duration tests (50 hours). The Combustion Subsystem drawings were CADAM released. The procurement process is in progress. An equipment specification and RFP were prepared for the new Low Pressure Cooling System (LPCS) and released for quotation. Work has been conducted on confirmation tests leading to final gas-side designs and studies to assist in channel fabrication.The final cathode gas-side design and the proposed gas-side designs of the anode and sidewall are presented. Anode confirmation tests and related analyses of anode wear mechanisms used in the selection of the proposed anode design are presented. Sidewall confirmation tests, which were used to select the proposed gas-side design, were conducted. The design for the full scale CDIF system was completed. A test program was initiated to investigate the practicality of using Avco current controls for current consolidation in the power takeoff (PTO) regions and to determine the cause of past current consolidation failures. Another important activity was the installation of 1A4-style coupons in the 1A1 channel. A description of the coupons and their location with 1A1 channel is presented herein.
Two-dimensional coupled fluid and electrodynamic calculations for a MHD DCW channel with slag layers
Liu, B. L.
1982-01-01
A fully coupled, two dimensional numerical method of modeling linear, coal-fired MHD generators is developed for the case of a plasma flow bounded by a slag layer on the channel walls. The governing partial differential equations for the plasma flow, slag layer and electrodynamics are presented and their coupling discussed. An iterative, numerical procedure employing non-uniform computational meshes and appropriate tridiagonal matrix solution schemes for the equations is presented. The method permits the investigation of the mutual plasma flow-slag layer development for prescribed wall temperatures, electrode geometry, slag properties and channel loading. In particular, the slag layer-plasma interface properties which require prior specification in an uncoupled analysis comprise part of the solution in the present approach. Results are presented for a short diagonally connected generator channel and include contour plots of the electric potential and current stream function as well as transverse and axial profiles of pertinent plasma properties. The results indicate that a thin electrode slag layer can be maintained in the presence of reasonable current density levels.
3D MHD Jet in a Non-Uniform Magnetic Field
Huang Hulin; Han Dong
2005-01-01
The purpose of this paper is to present a two-phase 3D magnetohydrodynamics (MHD) flow model that combines the volume of fluid (VOF) method with the technique derived from induced-magnetic-field equations for liquid metal free surface MHD-jet-flow. Analogy between the induced-magnetic-filed equation and the conventional computational fluid dynamics (CFD) equation is made, so that the equation can be conveniently accounted for by CFD. A penalty factor numerical method is introduced in order to force the local divergence-free condition of the magnetic fields and an extension of the void insulating calculation domain is applied to ensure that the induced-magnetic field at its boundaries is null. These simulation results for lithium liquid metal jets under magnetic field configurations of Magnetic Torus (Mtor) and National Spherical Torus Experiment (NSTX) outboard divertor have shown that three dimensional jet can not be annihilated by magnetic braking and its cross-section will deform in such a way that the momentum flux of the jet is conserved. 3D MHD effects from a magnetic field gradient cause return currents to interact with applied magnetic fields and produce unfavorable Lorentz forces.Under 3D applied non-uniform magnetic fields of the divertor, unfavorable Lorentz forces lead to a substantial change in flow pattern and a reduction in flow velocity, with the jet cross-section moving to one side of the jet space. These critical phenomena can not be revealed by 2D models.
Analysis of Linear MHD Power Generators
Witalis, E.A.
1965-02-15
The finite electrode size effects on the performance of an infinitely long MHD power generation duct are calculated by means of conformal mapping. The general conformal transformation is deduced and applied in a graphic way. The analysis includes variations in the segmentation degree, the Hall parameter of the gas and the electrode/insulator length ratio as well as the influence of the external circuitry and loading. A general criterion for a minimum of the generator internal resistance is given. The same criterion gives the conditions for the occurrence of internal current leakage between adjacent electrodes. It is also shown that the highest power output at a prescribed efficiency is always obtained when the current is made to flow between exactly opposed electrodes. Curves are presented showing the power-efficiency relations and other generator properties as depending on the segmentation degree and the Hall parameter in the cases of axial and transverse power extraction. The implications of limiting the current to flow between a finite number of identical electrodes are introduced and combined with the condition for current flow between opposed electrodes. The characteristics of generators with one or a few external loads can then be determined completely and examples are given in a table. It is shown that the performance of such generators must not necessarily be inferior to that of segmented generators with many independent loads. However, the problems of channel end losses and off-design loading have not been taken into consideration.
M. RAHIMI EOSBOEE,
2010-12-01
Full Text Available In this study magnetohydrodynamics (MHD boundary layer flow of an upper-convected Maxwell fluid has been investigated. Similarity transformation has been used to reduce the governing differential equations into an ordinary non-linear differential equation. homotopy perturbation Method (HPM has applied to solve this developed nonlinear equation. In this article firstly, the basic idea of the HPM for solving nonlinear differential equations is briefly ntroduced and then it is employed to derive solution of nonlinear governing equation of MHD boundary layer flow with highly nonlinear term. The obtained results from HPM have been compared with numerical Boundary Value problem Method (BVP to verify the accuracy of the proposed method. The effects of the Hartman number (M and Deborah number (β for various conditions have been shown through graphs.
Cessenat, M.; Genta, P.
1996-12-31
We use a method based on a separation of variables for solving a system of first order partial differential equations, in a very simple modelling of MHD. The method consists in introducing three unknown variables {phi}1, {phi}2, {phi}3 in addition of the time variable {tau} and then searching a solution which is separated with respect to {phi}1 and {tau} only. This is allowed by a very simple relation, called a `metric separation equation`, which governs the type of solutions with respect to time. The families of solutions for the system of equations thus obtained, correspond to a radial evolution of the fluid. Solving the MHD equations is then reduced to find the transverse component H{sub {Sigma}} of the magnetic field on the unit sphere {Sigma} by solving a non linear partial differential equation on {Sigma}. Thus we generalize ideas due to Courant-Friedrichs and to Sedov on dimensional analysis and self-similar solutions. (authors).
Vargas Toro, Agustín.
2014-05-01
Transient electronic devices are a new technology development whose main characteristic is that its components can disappear in a programmed and controlled way, which means such devices have a pre-engineered service life. Nowadays, transient electronics have a large application field, involving from the reduction of e-waste in the planet until the development of medical instruments and implants that can be discarded when the patients do not need it anymore, avoiding the trouble of having an extra procedure for them. These devices must be made from biocompatible materials avoiding long-term adverse effects in the environment and patients. It is fundamental to develop an analytical model that allows describing the behavior of these materials considering cases which its porosity may be constant or not, in presence of water or any other biofluid. In order to accomplish this analysis was solve the reactive diffusion equation based on Bromwich's integral and the Residue theorem for two material cases, those whose porosity is constant, and those whose porosity increases linearly in terms of its thickness, where was found a general expression. This allows to the analysis of the relation of the electric resistance (per unit length) and the rate of dissolution of the material.
Asoubar, Daniel; Wyrowski, Frank
2015-07-27
The computer-aided design of high quality mono-mode, continuous-wave solid-state lasers requires fast, flexible and accurate simulation algorithms. Therefore in this work a model for the calculation of the transversal dominant mode structure is introduced. It is based on the generalization of the scalar Fox and Li algorithm to a fully-vectorial light representation. To provide a flexible modeling concept of different resonator geometries containing various optical elements, rigorous and approximative solutions of Maxwell's equations are combined in different subdomains of the resonator. This approach allows the simulation of plenty of different passive intracavity components as well as active media. For the numerically efficient simulation of nonlinear gain, thermal lensing and stress-induced birefringence effects in solid-state active crystals a semi-analytical vectorial beam propagation method is discussed in detail. As a numerical example the beam quality and output power of a flash-lamp-pumped Nd:YAG laser are improved. To that end we compensate the influence of stress-induced birefringence and thermal lensing by an aspherical mirror and a 90° quartz polarization rotator.
Dipole Alignment in Rotating MHD Turbulence
Shebalin, John V.; Fu, Terry; Morin, Lee
2012-01-01
We present numerical results from long-term CPU and GPU simulations of rotating, homogeneous, magnetohydrodynamic (MHD) turbulence, and discuss their connection to the spherically bounded case. We compare our numerical results with a statistical theory of geodynamo action that has evolved from the absolute equilibrium ensemble theory of ideal MHD turbulence, which is based on the ideal MHD invariants are energy, cross helicity and magnetic helicity. However, for rotating MHD turbulence, the cross helicity is no longer an exact invariant, although rms cross helicity becomes quasistationary during an ideal MHD simulation. This and the anisotropy imposed by rotation suggests an ansatz in which an effective, nonzero value of cross helicity is assigned to axisymmetric modes and zero cross helicity to non-axisymmetric modes. This hybrid statistics predicts a large-scale quasistationary magnetic field due to broken ergodicity , as well as dipole vector alignment with the rotation axis, both of which are observed numerically. We find that only a relatively small value of effective cross helicity leads to the prediction of a dipole moment vector that is closely aligned (less than 10 degrees) with the rotation axis. We also discuss the effect of initial conditions, dissipation and grid size on the numerical simulations and statistical theory.
Proposal of a brand-new gyrokinetic algorithm for global MHD simulation
Naitou, Hiroshi; Kobayashi, Kenichi; Hashimoto, Hiroki; Andachi, Takehisa; Lee, Wei-Li; Tokuda, Shinji; Yagi, Masatoshi
2009-11-01
A new algorithm for the gyrokinetic PIC code is proposed. The basic equations are energy conserving and composed of (1) the gyrokinetic Vlasov (GKV) equation, (2) the Vortex equation, and (3) the generalized Ohm's law along the magnetic field. Equation (2) is used to advance electrostatic potential in time. Equation (3) is used to advance longitudinal component of vector potential in time as well as estimating longitudinal induced electric field to accelerate charged particles. The particle information is used to estimate pressure terms in equation (3). The idea was obtained in the process of reviewing the split-weight-scheme formalism. This algorithm was incorporated in the Gpic-MHD code. Preliminary results for the m=1/n=1 internal kink mode simulation in the cylindrical geometry indicate good energy conservation, quite low noise due to particle discreteness, and applicability to larger spatial scale and higher beta regimes. The advantage of new Gpic-MHD is that the lower order moments of the GKV equation are estimated by the moment equation while the particle information is used to evaluate the second order moment.
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.
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).
Understanding Accretion Disks through Three Dimensional Radiation MHD Simulations
Jiang, Yan-Fei
I study the structures and thermal properties of black hole accretion disks in the radiation pressure dominated regime. Angular momentum transfer in the disk is provided by the turbulence generated by the magneto-rotational instability (MRI), which is calculated self-consistently with a recently developed 3D radiation magneto-hydrodynamics (MHD) code based on Athena. This code, developed by my collaborators and myself, couples both the radiation momentum and energy source terms with the ideal MHD equations by modifying the standard Godunov method to handle the stiff radiation source terms. We solve the two momentum equations of the radiation transfer equations with a variable Eddington tensor (VET), which is calculated with a time independent short characteristic module. This code is well tested and accurate in both optically thin and optically thick regimes. It is also accurate for both radiation pressure and gas pressure dominated flows. With this code, I find that when photon viscosity becomes significant, the ratio between Maxwell stress and Reynolds stress from the MRI turbulence can increase significantly with radiation pressure. The thermal instability of the radiation pressure dominated disk is then studied with vertically stratified shearing box simulations. Unlike the previous results claiming that the radiation pressure dominated disk with MRI turbulence can reach a steady state without showing any unstable behavior, I find that the radiation pressure dominated disks always either collapse or expand until we have to stop the simulations. During the thermal runaway, the heating and cooling rates from the simulations are consistent with the general criterion of thermal instability. However, details of the thermal runaway are different from the predictions of the standard alpha disk model, as many assumptions in that model are not satisfied in the simulations. We also identify the key reasons why previous simulations do not find the instability. The thermal
LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS
赵继红; 刘桥
2014-01-01
This article proves the logarithmically improved Serrin’s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] (Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365: 806-808) and [18] (Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375: 799-802).
Radiation-driven MHD systems for space applications
Lee, J. H.; Jalufka, N. W.
High-power radiation such as concentrated solar or high-power laser radiation is considered as a driver for magnetohydrodynamic (MHD) systems which could be developed for efficient power generation and propulsion in space. Eight different systems are conceivable since the MHD systems can be classified in two: plasma and liquid-metal MHD's. Each of these systems is reviewed and solar- (or laser-) driven MHD thrusters are proposed.
Advanced MHD Algorithm for Solar and Space Science: lst Year Semi Annual Progress Report
Schnack, Dalton D.; Lionello, Roberto
2003-01-01
We report progress for the development of MH4D for the first and second quarters of FY2004, December 29, 2002 - June 6, 2003. The present version of MH4D can now solve the full viscous and resistive MHD equations using either an explicit or a semi-implicit time advancement algorithm. In this report we describe progress in the following areas. During the two last quarters we have presented poster at the EGS-AGU-EUG Joint Assembly in Nice, France, April 6-11, 2003, and a poster at the 2003 International Sherwood Theory Conference in Corpus Christi, Texas, April 28-30 2003. In the area of code development, we have implemented the MHD equations and the semi-implicit algorithm. The new features have been tested.
Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD
Gao, Song
2013-05-01
The Richtmyer-Meshkov instability occurs when density-stratified interfaces are impulsively accelerated, typically by a shock wave. We present a numerical method to simulate the Richtmyer-Meshkov instability in cylindrical geometry. The ideal MHD equations are linearized about a time-dependent base state to yield linear partial differential equations governing the perturbed quantities. Convergence tests demonstrate that second order accuracy is achieved for smooth flows, and the order of accuracy is between first and second order for flows with discontinuities. Numerical results are presented for cases of interfaces with positive Atwood number and purely azimuthal perturbations. In hydrodynamics, the Richtmyer-Meshkov instability growth of perturbations is followed by a Rayleigh-Taylor growth phase. In MHD, numerical results indicate that the perturbations can be suppressed for sufficiently large perturbation wavenumbers and magnetic fields.
Simulation of wave interactions with MHD
Batchelor, D; Bernholdt, D; Berry, L; Elwasif, W; Jaeger, E; Keyes, D; Klasky, S [Oak Ridge National Laboratory, Oak Ridge, TN 37331 (United States); Alba, C; Choi, M [General Atomics, San Diego, CA 92186 (United States); Bateman, G [Lehigh University, Bethlehem, PA 18015 (United States); Bonoli, P [Plasma Science and Fusion Center, MTT, Cambridge, MA 02139 (United States); Bramley, R [Indiana University, Bloomington, IN 47405 (United States); Breslau, J; Chance, M; Chen, J; Fu, G; Jardin, S [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Harvey, R [CompX, Del Mar, CA 92014 (United States); Jenkins, T [University of Wisconsin, Madison, WI 53706 (United States); Kruger, S [Tech-X, Boulder, CO 80303 (United States)], E-mail: batchelordb@ornl.gov (and others)
2008-07-15
The broad scientific objectives of the SWIM (Simulation 01 Wave Interaction with MHD) project are twofold: (1) improve our understanding of interactions that both radio frequency (RF) wave and particle sources have on extended-MHD phenomena, and to substantially improve our capability for predicting and optimizing the performance of burning plasmas in devices such as ITER: and (2) develop an integrated computational system for treating multiphysics phenomena with the required flexibility and extensibility to serve as a prototype for the Fusion Simulation Project. The Integrated Plasma Simulator (IPS) has been implemented. Presented here are initial physics results on RP effects on MHD instabilities in tokamaks as well as simulation results for tokamak discharge evolution using the IPS.
Simulation of wave interactions with MHD
Batchelor, Donald B [ORNL; Abla, G [General Atomics, San Diego; Bateman, Glenn [Lehigh University, Bethlehem, PA; Bernholdt, David E [ORNL; Berry, Lee A [ORNL; Bonoli, P. [Massachusetts Institute of Technology (MIT); Bramley, R [Indiana University; Breslau, J. [Princeton Plasma Physics Laboratory (PPPL); Chance, M. [Princeton Plasma Physics Laboratory (PPPL); Chen, J. [Princeton Plasma Physics Laboratory (PPPL); Choi, M. [General Atomics; Elwasif, Wael R [ORNL; Fu, GuoYong [Princeton Plasma Physics Laboratory (PPPL); Harvey, R. W. [CompX, Del Mar, CA; Jaeger, Erwin Frederick [ORNL; Jardin, S. C. [Princeton Plasma Physics Laboratory (PPPL); Jenkins, T [University of Wisconsin; Keyes, David E [Columbia University; Klasky, Scott A [ORNL; Kruger, Scott [Tech-X Corporation; Ku, Long-Poe [Princeton Plasma Physics Laboratory (PPPL); Lynch, Vickie E [ORNL; McCune, Douglas [Princeton Plasma Physics Laboratory (PPPL); Ramos, J. [Massachusetts Institute of Technology (MIT); Schissel, D. [General Atomics; Schnack, [University of Wisconsin; Wright, J. [Massachusetts Institute of Technology (MIT)
2008-07-01
The broad scientific objectives of the SWIM (Simulation of Wave Interaction with MHD) project are twofold: (1) improve our understanding of interactions that both radio frequency (RF) wave and particle sources have on extended-MHD phenomena, and to substantially improve our capability for predicting and optimizing the performance of burning plasmas in devices such as ITER: and (2) develop an integrated computational system for treating multiphysics phenomena with the required flexibility and extensibility to serve as a prototype for the Fusion Simulation Project. The Integrated Plasma Simulator (IPS) has been implemented. Presented here are initial physics results on RF effects on MHD instabilities in tokamaks as well as simulation results for tokamak discharge evolution using the IPS.
Lie Group Solutions of Magnetohydrodynamics Equations and Their Well-Posedness
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.
The Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media
Ghsemi, E; Soleimani, S; Barari, Amin
2012-01-01
The steady two-dimensional laminar forced magneto-hydrodynamic (MHD) Hiemenz flow against a flat plate with variable wall temperature in a porous medium is analyzed. The transformed nonlinear boundary-layer equations are solved analytically by homotopy analysis method (HAM). Results for the veloc...
Euler potentials for the MHD Kamchatnov-Hopf soliton solution
Semenov, VS; Korovinski, DB; Biernat, HK
2002-01-01
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invarian
Explosively-driven magnetohydrodynamic (MHD) generator studies
Agee, F.J.; Lehr, F.M. [Phillips Lab., Kirtland AFB, NM (United States); Vigil, M.; Kaye, R. [Sandia National Labs., Albuquerque, NM (United States); Gaudet, J.; Shiffler, D. [New Mexico Univ., Albuquerque, NM (United States)
1995-08-01
Plasma jet generators have been designed and tested which used an explosive driver and shocktube with a rectangular cross section that optimize the flow velocity and electrical conductivity. The latest in a series of designs has been tested using a reactive load to diagnose the electrical properties of the MHD generator/electromagnet combination. The results of these tests indicate that the plasma jet/MHD generator design does generate a flow velocity greater than 25 km/s and produces several gigawatts of pulsed power in a very small package size. A larger, new generator design is also presented.
1978-01-01
The purpose of this document is to develop an environmental, health and safety (EH and S) assessment and begin a site - specific assessment of these and socio - economic impacts for the magnetohydrodynamics program of the United States Department of Energy. This assessment includes detailed scientific and technical information on the specific EH and S issues mentioned in the MHD Environmental Development Plan. A review of current literature on impact-related subjects is also included. This document addresses the coal-fired, open-cycle MHD technology and reviews and assesses potential EH and S impacts resulting from operation of commercially-installed technology.
MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts. Final paper
Sidorenkov, S.I. [D.V. Efremov Scientific Research Inst. of Electrophysical Apparatus, St. Petersburg (Russian Federation); Hua, T.Q. [Argonne National Lab., IL (United States); Araseki, Hideo [Central Research Inst. of Electric Power Industry, Tokyo (Japan)
1994-07-01
Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. This paper describes four benchmark problems to validate magnetohydrodynamic (MHD) and heat transfer computer codes. The problems include rectangular duct geometry with uniform and nonuniform magnetic fields, with and without surface heat flux, and various rectangular cross sections. Two of the problems are based on experiments. Participants in this benchmarking activity come from three countries: The Russian Federation, The United States, and Japan. The solution methods to the problems are described. Results from the different computer codes are presented and compared.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
MHD Simulations of Core Collapse Supernovae with Cosmos++
Akiyama, Shizuka
2010-01-01
We performed 2D, axisymmetric, MHD simulations with Cosmos++ in order to examine the growth of the magnetorotational instability (MRI) in core--collapse supernovae. We have initialized a non--rotating 15 solar mass progenitor, infused with differential rotation and poloidal magnetic fields. The collapse of the iron core is simulated with the Shen EOS, and the parametric Ye and entropy evolution. The wavelength of the unstable mode in the post--collapse environment is expected to be only ~ 200 m. In order to achieve the fine spatial resolution requirement, we employed remapping technique after the iron core has collapsed and bounced. The MRI unstable region appears near the equator and angular momentum and entropy are transported outward. Higher resolution remap run display more vigorous overturns and stronger transport of angular momentum and entropy. Our results are in agreement with the earlier work by Akiyama et al. (2003) and Obergaulinger et al. (2009).
Non-Radial Oscillations in an Axisymmetric MHD Incompressible Fluid
A. Satya Narayanan
2000-09-01
It is well known from Helioseismology that the Sun exhibits oscillations on a global scale, most of which are non-radial in nature. These oscillations help us to get a clear picture of the internal structure of the Sun as has been demonstrated by the theoretical and observational (such as GONG) studies. In this study we formulate the linearised equations of motion for non-radial oscillations by perturbing the MHD equilibrium solution for an axisymmetric incompressible fluid. The fluid motion and the magnetic field are expressed as scalars , , and , respectively. In deriving the exact solution for the equilibrium state, we neglect the contribution due to meridional circulation. The perturbed quantities *, *, *, * are written in terms of orthogonal polynomials. A special case of the above formulation and its stability is discussed.
Viscous, resistive MHD 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 (MHD) 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 which appears general is that instability was 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.
Generation of sheet currents by high frequency fast MHD waves
Núñez, Manuel, E-mail: mnjmhd@am.uva.es
2016-07-01
The evolution of fast magnetosonic waves of high frequency propagating into an axisymmetric equilibrium plasma is studied. By using the methods of weakly nonlinear geometrical optics, it is shown that the perturbation travels in the equatorial plane while satisfying a transport equation which enables us to predict the time and location of formation of shock waves. For plasmas of large magnetic Prandtl number, this would result into the creation of sheet currents which may give rise to magnetic reconnection and destruction of the original equilibrium. - Highlights: • Regular solutions of quasilinear hyperbolic systems may evolve into shocks. • The shock location is found for high frequency fast MHD waves. • The result is applied to static axisymmetric equilibria. • The previous process may lead to the formation of sheet currents and destruction of the equilibrium.
Numerical study for MHD peristaltic flow in a rotating frame.
Hayat, T; Zahir, Hina; Tanveer, Anum; Alsaedi, A
2016-12-01
The aim of present investigation is to model and analyze the magnetohydrodynamic (MHD) peristaltic transport of Prandtl fluid in a channel with flexible walls. The whole system consisting of fluid and channel are in a rotating frame of reference with uniform angular velocity. Viscous dissipation in thermal equation is not ignored. The channel boundaries satisfy the convective conditions in terms of temperature. The arising complicated problems are reduced in solvable form using large wavelength and small Reynolds number assumptions. Numerical solution for axial and secondary velocities, temperature and heat transfer coefficient are presented. Main emphasis is given to the outcome of rotation and material parameters of Prandtl fluid on the physical quantities of interest.
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D.; Tassi, E.; Abdelhamid, H. M.; Morrison, P. J.
2017-01-01
A comprehensive study of the extended magnetohydrodynamic model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way, the energy conservation along with four families of Casimir invariants is naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular, normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
2D stationary resistive MHD flows: borderline to magnetic reconnection solutions
Nickeler, D H; Nickeler, Dieter H.; Fahr, Hans-Joerg
2005-01-01
We present the basic equations for stationary, incompressible resistive MHD flows in two dimensions. This leads to a system of differential equations for two flux functions, one elliptic partial differential equation (Grad-Shafranov-like) for the magnetic flux function and one for the stream function of the flow. In these equations two potentials appear: one potential is a generalized pressure. The second potential couples the magnetic and the flow shear components of the system. With the restriction to flux or at least line conserving flows one has to solve a modified Ohm's law. For the two dimensional case these are two coupled differential equations, which represent the borderline between the resistive but flux conserving (or line conserving) case, and that of reconnective solutions. We discuss some simplified solutions of these equations.
A new MHD code with adaptive mesh refinement and parallelization for astrophysics
Jiang, R.-L.; Fang, C.; Chen, P.-F.
2012-08-01
A new code, named MAP, is written in FORTRAN language for magnetohydrodynamics (MHD) simulations with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for computing the MHD part, namely, modified Mac Cormack Scheme (MMC), Lax-Friedrichs scheme (LF), and weighted essentially non-oscillatory (WENO) scheme. All of them are second-order, two-step, component-wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann solvers are also equipped. A high resolution can be achieved by the hierarchical block-structured AMR mesh. We use the extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced by the scheme in the magnetic induction equation. The numerical algorithms for the non-ideal terms, e.g., the resistivity and the thermal conduction, are also equipped in the code. The details of the AMR and MPI algorithms are described in the paper.
The Acceleration Mechanism of Resistive MHD Jets Launched from Accretion Disks
Kuwabara, T; Kudoh, T; Matsumoto, R
2004-01-01
We analyzed the results of non-linear resistive magnetohydrodynamical (MHD) simulations of jet formation to study the acceleration mechanism of axisymmetric, resistive MHD jets. The initial state is a constant angular momentum, polytropic torus threaded by weak uniform vertical magnetic fields. The time evolution of the torus is simulated by applying the CIP-MOCCT scheme extended for resistive MHD equations. We carried out simulations up to 50 rotation period at the innermost radius of the disk created by accretion from the torus. The acceleration forces and the characteristics of resistive jets were studied by computing forces acting on Lagrangian test particles. Since the angle between the rotation axis of the disk and magnetic field lines is smaller in resistive models than in ideal MHD models, magnetocentrifugal acceleration is smaller. The effective potential along a magnetic field line has maximum around $z \\sim 0.5r_0$ in resistive models, where $r_0$ is the radius where the density of the initial toru...
Stabilization of the SIESTA MHD Equilibrium Code Using Rapid Cholesky Factorization
Hirshman, S. P.; D'Azevedo, E. A.; Seal, S. K.
2016-10-01
The SIESTA MHD equilibrium code solves the discretized nonlinear MHD force F ≡ J X B - ∇p for a 3D plasma which may contain islands and stochastic regions. At each nonlinear evolution step, it solves a set of linearized MHD equations which can be written r ≡ Ax - b = 0, where A is the linearized MHD Hessian matrix. When the solution norm | x| is small enough, the nonlinear force norm will be close to the linearized force norm | r| 0 obtained using preconditioned GMRES. In many cases, this procedure works well and leads to a vanishing nonlinear residual (equilibrium) after several iterations in SIESTA. In some cases, however, | x|>1 results and the SIESTA code has to be restarted to obtain nonlinear convergence. In order to make SIESTA more robust and avoid such restarts, we have implemented a new rapid QR factorization of the Hessian which allows us to rapidly and accurately solve the least-squares problem AT r = 0, subject to the condition | x|QR method is based on a pairwise row factorization of the tri-diagonal Hessian. It provides a complete Cholesky factorization while preserving the memory allocation of A. This work was supported by the U.S. D.O.E. contract DE-AC05-00OR22725.
Nabert, Christian; Othmer, Carsten; Glassmeier, Karl-Heinz
2017-05-01
The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD) simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms) magnetosheath data to estimate Earth's dipole moment.
Evaluation of MHD materials for use in high-temperature fuel cells
Guidotti, R.
1978-06-15
The MHD and high-temperature fuel cell literature was surveyed for data pertaining to materials properties in order to identify materials used in MHD power generation which also might be suitable for component use in high-temperature fuel cells. Classes of MHD-electrode materials evaluated include carbides, nitrides, silicides, borides, composites, and oxides. Y/sub 2/O/sub 3/-stabilized ZrO/sub 2/ used as a reference point to evaluate materials for use in the solid-oxide fuel cell. Physical and chemical properties such as electrical resistivity, coefficient of thermal expansion, and thermodynamic stability toward oxidation were used to screen candidate materials. A number of the non-oxide ceramic MHD-electrode materials appear promising for use in the solid-electrolyte and molten-carbonate fuel cell as anodes or anode constituents. The MHD-insulator materials appear suitable candidates for electrolyte-support tiles in the molten-carbonate fuel cells. The merits and possible problem areas for these applications are discussed and additional needed areas of research are delineated.
Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole
Sadaka Georges
2011-11-01
Full Text Available FreeFem++ [11] is a software for the numerical solution of partial differential equations. It is based on finite element method. The FreeFem++ platform aims at facilitating teaching and basic research through prototyping. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic equations arising in Fusion Plasma in the context of the ITER project. First we consider the Grad-Shafranov equation, which is derived from the static ideal MHD equations assuming axisymetry. Some of the properties of the equation and its analytical solutions are discussed. Second we discretize a reduced resistive MHD model which admits solutions of the Grad-Shafranov equation as stationary solutions. Then the physical stability of these stationary solutions is investigated through numerical experiments and the numerical stability of the algorithm is discussed.
Pantellini, Filippo; Griton, Léa
2016-10-01
The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960's) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.
Application of ADER Scheme in MHD Simulation
ZHANG Yanyan; FENG Xueshang; JIANG Chaowei; ZHOU Yufen
2012-01-01
The Arbitrary accuracy Derivatives Riemann problem method（ADER） scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions： （ⅰ） Brio-Wu shock tube problem,（ⅱ） Dai-Woodward shock tube problem,（ⅲ） Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.
Pseudo-reconnection in MHD numerical simulation
无
2000-01-01
A class of pseudo-reconnections caused by a shifted mesh in magnetohydrodynamics (MHD) simulations is reported. In terms of this mesh system, some non-physical results may be obtained in certain circumstances, e.g. magnetic reconnection occurs without resistivity. After comparison, another kind of mesh is strongly recommended.
Azeem SHAHZAD
2013-02-01
Full Text Available In this article, we study the power law model of steady state, viscous, incompressible MHD flow over a vertically stretching sheet. Furthermore, heat transfer is also addressed by using the convective boundary conditions. The coupled partial differential equations are transformed into ordinary differential equations (ODEs using similarity transformations. The transformed highly non-linear ODEs are solved by using the Homotopy Analysis Method (HAM. The influence of different parameters on the velocity and temperature fields are analyzed and discussed.
Flux Emergence In The Solar Photosphere - Diagnostics Based On 3-D Rradiation-MHD Simulations
Yelles Chaouche, L.; Cheung, M.; Lagg, A.; Solanki, S.
2006-08-01
We investigate flux tube emergence in the solar photosphere using a diagnostic procedure based on analyzing Stokes signals from different spectral lines calculated in 3-D radiation-MHD simulations. The simulations include the effects of radiative transport and partial ionization and cover layers both above and below the solar surface. The simulations consider the emergence of a twisted magnetic flux tube through the solar surface. We consider different stages in the emergence process, starting from the early appearance of the flux tube at the solar surface, and following the emergence process until the emerged flux looks similar to a normal bipolar region. At every stage we compute line profiles by numerically solving the Unno-Rachkovsky equations at every horizontal grid point. Then, following observational practice, we apply Milne-Eddington-type inversions to the synthetic spectra in order to retrieve different atmospheric parameters. We include the influence of spatial smearing on the deduced atmospheric parameters to identify signatures of different stages of flux emergence in the solar photosphere.
Collisionless magnetic reconnection under anisotropic MHD approximation
Hirabayashi, Kota; Hoshino, Masahiro
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless magneto-hydro-dynamic (MHD) simulations based on the double adiabatic approximation, which is an important step to bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observation. According to our results, a pair of slow shocks does form in the reconnection layer. The resultant shock waves, however, are quite weak compared with those in an isotropic MHD from the point of view of the plasma compression and the amount of the magnetic energy released across the shock. Once the slow shock forms, the downstream plasma are heated in highly anisotropic manner and a firehose-sense (P_{||}>P_{⊥}) pressure anisotropy arises. The maximum anisotropy is limited by the marginal firehose criterion, 1-(P_{||}-P_{⊥})/B(2) =0. In spite of the weakness of the shocks, the resultant reconnection rate is kept at the same level compared with that in the corresponding ordinary MHD simulations. It is also revealed that the sequential order of propagation of the slow shock and the rotational discontinuity, which appears when the guide field component exists, changes depending on the magnitude of the guide field. Especially, when no guide field exists, the rotational discontinuity degenerates with the contact discontinuity remaining at the position of the initial current sheet, while with the slow shock in the isotropic MHD. Our result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.
Buttery, Richard
2011-08-01
This annual workshop on MHD Stability Control has been held since 1996 with a focus on understanding and developing control of MHD instabilities for future fusion reactors. The workshop generally covers a wide range of stability topics: from disruptions, to tearing modes, error fields, ELMs, resistive wall modes (RWMs) and ideal MHD. It spans many device types, particularly tokamaks, stellarators and reversed field pinches, to pull out commonalities in the physics and improve understanding. In 2010 the workshop was held on 15-17 November at the University of Wisconsin in Madison and was combined with the annual US-Japan MHD Workshop. The theme was `3D Magnetic Field Effects in MHD Control', with a focus on multidisciplinary sessions exploring issues of plasma response to 3D fields, the manifestation of such fields in the plasma, and how they influence stability. This has been a topic of renewed interest, with utilisation of 3D fields for ELM control now planned in ITER, and a focus on the application of such fields for error field correction, disruption avoidance, and RWM control. Key issues included the physics of the interaction, types of coils and harmonic spectra needed to control instabilities, and subsidiary effects such as braking (or rotating) the plasma. More generally, a wider range of issues were discussed including RWM physics, tearing mode physics, disruption mitigation, ballooning stability, the snowflake divertor concept, and the line tied pinch! A novel innovation to the meeting was a panel discussion session, this year on Neoclassical Toroidal Viscosity, which ran well; more will be tried next year. In this special section of Plasma Physics and Controlled Fusion we present several of the invited and contributed papers from the 2010 workshop, which have been subject to the normal refereeing procedures of the journal. These papers give a sense of the exceptional quality of the presentations at this workshop, all of which may be found at http://fusion.gat.com/conferences/mhd
Nakamizo, A.; Tanaka, T.
2006-12-01
Existing global models of the solar-wind/IMF expanding to the Earth's orbit are basically grounded in the idea of "source surface." It is widely accepted that the sector structure and the solar wind speed are primarily controlled by the magnetic field at the source surface and the so-called "expansion factor." On the other hand, 3-D MHD model is still off from practical use because both of scientific and technical problems. One of the former problems is the reproduction of supersonic solar-wind. From the viewpoint of the physics of the solar wind, coronal heating and outward acceleration mechanisms are invoked to explain the supersonic evolution of the solar wind. Since the mechanism responsible for the heating/acceleration is still one of the primary subjects of the physics of the solar wind, many MHD models have taken into account their effects by incorporating additional source terms corresponding to promising candidates such as thermal conductions, radiation losses and wave pressures. However there are few MHD models considering the effect of the expansion factor, which determines the solar-wind speed in the series of source surface models. In this study we newly incorporate the flux tube expansion rate into the MHD equation system including heat source function in the energy equation. Appling the unstructured grid system, we achieved the dense grid spacing at the inner boundary, which enable us to adopt realistic solar magnetic fields, and a size of simulation space of 1AU. Photospheric magnetic field data is used as the inner boundary condition.The simulation results are summarized as: (1) The variation of solar wind speed is well controlled by the structure of magnetic fields at and little above the solar surface and (2) Far above the solar surface, the interface between high and low speed flows evolves to a structure suggestive of CIRs. Comparing the data from simulation with the actual solar wind data obtained by spacecrafts, we will discuss the future
MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux
Anuar Ishak; Roslinda Nazar; Ioan Pop
2009-01-01
The steady magnetohydrodynamic (MHD) mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing flow.
Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface
Jia Qing
2016-04-01
Full Text Available In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation and nanoparticle concentration. Similarity transformation variables have been used to transform the governing coupled partial differential equations into ordinary differential equations. The resulting highly nonlinear coupled ordinary differential equations have been solved numerically with the help of Successive linearization method (SLM and Chebyshev spectral collocation method. The impacts of various pertinent parameters of interest are discussed for velocity profile, temperature profile, concentration profile and entropy profile. The expression for local Nusselt number and local Sherwood number are also analyzed and discussed with the help of tables. Furthermore, comparison with the existing is also made as a special case of our study.
Laser-Plasma Modeling Using PERSEUS Extended-MHD Simulation Code for HED Plasmas
Hamlin, Nathaniel; Seyler, Charles
2016-10-01
We discuss the use of the PERSEUS extended-MHD simulation code for high-energy-density (HED) plasmas in modeling laser-plasma interactions in relativistic and nonrelativistic regimes. By formulating the fluid equations as a relaxation system in which the current is semi-implicitly time-advanced using the Generalized Ohm's Law, PERSEUS enables modeling of two-fluid phenomena in dense plasmas without the need to resolve the smallest electron length and time scales. For relativistic and nonrelativistic laser-target interactions, we have validated a cycle-averaged absorption (CAA) laser driver model against the direct approach of driving the electromagnetic fields. The CAA model refers to driving the radiation energy and flux rather than the fields, and using hyperbolic radiative transport, coupled to the plasma equations via energy source terms, to model absorption and propagation of the radiation. CAA has the advantage of not requiring adequate grid resolution of each laser wavelength, so that the system can span many wavelengths without requiring prohibitive CPU time. For several laser-target problems, we compare existing MHD results to extended-MHD results generated using PERSEUS with the CAA model, and examine effects arising from Hall physics. This work is supported by the National Nuclear Security Administration stewardship sciences academic program under Department of Energy cooperative agreements DE-FOA-0001153 and DE-NA0001836.
Three-Dimensional Multiscale MHD Model of Cometary Plasma Environments
Gombosi, Tamas I.; DeZeeuw, Darren L.; Haberli, Roman M.; Powell, Kenneth G.
1996-01-01
First results of a three-dimensional multiscale MHD model of the interaction of an expanding cometary atmosphere with the magnetized solar wind are presented. The model starts with a supersonic and super-Alfvenic solar wind far upstream of the comet (25 Gm upstream of the nucleus) with arbitrary interplanetary magnetic field orientation. The solar wind is continuously mass loaded with cometary ions originating from a 10-km size nucleus. The effects of photoionization, electron impact ionization, recombination, and ion-neutral frictional drag are taken into account in the model. The governing equations are solved on an adaptively refined unstructured Cartesian grid using our new multiscale upwind scalar conservation laws-type numerical technique (MUSCL). We have named this the multiscale adaptive upwind scheme for MHD (MAUS-MHD). The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the diamagnetic cavity of the comet. The main findings are the following: (1) Mass loading decelerates the solar wind flow upstream of the weak cometary shock wave (M approximately equals 2, M(sub A) approximately equals 2), which forms at a subsolar standoff distance of about 0.35 Gm. (2) A cometary plasma cavity is formed at around 3 x 10(exp 3) km from the nucleus. Inside this cavity the plasma expands outward due to the frictional interaction between ions and neutrals. On the nightside this plasma cavity considerably narrows and a relatively fast and dense cometary plasma beam is ejected into the tail. (3) Inside the plasma cavity a teardrop-shaped inner shock is formed, which is terminated by a Mach disk on the nightside. Only the region inside the inner shock is the 'true' diamagnetic cavity. (4) The model predicts four distinct current systems in the inner coma: the density peak current, the cavity boundary current, the inner shock current, and finally the cross-tail current
Spicule-like structures observed in 3D realistic MHD simulations
Martinez-Sykora, J; De Pontieu, B; Carlsson, M
2009-01-01
We analyze features that resemble type i spicules in two different 3D numerical simulations in which we include horizontal magnetic flux emergence in a computational domain spanning the upper layers of the convection zone to the lower corona. The two simulations differ mainly in the preexisting ambient magnetic field strength and in the properties of the inserted flux tube. We use the Oslo Staggered Code (OSC) to solve the full MHD equations with non-grey and non-LTE radiative transfer and thermal conduction along the magnetic field lines. We find a multitude of features that show a spatiotemporal evolution that is similar to that observed in type i spicules, which are characterized by parabolic height vs. time profiles, and are dominated by rapid upward motion at speeds of 10-30 km/s, followed by downward motion at similar velocities. We measured the parameters of the parabolic profile of the spicules and find similar correlations between the parameters as those found in observations. The values for height (...
Prasad Kerehalli
2015-01-01
Full Text Available An analysis is carried out to study the effects of temperature-dependent transport properties on the fully developed free and forced MHD convection flow in a vertical channel. In this model, viscous and Ohmic dissipation terms are also included. The governing nonlinear equations (in non-dimensional form are solved numerically by a second order finite difference scheme. A parametric study is performed in order to illustrate the interactive influences of the model parameters; namely, the magnetic parameter, the variable viscosity parameter, the mixed convection parameter, the variable thermal conductivity parameter, the Brinkmann number and the Eckert number. The velocity field, the temperature field, the skin friction and the Nusselt number are evaluated for several sets of values of these parameters. For some special cases, the obtained numerical results are compared with the available results in the literature: Good agreement is found. Of all the parameters, the variable thermo-physical transport property has the strongest effect on the drag, heat transfer characteristics, the stream-wise velocity, and the temperature field.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Spectral-Homotopy Perturbation Method for Solving Governing MHD Jeffery-Hamel Problem
Ahmed A. Khidir
2014-01-01
Full Text Available We present a new modification of the homotopy perturbation method (HPM for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the MHD Jeffery-Hamel flow and the effect of MHD on the flow has been discussed. Comparisons are made between the proposed technique, the previous studies, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the presented approach. The results demonstrate that the new modification is more efficient and converges faster than the standard homotopy perturbation method at small orders. The MATLAB software has been used to solve all the equations in this study.
Linear Two-Dimensional MHD of Accretion Disks: Crystalline structure and Nernst coefficient
Montani, Giovanni
2009-01-01
We analyse the two-dimensional MHD configurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline structure outlined in Coppi (2005), dealing with a local model too, when a specific accretion rate is taken into account. We limit our attention to the linearised MHD formulation of the electromagnetic back-reaction characterising the equilibrium, by fixing the structure of the radial, vertical and azimuthal profiles. Since we deal with toroidal currents only, the consistency of the model is ensured by the presence of a small collisional effect, phenomenologically described by a non-zero constant Nernst coefficient (thermal power of the plasma). Such an effect provides a proper balance of the electron force equation via non zero temperature gradients, related directly to the radial and vertical velocity components. We show that the obtained profile has the typical oscillating feat...
Extension of the MURaM radiative MHD code for coronal simulations
Rempel, Matthias
2016-01-01
We present a new version of the MURaM radiative MHD code that allows for simulations spanning from the upper convection zone into the solar corona. We implemented the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction and an equilibrium ionization equation of state. We artificially limit the coronal Alfv{\\'e}n and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantify the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be...
Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
Brachet, M E; Krstulovic, G; Mininni, P D; Pouquet, A; Rosenberg, D
2012-01-01
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 four-fold 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 re-gridding 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 ones on grids of 4096^3 points. We find that at the highest resolution, two different current and vorticity sheet systems collide, producing two successive accelerations in the development of small scales with, at the latest time, a convergence of magnetic field lines to the location of maximum current, probably leading locally to a strong bending and directional variability of such lines.
Ring-shaped discharge structures in a closed cycle MHD disk generator
Fukuda, H.; Kabashima, S.
1987-06-01
Numerical simulations are carried out to study plasma properties in a nonequilibrium disk-type MHD generator. The analysis is based on a two-dimensional time-dependent MHD equation, and is performed in the r-z plane. From the r-z analysis, the current distributions in the boundary layer, electrode regions are obtained, as well as the channel main flow region. The two-state nature of plasma, i.e., the formation of streamers and their dynamical behavior in the channel is confirmed. The dependence of the streamer properties on the magnetic field strength and load resistance is examined. The calculations suggest the existence of an eddy current in the boundary layer for the high-loading parameter. Some enhanced eddy currents in the nozzle region and the intensive eddy current at the upper-stream edge of the cathode are obtained for some plasma parameters. 19 references.
Global well-posedness for axisymmetric MHD system with only vertical viscosity
Jiu, Quansen; Yu, Huan; Zheng, Xiaoxin
2017-09-01
In this paper, we are concerned with the global well-posedness of a tri-dimensional MHD system with only vertical viscosity in velocity equation for the large axisymmetric initial data. By making good use of the axisymmetric structure of flow and the maximal smoothing effect of vertical diffusion, we show that sup 2 ≤ p vertical first derivative of velocity vector field, we further establish losing estimates for the anisotropy tri-dimensional MHD system to get the high regularity of (u , b), which guarantees that ∫0t ‖ ∇u (τ) ‖ L∞ dτ < ∞. This together with the classical commutator estimate entails the global regularity of a smooth solution.
Newtonian CAFE: a new ideal MHD code to study the solar atmosphere
González-Avilés, J. J.; Cruz-Osorio, A.; Lora-Clavijo, F. D.; Guzmán, F. S.
2015-12-01
We present a new code designed to solve the equations of classical ideal magnetohydrodynamics (MHD) in three dimensions, submitted to a constant gravitational field. The purpose of the code centres on the analysis of solar phenomena within the photosphere-corona region. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As solar tests we present the transverse oscillations of Alfvénic pulses in coronal loops using a 2.5D model, and as 3D tests we present the propagation of impulsively generated MHD-gravity waves and vortices in the solar atmosphere. The code is based on high-resolution shock-capturing methods, uses the Harten-Lax-van Leer-Einfeldt (HLLE) flux formula combined with Minmod, MC, and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the Flux Constrained Transport method.
Newtonian CAFE: a new ideal MHD code to study the solar atmosphere
Gonzalez-Aviles, J J; Lora-Clavijo, F D; Guzman, F S
2015-01-01
We present a new code designed to solve the equations of classical ideal magneto-hydrodynamics (MHD) in three dimensions, submitted to a constant gravitational field. The purpose of the code centers on the analysis of solar phenomena within the photosphere-corona region. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As solar tests we present the transverse oscillations of Alfvenic pulses in coronal loops using a 2.5D model, and as 3D tests we present the propagation of impulsively generated MHD-gravity waves and vortices in the solar atmosphere. The code is based on high-resolution shock-capturing methods, uses the HLLE flux formula combined with Minmod, MC and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the Flux Constrained Transport method.
VisAn MHD: a toolbox in Matlab for MHD computer model data visualisation and analysis
P. Daum
2007-03-01
Full Text Available Among the many challenges facing modern space physics today is the need for a visualisation and analysis package which can examine the results from the diversity of numerical and empirical computer models as well as observational data. Magnetohydrodynamic (MHD models represent the latest numerical models of the complex Earth's space environment and have the unique ability to span the enormous distances present in the magnetosphere from several hundred kilometres to several thousand kilometres above the Earth surface. This feature enables scientist to study complex structures of processes where otherwise only point measurements from satellites or ground-based instruments are available. Only by combining these observational data and the MHD simulations it is possible to enlarge the scope of the point-to-point observations and to fill the gaps left by measurements in order to get a full 3-D representation of the processes in our geospace environment. In this paper we introduce the VisAn MHD toolbox for Matlab as a tool for the visualisation and analysis of observational data and MHD simulations. We have created an easy to use tool which is capable of highly sophisticated visualisations and data analysis of the results from a diverse set of MHD models in combination with in situ measurements from satellites and ground-based instruments. The toolbox is being released under an open-source licensing agreement to facilitate and encourage community use and contribution.
MHD Shallow Water Waves: Linear Analysis
Heng, Kevin
2009-01-01
We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincare modes and one magneto-Rossby mode) are previously known. The other two wave modes are strongly influenced by the magnetic field and rotation, and have substantially lower angular frequencies; as such, we term them "magnetostrophic modes". We obtain analytical functions for the velocity, height and magnetic field perturbations in the limit that the magnitude of the MHD analogue of Lamb's parameter is large. On a sphere, the magnetostrophic modes reside near the poles, while the other modes are equatorially confined. Magnetostrophic modes may be an ingredient in explaining the frequency drifts observed in Type I X-ray bursts from neutron stars.
Type I Planetary Migration with MHD Turbulence
Laughlin, G; Adams, F; Laughlin, Gregory; Steinacker, Adriane; Adams, Fred
2004-01-01
This paper examines how type I planet migration is affected by the presence of turbulent density fluctuations in the circumstellar disk. For type I migration, the planet does not clear a gap in the disk and its secular motion is driven by torques generated by the wakes it creates in the surrounding disk fluid. MHD turbulence creates additional density perturbations that gravitationally interact with the planet and can dominate the torques produced by the migration mechanism itself. This paper shows that conventional type I migration can be readily overwhelmed by turbulent perturbations and hence the usual description of type I migration should be modified in locations where the magnetorotational instability is active. In general, the migrating planet does not follow a smooth inward trned, but rather exhibits a random walk through phase space. Our main conclusion is that MHD turbulence will alter the time scales for type I planet migration and -- because of chaos -- requires the time scales to be described by ...
Magnetic Reconnection in a Compressible MHD Plasma
Hesse, Michael; Birn, Joachim; Zenitani, Seiji
2011-01-01
Using steady-state resistive MHD, magnetic reconnection is reinvestigated for conditions of high resistivity/low magnetic Reynolds number, when the thickness of the diffusion region is no longer small compared to its length. Implicit expressions for the reconnection rate and other reconnection parameters are derived based on the requirements of mass, momentum, and energy conservation. These expressions are solved via simple iterative procedures. Implications specifically for low Reynolds number/high resistivity are being discussed
MHD simulations on an unstructured mesh
Strauss, H.R. [New York Univ., NY (United States); Park, W.; Belova, E.; Fu, G.Y. [Princeton Univ., NJ (United States). Plasma Physics Lab.; Longcope, D.W. [Univ. of Montana, Missoula, MT (United States); Sugiyama, L.E. [Massachusetts Inst. of Tech., Cambridge, MA (United States)
1998-12-31
Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D.
Design Study: Rocket Based MHD Generator
1997-01-01
This report addresses the technical feasibility and design of a rocket based MHD generator using a sub-scale LOx/RP rocket motor. The design study was constrained by assuming the generator must function within the performance and structural limits of an existing magnet and by assuming realistic limits on (1) the axial electric field, (2) the Hall parameter, (3) current density, and (4) heat flux (given the criteria of heat sink operation). The major results of the work are summarized as follows: (1) A Faraday type of generator with rectangular cross section is designed to operate with a combustor pressure of 300 psi. Based on a magnetic field strength of 1.5 Tesla, the electrical power output from this generator is estimated to be 54.2 KW with potassium seed (weight fraction 3.74%) and 92 KW with cesium seed (weight fraction 9.66%). The former corresponds to a enthalpy extraction ratio of 2.36% while that for the latter is 4.16%; (2) A conceptual design of the Faraday MHD channel is proposed, based on a maximum operating time of 10 to 15 seconds. This concept utilizes a phenolic back wall for inserting the electrodes and inter-electrode insulators. Copper electrode and aluminum oxide insulator are suggested for this channel; and (3) A testing configuration for the sub-scale rocket based MHD system is proposed. An estimate of performance of an ideal rocket based MHD accelerator is performed. With a current density constraint of 5 Amps/cm(exp 2) and a conductivity of 30 Siemens/m, the push power density can be 250, 431, and 750 MW/m(sup 3) when the induced voltage uB have values of 5, 10, and 15 KV/m, respectively.
Final Report: "Large-Eddy Simulation of Anisotropic MHD Turbulence"
Zikanov, Oleg
2008-06-23
To acquire better understanding of turbulence in flows of liquid metals and other electrically conducting fluids in the presence of steady magnetic fields and to develop an accurate and physically adequate LES (large-eddy simulation) model for such flows. The scientific objectives formulated in the project proposal have been fully completed. Several new directions were initiated and advanced in the course of work. Particular achievements include a detailed study of transformation of turbulence caused by the imposed magnetic field, development of an LES model that accurately reproduces this transformation, and solution of several fundamental questions of the interaction between the magnetic field and fluid flows. Eight papers have been published in respected peer-reviewed journals, with two more papers currently undergoing review, and one in preparation for submission. A post-doctoral researcher and a graduate student have been trained in the areas of MHD, turbulence research, and computational methods. Close collaboration ties have been established with the MHD research centers in Germany and Belgium.
Intensity contrast from MHD simulations and from HINODE observations
Afram, N; Solanki, S K; Schuessler, M; Lagg, A; Voegler, A
2010-01-01
Changes in the solar surface area covered by small-scale magnetic elements are thought to cause long-term changes in the solar spectral irradiance, which are important for determining the impact on Earth's climate. To study the effect of small-scale magnetic elements on total and spectral irradiance, we derive their contrasts from 3-D MHD simulations of the solar atmosphere. Such calculations are necessary since measurements of small-scale flux tube contrasts are confined to a few wavelengths and suffer from scattered light and instrument defocus, even for space observations. To test the contrast calculations, we compare rms contrasts from simulations with those obtained with the broad-band filter imager mounted on the Solar Optical Telescope (SOT) onboard the Hinode satellite and also analyse centre-to-limb variations (CLV). The 3-D MHD simulations include the interaction between convection and magnetic flux tubes. They have been run with non-grey radiative transfer using the MURaM code. Simulations have an ...
MHD (magnetohydrodynamic) undersea propulsion: A novel concept with renewed interest
Doss, E.D.; Geyer, H.K. (Argonne National Lab., IL (USA)); Roy, G.D. (Office of Naval Research, Arlington, VA (USA))
1990-01-01
This paper discusses the reasons for the national and international renewed interest in the concept of MHD seawater propulsion. The main advantages of this concept are presented, together with some of the technical challenges that need to be overcome to achieve reliability, performance, and stealth. The paper discusses in more detail some of the technical issues and loss mechanisms influencing the thruster performance in terms of its electrical efficiency. Among the issues discussed are the jet losses and nozzle efficiency. Ohmic losses and frictional losses inside the thruster. Also discussed are the electrical end losses caused by the fringing magnetic field near the end of the electrodes. It has been shown that the frictional and end losses can have strong adverse effects on the thruster performance. Furthermore, a parametric study has been performed to investigate the effects of several parameters on the performance of the MHD thrusters. Those parameters include the magnetic field, thruster diameter, all roughness, flow velocity, and electrical load factor. The results of the parametric study indicate that the thruster efficiency increases with the strength of the magnetic field and thruster diameter, and decreases with the wall roughness and the flow velocity. 8 refs., 8 figs.
Sunspot Modeling: From Simplified Models to Radiative MHD Simulations
Rolf Schlichenmaier
2011-09-01
Full Text Available We review our current understanding of sunspots from the scales of their fine structure to their large scale (global structure including the processes of their formation and decay. Recently, sunspot models have undergone a dramatic change. In the past, several aspects of sunspot structure have been addressed by static MHD models with parametrized energy transport. Models of sunspot fine structure have been relying heavily on strong assumptions about flow and field geometry (e.g., flux-tubes, "gaps", convective rolls, which were motivated in part by the observed filamentary structure of penumbrae or the necessity of explaining the substantial energy transport required to maintain the penumbral brightness. However, none of these models could self-consistently explain all aspects of penumbral structure (energy transport, filamentation, Evershed flow. In recent years, 3D radiative MHD simulations have been advanced dramatically to the point at which models of complete sunspots with sufficient resolution to capture sunspot fine structure are feasible. Here overturning convection is the central element responsible for energy transport, filamentation leading to fine-structure and the driving of strong outflows. On the larger scale these models are also in the progress of addressing the subsurface structure of sunspots as well as sunspot formation. With this shift in modeling capabilities and the recent advances in high resolution observations, the future research will be guided by comparing observation and theory.
Kinetic effects of energetic particles on resistive MHD stability.
Takahashi, R; Brennan, D P; Kim, C C
2009-04-03
We show that the kinetic effects of energetic particles can play a crucial role in the stability of the m/n=2/1 tearing mode in tokamaks (e.g., JET, JT-60U, and DIII-D), where the fraction of energetic particle beta(frac) is high. Using model equilibria based on DIII-D experimental reconstructions, the nonideal MHD linear stability of cases unstable to the 2/1 mode is investigated including a deltaf particle-in-cell model for the energetic particles coupled to the nonlinear 3D resistive MHD code NIMROD [C. C. Kim et al., Phys. Plasmas 15, 072507 (2008)10.1063/1.2949704]. It is observed that energetic particles have significant damping and stabilizing effects at experimentally relevant beta, beta(frac), and S, and excite a real frequency of the 2/1 mode. Extrapolation of the results is discussed for implications to JET and ITER, where the effects are projected to be significant.
An unsplit, cell-centered Godunov method for ideal MHD
Crockett, Robert K.; Colella, Phillip; Fisher, Robert T.; Klein, Richard I.; McKee, Christopher F.
2003-08-29
We present a second-order Godunov algorithm for multidimensional, ideal MHD. Our algorithm is based on the unsplit formulation of Colella (J. Comput. Phys. vol. 87, 1990), with all of the primary dependent variables centered at the same location. To properly represent the divergence-free condition of the magnetic fields, we apply a discrete projection to the intermediate values of the field at cell faces, and apply a filter to the primary dependent variables at the end of each time step. We test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions. The test suite includes rotated planar linear waves, MHD shock tube problems, low-beta flux tubes, and a magnetized rotor problem. For all of these cases, we observe that the algorithm is second-order accurate for smooth solutions, converges to the correct weak solution for problems involving shocks, and exhibits no evidence of instability or loss of accuracy due to the possible presence of non-solenoidal fields.
An Unsplit, Cell-Centered Godunov Method for Ideal MHD
Fisher, R; Crockett, R; Colella, P; Klein, R; McKee, C
2003-10-16
We present a second-order Godunov algorithm for multidimensional, ideal MHD. Our algorithm is based on the unsplit formulation of Colella, with all of the primary dependent variables centered at the same location. To properly represent the divergence-free condition of the magnetic fields, we apply a discrete projection to the intermediate values of the field at cell faces, and apply a filter to the primary dependent variables at the end of each time step. We apply the method to a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions. The test suite includes rotated planar linear waves, MHD shock tube problems, and low-beta flux tubes. For all of these cases, we observe that the algorithm is second-order accurate for smooth solutions, converges to the correct weak solution for problems involving shocks, and exhibits no evidence of instability or loss of accuracy due to the possible presence of non-solenoidal fields.
Fully implicit adaptive mesh refinement algorithm for reduced MHD
Philip, Bobby; Pernice, Michael; Chacon, Luis
2006-10-01
In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technology to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite grid --FAC-- algorithms) for scalability. We demonstrate that the concept is indeed feasible, featuring near-optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations in challenging dissipation regimes will be presented on a variety of problems that benefit from this capability, including tearing modes, the island coalescence instability, and the tilt mode instability. L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) B. Philip, M. Pernice, and L. Chac'on, Lecture Notes in Computational Science and Engineering, accepted (2006)
Inductive ionospheric solver for magnetospheric MHD simulations
H. Vanhamäki
2011-01-01
Full Text Available We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances and similar output is produced (ionospheric electric field. The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km^{−1} in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981.
The Statistical Mechanics of Ideal MHD Turbulence
Shebalin, John V.
2003-01-01
Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.
MHD thrust vectoring of a rocket engine
Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic
2016-09-01
In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.
Inductive ionospheric solver for magnetospheric MHD simulations
Vanhamäki, H.
2011-01-01
We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).
Nonlinear MHD dynamo operating at equipartition
Archontis, V.; Dorch, Bertil; Nordlund, Åke
2007-01-01
Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......-equipartition and a turbulent state. The generation and evolution of such strong magnetic fields is relevant for the understanding of dynamo action that occurs in stars and other astrophysical objects. Aims.We study the mode of operation of this dynamo, in the linear and non-linear saturation regimes. We also consider...... the effect of varying the magnetic and fluid Reymolds number on the non-linear behaviour of the system. Methods.We perform three-dimensional non-linear MHD simulations and visualization using a high resolution numerical scheme. Results.We find that this dynamo has a high growth rate in the linear regime...
Md. Jashim Uddin
2012-01-01
Full Text Available Steady viscous incompressible MHD laminar boundary layer slip flow of an electrically conducting nanofluid over a convectively heated permeable moving linearly stretching sheet has been investigated numerically. The effects of Brownian motion, thermophoresis, magnetic field, and heat generation/absorption are included in the nanofluid model. The similarity transformations for the governing equations are developed. The effects of the pertinent parameters, Lewis number, magnetic field, Brownian motion, heat generation, thermophoretic, momentum slip and Biot number on the flow field, temperature, skin friction factor, heat transfer rate, and nanoparticle, volume fraction rate are displayed in both graphical and tabular forms. Comparisons of analytical (for special cases and numerical solutions with the existing results in the literature are made and is found a close agreement, that supports the validity of the present analysis and the accuracy of our numerical computations. Results for the reduced Nusselt and Sherwood numbers are provided in tabular and graphical forms for various values of the flow controlling parameters which govern the momentum, energy, and the nanoparticle volume fraction transport in the MHD boundary layer.
Coronal Heating and Acceleration of the High/Low-Speed Solar Wind by Fast/Slow MHD Shock Trains
Suzuki, T K
2004-01-01
We investigate coronal heating and acceleration of the high- and low-speed solar wind in the open field region by dissipation of fast and slow magnetohydrodynamical (MHD) waves through MHD shocks. Linearly polarized \\Alfven (fast MHD) waves and acoustic (slow MHD) waves travelling upwardly along with a magnetic field line eventually form fast switch-on shock trains and hydrodynamical shock trains (N-waves) respectively to heat and accelerate the plasma. We determine one dimensional structure of the corona from the bottom of the transition region (TR) to 1AU under the steady-state condition by solving evolutionary equations for the shock amplitudes simultaneously with the momentum and proton/electron energy equations. Our model reproduces the overall trend of the high-speed wind from the polar holes and the low-speed wind from the mid- to low-latitude streamer except the observed hot corona in the streamer. The heating from the slow waves is effective in the low corona to increase the density there, and plays ...
MHD biconvective flow of Powell Eyring nanofluid over stretched surface
Naseem, Faiza; Shafiq, Anum; Zhao, Lifeng; Naseem, Anum
2017-06-01
The present work is focused on behavioral characteristics of gyrotactic microorganisms to describe their role in heat and mass transfer in the presence of magnetohydrodynamic (MHD) forces in Powell-Eyring nanofluids. Implications concerning stretching sheet with respect to velocity, temperature, nanoparticle concentration and motile microorganism density were explored to highlight influential parameters. Aim of utilizing microorganisms was primarily to stabilize the nanoparticle suspension due to bioconvection generated by the combined effects of buoyancy forces and magnetic field. Influence of Newtonian heating was also analyzed by taking into account thermophoretic mechanism and Brownian motion effects to insinuate series solutions mediated by homotopy analysis method (HAM). Mathematical model captured the boundary layer regime that explicitly involved contemporary non linear partial differential equations converted into the ordinary differential equations. To depict nanofluid flow characteristics, pertinent parameters namely bioconvection Lewis number Lb, traditional Lewis number Le, bioconvection Péclet number Pe, buoyancy ratio parameter Nr, bioconvection Rayleigh number Rb, thermophoresis parameter Nt, Hartmann number M, Grashof number Gr, and Eckert number Ec were computed and analyzed. Results revealed evidence of hydromagnetic bioconvection for microorganism which was represented by graphs and tables. Our findings further show a significant effect of Newtonian heating over a stretching plate by examining the coefficient values of skin friction, local Nusselt number and the local density number. Comparison was made between Newtonian fluid and Powell-Eyring fluid on velocity field and temperature field. Results are compared of with contemporary studies and our findings are found in excellent agreement with these studies.
Global existence and uniqueness of nonlinear evolutionary fluid equations
Qin, Yuming; Wang, Taige
2015-01-01
This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equations, compressible viscous micropolar fluid equations, the full non-Newtonian fluid equations and non-autonomous compressible Navier-Stokes equations. These types of partial differential equations arise in many fields of mathematics, but also in other branches of science such as physics and fluid dynamics. This book will be a valuable resource for graduate students and researchers interested in partial differential equations, and will also benefit practitioners in physics and engineering.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects
M Ramzan; M Farooq; T Hayat; A Alsaedi; J Cao
2015-01-01
Combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained. Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.
FOI-PERFECT code: 3D relaxation MHD modeling and Applications
Wang, Gang-Hua; Duan, Shu-Chao; Comutational Physics Team Team
2016-10-01
One of the challenges in numerical simulations of electromagnetically driven high energy density (HED) systems is the existence of vacuum region. FOI-PERFECT code adopts a full relaxation magnetohydrodynamic (MHD) model. The electromagnetic part of the conventional model adopts the magnetic diffusion approximation. The vacuum region is approximated by artificially increasing the resistivity. On one hand the phase/group velocity is superluminal and hence non-physical in the vacuum region, on the other hand a diffusion equation with large diffusion coefficient can only be solved by implicit scheme which is difficult to be parallelized and converge. A better alternative is to solve the full electromagnetic equations. Maxwell's equations coupled with the constitutive equation, generalized Ohm's law, constitute a relaxation model. The dispersion relation is given to show its transition from electromagnetic propagation in vacuum to resistive MHD in plasma in a natural way. The phase and group velocities are finite for this system. A better time stepping is adopted to give a 3rd full order convergence in time domain without the stiff relaxation term restriction. Therefore it is convenient for explicit & parallel computations. Some numerical results of FOI-PERFECT code are also given. Project supported by the National Natural Science Foundation of China (Grant No. 11571293) And Foundation of China Academy of Engineering Physics (Grant No. 2015B0201023).
MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate
Krishnendu Bhattacharyya; Swati Mukhopadhyay; G.C.Layek
2011-01-01
An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.%@@ An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented.A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method.In the boundary slip condition no local similarity occurs.Velocity and temperature distributions within the boundary layer are presented.Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.
On The Role of MHD Waves in Heating Localised Magnetic Structures
Erdélyi, R.; Nelson, C. J.
2016-04-01
Satellite and ground-based observations from e.g. SOHO, TRACE, STEREO, Hinode, SDO and IRIS to DST/ROSA, IBIS, CoMP, STT/CRISP have provided a wealth of evidence of waves and oscillations present in a wide range of spatial scales of the magnetised solar atmosphere. Our understanding about localised solar structures has been considerably changed in light of these high spatial and time resolution observations. However, MHD waves not only enable us to perform sub-resolution magneto-seismology of magnetic waveguides but are also potential candidates to carry and damp the necessary non-thermal energy in these localised waveguides. First, we will briefly outline the basic recent developments in MHD wave theory focussing on linear waves. Next, we discuss the role of the most frequently studied wave classes, including the Alfven, and magneto-acoustic kink and sausage waves. The current theoretical (and often difficult) interpretations of the detected solar atmospheric wave and oscillatory phenomena within the framework of MHD will be shown. Last, the latest reported observational findings of potential MHD wave flux, in terms of localised plasma heating, in the solar atmosphere is discussed, bringing us closer to solve the coronal heating problem.
Towards a Scalable Fully-Implicit Fully-coupled Resistive MHD Formulation with Stabilized FE Methods
Shadid, J N; Pawlowski, R P; Banks, J W; Chacon, L; Lin, P T; Tuminaro, R S
2009-06-03
This paper presents an initial study that is intended to explore the development of a scalable fully-implicit stabilized unstructured finite element (FE) capability for low-Mach-number resistive MHD. The discussion considers the development of the stabilized FE formulation and the underlying fully-coupled preconditioned Newton-Krylov nonlinear iterative solver. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by the Newton linearization, fully-coupled algebraic multilevel preconditioners are employed. Verification results demonstrate the expected order-of-acuracy for the stabilized FE discretization of a 2D vector potential form for the steady and transient solution of the resistive MHD system. In addition, this study puts forth a set of challenging prototype problems that include the solution of an MHD Faraday conduction pump, a hydromagnetic Rayleigh-Bernard linear stability calculation, and a magnetic island coalescence problem. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.
Multimegawatt nuclear electric propulsion with gaseous and vapor core reactors with MHD
Knight, Travis; Anghaie, Samim; Smith, Blair; Houts, Michael
2001-02-01
This study investigated the development of a system concept for space power generation and nuclear electric propulsion based on a fissioning plasma core reactor (FPCR) with magnetohydrodynamic (MHD) power conversion system, coupled to a magnetoplasmadynamic (MPD) thruster. The FPCR is a liquid-vapor core reactor concept operating with metallic uranium or uranium tetrafluoride (UF4) vapor as the fissioning fuel and alkali metals or their fluorides as working fluid in a closed Rankine cycle with MHD energy conversion. Candidate working fluids include K, Li, Na, KF, LiF, NaF, etc. The system features core outlet temperatures of 3000 to 4000 K at pressures of about 1 to 10 MPa, MHD temperatures of 2000 to 3000 K, and radiator temperatures of 1200 to 2000 K. This combination of parameters offers the potential for low total system specific mass in the range of 0.4 to 0.6 kg/kWe. The MHD output could be coupled with minimal power conditioning to the variable specific impulse magnetoplasma rocket (VASIMR), MPD thrusters or other types of thruster for producing thrust at very high specific impulse (Isp=1500 to 10,000 s). .
Study of extended MHD effects on interchange modes in spheromak equilibria
Howell, E. C.; Sovinec, C. R.
2014-10-01
A study of extended MHD effects on linear interchange modes is performed using the NIMROD code [Sovinec & King JCP 2010]. A linear cylindrical equilibrium model is adapted from [Jardin NF 1982] to allow finite toroidal current at the edge. These equilibria are representative of SSPX discharges where currents are driven on the open field to keep the safety factor above 1/2 across the profile [McLean et al., POP 2006]. These spheromaks have weak magnetic shear, and interchange stability is an important consideration. The Suydam parameter, D, is scaled to study resistive and ideal interchange modes. The calculated MHD growth rate increases with D. The resistive interchange scaling γ ~η 1 / 3 is observed for D <1/4 . Calculations using the full extended MHD model are performed for a range of hall parameters Λ. This model includes gyro-viscosity, the hall term, equilibrium diamagnetic flows, and the cross-field diamagnetic heat flux. Two fluid effects in the full model are always destabilizing at large Λ. However, some cases exhibit a range of Λ where the growth rate for the full model is reduced relative to the MHD growth rate. Work supported by US DOE.
JHANKAL ANUJ
2015-01-01
Full Text Available MHD boundary layer flow near stagnation point of linear stretching sheet with variable thermal conductivity are solved using He’s Homotopy Perturbation Method (HPM, which is one of the semi-exact method. Similarity transformation has been used to reduce the governing differential equations into an ordinary non-linear differential equation. The main advantage of HPM is that it does not require the small parameter in the equations and hence the limitations of traditional perturbations can be eliminated. In this paper firstly, the basic idea of the HPM for solving nonlinear differential equations is briefly introduced and then it is employed to derive solution of nonlinear governing equations of MHD boundary layer flow with nonlinear term. The influence of various relevant physical characteristics are presented and discussed.
Dr. G. Prabhakara Rao,
2015-04-01
Full Text Available We consider a two-dimensional MHD natural convection flow of an incompressible viscous and electrically conducting fluid through porous medium past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations of velocity and temperature fields with appropriate boundary conditions are solved by the ordinary differential equations by introducing appropriate coordinate transformations. We solve that ordinary differential equations and find the velocity profiles, temperature profile, the skin friction and nusselt number. The effects of Grashof number (Gr, Hartmann number (M and Prandtl number (Pr, Darcy parameter (D-1 on velocity profiles and temperature profiles are shown graphically.
Kazi Humayun Kabir
2015-01-01
Full Text Available An analysis is presented to investigate the influences of viscous and pressure stress work on MHD natural convection flow along a uniformly heated vertical wavy surface. The governing equations are first modified and then transformed into dimensionless non-similar equations by using set of suitable transformations. The transformed boundary layer equations are solved numerically using the implicit finite difference method, known as Keller-box scheme. Numerical results for the velocity profiles, temperature profiles, skin friction coefficient, the rate of heat transfers, streamlines and isotherms are shown graphically. Some results of skin friction, rate of heat transfer are presented in tabular form for selected values of physical parameters.
MHD modeling on geodesic grids
Florinski, V; Balsara, D S; Meyer, C
2013-01-01
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional "Cartesian" frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a sim...
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.
3D simulations of disc-winds extending radially self-similar MHD models
Stute, Matthias; Vlahakis, Nektarios; Tsinganos, Kanaris; Mignone, Andrea; Massaglia, Silvano
2014-01-01
Disc-winds originating from the inner parts of accretion discs are considered as the basic component of magnetically collimated outflows. The only available analytical MHD solutions to describe disc-driven jets are those characterized by the symmetry of radial self-similarity. However, radially self-similar MHD jet models, in general, have three geometrical shortcomings, (i) a singularity at the jet axis, (ii) the necessary assumption of axisymmetry, and (iii) the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis, by solving the full three-dimensional equations of MHD and impose a termination radius at finite radial distance. We focus here on studying the effects of relaxing the (ii) assumption of axisymmetry, i.e. of performing full 3D numerical simulations of a disc-wind crossing all magnetohydrodynamic critical surfaces. We compare the results of these runs with previou...
On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes
Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo; Aloy, Miguel-Ángel; Müller, Ewald
2017-06-01
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.
MHD stability limits in the TCV Tokamak
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
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
Pressure, Chaotic Magnetic Fields and MHD Equilibria
S.R. Hudson & N. Nakajima
2010-05-12
Analyzes of plasma behavior often begin with a description of the ideal magnetohydrodynamic equilibrium, this being the simplest model capable of approximating macroscopic force balance. Ideal force balance is when the pressure gradient is supported by the Lorentz force, ∇p = j x B. We discuss the implications of allowing for a chaotic magnetic field on the solutions to this equation. We argue that the solutions are pathological and not suitable for numerical calculations. If the pressure and magnetic Field are continuous, the only non-trivial solutions have an uncountable infinity of discontinuities in the pressure gradient and current. The problems arise from the arbitrarily small length scales in the structure of the field, and the consequence of ideal force balance that the pressure is constant along the Field-lines, B • ∇p = 0. A simple method to ameliorate the singularities is to include a small but Finite perpendicular diffusion. A self-consistent set of equilibrium equations is described and some algorithmic approaches aimed at solving these equations are discussed.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Two-fluid turbulence including electron inertia
Andrés, Nahuel, E-mail: nandres@iafe.uba.ar; Gómez, Daniel [Instituto de Astronomía y Física del Espacio, CC. 67, suc. 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, 1428 Buenos Aires (Argentina); Gonzalez, Carlos; Martin, Luis; Dmitruk, Pablo [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, 1428 Buenos Aires (Argentina)
2014-12-15
We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure, and electron inertia. According to this description, each plasma species introduces a new spatial scale: the ion inertial length λ{sub i} and the electron inertial length λ{sub e}, which are not present in the traditional MHD description. In the present paper, we seek for possible changes in the energy power spectrum in fully developed turbulent regimes, using numerical simulations of the two-fluid equations in two-and-a-half dimensions. We have been able to reproduce different scaling laws in different spectral ranges, as it has been observed in the solar wind for the magnetic energy spectrum. At the smallest wavenumbers where plain MHD is valid, we obtain an inertial range following a Kolmogorov k{sup −5∕3} law. For intermediate wavenumbers such that λ{sub i}{sup −1}≪k≪λ{sub e}{sup −1}, the spectrum is modified to a k{sup −7∕3} power-law, as has also been obtained for Hall-MHD neglecting electron inertia terms. When electron inertia is retained, a new spectral region given by k>λ{sub e}{sup −1} arises. The power spectrum for magnetic energy in this region is given by a k{sup −11∕3} power law. Finally, when the terms of electron inertia are retained, we study the self-consistent electric field. Our results are discussed and compared with those obtained in the solar wind observations and previous simulations.
3D MHD Simulations of Tokamak Disruptions
Woodruff, Simon; Stuber, James
2014-10-01
Two disruption scenarios are modeled numerically by use of the CORSICA 2D equilibrium and NIMROD 3D MHD codes. The work follows the simulations of pressure-driven modes in DIII-D and VDEs in ITER. The aim of the work is to provide starting points for simulation of tokamak disruption mitigation techniques currently in the CDR phase for ITER. Pressure-driven instability growth rates previously observed in simulations of DIIID are verified; Halo and Hiro currents produced during vertical displacements are observed in simulations of ITER with implementation of resistive walls in NIMROD. We discuss plans to exercise new code capabilities and validation.
Evaluation of feedback in conductive MHD devices
Grinberg, G.K.
1977-01-01
A method is recommended for computing feedback and the self-energizing threshold of conducting MHD devices. Circuits of equivalent magnetizing currents are used for this purpose in addition to equivalent electrical circuits. This kind of an approach makes it possible to reflect the influence of R/sub m/ on the operation of the device. Dimensionless functions were found which determine the critical value of the Reynolds magnetic number. The computations demonstrated that the redistribution of the magnetic field in the machine's operating zone under the influence of an induced field must be considered.
Vlaykov, Dimitar G; Schmidt, Wolfram; Schleicher, Dominik R G
2016-01-01
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LES), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale (SGS) dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator (W.K. Yeo CUP 1993, ed. Galperin & Orszag) and require no assumptions about the nature of the flow or magnetic field. Thus the scope of their applicability ranges from the sub- to ...
Superconducting magnet system for an experimental disk MHD facility
Knoopers, H.G.; Kate, ten H.H.J.; Klundert, van de L.J.M.
1991-01-01
A predesign of a split-pair magnet for a magnetohydrodynamic (MHD) facility for testing a 10-MW open-cycle disk or a 5-MW closed-cycle disk generator is presented. The magnet system consists of a NbTi and a Nb 3Sn section, which provide a magnetic field of 9 T in the active area of the MHD channel.
The Hamiltonian Structure of the Maxwell-Vlasov Equations.
1981-02-01
principle of Percival [1979). 4. By using an appropriate Darboux theorem, (see Marsden [1981], lecture 1), one can show that Of admits canonically...get the Vlasov-Poisson equation. It would also be of interest to realize both the Vlasov-Maxwell and MHD equations as limiting cases of a grand...de Vries equation, Springer Lecture Notes, #755, 1-15 and Inv. Math. 50, 219-248. J. Arms (1979]. Linearization stability of gravitational and gauge
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
A comparative study on 3-D solar wind structure observed by Ulysses and MHD simulation
FENG Xueshang; XIANG Changqing; ZHONG Dingkun; FAN Quanlin
2005-01-01
During Ulysses' first rapid pole-to-pole transit from September 1994 to June 1995, its observations showed that middle- or high-speed solar winds covered all latitudes except those between -20° and +20° near the ecliptic plane,where the velocity was 300-450 km/s. At poleward 40°,however, only fast solar winds at the speed of 700-870 km/s were observed. In addition, the transitions from low-speed wind to high-speed wind or vice versa were abrupt. In this paper, the large-scale structure of solar wind observed by Ulysses near solar minimum is simulated by using the three-dimensional numerical MHD model. The model combines TVD Lax-Friedrich scheme and MacCormack Ⅱ scheme and decomposes the calculation region into two regions: one from 1 to 22 Rs and the other from 18 Rs to 1 AU.Based on the observations of the solar photospheric magnetic field and an addition of the volumetric heating to MHD equations, the large-scale solar wind structure mentioned above is reproduced by using the three-dimensional MHD model and the numerical results are roughly consistent with Ulysses' observations. Our simulation shows that the initial magnetic field topology and the addition of volume heating may govern the bimodal structure of solar wind observed by Ulysses and also demonstrates that the three-dimensional MHD numerical model used here is efficient in modeling the large-scale solar wind structure.
Three-dimensional MHD modeling of vertical kink oscillations in an active region plasma curtain
Ofman, L.; Parisi, M.; Srivastava, A. K.
2015-10-01
Context. Observations on 2011 August 9 of an X 6.9-class flare in active region (AR) 11263 by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO), were followed by a rare detection of vertical kink oscillations in a large-scale coronal active region plasma curtain in extreme UV coronal lines with periods in the range 8.8-14.9 min. Aims: Our aim is to study the generation and propagation of the magnetohydrodynamic (MHD) oscillations in the plasma curtain taking the realistic 3D magnetic and the density structure of the curtain into account. We also aim to test and improve coronal seismology for a more accurate determination of the magnetic field than with the standard method. Methods: We use the observed morphological and dynamical conditions, as well as plasma properties of the coronal curtain, to initialize a 3D MHD model of the observed vertical and transverse oscillations. To accomplish this, we implemented the impulsively excited velocity pulse mimicking the flare-generated nonlinear fast magnetosonic propagating disturbance interacting obliquely with the curtain. The model is simplified by utilizing an initial dipole magnetic field, isothermal energy equation, and gravitationally stratified density guided by observational parameters. Results: Using the 3D MHD model, we are able to reproduce the details of the vertical oscillations and study the process of their excitation by a nonlinear fast magnetosonic pulse, propagation, and damping, finding agreement with the observations. Conclusions: We estimate the accuracy of simplified slab-based coronal seismology by comparing the determined magnetic field strength to actual values from the 3D MHD modeling results, and demonstrate the importance of taking more realistic magnetic geometry and density for improving coronal seismology into account. A movie associated to Fig. 1 is available in electronic form at http://www.aanda.org
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
Thin film flow in MHD third grade fluid on a vertical belt with temperature dependent viscosity.
Taza Gul
Full Text Available In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM. In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM. The physical characteristics of the problem have been well discussed in graphs for several parameter of interest.
Thin film flow in MHD third grade fluid on a vertical belt with temperature dependent viscosity.
Gul, Taza; Islam, Saed; Shah, Rehan Ali; Khan, Ilyas; Shafie, Sharidan
2014-01-01
In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD) third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM). In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM). The physical characteristics of the problem have been well discussed in graphs for several parameter of interest.
Analytical description of stationary ideal MHD flows with constant total pressure
Golovin, Sergey V
2009-01-01
Incompressible stationary flows of ideal plasma are observed. By introduction of curvilinear system of coordinates in which streamlines and magnetic force lines form a family of coordinate surfaces, MHD equations are partially integrated and brought to a certain convenient form. It is demonstrated that the admissible group of Bogoyavlenskij's symmetry transformations performs as a scaling transformation for the curvilinear coordinates. Analytic description of stationary flows with constant total pressure is given. It is shown, that contact magnetic surfaces of such flows are translational surfaces, i.e. are swept out by translating one curve rigidly along another curve. Explicit examples of solutions with constant total pressure possessing a significant functional arbitrariness are given.
NATURAL CONVECTION IN MHD TRANSIENT FLOW PAST AN ACCELERATED VERTICAL PLATE WITH HEAT SINK
N. AHMED
2014-09-01
Full Text Available The problem of an MHD heat and mass transfer flow past an accelerated infinite vertical plate in a porous medium in presence of chemical reaction, thermal diffusion and first order heat sink is studied. A magnetic field of uniform strength is assumed to be applied normal to the field directed to the fluid region. The resulting system of equations governing the fluid motion is solved by adopting Laplace Transform technique in closed form. The effects of the physical parameters involved in the problem on the flow and the transport characteristics are studied graphs.
Jahan, Shah; Sakidin, Hamzah; Nazar, Roslinda Mohd
2016-11-01
The behavior of magnetohydrodynamics (MHD) flow of viscous fluid near the stagnation point over a stretching cylinder with variable thermal conductivity is analyzed. Thermal conductivity is assumed to be linearly related with temperature. The joule heating effects due to magnetic field is also encountered here. Analytical solutions are developed for both momentum and energy equations by using the homotopy analysis method (HAM). The variations of different parameters on the velocity and temperature distributions along with the skin friction coefficient and local Nusselt number are displayed graphically. Numerical values for the skin friction coefficient are calculated and discussed
A Constrained Transport Scheme for MHD on Unstructured Static and Moving Meshes
Mocz, Philip; Hernquist, Lars
2014-01-01
Magnetic fields play an important role in many astrophysical systems and a detailed understanding of their impact on the gas dynamics requires robust numerical simulations. Here we present a new method to evolve the ideal magnetohydrodynamic (MHD) equations on unstructured static and moving meshes that preserves the magnetic field divergence-free constraint to machine precision. The method overcomes the major problems of using a cleaning scheme on the magnetic fields instead, which is non-conservative, not fully Galilean invariant, does not eliminate divergence errors completely, and may produce incorrect jumps across shocks. Our new method is a generalization of the constrained transport (CT) algorithm used to enforce the $\
Inertial Current Generators of Poynting Flux in MHD Simulations of Black Hole Ergospheres
Punsly, B
2005-01-01
This Letter investigates the physics that is responsible for creating the current system that supports the outgoing Poynting flux emanating from the ergosphere of a rotating black hole in the limit that the magnetic energy density greatly exceeds the plasma rest mass density (magnetically dominated limit). The underlying physics is derived from published three-dimensional simulations that obey the general relativistic equations of perfect magnetohydrodynamics (MHD). It is found that the majority of the Poynting flux emitted from the magnetically dominated regions of the ergosphere has a source associated with inertial effects outside of the event horizon.
MHD non-Newtonian micropolar fluid flow and heat transfer in channel with stretching walls
M. ASHRAF; N. JAMEEL; K. ALI
2013-01-01
A study is presented for magnetohydrodynamics (MHD) flow and heat trans-fer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing.
Calculation of three-dimensional MHD equilibria with islands and stochastic regions
Reiman, A.; Greenside, H.
1986-08-01
A three-dimensional MHD equilibrium code is described that does not assume the existence of good surfaces. Given an initial guess for the magnetic field, the code proceeds by calculating the pressure-driven current and then by updating the field using Ampere's law. The numerical algorithm to solve the magnetic differential equation for the pressure-driven current is described, and demonstrated for model fields having islands and stochastic regions. The numerical algorithm which solves Ampere's law in three dimensions is also described. Finally, the convergence of the code is illustrated for a particular stellarator equilibrium with no large islands.
MHD flow of tangent hyperbolic fluid over a stretching cylinder: Using Keller box method
Malik, M.Y.; Salahuddin, T., E-mail: taimoor_salahuddin@yahoo.com; Hussain, Arif; Bilal, S.
2015-12-01
A numerical solution of MHD flow of tangent hyperbolic fluid model over a stretching cylinder is obtained in this paper. The governing boundary layer equation of tangent hyperbolic fluid is converted into an ordinary differential equation using similarity transformations, which is then solved numerically by applying the implicit finite difference Keller box method. The effects of various parameters on velocity profiles are analyzed and discussed in detail. The values of skin friction coefficient are tabulated and plotted in order to understand the flow behavior near the surface of the cylinder. For validity of the model a comparison of the present work with the literature has been made. - Highlights: • Non-Newtonian (tangent hyperbolic) fluid is taken by using boundary layer approximation. • MHD effects are assumed. • To solve the highly non-linear equations by numerical approach (Keller box Method). • Keller box method is one of the best computational methods capable of solving different engineering problems in fluid mechanics. • Keller box method is an implicit method and has truncation error of order h{sup 2}.
Radiation Effects on MHD Stagnation-Point Flow in a Nanofluid
Mohammad Eftekhari Yazdi
2013-05-01
Full Text Available In this study, the two-dimensional Magnetohydrodynamic (MHD boundary layer of stagnation-point flow in a nanofluid in the presence of thermal radiation is investigated. Using a similarity transform, the Navier-Stokes equations are reduced to a set of nonlinear ordinary differential equations. The similarity equations are solved numerically for three types of nanoparticles, namely copper (Cu, alumina (Al2O3 and titania (TiO2 in water as the base fluid. The skin-friction coefficient and Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters are presented graphically and discussed. Effects of the nanoparticle volume fraction on the flow and heat transfer characteristics are thoroughly examined.
Effects of Hall current and radiation absorption on MHD micropolar fluid in a rotating system
P.V. Satya Narayana
2013-12-01
Full Text Available The objective of this paper is to study the effects of Hall current and radiation absorption on MHD free convection mass transfer flow of a micropolar fluid in a rotating frame of reference. A uniform magnetic field acts perpendicular to the porous surface in which absorbs micropolar fluid with a constant suction velocity. The entire system rotates about the axes normal to the plate with uniform angular velocity Ω. The dimensionless governing equations for this investigation are reduced to a system of linear differential equations using regular perturbation method, and equations are solved analytically. The influence of various flow parameters of the flow field has been discussed and explained graphically. The present study is of immediate interest in geophysical, cosmically fluid dynamics, medicine, biology, and all those processes which are greatly embellished by a strong magnetic field with a low density of the gas.
Tasawar Hayat
Full Text Available This paper investigates the unsteady MHD flow of viscous fluid between two parallel rotating disks. Fluid fills the porous space. Energy equation has been constructed by taking Joule heating, thermal stratification and radiation effects into consideration. We convert system of partial differential equations into system of highly nonlinear ordinary differential equations after employing the suitable transformations. Convergent series solutions are obtained. Behavior of different involved parameters on velocity and temperature profiles is examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and inspected. It is found that tangential velocity profile is increasing function of rotational parameter. Fluid temperature reduces for increasing values of thermal stratification parameter. At upper disk heat transfer rate enhances for larger values of Eckert and Prandtl numbers.
Hayat, Tasawar; Qayyum, Sumaira; Imtiaz, Maria; Alsaedi, Ahmed
2016-01-01
This paper investigates the unsteady MHD flow of viscous fluid between two parallel rotating disks. Fluid fills the porous space. Energy equation has been constructed by taking Joule heating, thermal stratification and radiation effects into consideration. We convert system of partial differential equations into system of highly nonlinear ordinary differential equations after employing the suitable transformations. Convergent series solutions are obtained. Behavior of different involved parameters on velocity and temperature profiles is examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and inspected. It is found that tangential velocity profile is increasing function of rotational parameter. Fluid temperature reduces for increasing values of thermal stratification parameter. At upper disk heat transfer rate enhances for larger values of Eckert and Prandtl numbers.
Heat transfer with thermal radiation on MHD particle-fluid suspension induced by metachronal wave
Bhatti, M. M.; Zeeshan, A.; Ellahi, R.
2017-09-01
In this article, effects of heat transfer on particle-fluid suspension induced by metachronal wave have been examined. The influence of magnetohydrodynamics (MHD) and thermal radiation are also taken into account with the help of Ohm's law and Roseland's approximation. The governing flow problem for Casson fluid model is based on continuity, momentum and thermal energy equation for fluid phase and particle phase. Taking the approximation of long wavelength and zero Reynolds number, the governing equations are simplified. Exact solutions are obtained for the coupled partial differential equations. The impact of all the embedding parameters is discussed with the help of graphs. In particular, velocity profile, pressure rise, temperature profile and trapping phenomena are discussed for all the emerging parameters. It is observed that while fluid parameter enhances the velocity profile, Hartmann number and particle volume fraction oppose the flow.
Dissipation on Steady MHD Marangoni Convection Flow over a Flat Surface with Suction and Injection
S. Mohammed Ibrahim
2013-01-01
Full Text Available The combined effects of radiation and mass transfer on a steady MHD two-dimensional Marangoni convection flow over a flat surface in presence of Joule heating and viscous dissipation under influence of suction and injection is studied numerically. The general governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta method along with shooting technique. The effects of governing parameters on velocity, temperature, and concentration as well as interface velocity, the surface temperature gradient, and the surface concentration gradient were presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement.
P. LOGANATHAN,
2010-11-01
Full Text Available The numerical study of effects of thermal conductivity on unsteady MHD free convective flow over an isothermal semi infinite vertical plate is presented. It is assumed that the thermal conductivity of the fluid as a linear function of temperature. A magnetic field is applied transversely to the direction of the flow. The boundary layer equations of continuity, momentum and energy equations are transformed into non-linear coupled equations and then solved using implicit finite-difference method of Crank-Nicholson type. A parametric study is performed to illustrate the influence of thermal conductivity, magnetic parameter and Prandtl number on the velocity and temperature profiles. In addition, the local and average skin friction, Nusselt number at the plate are shown graphically for both air and water. An analysis of the results obtained shows that the flowfield is influenced appreciably by the strength of magnetic field, thermal conductivity at the wall of the plate.
A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet
Ahmed, Jawad; Shahzad, Azeem; Khan, Masood; Ali, Ramzan
2015-11-01
This article focuses on the exact solution regarding convective heat transfer of a magnetohydrodynamic (MHD) Jeffrey fluid over a stretching sheet. The effects of joule and viscous dissipation, internal heat source/sink and thermal radiation on the heat transfer characteristics are taken in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function. The influence of the pertinent parameters on the temperature profile is examined. In addition the results for the wall temperature gradient are also discussed in detail.
A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet
Ahmed, Jawad; Shahzad, Azeem [Department of Basic Sciences, University of Engineering and Technology, Taxila 47050 (Pakistan); Khan, Masood [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Ali, Ramzan, E-mail: alian.qau@gmail.com [Department of Applied Mathematics, TU-Dortmund (Germany); University of Central Asia, 720001 Bishkek (Kyrgyzstan)
2015-11-15
This article focuses on the exact solution regarding convective heat transfer of a magnetohydrodynamic (MHD) Jeffrey fluid over a stretching sheet. The effects of joule and viscous dissipation, internal heat source/sink and thermal radiation on the heat transfer characteristics are taken in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function. The influence of the pertinent parameters on the temperature profile is examined. In addition the results for the wall temperature gradient are also discussed in detail.
A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet
Jawad Ahmed
2015-11-01
Full Text Available This article focuses on the exact solution regarding convective heat transfer of a magnetohydrodynamic (MHD Jeffrey fluid over a stretching sheet. The effects of joule and viscous dissipation, internal heat source/sink and thermal radiation on the heat transfer characteristics are taken in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST and prescribed heat flux (PHF. Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function. The influence of the pertinent parameters on the temperature profile is examined. In addition the results for the wall temperature gradient are also discussed in detail.
Muhammad Mubashir Bhatti
2016-05-01
Full Text Available In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations with the help of similarity variables. The solution of the resulting nonlinear differential equations is solved numerically with the help of the successive linearization method and Chebyshev spectral collocation method. The influence of all the emerging parameters is discussed with the help of graphs and tables. It is observed that the influence of magnetic field and fluid parameters oppose the flow. It is also analyzed that thermal radiation effects and the Prandtl number show opposite behavior on temperature profile. Furthermore, it is also observed that entropy profile increases for all the physical parameters.
MHD mixed convection flow through a diverging channel with heated circular obstacle
Alam, Md. S.; Shaha, J.; Khan, M. A. H.; Nasrin, R.
2016-07-01
A numerical study of steady MHD mixed convection heat transfer and fluid flow through a diverging channel with heated circular obstacle is carried out in this paper. The circular obstacle placed at the centre of the channel is hot with temperature Th. The top and bottom walls are non-adiabatic. The basic nonlinear governing partial differential equations are transformed into dimensionless ordinary differential equations using similarity transformations. These equations have been solved numerically for different values of the governing parameters, namely Reynolds number (Re), Hartmann number (Ha), Richardson number (Ri) and Prandtl number (Pr) using finite element method. The streamlines, isotherms, average Nusselt number and average temperature of the fluid for various relevant dimensionless parameters are displayed graphically. The study revealed that the flow and thermal fields in the diverging channel depend significantly on the heated body. In addition, it is observed that the magnetic field acts to increase the rate of heat transfer within the channel.
Heat transfer with thermal radiation on MHD particle–fluid suspension induced by metachronal wave
M M BHATTI; A ZEESHAN; R ELLAHI
2017-09-01
In this article, effects of heat transfer on particle–fluid suspension induced by metachronal wave have been examined. The influence of magnetohydrodynamics (MHD) and thermal radiation are also taken into account with the help of Ohm’s law and Roseland’s approximation. The governing flow problem for Casson fluid model is based on continuity, momentum and thermal energy equation for fluid phase and particle phase. Taking the approximation of long wavelength and zero Reynolds number, the governing equations are simplified. Exact solutions are obtained for the coupled partial differential equations. The impact of all the embedding parameters is discussed with the help of graphs. In particular, velocity profile, pressure rise, temperature profile and trapping phenomena are discussed for all the emerging parameters. It is observed that while fluid parameter enhances the velocity profile, Hartmann number and particle volume fraction oppose the flow.
Effects of Joule Heating and Viscous Dissipation on MHD Marangoni Convection Boundary Layer Flow
Rohana Abdul Hamid
2011-09-01
Full Text Available An analysis is performed to study the effects of the Joule heating and viscous dissipation on the magnetohydrodynamics (MHD Marangoni convection boundary layer flow. The governing partial differential equations are reduced to a system of ordinary differential equations via the similarity transformations. Numerical results of the similarity equations are obtained using the Runge-Kutta-Fehlberg method. Effects of the magnetic field parameter, and the combined effects of the Joule heating and the viscous dissipation are investigated and the numerical results are tabulated in tables and figures. It is found that the magnetic field reduces the fluid velocity but increases the fluid temperature. On the other hand, the combined effects of the Joule heating and viscous dissipation have significantly influenced the surface temperature gradient.
Neutrino oscillations in MHD supernova explosions
Kawagoe, S; Kotake, K [Division of Theoretical Astronomy, National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588 (Japan); Takiwaki, T, E-mail: shio.k@nao.ac.j [Center for Computational Astrophysics, National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588 (Japan)
2010-01-01
We calculate the neutrino oscillations numerically in magnetohydrodynamic (MHD) explosion models to see how asphericity has impacts on neutrino spectra. Magneto-driven explosions are one of the most attracting scenarios for producing large scale departures from spherical symmetric geometry, that are reported by many observational data. We find that the event rates at Super-Kamiokande (SK) seen from the polar direction (e.g., the rotational axis of the supernovae) decrease when the shock wave is propagating through H-resonance. In addition, we find that L-resonance in this situation becomes non-adiabatic, and the effect of L-resonance appears in the neutrino signal, because the MHD shock can propagate to the stellar surface without shock-stall after core bounce, and the shock reaches the L-resonance at earlier stage than the conventional spherical supernova explosion models. Our results suggest that we may obtain the observational signatures of the two resonances in SK for Galactic supernova.
MHD Forces in Quasi-Static Evolution, Catastrophe, and ``Failed'' Eruption of Solar Flux Ropes
Chen, James
2017-08-01
This paper presents the first unified theoretical model of flux rope dynamics---a single set of flux-rope equations in ideal MHD---to describe as one dynamical process the quasi-static evolution, catastrophic transition to eruption, cessation (``failure'') of eruption, and the post-eruption quasi-equilibria. The model is defined by the major radial {\\it and} minor radial equations of motion including pressure. The initial equilibrium is a flux rope in a background plasma with pressure $p_c(Z)$ and an overlying magnetic field $B_c(Z)$. The flux rope is initially force-free, but theevolution is not required to be force- free. A single quasi-static control parameter, the rate of increase in poloidal flux, is used for the entire process. As this parameter is slowly increased, the flux rope rises, following a sequence of quasi-static equilibria. As the apex of the flux rope rises past a critical height $Z_{crt}$, it expands on a dynamical (Alfvénic) timescale. The eruption rapidly ceases, as the stored magnetic energy of eruption is exhausted, and a new equilibrium is established at height $Z_1 > Z_{crt}$. The calculated velocity profile resembles the observed velocity profiles in ``failed'' eruptions including a damped oscillation. In the post-eruption equilibria, the outward hoop force is balanced by the tension of the toroidal self magnetic field and pressure gradient force. Thus, the flux rope does not evolve in a force-free manner. The flux rope may also expand without reaching a new equilibrium, provided a sufficient amount of poloidal flux is injected on the timescale of eruption. This scenario results in a full CME eruption. It is shown that the minor radial expansion critically couples the evolution of the toroidal self-field and pressure gradient force. No parameter regime is found in which the commonly used simplifications---near-equilibrium minor radial expansion, force-free expansion, and constant aspect ratio $R/a$ (e.g., the torus instability equation
Ionospheric conductance distribution and MHD wave structure: observation and model
F. Budnik
Full Text Available The ionosphere influences magnetohydrodynamic waves in the magnetosphere by damping because of Joule heating and by varying the wave structure itself. There are different eigenvalues and eigensolutions of the three dimensional toroidal wave equation if the height integrated Pedersen conductivity exceeds a critical value, namely the wave conductance of the magnetosphere. As a result a jump in frequency can be observed in ULF pulsation records. This effect mainly occurs in regions with gradients in the Pedersen conductances, as in the auroral oval or the dawn and dusk areas. A pulsation event recorded by the geostationary GOES-6 satellite is presented. We explain the observed change in frequency as a change in the wave structure while crossing the terminator. Furthermore, selected results of numerical simulations in a dipole magnetosphere with realistic ionospheric conditions are discussed. These are in good agreement with the observational data.
Key words. Ionosphere · (Ionosphere · magnetosphere interactions · Magnetospheric physics · Magnetosphere · ionosphere interactions · MHD waves and instabilities.
Wall functions for numerical modeling of laminar MHD flows
Widlund, O
2003-01-01
general wall function treatment is presented for the numerical modeling of laminar magnetohydrodynamic (MHD) flows. The wall function expressions are derived analytically from the steady-state momentum and electric potential equations, making use only of local variables of the numerical solution. No assumptions are made regarding the orientation of the magnetic field relative to the wall, nor of the magnitude of the Hartmann number, or the wall conductivity. The wall functions are used for defining implicit boundary conditions for velocity and electric potential, and for computing mass flow and electrical currents in near wall-cells. The wall function treatment was validated in a finite volume formulation, and compared with an analytic solution for a fully developed channel flow in a transverse magnetic field. For the case with insulating walls, a uniform 20 x 20 grid, and Hartmann numbers Ha = [10,30,100], the accuracy of pressure drop and wall shear stress predictions was [1.1%,1.6%,0.5%], respectively. Com...
Two-dimensional MHD model of the reconnection diffusion region
N. V. Erkaev
2002-01-01
Full Text Available Magnetic reconnection is an important process providing a fast conversion of magnetic energy into thermal and kinetic plasma energy. In this concern, a key problem is that of the resistive diffusion region where the reconnection process is initiated. In this paper, the diffusion region is associated with a nonuniform conductivity localized to a small region. The nonsteady resistive incompressible MHD equations are solved numerically for the case of symmetric reconnection of antiparallel magnetic fields. A Petschek type steady-state solution is obtained as a result of time relaxation of the reconnection layer structure from an arbitrary initial stage. The structure of the diffusion region is studied for various ratios of maximum and minimum values of the plasma resistivity. The effective length of the diffusion region and the reconnection rate are determined as functions of the length scale and the maximum of the resistivity. For sufficiently small length scale of the resistivity, the reconnection rate is shown to be consistent with Petschek's formula. By increasing the resistivity length scale and decreasing the resistivity maximum, the reconnection layer tends to be wider, and correspondingly, the reconnection rate tends to be more consistent with that of the Parker-Sweet regime.
2012-02-29
pressible flow via adaptive nonlinear filtering, International Journal for Numerical Methods in Fluids, (2012). [5] M. Gunzburger, C. Trenchea, and C...errors of IMEX methods for magnetohydrodynamics flows at small Reynolds number [12] The MHD flows are governed by the Navier-Stokes equations coupled...require different meshes, time steps and methods. We introduce a implicit- explicit (IMEX) method where the MHD equations can be evolved in time by calls to
Realistic radiative MHD simulation of a solar flare
Rempel, Matthias D.; Cheung, Mark; Chintzoglou, Georgios; Chen, Feng; Testa, Paola; Martinez-Sykora, Juan; Sainz Dalda, Alberto; DeRosa, Marc L.; Viktorovna Malanushenko, Anna; Hansteen, Viggo H.; De Pontieu, Bart; Carlsson, Mats; Gudiksen, Boris; McIntosh, Scott W.
2017-08-01
We present a recently developed version of the MURaM radiative MHD code that includes coronal physics in terms of optically thin radiative loss and field aligned heat conduction. The code employs the "Boris correction" (semi-relativistic MHD with a reduced speed of light) and a hyperbolic treatment of heat conduction, which allow for efficient simulations of the photosphere/corona system by avoiding the severe time-step constraints arising from Alfven wave propagation and heat conduction. We demonstrate that this approach can be used even in dynamic phases such as a flare. We consider a setup in which a flare is triggered by flux emergence into a pre-existing bipolar active region. After the coronal energy release, efficient transport of energy along field lines leads to the formation of flare ribbons within seconds. In the flare ribbons we find downflows for temperatures lower than ~5 MK and upflows at higher temperatures. The resulting soft X-ray emission shows a fast rise and slow decay, reaching a peak corresponding to a mid C-class flare. The post reconnection energy release in the corona leads to average particle energies reaching 50 keV (500 MK under the assumption of a thermal plasma). We show that hard X-ray emission from the corona computed under the assumption of thermal bremsstrahlung can produce a power-law spectrum due to the multi-thermal nature of the plasma. The electron energy flux into the flare ribbons (classic heat conduction with free streaming limit) is highly inhomogeneous and reaches peak values of about 3x1011 erg/cm2/s in a small fraction of the ribbons, indicating regions that could potentially produce hard X-ray footpoint sources. We demonstrate that these findings are robust by comparing simulations computed with different values of the saturation heat flux as well as the "reduced speed of light".
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.
Sakurai, Takashi; Goossens, Marcel; Hollweg, Joseph V.
1991-01-01
The present method of addressing the resonance problems that emerge in such MHD phenomena as the resonant absorption of waves at the Alfven resonance point avoids solving the fourth-order differential equation of dissipative MHD by recourse to connection formulae across the dissipation layer. In the second part of this investigation, the absorption of solar 5-min oscillations by sunspots is interpreted as the resonant absorption of sounds by a magnetic cylinder. The absorption coefficient is interpreted (1) analytically, under certain simplifying assumptions, and numerically, under more general conditions. The observed absorption coefficient magnitude is explained over suitable parameter ranges.
Shiraishi, Junya; Miyato, Naoaki; Matsunaga, Go
2016-01-01
It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle’s Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas. PMID:27160346
Shateyi, Stanford
2017-07-01
The spectral relaxation method is employed to examine natural convective heat and mass transfer, MHD flow over a permeable moving vertical plate with convective boundary condition in the presence of viscous dissipation, thermal radiation and chemical reaction. The governing partial differential equations were transformed into a system of nonlinear ordinary differential equations by using a similarity approach. The pertinent results are then displayed in tabular form and graphically.
Picologlou, B.F.; Doss, E.D.; Geyer, H.K. (Argonne National Lab., IL (United States)); Sikes, W.C.; Ranellone, R.F. (Newport News Shipbuilding and Dry Dock Co., VA (United States))
1992-01-01
A two Tesla test facility was designed, built, and operated to investigate the performance of magnetohydrodynamic (MHD) seawater thrusters. The results of this investigation are used to validate a design oriented MHD thruster performance computer code. The thruster performance code consists of a one-dimensional MHD hydrodynamic model coupled to a two-dimensional electrical model. The code includes major loss mechanisms affecting the performance of the thruster. Among these losses are the joule dissipation losses, frictional losses, electrical end losses, and single electrode potential losses. The facility test loop, its components, and their design are presented in detail. Additionally, the test matrix and its rationale are discussed. Representative experimental results of the test program are presented, and are compared to pretest computer model predictions. Good agreement between predicted and measured data has served to validate the thruster performance computer models.
Study of the processes resulting from the use of alkaline seed in natural gas-fired MHD facilities
Styrikovich, M.A.; Mostinskii, I.L.
1977-01-01
Various ways of ionizing seed injection and recovery, applicable to open-cycle magnetohydrodynamic (MHD) power generation facilities, operating on sulfur-free gaseous fossil fuel, are discussed and experimentally verified. The physical and chemical changes of the seed and the heat and mass transfer processes resulting from seed application are investigated using the U-02 experimental MHD facility and laboratory test facilities. Engineering methods for calculating the processes of seed droplet vaporization, condensation and the precipitation of submicron particles of K/sub 2/CO/sub 3/ on the heat exchange surface are also included.
Huang, Zhenguang; Tóth, Gábor; Gombosi, Tamas I.; Jia, Xianzhe; Rubin, Martin; Fougere, Nicolas; Tenishev, Valeriy; Combi, Michael R.; Bieler, Andre; Hansen, Kenneth C.; Shou, Yinsi; Altwegg, Kathrin
2016-05-01
The neutral and plasma environment is critical in understanding the interaction of the solar wind and comet 67P/Churyumov-Gerasimenko (CG), the target of the European Space Agency's Rosetta mission. To serve this need and support the Rosetta mission, we have developed a 3-D four-fluid model, which is based on BATS-R-US (Block-Adaptive Tree Solarwind Roe-type Upwind Scheme) within SWMF (Space Weather Modeling Framework) that solves the governing multifluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates different mass loading processes, including photoionization and electron impact ionization, charge exchange, dissociative ion-electron recombination, and collisional interactions between different fluids. We simulated the plasma and neutral gas environment near perihelion in three different cases: an idealized comet with a spherical body and uniform neutral gas outflow, an idealized comet with a spherical body and illumination-driven neutral gas outflow, and comet CG with a realistic shape model and illumination-driven neutral gas outflow. We compared the results of the three cases and showed that the simulations with illumination-driven neutral gas outflow have magnetic reconnection, a magnetic pileup region and nucleus directed plasma flow inside the nightside reconnection region, which have not been reported in the literature.
Resistive MHD reconstruction of two-dimensional coherent structures in space
W.-L. Teh
2010-11-01
Full Text Available We present a reconstruction technique to solve the steady resistive MHD equations in two dimensions with initial inputs of field and plasma data from a single spacecraft as it passes through a coherent structure in space. At least two components of directly measured electric fields (the spacecraft spin-plane components are required for the reconstruction, to produce two-dimensional (2-D field and plasma maps of the cross section of the structure. For convenience, the resistivity tensor η is assumed diagonal in the reconstruction coordinates, which allows its values to be estimated from Ohm's law, E+v×B=η·j. In the present paper, all three components of the electric field are used. We benchmark our numerical code by use of an exact, axi-symmetric solution of the resistive MHD equations and then apply it to synthetic data from a 3-D, resistive, MHD numerical simulation of reconnection in the geomagnetic tail, in a phase of the event where time dependence and deviations from 2-D are both weak. The resistivity used in the simulation is time-independent and localized around the reconnection site in an ellipsoidal region. For the magnetic field, plasma density, and pressure, we find very good agreement between the reconstruction results and the simulation, but the electric field and plasma velocity are not predicted with the same high accuracy.
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
MHD Turbulence in Accretion Disk Boundary Layers
Chan, Chi-kwan
2012-01-01
The physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations...
Drag reduction in turbulent MHD pipe flows
Orlandi, P.
1996-01-01
This is a preliminary study devoted to verifying whether or not direct simulations of turbulent Magneto-Hydro-Dynamic (MHD) flows in liquid metals reproduce experimental observations of drag reduction. Two different cases have been simulated by a finite difference scheme which is second order accurate in space and time. In the first case, an external azimuthal magnetic field is imposed. In this case, the magnetic field acts on the mean axial velocity and complete laminarization of the flow at N(sub a) = 30 has been achieved. In the second case, an axial magnetic field is imposed which affects only fluctuating velocities, and thus the action is less efficient. This second case is more practical, but comparison between numerical and experimental results is only qualitative.
The Biermann Catastrophe in Numerical MHD
Graziani, Carlo; Lee, Dongwook; Lamb, Donald Q; Weide, Klaus; Fatenejad, Milad; Miller, Joshua
2014-01-01
The Biermann Battery effect is a popular mechanism for generating magnetic fields in initially unmagnetized plasmas, and is frequently invoked in cosmic magnetogenesis and studied in High-Energy Density laboratory physics experiments. Generation of magnetic fields by the Biermann effect due to mis-aligned density and temperature gradients in smooth flow _behind_ shocks is well known. We show that a magnetic field is also generated _within_ shocks as a result of the electron-ion charge separation that they induce. A straightforward implementation of the Biermann effect in MHD codes does not capture this physical process, and worse, produces unphysical magnetic fields at shocks whose value does not converge with resolution. We show that this breakdown of convergence is due to naive discretization. We show that a careful consideration of the kinetic picture of ion viscous shocks leads to a formulation of the Biermann effect in terms of the electron temperature -- which is continuous across shocks -- that gives r...
MHD power generation with fully ionized seed
Yamasaki, H.; Shioda, S.
1977-01-01
Recovery of power density in the regime of fully ionized seed has been demonstrated experimentally using an MHD disk generator with the effective Hall parameter up to 5.0 when the seed was fully ionized. The experiments were conducted with a shock-heated and potassium-seeded argon plasma under the following conditions: stagnation gas pressure = 0.92 atm, stagnation gas temperature = 2750 K, flow Mach number = 2.5, and seed fraction = 1.4 x 10/sup -5/. Measurements of electron-number density and spectroscopic observations of both potassium and argon lines confirmed that the recovery of power output was due to the reduction of ionization instability. This fact indicates that the successful operation of a disk generator utilizing nonequilibrium ionization seems to be possible and that the suppression of ionization instability can also provide higher adiabatic efficiency. Furthermore, the lower seed fraction offers technological advantages related to seed problems.
3-D nonlinear evolution of MHD instabilities
Bateman, G.; Hicks, H. R.; Wooten, J. W.
1977-03-01
The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed.
A helically distorted MHD flux rope model
Theobald, Michael L.; Montgomery, David
1990-01-01
A flux rope model is proposed which has a variable degree of helical distortion from axisymmetry. The basis for this suggestion is a series of numerical and analytical investigations of magnetohydrodynamic states which result when an axial electric current is directed down on dc magnetic field. The helically distorted states involve a flow velocity and seem to be favored because of their lower rate of energy dissipation. Emphasis is on the magnetometer and particle energy analyzer traces that might be characteristic of such flux ropes. It is shown that even a fractionally small helical distortion may considerably alter the traces in minimum-variance coordinates. In short, what may be fairly common MHD processes can render a flux rope almost unrecognizable under standard diagnostics, even if the departures from axisymmetry are not great.
Global MHD Models of the Solar Corona
Suess, S. T.; Rose, Franklin (Technical Monitor)
2001-01-01
Global magnetohydrodynamic (MHD) models of the solar corona are computationally intensive, numerically complex simulations that have produced important new results over the past few years. After a brief overview of how these models usually work, I will address three topics: (1) How these models are now routinely used to predict the morphology of the corona and analyze Earth and space-based remote observations of the Sun; (2) The direct application of these models to the analysis of physical processes in the corona and chromosphere and to the interpretation of in situ solar wind observations; and (3) The use of results from global models to validate the approximations used to make detailed studies of physical processes in the corona that are not otherwise possible using the global models themselves.
The Biermann catastrophe of numerical MHD
Graziani, C.; Tzeferacos, P.; Lee, D.; Lamb, D. Q.; Weide, K.; Fatenejad, M.; Miller, J.
2016-05-01
The Biermann Battery effect is frequently invoked in cosmic magnetogenesis and studied in High-Energy Density laboratory physics experiments. Unfortunately, direct implementation of the Biermann effect in MHD codes is known to produce unphysical magnetic fields at shocks whose value does not converge with resolution. We show that this convergence breakdown is due to naive discretization, which fails to account for the fact that discretized irrotational vector fields have spurious solenoidal components that grow without bound near a discontinuity. We show that careful consideration of the kinetics of ion viscous shocks leads to a formulation of the Biermann effect that gives rise to a convergent algorithm. We note a novel physical effect a resistive magnetic precursor in which Biermann-generated field in the shock “leaks” resistively upstream. The effect appears to be potentially observable in experiments at laser facilities.
Activation of MHD reconnection on ideal timescales
Landi, S; Del Zanna, L; Tenerani, A; Pucci, F
2016-01-01
Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number $S$, up to $10^7$. Results confirm that when the critical aspect ratio of $S^{1/3}$ is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfv\\'enic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be ro...
Resonant interactions of perturbations in MHD flows
Sagalakov, A.M.; Shtern, V.N.
1977-01-17
The nonlinear theory of hydrodynamic stability differentiates three types of interactions: deformation of the initial velocity profile by Reynolds stress pulsations, multiplication of harmonics, and the resonant interaction of harmonics with dissimilar wave numbers and frequencies. This article analyzes an approach considering the first and third of these non-linear mechanisms, producing an acceptable approximation of the averaged characteristics of a developing pulsation movement, particularly the averaged turbulent velocity profile. The approach consists in analysis of triharmonic oscillations, the parameters of which satisfy the resonant relationships. A model of a triharmonic pulsation mode is studied which is applicable to MHD flows. It is shown in particular how a magnetic field transverse to the flow plane suppresses the resonant interaction of three-dimensional perturbations. This agrees with experimental studies on two-dimensional turbulence conducted earlier. 11 references, 3 figures.
Modeling of the subgrid-scale term of the filtered magnetic field transport equation
Balarac, Guillaume; Kosovichev, Alexander; Brugière, Olivier; Wray, Alan; Mansour, Nagi
2010-01-01
Accurate subgrid-scale turbulence models are needed to perform realistic numerical magnetohydrodynamic (MHD) simulations of the subsurface flows of the Sun. To perform large-eddy simulations (LES) of turbulent MHD flows, three unknown terms have to be modeled. As a first step, this work proposes to use a priori tests to measure the accuracy of various models proposed to predict the SGS term appearing in the transport equation of the filtered magnetic field. It is proposed to evaluate the SGS ...
Magnetorotational Instability of Dissipative MHD Flows
HERRON, ISOM H
2010-07-10
Executive summary Two important general problems of interest in plasma physics that may be addressed successfully by Magnetohydrodynamics (MHD) are: (1) Find magnetic field configurations capable of confining a plasma in equilibrium. (2) Study the stability properties of each such an equilibrium. It is often found that the length scale of many instabilities and waves that are able to grow or propagate in a system, are comparable with plasma size, such as in magnetically confined thermonuclear plasmas or in astrophysical accretion disks. Thus MHD is able to provide a good description of such large-scale disturbances. The Magnetorotational instability (MRI) is one particular instance of a potential instability. The project involved theoretical work on fundamental aspects of plasma physics. Researchers at the Princeton Plasma Physics Laboratory (PPPL) began to perform a series of liquid metal Couette flow experiments between rotating cylinders. Their purpose was to produce MRI, which they had predicted theoretically 2002, but was only observed in the laboratory since this project began. The personnel on the project consisted of three persons: (1) The PI, who was partially supported on the budget during each of four summers 2005-2008. (2) Two graduate research assistants, who worked consecutively on the project throughout the years 2005-2009. As a result, the first student, Fritzner Soliman, obtained an M.S. degree in 2006; the second student, Pablo Suarez obtained the Ph.D. degree in 2009. The work was in collaboration with scientists in Princeton, periodic trips were made by the PI as part of the project. There were 4 peer-reviewed publications and one book produced.
Eigenanalysis of Ideal Hall MHD Turbulence
Fu, T.; Shebalin, J. V.
2011-12-01
Ideal, incompressible, homogeneous, Hall magnetohydrodynamic (HMHD) turbulence may be investigated through a Fourier spectral method. In three-dimensional periodic geometry, the independent Fourier coefficients represent a canonical ensemble described by a Gaussian probability density. The canonical ensemble is based on the conservation of three invariants: total energy, generalized helicity, and magnetic helicity. Generalized helicity in HMHD takes the place of cross helicity in MHD. The invariants determine the modal probability density giving the spectral structure and equilibrium statistics of ideal HMHD, which are compared to known MHD results. New results in absolute equilibrium ensemble theory are derived using a novel approach that involves finding the eigenvalues of a Hermitian covariance matrix for each modal probability density. The associated eigenvectors transform the original phase space variables into eigenvariables through a special unitary transformation. These are the normal modes which facilitate the analysis of ideal HMHD non-linear dynamics. The eigenanalysis predicts that the low wavenumber modes with very small eigenvalues may have mean values that are large compared to their standard deviations, contrary to the ideal ensemble prediction of zero mean values. (Expectation values may also be relatively large at the highest wave numbers, but the addition of even small levels of dissipation removes any relevance this may have for real-world turbulence.) This behavior is non-ergodic over very long times for a numerical simulation and is termed 'broken ergodicity'. For fixed values of the ideal invariants, the effect is seen to be enhanced with increased numerical grid size. Broken ergodicity at low wave number modes gives rise to large-scale, quasi-stationary, coherent structure. Physically, this corresponds to plasma relaxation to force-free states. For real HMHD turbulence with dissipation, broken ergodicity and coherent structure are still
Global MHD simulations of Neptune's magnetosphere
Mejnertsen, L.; Eastwood, J. P.; Chittenden, J. P.; Masters, A.
2016-08-01
A global magnetohydrodynamic (MHD) simulation has been performed in order to investigate the outer boundaries of Neptune's magnetosphere at the time of Voyager 2's flyby in 1989 and to better understand the dynamics of magnetospheres formed by highly inclined planetary dipoles. Using the MHD code Gorgon, we have implemented a precessing dipole to mimic Neptune's tilted magnetic field and rotation axes. By using the solar wind parameters measured by Voyager 2, the simulation is verified by finding good agreement with Voyager 2 magnetometer observations. Overall, there is a large-scale reconfiguration of magnetic topology and plasma distribution. During the "pole-on" magnetospheric configuration, there only exists one tail current sheet, contained between a rarefied lobe region which extends outward from the dayside cusp, and a lobe region attached to the nightside cusp. It is found that the tail current always closes to the magnetopause current system, rather than closing in on itself, as suggested by other models. The bow shock position and shape is found to be dependent on Neptune's daily rotation, with maximum standoff being during the pole-on case. Reconnection is found on the magnetopause but is highly modulated by the interplanetary magnetic field (IMF) and time of day, turning "off" and "on" when the magnetic shear between the IMF and planetary fields is large enough. The simulation shows that the most likely location for reconnection to occur during Voyager 2's flyby was far from the spacecraft trajectory, which may explain the relative lack of associated signatures in the observations.
A Two-Fluid, MHD Coronal Model
Suess, S. T.; Wang, A.-H.; Wu, S. T.; Poletto, G.; McComas, D. J.
1999-01-01
We describe first results from a numerical two-fluid MHD model of the global structure of the solar Corona. The model is two-fluid in the sense that it accounts for the collisional energy exchange between protons and electrons. As in our single-fluid model, volumetric heat and Momentum sources are required to produce high speed wind from Corona] holes, low speed wind above streamers, and mass fluxes similar to the empirical solar wind. By specifying different proton and electron heating functions we obtain a high proton temperature in the coronal hole and a relatively low proton temperature above the streamer (in comparison with the electron temperature). This is consistent with inferences from SOHO/UltraViolet Coronagraph Spectrometer instrument (UVCS), and with the Ulysses/Solar Wind Observations Over the Poles of the Sun instrument (SWOOPS) proton and electron temperature measurements which we show from the fast latitude scan. The density in the coronal hole between 2 and 5 solar radii (2 and 5 R(sub S)) is similar to the density reported from SPARTAN 201.-01 measurements by Fisher and Guhathakurta [19941. The proton mass flux scaled to 1 AU is 2.4 x 10(exp 8)/sq cm s, which is consistent with Ulysses observations. Inside the closed field region, the density is sufficiently high so that the simulation gives equal proton and electron temperatures due to the high collision rate. In open field regions (in the coronal hole and above the streamer) the proton and electron temperatures differ by varying amounts. In the streamer the temperature and density are similar to those reported empirically by Li et al. [1998], and the plasma beta is larger than unity everywhere above approx. 1.5 R(sub S), as it is in all other MHD coronal streamer models [e.g., Steinolfson et al., 1982; also G. A. Gary and D. Alexander, Constructing the coronal magnetic field, submitted to Solar Physics, 1998].
MHD stability limits in the TCV Tokamak
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
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
A.S. Idowu
2015-03-01
Full Text Available Radiation on magnetohydrodynamic (MHD boundary layer flow of a viscous fluid over an exponentially stretching sheet was considered together with it’s effects. The new technique of homotopy analysis method (nHAM was used to obtain the convergent series expressions for velocity and temperature, where the governig system of partial differential equations has been transformed into ordinary differential equations. The interpretation to these expressions is shown physically through graphs. We observed that the effects of Prandtl and Magnetic number acts in opposite to each other on the temperature.
S.P. Anjali Devi
2010-01-01
Full Text Available Viscous and Joule dissipation effects are considered on MHD nonlinear flow and heat transfer past a stretching porous surface embedded in a porous medium under a transverse magnetic field. Analytical solutions of highly nonlinear momentum equation and confluent hypergeometric similarity solution of heat transfer equations in the case when the plate stretches with velocity varying linearly with distance are obtained. The effect of various parameters like suction parameter, Prandtl number, Magnetic parameter, and Eckert number entering into the velocity field, temperature distribution and skin friction co-efficient at the wall are discussed with the aid of graphs.
S. Mohammed Ibrahim
2014-01-01
Full Text Available The steady two-dimensional radiative MHD boundary layer flow of an incompressible, viscous, electrically conducting fluid caused by a nonisothermal linearly stretching sheet placed at the bottom of fluid saturated porous medium in the presence of viscous dissipation and chemical reaction is studied. The governing system of partial differential equations is converted to ordinary differential equations by using the similarity transformations, which are then solved by shooting method. The dimensionless velocity, temperature, and concentration are computed for different thermophysical parameters, namely, the magnetic parameter, permeability parameter, radiation parameter, wall temperature parameter, Prandtl number, Eckert number, Schmidt number, and chemical reaction.
Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model
Frank, Adam; Jones, T. W.; Ryu, Dongsu
1995-01-01
Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.
Simpson, J. J.; Taflove, A.
2006-12-01
We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations for sub-30 kHz electromagnetic (EM) propagation in the Earth-ionosphere waveguide. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain calculation of EM propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. This is unlike previous FDTD models which assumed azimuthal symmetry about a vertical current source excitation representing a lightning channel. Our model is therefore unique in that it includes fully 3-D anisotropic plasma phenomena in the ionosphere as influenced by the full-vector geomagnetic field. In this study, we show results for EM propagation from lightning strikes using a spherical-coordinate (latitude- longitude) grid having a 1 x 1 x 1 km resolution. Our new model provides additional capabilities to simulate EM wave phenomena arising from whistlers and other lightning-related events, as well as for better understanding anomalous ionospheric phenomena reported to have occurred prior to and during major earthquakes.
Tripathi, Bhavya
2016-01-01
In this paper, effects of heat transfer on the blood flow through a stenosed, inclined non-tapered porous artery subject to the action of external magnetic field is investigated. Viscosity is assumed as variable viscosity with variable Hematocrit throughout the region of the artery. Governing equations have been modeled by taking blood as incompressible magnetohydrodynamic (MHD) Newtonian fluid. The energy equation is formulated by taking an extra factor of the heat source in its equation. The nonlinear momentum equations are simplified under the assumption of mild stenosis. Homotopy perturbation method (HPM) is used to solve nonlinear equations of velocity and temperature profiles. Effects of porosity parameter (Z), applied magnetic field parameter (M), variable hematocrit parameter(Hr), Brinkman number (Br), heat source parameter (Q) and the Grashof number (Gr) on velocity and temperature profiles are discussed graphically.
Chatterjee, Dipankar; Amiroudine, Sakir
2011-02-01
A comprehensive non-isothermal Lattice Boltzmann (LB) algorithm is proposed in this article to simulate the thermofluidic transport phenomena encountered in a direct-current (DC) magnetohydrodynamic (MHD) micropump. Inside the pump, an electrically conducting fluid is transported through the microchannel by the action of an electromagnetic Lorentz force evolved out as a consequence of the interaction between applied electric and magnetic fields. The fluid flow and thermal characteristics of the MHD micropump depend on several factors such as the channel geometry, electromagnetic field strength and electrical property of the conducting fluid. An involved analysis is carried out following the LB technique to understand the significant influences of the aforementioned controlling parameters on the overall transport phenomena. In the LB framework, the hydrodynamics is simulated by a distribution function, which obeys a single scalar kinetic equation associated with an externally imposed electromagnetic force field. The thermal history is monitored by a separate temperature distribution function through another scalar kinetic equation incorporating the Joule heating effect. Agreement with analytical, experimental and other available numerical results is found to be quantitative.
MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts
Sidorenkov, S.I. [D.V. Efremov Scientific Research Inst. of Electrophysical Apparatus, St. Petersburg (Russian Federation); Hua, T.Q. [Argonne National Lab., IL (United States); Araseki, H. [Central Research Inst. of Electric Power Industry, Tokoyo (Japan)
1994-12-31
Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. Argonne National Laboratory and The Efremov Institute have jointly defined several benchmark problems for code validation. The problems, described in this paper, are based on two series of rectangular duct experiments conducted at ANL; one of the series is a joint ANL/Efremov experiment. The geometries consist of variation of aspect ratio and wall thickness (thus wall conductance ratio). The transverse magnetic fields are uniform and nonuniform in the axial direction.
A Novel High-Order, Entropy Stable, 3D AMR MHD Solver with Guaranteed Positive Pressure
Derigs, Dominik; Gassner, Gregor J; Walch, Stefanie
2016-01-01
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code $\\texttt{FLASH}$ (http://flash.uchicago.edu). The accuracy, robustness and computational efficiency is demonstrated with a number of tests, including comparisons to available MHD implementations in $\\texttt{FLASH}$.
Intermittent heating in the solar corona employing a 3D MHD model
Bingert, Sven
2011-01-01
We investigate the spatial and temporal evolution of the heating of the corona of a cool star such as our Sun in a three-dimensional magneto-hydrodynamic (3D MHD) model. We solve the 3D MHD problem numerically in a box representing part of the (solar) corona. The energy balance includes Spitzer heat conduction along the magnetic field and optically thin radiative losses. The self-consistent heating mechanism is based on the braiding of magnetic field lines rooted in the convective photosphere. Magnetic stress induced by photospheric motions leads to currents in the atmosphere which heat the corona through Ohmic dissipation. While the horizontally averaged quantities, such as heating rate, temperature or density, are relatively constant in time, the simulated corona is highly variable and dynamic, on average reaching temperatures and densities as found in observations. The strongest heating per particle is found in the transition region from the chromosphere to the corona. The heating is concentrated in curren...
Alfvén ionization in an MHD-gas interactions code
Wilson, A. D.; Diver, D. A.
2016-07-01
A numerical model of partially ionized plasmas is developed in order to capture their evolving ionization fractions as a result of Alfvén ionization (AI). The mechanism of, and the parameter regime necessary for, AI is discussed and an expression for the AI rate based on fluid parameters, from a gas-MHD model, is derived. This AI term is added to an existing MHD-gas interactions' code, and the result is a linear, 2D, two-fluid model that includes momentum transfer between charged and neutral species as well as an ionization rate that depends on the velocity fields of both fluids. The dynamics of waves propagating through such a partially ionized plasma are investigated, and it is found that AI has a significant influence on the fluid dynamics as well as both the local and global ionization fraction.
A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG
M. K. Griffiths; V. Fedun; R.Erdélyi
2015-03-01
Parallelization techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs), possessing hundreds of processor cores. The opportunity has been recognized by the computational sciences and engineering communities, who have recently harnessed successfully the numerical performance of GPUs. For example, parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Here, we describe the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1–3D MHD code capable of modelling magnetized and gravitationally stratified plasma. The objective of this paper is to present the numerical methods and techniques used for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the performance benchmarks and validation results demonstrating that the code successfully simulates the physics for a range of test scenarios including a full 3D realistic model of wave propagation in the solar atmosphere.
Generalized similarity method in unsteady two-dimensional MHD ...
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International Journal of Engineering, Science and Technology. Vol. 1, No. ... Controlling of crystallization processes in metallurgy and influence of magnetic field on discrete chemical systems bring. MHD and heat ...... Nomenclature. B. [T].
Unsteady MHD free convective flow past a vertical porous plate ...
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2000 Mathematics subject classification: 76 W 05. Keywords: Free ... the design of MHD generators and accelerators, underground water energy storage system etc. ... In many works on plasma physics, the Hall effect is disregarded. But if the.
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...
Raju, C. S. K.; Sandeep, N.; Malvandi, A.
2016-12-01
Nanofluids are potential heat transfer fluids with enhanced thermal and physical properties can be applied in many areas. External magnetic field have tendency to set the thermal and physical properties of nanofluids. With this motivation, we investigated the effects of temperature dependent viscosity, heat source/sink and viscous dissipation on natural convective heat transfer of radiative magnetohydrodynamic (MHD) non-Newtonian nanofluid caused by a cone. For this study, a simulation is performed by mixing of copper nanoparticles in the kerosene. The self similar transformed governing equations are solved by enforcing Runge-Kutta based shooting technique. We acquire the significant accuracy of the recent results by comparing with the published results. In addition, it is indicated that the dual solutions exist for both the base fluid and nanofluid cases. The effects of dimensionless parameters including Eckert number, Weissenberg number, Power-law index, viscous variation parameter, heat source/sink, thermal radiation parameter, and magnetic field parameter on velocity and temperature fields along with the friction factor coefficient and the local Nusselt number are discussed with the help of graphs and tables. It is shown that nanoparticles inclusion into the non-Newtonian fluids has a positive effect on thermal performance. In addition, the viscous variation parameter has a tendency to encourage the friction factor coefficient as well as the heat transfer rate. Moreover, Cu-kerosene nanofluid signifies a better thermal performance than the Ag-kerosene nanofluid.
Passive stabilization in a linear MHD stability code
Todd, A.M.M.
1980-03-01
Utilizing a Galerkin procedure to calculate the vacuum contribution to the ideal MHD Lagrangian, the implementation of realistic boundary conditions are described in a linear stability code. The procedure permits calculation of the effect of arbitrary conducting structure on ideal MHD instabilities, as opposed to the prior use of an encircling shell. The passive stabilization of conducting coils on the tokamak vertical instability is calculated within the PEST code and gives excellent agreement with 2-D time dependent simulations of PDX.
Extraction of MHD Signal Based on Wavelet Transform
赵晴初; 赵彤; 李旻; 黄胜华; 徐佩霞
2002-01-01
Mirnov signals mixed with interferences are a kind of non-stationary signal. It can not obtain satisfactory effects to extract MHD signals from mirnov signals by Fourier Transform. This paper suggests that the wavelet transform can be used to treat mirnov signals. Theoretical analysis and experimental result have indicated that using the time-frequency analysis characteristics of the wavelet transform to filter mirnov signals can remove effectively interferences and extract useful MHD signals.
Magnetohydrodynamic (MHD) flow of Cu-water nanofluid due to a rotating disk with partial slip
Hayat, Tasawar [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia); Rashid, Madiha; Imtiaz, Maria, E-mail: mi-qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, Ahmed [Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2015-06-15
This paper investigates MHD steady flow of viscous nanofluid due to a rotating disk. Water is treated as a base fluid and copper as nanoparticle. Nanofluid fills the porous medium. Effects of partial slip, viscous dissipation and thermal radiation are also considered. Similarity transformations reduce the nonlinear partial differential equations to ordinary differential equations. Flow and heat transfer characteristics are computed by HAM solutions. Also computations for skin friction coefficient and Nusselt number are presented and examined for pertinent parameters. It is noted that higher velocity slip parameter decreases the radial and azimuthal velocities while temperature decreases for larger values of the thermal slip parameter. Also the rate of heat transfer enhances when the nanoparticle volume fraction increases.
Unsteady MHD free convective Couette flow between vertical porous plates with thermal radiation
Basant K. Jha
2015-10-01
Full Text Available This study investigates the unsteady MHD free convective Couette flow of viscous incompressible electrically conducting fluid between two infinite vertical porous plates in the presence of transverse magnetic field and thermal radiation. Solutions for time dependent energy and momentum equations are obtained by the implicit finite difference method. To check the accuracy of the numerical solutions, steady state solutions for energy and momentum equations are obtained by using the perturbation method. The effect of various parameters controlling the physical situation is discussed with the aid of line graphs. Significant results from this study are that both velocity and temperature increase with the increase in thermal radiation parameter and time. A series of numerical experiments show that steady state velocity and temperature occur when the dimensionless time approaches the values of Prandtl number of the fluid. During the course of numerical computation, an excellent agreement was found between unsteady and steady state solutions at large value of time.
Impact of Chemical Reaction on MHD Mixed Convection Heat and Mass Transfer Flow with Thermophoresis
Prabir Kumar KUNDU
2014-02-01
Full Text Available A mathematical model is analyzed in order to study the effects of chemical reaction and thermophoresis on MHD mixed convection boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium, by taking into account the radiative heat flux and variable suction. The governing partial differential equations are transformed into a set of coupled ordinary differential equations which are solved analytically using the regular perturbation technique. Numerical results for dimensionless velocity, temperature, concentration as well as the skin friction coefficient, Nusselt number and Sherwood number are presented through graphs and a table for pertinent parameters to show interesting aspects of the solution.doi:10.14456/WJST.2014.35
Relativistic modeling capabilities in PERSEUS extended MHD simulation code for HED plasmas
Hamlin, Nathaniel D., E-mail: nh322@cornell.edu [438 Rhodes Hall, Cornell University, Ithaca, NY, 14853 (United States); Seyler, Charles E., E-mail: ces7@cornell.edu [Cornell University, Ithaca, NY, 14853 (United States)
2014-12-15
We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest hybrid X-pinch simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as X-pinches and laser-plasma interactions. By suitable formulation of the relativistic generalized Ohm’s law as an evolution equation, we have reduced the recovery of primitive variables, a major technical challenge in relativistic codes, to a straightforward algebraic computation. Our code recovers expected results in the non-relativistic limit, and reveals new physics in the modeling of electron beam acceleration following an X-pinch. Through the use of a relaxation scheme, relativistic PERSEUS is able to handle nine orders of magnitude in density variation, making it the first fluid code, to our knowledge, that can simulate relativistic HED plasmas.
MHD flow of dusty nanofluid over a stretching surface with volume fraction of dust particles
Sandeep Naramgari
2016-06-01
Full Text Available In this study we analyzed the momentum and heat transfer behavior of MHD nanofluid embedded with conducting dust particles past a stretching surface in the presence of volume fraction of dust particles. The governing equations of the flow and heat transfer are transformed into nonlinear ordinary differential equations by using similarity transformation and then solved numerically using Runge–Kutta based shooting technique. The effect of non-dimensional governing parameters on velocity and temperature profiles of the flow are discussed and presented through graphs. Additionally friction factor and the Nusselt number have also been computed. Under some special conditions, numerical results obtained by the present study were compared with the existed studies. The result of the present study proves to be highly satisfactory. The results indicate that an increase in the interaction between the fluid and particle phase enhances the heat transfer rate and reduces the friction factor.
Momentum and Heat Transfer in MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet
T. R. Mahapatra
2013-01-01
Full Text Available In this paper we present a mathematical analysis for the magneto hydrodynamic (MHD axi-symmetric stagnation-point flow and heat transfer over a shrinking sheet which shrinks axi-symmetrically in its own plane. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then these equations are solved numerically by shooting technique. Thermal conductivity is assumed to vary linearly with the temperature. Temperature profiles are obtained for two different types of heating process namely (i the sheet with prescribed surface temperature (PST and (ii the sheet with prescribed surface heat flux (PHF. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.
UNSTEADY PLANE MHD BOUNDARY LAYER FLOW OF A FLUID OF VARIABLE ELECTRICAL CONDUCTIVITY
Zoran B Boričić
2010-01-01
Full Text Available This paper is devoted to the analysis of unsteady plane laminar magnetohydrodynamic (MHD boundary layer flow of incompressible and variable electrical conductivity fluid. The present magnetic field is homogenous and perpendicular to the body surface. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in induction-less approximation. Free stream velocity is an arbitrary differentiable function. Fluid electrical conductivity is decreasing function of velocity ratio. In order to solve the described problem multiparametric (generalized similarity method is used and so-called universal equations are obtained. Obtained universal equations are solved numerically in appropriate approximation and a part of obtained results is given in the form of figures and corresponding conclusions.
M.S Uddin
2011-01-01
Full Text Available The paper is concerned to find the distribution of the chemically reactant solute in the MHD flow of an electrically conducting viscous incompressible fluid over a stretching surface. The first order chemical reaction and the variable solute distribution along the surface are taken into consideration. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of non-linear self-similar ordinary differential equations by using scaling group of transformations. An exact analytic solution is obtained for the velocity field. Using this velocity field, we obtain numerical solution for the reactant concentration field. It reveals from the study that the values of concentration profile enhances with the increase of the magnetic field and decreases with increase of Schmidt number as well as the reaction rate parameter. Most importantly, when the solute distribution along the surface increases then the concentration profile decreases.
Radiation Effect on Mhd Heat and Mass Transfer Flow over a Shrinking Sheet with Mass Suction
patkar ramesh
2014-01-01
Full Text Available A numerical analysis has been carried out to study the effects radiation and heat source/sink on the steady two dimensional magnetohydrodynamic (MHD boundary layer flow of heat and mass transfer past a shrinking sheet with wall mass suction. In the dynamic system, a uniform magnetic field acts normal to the plane of flow. The governing partial differential equations are transformed into self-similar equations are solved by employing finite difference using the quasilinearization technique. From the analysis it is found that the velocity inside the boundary layer increases with increase of wall mass suction and magnetic field and accordingly the thickness of the momentum boundary layer decreases. The temperature decreases with Hartmann number, Prandtl number, and heat sink parameter and the temperature increases with heat source parameter, radiation parameter. The concentration decreases with an increase of Hartmann number, mass suction parameter, Schmidt number, chemical reaction parameter.
Heat Transfer Analysis of MHD Water Functionalized Carbon Nanotube Flow over a Static/Moving Wedge
Waqar A. Khan
2015-01-01
Full Text Available The MHD flow and heat transfer from water functionalized CNTs over a static/moving wedge are studied numerically. Thermal conductivity and viscosity of both single and multiple wall carbon nanotubes (CNTs within a base fluid (water of similar volume are investigated to determine the impact of these properties on thermofluid performance. The governing partial differential equations are converted into nonlinear, ordinary, and coupled differential equations and are solved using an implicit finite difference method with quasi-linearization techniques. The effects of volume fraction of CNTs and magnetic and wedge parameters are investigated and presented graphically. The numerical results are compared with the published data and are found to be in good agreement. It is shown that the magnetic field reduces boundary layer thickness and increases skin friction and Nusselt numbers. Due to higher density and thermal conductivity, SWCNTs offer higher skin friction and Nusselt numbers.
Hayek, W; Carlsson, M; Trampedach, R; Collet, R; Gudiksen, B V; Hansteen, V H; Leenaarts, J
2010-01-01
We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes and improved resolution of hydrodynamical structures. We apply the code to simulate the surface granulation in a solar-type star, ignoring magnetic fields, and investigate the importance of coherent scattering for the atmospheric structure. A scattering term is added to the radiative transfer equation, requiring an iterative computation of the radiation field. We use a short-characteristics-based Gauss-Seidel acceleration scheme to compute radiative flux divergences for the energy equation. The effects of coherent scattering are tested by comparing the temperature stratification of three 3D time-dependent hydrodynamical atmosphere models of a solar-type star: without scattering, with continuum scattering only, and with bo...
Wang, A. H.; Wu, S. T.; Liu, Yang; Hathaway, D.
2008-01-01
We introduce a numerical simulation method for recovering the photospheric velocity field from the vector magnetograms. The traditional method is local correlation tracking (LCT) which is based on measuring the relative displacements of features in blocks of pixels between successive white-light images or magnetograms. Within this method, there are a variety of implementations. One of recently developed implementations is induction local correlation tracking (ILCT) as described by Welsch et al. (2004). They employ the normal component of magnetic induction equation as a constraint to assure consistent solutions. Our numerical method uses the fully three-dimensional MHD equations to recover the photospheric velocity field with individual vector magnetograms. We compare our method to the ILCT method using NOAA AR8210 as an example. The differences and similarities are discussed in detail.
Approximate analytical solution of MHD flow of an Oldroyd 8-constant fluid in a porous medium
Faisal Salah
2014-12-01
Full Text Available The steady flow in an incompressible, magnetohydrodynamic (MHD Oldroyd 8-constant fluid in a porous medium with the motion of an infinite plate is investigated. Using modified Darcy’s law of an Oldroyd 8-constant fluid, the equations governing the flow are modelled. The resulting nonlinear boundary value problem is solved using the homotopy analysis method (HAM. The obtained approximate analytical solutions clearly satisfy the governing nonlinear equations and all the imposed initial and boundary conditions. The convergence of the HAM solutions for different orders of approximation is demonstrated. For the Newtonian case, the approximate analytical solution via HAM is shown to be in close agreement with the exact solution. Finally, the variations of velocity field with respect to the magnetic field, porosity and non-Newtonian fluid parameters are graphically shown and discussed.
Study of MHD activities in the plasma of SST-1
Dhongde, Jasraj; Bhandarkar, Manisha; Pradhan, Subrata, E-mail: pradhan@ipr.res.in; Kumar, Sameer
2016-10-15
Highlights: • An account of MHD activity in the plasma of SST-1 • Observation of MHD instabilities with mode m = 2, n = 1 in SST-1 plasma. • MHD instabilities study of characteristic growth time, growth rate of island and island width etc. in SST-1 plasma. - Abstract: Steady State Superconducting Tokamak (SST-1) is a medium size Tokamak in operation at the Institute for Plasma Research, India. SST-1 has been consistently producing plasma currents in excess of 60 kA, with plasma durations above 400 ms and a central magnetic field of 1.5 T over last few experimental campaigns of 2014. Investigation of these experimental data suggests the presence of MHD activity in the SST-1 plasma. Further analysis clearly explains the behavior of MHD instabilities observed (i.e. tearing modes with m = 2, n = 1), estimating the growth rate and the island width in the SST-1 plasma. Poloidal magnetic field and Toroidal magnetic field fluctuations in SST-1 are observed using Mirnov coils. Onsets of disruptions in connection with MHD activities have been correlated with other diagnostics such as ECE, Density and Hα etc. The observations have been cross compared with the theoretical calculations and are found to be in good agreement.
Wexler, David B.; Hollweg, Joseph V.; Jensen, Elizabeth; Lionello, Roberto; Macneice, Peter J.; Coster, Anthea J.
2017-08-01
Study of coronal MHD wave energetics relies upon accurate representation of plasma particle number densities (ne) and magnetic field strengths. In the lower corona, these parameters are obtained indirectly, and typically presented as empirical equations as a function of heliocentric radial distance (solar offset, SO). The development of coronal global models using synoptic solar surface magnetogram inputs has provided refined characterization of the coronal plasma organization and magnetic field. We present a cross-analysis between a MHD thermodynamic simulation and Faraday rotation (FR) observations over SO 1.63-1.89 solar radii (Rs) near solar minimum. MESSENGER spacecraft radio signals with a line of sight (LOS) passing through the lower corona were recorded in dual polarization using the Green Bank Telescope in November 2009. Polarization position angle changes were obtained from Stokes parameters. The magnetic field vector (B) and ne along the LOS were obtained from a MHD thermodynamic simulation provided by the Community Coordinated Modeling Center. The modeled FR was computed as the integrated product of ne and LOS-aligned B component. The observations over the given SO range yielded an FR change of 7 radians. The simulation reproduced this change when the modeled ne was scaled up by 2.8x, close to values obtained using the Allen-Baumbach equation. No scaling of B from the model was necessary. A refined fit to the observations was obtained when the observationally based total electron content (TEC) curves were introduced. Changes in LOS TEC were determined from radio frequency shifts as the signal passed to successively lower electron concentrations during egress. A good fit to the observations was achieved with an offset of 7e21 m-2 added. Back-calculating ne along the LOS from the TEC curves, we found that the equivalent ne scaling compared to the model output was higher by a factor of 3. The combination of solar surface magnetogram-based MHD coronal
Maget, P.; Huysmans, G. T. A.; Lütjens, H.; Ottaviani, M.; Moreau, Ph; Ségui, J.-L.
2009-06-01
Attempts to run non-inductive plasma discharges on Tore Supra sometimes fail due to the triggering of magneto-hydro-dynamic (MHD) instabilities that saturate at a large amplitude, producing degraded confinement and loss of wave driven fast electrons (the so-called MHD regime (Maget et al 2005 Nucl. Fusion 45 69-80)). In this paper we investigate the transition to this soft (in the sense of non-disruptive) MHD limit from experimental observations, and compare it with non-linear code predictions. Such a comparison suggests that different non-linear regimes, with periodic relaxations or saturation, are correctly understood. However, successful non-inductive discharges without detectable magnetic island at q = 2 cannot be reproduced if realistic transport coefficients are used in the computation. Additional physics seems mandatory for explaining these discharges, such as diamagnetic effects, that could also justify cases of abrupt transition to the MHD regime.
CAFE: A NEW RELATIVISTIC MHD CODE
Lora-Clavijo, F. D.; Cruz-Osorio, A. [Instituto de Astronomía, Universidad Nacional Autónoma de México, AP 70-264, Distrito Federal 04510, México (Mexico); Guzmán, F. S., E-mail: fdlora@astro.unam.mx, E-mail: aosorio@astro.unam.mx, E-mail: guzman@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo. Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán, México (Mexico)
2015-06-22
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin–Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin–Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
CAFE: A New Relativistic MHD Code
Lora-Clavijo, F D; Guzman, F S
2014-01-01
We present CAFE, a new independent code designed to solve the equations of Relativistic ideal Magnetohydrodynamics (RMHD) in 3D. We present the standard tests for a RMHD code and for the Relativistic Hydrodynamics (RMD) regime since we have not reported them before. The tests include the 1D Riemann problems related to blast waves, head-on collision of streams and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the 2D tests, without magnetic field we include the 2D Riemann problem, the high speed Emery wind tunnel, the Kelvin-Helmholtz instability test and a set of jets, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion and the Kelvin-Helmholtz instability. The code uses High Resolution Shock Capturing methods and as a standard set up we present the error analysis with a simple combination that uses the HLLE flux formula combined with linear, PPM ...
CAFE: A New Relativistic MHD Code
Lora-Clavijo, F. D.; Cruz-Osorio, A.; Guzmán, F. S.
2015-06-01
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin-Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin-Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
Pulse Detonation Rocket MHD Power Experiment
Litchford, Ron J.; Cook, Stephen (Technical Monitor)
2002-01-01
A pulse detonation research engine (MSFC (Marshall Space Flight Center) Model PDRE (Pulse Detonation Rocket Engine) G-2) has been developed for the purpose of examining integrated propulsion and magnetohydrodynamic power generation applications. The engine is based on a rectangular cross-section tube coupled to a converging-diverging nozzle, which is in turn attached to a segmented Faraday channel. As part of the shakedown testing activity, the pressure wave was interrogated along the length of the engine while running on hydrogen/oxygen propellants. Rapid transition to detonation wave propagation was insured through the use of a short Schelkin spiral near the head of the engine. The measured detonation wave velocities were in excess of 2500 m/s in agreement with the theoretical C-J velocity. The engine was first tested in a straight tube configuration without a nozzle, and the time resolved thrust was measured simultaneously with the head-end pressure. Similar measurements were made with the converging-diverging nozzle attached. The time correlation of the thrust and head-end pressure data was found to be excellent. The major purpose of the converging-diverging nozzle was to configure the engine for driving an MHD generator for the direct production of electrical power. Additional tests were therefore necessary in which seed (cesium-hydroxide dissolved in methanol) was directly injected into the engine as a spray. The exhaust plume was then interrogated with a microwave interferometer in an attempt to characterize the plasma conditions, and emission spectroscopy measurements were also acquired. Data reduction efforts indicate that the plasma exhaust is very highly ionized, although there is some uncertainty at this time as to the relative abundance of negative OH ions. The emission spectroscopy data provided some indication of the species in the exhaust as well as a measurement of temperature. A 24-electrode-pair segmented Faraday channel and 0.6 Tesla permanent
Pulse Detonation Rocket MHD Power Experiment
Litchford, Ron J.; Cook, Stephen (Technical Monitor)
2002-01-01
A pulse detonation research engine (MSFC (Marshall Space Flight Center) Model PDRE (Pulse Detonation Rocket Engine) G-2) has been developed for the purpose of examining integrated propulsion and magnetohydrodynamic power generation applications. The engine is based on a rectangular cross-section tube coupled to a converging-diverging nozzle, which is in turn attached to a segmented Faraday channel. As part of the shakedown testing activity, the pressure wave was interrogated along the length of the engine while running on hydrogen/oxygen propellants. Rapid transition to detonation wave propagation was insured through the use of a short Schelkin spiral near the head of the engine. The measured detonation wave velocities were in excess of 2500 m/s in agreement with the theoretical C-J velocity. The engine was first tested in a straight tube configuration without a nozzle, and the time resolved thrust was measured simultaneously with the head-end pressure. Similar measurements were made with the converging-diverging nozzle attached. The time correlation of the thrust and head-end pressure data was found to be excellent. The major purpose of the converging-diverging nozzle was to configure the engine for driving an MHD generator for the direct production of electrical power. Additional tests were therefore necessary in which seed (cesium-hydroxide dissolved in methanol) was directly injected into the engine as a spray. The exhaust plume was then interrogated with a microwave interferometer in an attempt to characterize the plasma conditions, and emission spectroscopy measurements were also acquired. Data reduction efforts indicate that the plasma exhaust is very highly ionized, although there is some uncertainty at this time as to the relative abundance of negative OH ions. The emission spectroscopy data provided some indication of the species in the exhaust as well as a measurement of temperature. A 24-electrode-pair segmented Faraday channel and 0.6 Tesla permanent
Present understanding of MHD and heat transfer phenomena for liquid metal blankets
Kirillov, I.R. [D.V. Efremov Scientific Research Institute of Electrophysical Apparatus (Russia); Barleon, L. [Kernforschungszentrum Karlsruhe GmbH (Germany); Reed, C.B. [Argonne National Lab., IL (United States); Miyazaki, K. [Osaka Univ., Suita (Japan). Faculty of Engineering
1994-07-01
A review of experimental work on magnetohydrodynamic (MHD) and heat transfer (HT) characteristics of liquid metal flows in fusion relevant conditions is presented. Experimental data on MHD flow pressure drop in straight channels of round and rectangular cross-section with electroconducting walls in a transverse magnetic field show good agreement with theoretical predictions, and simple engineering formulas are confirmed. Less data are available on velocity distribution and HT characteristics, and even less data are available for channels with electroinsulating walls or artificially made self-heating electroinsulating coatings. Some experiments show an interesting phenomena of HT increase in the presence of a transverse or axial magnetic field. For channels of complex geometry -- expansions, contractions, bends, and manifolds -- few experimental data are available. Future efforts should be directed toward investigation of MHD/HT in straight channels with perfect and nonperfect electroinsulated walls, including walls with controlled imperfections, and in channels of complex geometry. International cooperation in manufacturing and operating experimental facilities with magnetic fields at, or even higher than, 5--7 T with comparatively large volumes may be of great help.
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
Ramakanth Munipalli; P.-Y.Huang; C.Chandler; C.Rowell; M.-J.Ni; N.Morley; S.Smolentsev; M.Abdou
2008-06-05
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as “canonical”,) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
Yang, H.; Bhattacharjee, A.; Forbes, T. G.
2008-12-01
It has long been suggested that eruptive phenomena such as coronal mass ejections, prominence eruptions, and large flares might be caused by a loss of equilibrium in a coronal flux rope (Van Tend and Kuperus, 1978). Forbes et al. (1994) developed an analytical two-dimensional model in which eruptions occur due to a catastrophic loss of equilibrium and relaxation to a lower-energy state containing a thin current sheet. Magnetic reconnection then intervenes dynamically, leading to the release of magnetic energy and expulsion of a plasmoid. We have carried out high-Lundquist-number simulations to test the loss-of equilibrium mechanism, and demonstrated that it does indeed occur in the quasi-ideal limit. We have studied the subsequent dynamical evolution of the system in resistive and Hall MHD models for single as well as multiple arcades. The typical parallel electric fields are super-Dreicer, which makes it necessary to include collisionless effects via a generalized Ohm's law. It is shown that the nature of the local dissipation mechanism has a significant effect on the global geometry and dynamics of the magnetic configuration. The presence of Hall currents is shown to alter the length of the current sheet and the jets emerging from the reconnection site, directed towards the chromosphere. Furthermore, Hall MHD effects break certain symmetries of resistive MHD dynamics, and we explore their observational consequences.
Klimas, A. J.; Uritsky, V.; Vassiliadis, D.; Baker, D. N.
2005-01-01
Loading and consequent unloading of magnetic flux is an essential element of the substorm cycle in Earth's magnetotail. We are unaware of an available global MHD magnetospheric simulation model that includes a loading- unloading cycle in its behavior. Given the central role that MHD models presently play in the development of our understanding of magnetospheric dynamics, and given the present plans for the central role that these models will play in ongoing space weather prediction programs, it is clear that this failure must be corrected. A 2-dimensional numerical driven current-sheet model has been developed that incorporates an idealized current- driven instability with a resistive MHD system. Under steady loading, the model exhibits a global loading- unloading cycle. The specific mechanism for producing the loading-unloading cycle will be discussed. It will be shown that scale-free avalanching of electromagnetic energy through the model, from loading to unloading, is carried by repetitive bursts of localized reconnection. Each burst leads, somewhat later, to a field configuration that is capable of exciting a reconnection burst again. This process repeats itself in an intermittent manner while the total field energy in the system falls. At the end of an unloading interval, the total field energy is reduced to well below that necessary to initiate the next unloading event and, thus, a loading-unloading cycle results. It will be shown that, in this model, it is the topology of bursty localized reconnection that is responsible for the appearance of the loading-unloading cycle.
A Resistive MHD Simulation of the Shear Flow Effects on the Structure of Reconnection Layer
SUN Xiaoxia; WANG Chunhua; LIN Yu; WANG Xiaogang
2007-01-01
By using a one-dimensional resistive magnetohydrodynamic (MHD) model, the Rie-mann problem is solved numerically for the structure of the reconnection layer under a sheared flow along the anti-parallel magnetic field components. The simulation is carried out for general cases with symmetric or asymmetric plasma densities and magnetic fields on the two sides of the initial current sheet, and cases with or without a guide magnetic field, as in various space and fusion plasmas. The generation of MHD discontinuities in the reconnection layer is discussed, including time-dependent intermediate shocks, intermediate shocks, slow shocks, slow expansion waves, and the contact discontinuity. It is shown that the structure of the reconnection layer is significantly affected by the presence of the shear flow. For an initial symmetric current sheet, the symmetry condition is altered due to the shear flow. For cases with an asymmetric initial current sheet, as at the Earth's magnetopause, the strengths of MHD discontinuities change significantly with the shear flow speed. Moreover, the general results for the reconnection layers in the outflow regions on either side of the X line are discussed systematically for the first time.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Computer controlled MHD power consolidation and pulse-generation system
Johnson, R.
The major goal of this project is to establish the feasibility of a power conversion technology which will permit the direct synthesis of computer programmable pulse power. Feasibility will be established in this project by demonstration of direct synthesis of commercial frequency power by means of computer control. The power input to the conversion system is assumed to be a magnetohydrodynamic (MHD) Faraday connected generator which may be viewed as a multi-terminal d.c. source. This consolidation/inversion process is referred to subsequently as Pulse-Amplitude-Synthesis-and-Control (PASC). A secondary goal is to deliver a controller subsystem consisting of a computer, software, and computer interface board which can serve as one of the building blocks for a possible Phase 2 prototype system. This report covers the initial six months portion of the project and includes discussions on the following areas: (1) selection of a control computer with software tool kit for development of the PASC controller contract requirement; (2) problem formulation considerations for simulation of the PASC technique on digital computers; (3) initial simulation results for the PASC transformer, including simulation results obtained using SPICE and the INTEG program; (4) a survey of available gate-turn-off (GTO's), power semiconductors, power field effect transistors (PFET's), and fiber optics signal cabling and transducers.
Ghoumaid, A.; Benamira, F.; Guechi, L. [Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université des Frères Mentouri, Constantine, Route d’Ain El Bey, Constantine (Algeria)
2016-02-15
It is shown that the application of the Nikiforov-Uvarov method by Ikhdair for solving the Dirac equation with the radial Rosen-Morse potential plus the spin-orbit centrifugal term is inadequate because the required conditions are not satisfied. The energy spectra given is incorrect and the wave functions are not physically acceptable. We clarify the problem and prove that the spinor wave functions are expressed in terms of the generalized hypergeometric functions {sub 2}F{sub 1}(a, b, c; z). The energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function.
MHD Disc Winds and Linewidth Distributions
Chajet, Laura S
2013-01-01
We study AGN emission line profiles combining an improved version of the accretion disc-wind model of Murray & Chiang with the magneto-hydrodynamic model of Emmering et al. We show how the shape, broadening and shift of the C IV line depend not only on the viewing angle to the object but also on the wind launching angle, especially for small launching angles. We have compared the dispersions in our model C IV linewidth distributions to observational upper limit on that dispersion, considering both smooth and clumpy torus models. As the torus half-opening angle (measured from the polar axis) increases above about 18? degrees, increasingly larger wind launching angles are required to match the observational constraints. Above a half-opening angle of about 47? degrees, no wind launch angle (within the maximum allowed by the MHD solutions) can match the observations. Considering a model that replaces the torus by a warped disc yields the same constraints obtained with the two other models.
Nonlinear MHD waves in a Prominence Foot
Ofman, Leon; Kucera, Therese; Schmieder, Brigitte
2015-01-01
We study nonlinear waves in a prominence foot using 2.5D MHD model motivated by recent high-resolution observations with Hinode/SOT in Ca~II emission of a prominence on October 10, 2012 showing highly dynamic small-scale motions in the prominence material. Observations of H$\\alpha$ intensities and of Doppler shifts show similar propagating fluctuations. However the optically thick nature of the emission lines inhibits unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity ($\\delta I/I\\sim \\delta n/n$). The waves are evident as significant density fluctuations that vary with height, and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with typical period in the range of 5-11 minutes, and wavelengths $\\sim <$2000 km. Recent Doppler shift observations show the transverse displacement of the propagating wav...
Activation of MHD reconnection on ideal timescales
Landi, S.; Papini, E.; Del Zanna, L.; Tenerani, A.; Pucci, F.
2017-01-01
Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number S, up to 107. Results confirm that when the critical aspect ratio of S 1/3 is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfvénic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be robust, as the predicted scaling is measured both in inviscid simulations and when using a Prandtl number P = 1 in the viscous regime.
Corrosion and arc erosion in MHD channels
Rosa, R.J. (Montana State Univ., Bozeman, MT (United States). Dept. of Mechanical Engineering); Pollina, R.J. (Montana State Univ., Bozeman, MT (United States). Dept. of Mechanical Engineering EG and G Energy Measurements, Inc., Las Vegas, NV (United States))
1992-08-01
The problems connected with gas side corrosion for the design of the lA4 (POC) channel hardware are explored and results of gas side wear rate tests in the Textron Mark VII facility are presented. It is shown that the proposed designs meet a 2000 hour lifetime criterion based upon these materials tests. Improvement in cathode lifetime is demonstrated with lower voltage intercathode gaps. The corrosion of these materials is discussed and it is shown how lifetimes are dependent upon gap voltage and average metal temperature. The importance of uniformity of slagging to the durability of the anode wall is demonstrated. The wear mechanism of the anodes in the MHD channel is analyzed. In addition to gas-side corrosion, the results of specific water corrosion tests of sidewall materials are discussed. All of the tests reported here were carried out to confirm the gas-side performance and the manufacturability of anode and sidewall designs and to address questions posed about the durability of tungsten-copper on the waterside. the results of water corrosion tests of the tungsten copper alloy sidewall material are presented to show that with proper control of waterside pH and, if necessary, dissolved oxygen, one can obtain reliable performance with no degradation of heat transfer with this material. The final choice of materials was determined primarily by the outcome of these tests and also by the question of the manufacturability of the prospective designs.
Boulbe, C
2007-10-15
Interaction between a plasma and a magnetic field appears and has an important role in various domains such as thermonuclear fusion by magnetic confinement or astrophysical plasmas for example. In evolution, these interactions are described by the equations of magnetohydrodynamics (MHD). At equilibrium, the MHD equations result in the magnetostatic equations involving the magnetic field and the kinetic pressure of the plasma. The magnetostatic equations form a system of 3-dimensional non linear partial differential equations involving a magnetic field and a kinetic plasma pressure. When the pressure is supposed negligible, the magnetic field is known as Beltrami field. In a first time, we propose to solve numerically the Beltrami field problem using a fixed point iterative algorithm associated with finite element methods. This iterative strategy is extended in a second time to the computation of magnetostatic configurations with pressure. In the sequel, we interest in the approximation of ideal MHD equations. This system forms a nonlinear hyperbolic conservation law. We propose to use a finite volume approach, in which fluxes are calculated by a Roe's method on a tetrahedral mesh. Fluxes of the magnetic field are modified in order to satisfy the constraint of divergence free imposed on it. The proposed methods have been implemented in two new 3-dimensional codes called TETRAFFF for equilibrium, and TETRAMHD for MHD. The obtained numerical results confirm the high performance of these methods. (author)
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V
2007-01-01
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given.
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru
2008-07-04
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
Doss, E.D. [ed.] [Argonne National Lab., IL (United States); Sikes, W.C. [ed.] [Newport News Shipbuilding and Dry Dock Co., VA (United States)
1992-09-01
This report describes the work performed during Phase 1 and Phase 2 of the collaborative research program established between Argonne National Laboratory (ANL) and Newport News Shipbuilding and Dry Dock Company (NNS). Phase I of the program focused on the development of computer models for Magnetohydrodynamic (MHD) propulsion. Phase 2 focused on the experimental validation of the thruster performance models and the identification, through testing, of any phenomena which may impact the attractiveness of this propulsion system for shipboard applications. The report discusses in detail the work performed in Phase 2 of the program. In Phase 2, a two Tesla test facility was designed, built, and operated. The facility test loop, its components, and their design are presented. The test matrix and its rationale are discussed. Representative experimental results of the test program are presented, and are compared to computer model predictions. In general, the results of the tests and their comparison with the predictions indicate that thephenomena affecting the performance of MHD seawater thrusters are well understood and can be accurately predicted with the developed thruster computer models.
MHD modeling of coronal loops: the transition region throat
Guarrasi, M; Orlando, S; Mignone, A; Klimchuk, J A
2014-01-01
The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. We study the area response with a time-dependent 2D MHD loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal conduction and radiation from optically thin plasma. We run a simulation for a loop 50 Mm long and quasi-statically heated to about 4 MK. We find that the area can change substantially with the quasi-steady heating rate, e.g. by ~40% at 0.5 MK as the loop temperature varies between 1 and 4 MK, and, therefore, affects the interpretation of DEM(T) curves.
Magnetosheath Turbulence at MHD Scales: A Statistical Study
Huang, Shiyong; Sahraoui, Fouad; Hadid, Lina; Yuan, Zhigang
2015-04-01
Turbulence is ubiquitous in space plasmas, such as terrestrial magnetotail and magnetosheath, solar wind, or the interstellar medium. In the solar wind, it is well established that at MHD scales, the magnetic energy spectra generally follow the so-called Kolmogorov's spectrum f-5/3. In the magnetosheath, Alexandrova et al. [2006] observed a Kolmogorov-like inertial range in the frequency range f < fci. In this study, we used three years data from the Cluster mission to statistically investigate the existence of the Kolmogorov inertial range in the whole magnetosheath, including flanks and subsolar regions. Statistical results show that most spectra are shallower than the Kolmogorov one, and have a scaling ~ f-1recalling the energy containing scales of solarwind turbulence. These spectra were found to be populated by uncorrelated fluctuations. The Kolmogorov scaling is observed only away from the bock shock and in the flanks region. These results suggest that random-like fluctuations are generated behind the shock, which reach a fully developed turbulence state only after some time corresponding to their propagation (or advection) away from the shock. At kinetic scales no dependence of the turbulence scaling on the location in the magnetosheath was found.
New aspects of plasma sheet dynamics - MHD and kinetic theory
H. Wiechen
Full Text Available Magnetic reconnection is a process of fundamental importance for the dynamics of the Earth's plasma sheet. In this context, the development of thin current sheets in the near-Earth plasma sheet is a topic of special interest because they could be a possible cause of microscopic fluctuations acting as collective non-idealness from a macroscopic point of view. Simulations of the near-Earth plasma sheet including boundary perturbations due to localized inflow through the northern (or southern plasma sheet boundary show developing thin current sheets in the near-Earth plasma sheet about 810 R_{E} tailwards of the Earth. This location is largely independent from the localization of the perturbation. The second part of the paper deals with the problem of the macroscopic non-ideal consequences of microscopic fluctuations. A new model is presented that allows the quantitative calculation of macroscopic non-idealness without considering details of microscopic instabilities or turbulence. This model is only based on the assumption of a strongly fluctuating, mixing dynamics on microscopic scales in phase space. The result of this approach is an expression for anomalous non-idealness formally similar to the Krook resistivity but now describing the macroscopic consequences of collective microscopic fluctuations, not of collisions.
Key words. Magnetospheric physics (plasma sheet · Space plasma physics (kinetic and MHD theory; magnetic reconnection
3D MHD modeling of twisted coronal loops
Reale, F; Guarrasi, M; Mignone, A; Peres, G; Hood, A W; Priest, E R
2016-01-01
We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the high-beta chromosphere to the low-beta corona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ~30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and X-ray bands. The plasma confined in the flux tube is heated to active region temperatures (~3 MK) after ~2/3 hr. Upflows from the chromosphere up to ~100 km/s fill the core of the flux tube to densities above 10^9 cm^-3. More heating is released in the low corona than the high corona and is finely ...
MHD simulations with resistive wall and magnetic separatrix
Strauss, H. R.; Pletzer, A.; Park, W.; Jardin, S.; Breslau, J.; Sugiyama, L.
2004-12-01
A number of problems in resistive MHD magnetic fusion simulations describe plasmas with three regions: the core, the halo region, and the resistive boundary. Treating these problems requires maintenance of an adequate resistivity contrast between the core and halo. This can be helped by the presence of a magnetic separatrix, which in any case is required for reasons of realistic modeling. An appropriate mesh generation capability is also needed to include the halo region when a separatrix is present. Finally a resistive wall boundary condition is required, to allow both two dimensional and three dimensional magnetic perturbations to penetrate the wall. Preliminary work is presented on halo current simulations in ITER. The first step is the study of VDE (vertical displacement event) instabilities. The growth rate is consistent with scaling inversely proportional to the resistive wall penetration time. The simulations have resistivity proportional to the -3/2 power of the temperature. Simulations have been done with resistivity contrast between the plasma core and wall of 1000 times, to model the vacuum region between the core and resistive shell. Some 3D simulations are shown of disruptions competing with VDEs. Toroidal peaking factors are up to about 3.
3D MHD modeling of twisted coronal loops
Reale, F.; Orlando, S.; Guarrasi, M.; Mignone, A.; Peres, G.; Hood, A. W.; Priest, E. R.
2016-10-01
We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube in the solar atmosphere extending from the high-β chromosphere to the low-β corona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ∼30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and X-ray bands. The plasma confined in the flux tube is heated to active region temperatures (∼3 MK) after ∼2/3 hr. Upflows from the chromosphere up to ∼100 km s‑1 fill the core of the flux tube to densities above 109 cm‑3. More heating is released in the low corona than the high corona and is finely structured both in space and time.
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
M.V.D.N.S.Madhavi
2017-03-01
Full Text Available We analysed in this paper the problem of MHD mixed convection flow from a vertical plate embedded in a saturated porous medium in the presence of melting, thermal dispersion, radiation and heat absorption or generation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by Runge-Kutta fourth order method coupled with shooting technique. The effect of melting and heat absorption or generation under different parametric conditions on velocity, temperature and heat transfer was analyzed for both aiding and opposing flows
Dynamo action in dissipative, forced, rotating MHD turbulence
Shebalin, John V.
2016-06-01
Magnetohydrodynamic (MHD) turbulence is an inherent feature of large-scale, energetic astrophysical and geophysical magnetofluids. In general, these are rotating and are energized through buoyancy and shear, while viscosity and resistivity provide a means of dissipation of kinetic and magnetic energy. Studies of unforced, rotating, ideal (i.e., non-dissipative) MHD turbulence have produced interesting results, but it is important to determine how these results are affected by dissipation and forcing. Here, we extend our previous work and examine dissipative, forced, and rotating MHD turbulence. Incompressibility is assumed, and finite Fourier series represent turbulent velocity and magnetic field on a 643 grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields.
Results from a large-scale MHD propulsion experiment
Petrick, M.; Libera, J.; Bouillard, J. X.; Pierson, E. S.; Hill, D.
Magnetohydrodynamic (MHD) thrusters have long been recognized as potentially attractive candidates for ship propulsion because such systems eliminate the conventional rotating drive components. The MHD thruster is essentially an electromagnetic (EM) pump operating in seawater. An electrical current is passed directly through the seawater and interacts with an applied magnetic field; the interaction of the magnetic field and the electrode current in the seawater results in a Lorentz force acting on the water, and the reaction to this force propels the vessel forward. The concept of EM propulsion has been examined periodically during the past 35 years as an alternative method of propulsion for surface ships and submersibles. The conclusions reached in early studies were that MHD thrusters restricted to fields of 2 T (the state-of-the-art at that time) were impractical and very inefficient. With the evolution of superconducting magnet technology, later studies investigated the performance of MHD thrusters with much higher magnetic field strengths and concluded that at higher fields (greater than 6-T) practical MHD propulsion systems appear possible. The feasibility of attaining the requisite higher magnetic fields has increased markedly because of rapid advances in building high-field superconducting magnets and the recent evolution of high-temperature superconductors.
Benchmarking a hybrid MHD/kinetic code with C-2 experimental data
Magee, Richard; Clary, Ryan; Dettrick, Sean; Korepanov, Sergey; Onofri, Marco; Smirnov, Artem; TAE Team
2013-10-01
The C-2 device creates field-reversed configuration (FRC) plasmas via the dynamic merging of two compact toroids and heated with neutral beams. Simulations of these plasmas are performed with Q2D - a hybrid MHD/Monte Carlo code that evolves the plasma according to the resistive MHD equations and treats the neutral beam injected fast ions as a minority kinetic species. Recent Q2D runs have resulted in testable predictions, namely that the axial profile of the fast ions is double-peaked, and charge-exchange neutrals are localized in pitch-angle. In some simulations, the fast particle population can induce magnetic fluctuations. These fluctuations are largest in the radial component, have a characteristic frequency approximately equal to the fast ion bounce frequency (f ~ 150 kHz), and a broad k spectrum. These fluctuations have the beneficial effect of smoothing out the double-peaked axial fast ion density profile, resulting in an increased fast ion density at the mid-plane. We will present results from a benchmarking study to quantitatively compare the results of Q2D runs to existing C-2 experimental data.
Kinetic cascade beyond MHD of solar wind turbulence in two-dimensional hybrid simulations
Verscharen, Daniel; Motschmann, Uwe; Müller, Joachim
2012-01-01
The nature of solar wind turbulence in the dissipation range at scales much smaller than the large MHD scales remains under debate. Here a two-dimensional model based on the hybrid code abbreviated as A.I.K.E.F. is presented, which treats massive ions as particles obeying the kinetic Vlasov equation and massless electrons as a neutralizing fluid. Up to a certain wavenumber in the MHD regime, the numerical system is initialized by assuming a superposition of isotropic Alfv\\'en waves with amplitudes that follow the empirically confirmed spectral law of Kolmogorov. Then turbulence develops and energy cascades into the dispersive spectral range, where also dissipative effects occur. Under typical solar wind conditions, weak turbulence develops as a superposition of normal modes in the kinetic regime. Spectral analysis in the direction parallel to the background magnetic field reveals a cascade of left-handed Alfv\\'en/ion-cyclotron waves up to wave vectors where their resonant absorption sets in, as well as a cont...
Extension of the MURaM Radiative MHD Code for Coronal Simulations
Rempel, M.
2017-01-01
We present a new version of the MURaM radiative magnetohydrodynamics (MHD) code that allows for simulations spanning from the upper convection zone into the solar corona. We implement the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction, and an equilibrium ionization equation of state. We artificially limit the coronal Alfvén and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantify the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be obtained with values of the reduced speed of light just marginally larger than the maximum sound speed. Overall this leads to a fully explicit code that can compute the time evolution of the solar corona in response to photospheric driving using numerical time steps not much smaller than 0.1 s. Numerical simulations of the coronal response to flux emergence covering a time span of a few days are well within reach using this approach.
A New Axisymmetric MHD Model of the Interaction of the Solar Wind with Venus
DeZeeuw, Darren L.; Nagy, Andrew F.; Gombosi, Tamas I.; Powell, Kenneth G.; Luhmann, Janet G.
1996-01-01
A new two-dimensional axisymmetric MHD model is used to study the interaction of the solar wind with Venus under conditions where the interplanetary field is approximately aligned with the solar wind velocity. This numerical model solves the MHD transport equations for density, velocity, pressure, and magnetic field on an adaptively refined, unstructured grid system. This use of an adaptive grid allows high spatial resolution in regions of large density/velocity gradients and yet can be run on a workstation. The actual grid sizes vary from about 0.06 R(sub v) near the bowshock to 2 R(sub v) in the unperturbed solar wind. The results of the calculations are compared with observed magnetic field values obtained from the magnetometer on the Pioneer Venus Orbiter, at a time when the angle between the solar wind velocity vector and the interplanetary magnetic field (IMF) was only 7.6 deg. Good qualitative agreement between the observed and calculated field behavior is found. The overall results suggest that the induced magnetotail disappears when the IMF is radial for an extended time period and implies that it weakens when the field rotated through a near-radial orientation.
CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel
2017-08-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD
Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie
2017-02-01
Entropy stable schemes can be constructed with a specific choice of the numerical flux function. First, an entropy conserving flux is constructed. Secondly, an entropy stable dissipation term is added to this flux to guarantee dissipation of the discrete entropy. Present works in the field of entropy stable numerical schemes are concerned with thorough derivations of entropy conservative fluxes for ideal MHD. However, as we show in this work, if the dissipation operator is not constructed in a very specific way, it cannot lead to a generally stable numerical scheme. The two main findings presented in this paper are that the entropy conserving flux of Ismail & Roe can easily break down for certain initial conditions commonly found in astrophysical simulations, and that special care must be taken in the derivation of a discrete dissipation matrix for an entropy stable numerical scheme to be robust. We present a convenient novel averaging procedure to evaluate the entropy Jacobians of the ideal MHD and the compressible Euler equations that yields a discretization with favorable robustness properties.
A novel code for numerical 3-D MHD studies of CME expansion
J. Kleimann
2009-03-01
Full Text Available A recent third-order, essentially non-oscillatory central scheme to advance the equations of single-fluid magnetohydrodynamics (MHD in time has been implemented into a new numerical code. This code operates on a 3-D Cartesian, non-staggered grid, and is able to handle shock-like gradients without producing spurious oscillations.
To demonstrate the suitability of our code for the simulation of coronal mass ejections (CMEs and similar heliospheric transients, we present selected results from test cases and perform studies of the solar wind expansion during phases of minimum solar activity. We can demonstrate convergence of the system into a stable Parker-like steady state for both hydrodynamic and MHD winds. The model is subsequently applied to expansion studies of CME-like plasma bubbles, and their evolution is monitored until a stationary state similar to the initial one is achieved. In spite of the model's (current simplicity, we can confirm the CME's nearly self-similar evolution close to the Sun, thus highlighting the importance of detailed modelling especially at small heliospheric radii.
Additionally, alternative methods to implement boundary conditions at the coronal base, as well as strategies to ensure a solenoidal magnetic field, are discussed and evaluated.
Key contributions in MHD power generation. Quarterly report, 1 June 1979-31 August 1979
Louis, J F
1979-11-01
Activities during the third quarter of the contract period are reported in detail. The tasks reported on include: (1) investigation of electrical behavior in the vicinity of electrode and insulating walls; (2) studies of critical performance issues in the development of combustion disk generators; (3) development and testing of electrode modules, including studies of insulator properties; and (4) determination of coal combustion kinetics and ash behavior relevant to two-stage MHD combustors, and investigation of the mixing and flow aerodynamics of a high swirl geometry second stage.