Ideal magnetohydrodynamic (MHD) equations and multi-parallel-fluid MHD theory

2019 ◽  
Author(s):  
Linjin Zheng
Keyword(s):  
Mhd Equations ◽  
Ideal Magnetohydrodynamic

Axisymmetric Magnetohydrodynamic Equilibria without a Wall

1993 ◽  
Vol 48 (12) ◽  
pp. 1131-1150
Author(s):  
D. Lortz ◽  
W. Haimerl
Keyword(s):  
Magnetic Field ◽  
Homogeneous Magnetic Field ◽  
Mhd Equations ◽  
External Current ◽  
Flux Function ◽  
Plasma Torus ◽  
Ideal Magnetohydrodynamic ◽  
Axisymmetric Configuration ◽  
A Current ◽  
The Ideal

Abstract Starting from the ideal magnetohydrodynamic (MHD) equations, we consider the following axisymmetric configuration: a current-carrying plasma torus in a homogeneous magnetic field that is aligned parallel to the torus axis. At a certain field strength this configuration is in equilibrium without need of external current singularities such as wires or walls.The magnetic flux function is expanded in small inverse aspect ratio. The geometry of this configuration is completely determined to second order as a function of the profile parameters.

scholarly journals DYNAMO EFFECTS IN MAGNETIZED IDEAL PLASMA COSMOLOGIES

2008 ◽  
Vol 23 (11) ◽  
pp. 1697-1710 ◽  
Author(s):  
KOSTAS KLEIDIS ◽  
APOSTOLOS KUIROUKIDIS ◽  
DEMETRIOS PAPADOPOULOS ◽  
LOUKAS VLAHOS
Keyword(s):  
Magnetic Field ◽  
Cosmological Model ◽  
Homogeneous Magnetic Field ◽  
Mhd Equations ◽  
Cosmological Perturbations ◽  
Gravitational Instabilities ◽  
Ideal Magnetohydrodynamic ◽  
The Magnetic Field ◽  
Ideal Plasma ◽  
The Ideal

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what is most important, is that, at late times, the magnetic-induction contrast(δB/B) grows, resulting in the enhancement of the ambient magnetic field. This process can be particularly favored by condensations, formed within the plasma fluid due to gravitational instabilities.

A new decay channel for compressional Alfvén waves in plasmas

2008 ◽  
Vol 74 (1) ◽  
pp. 99-105 ◽  
Author(s):  
G. BRODIN ◽  
P. K. SHUKLA ◽  
L. STENFLO
Keyword(s):  
Decay Channel ◽  
Magnetized Plasma ◽  
Mhd Equations ◽  
Alfven Wave ◽  
Wave Interactions ◽  
Decay Products ◽  
Laboratory Plasmas ◽  
Ideal Magnetohydrodynamic ◽  
Hall Mhd ◽  
The Ideal

AbstractWe present a new efficient wave decay channel involving nonlinear interactions between a compressional Alfvén wave, a kinetic Alfvén wave, and a modified ion sound wave in a magnetized plasma. It is found that the wave coupling strength of the ideal magnetohydrodynamic (MHD) theory is much increased when the effects due to the Hall current are included in a Hall–MHD description of wave–wave interactions. In particular, with a compressional Alfvén pump wave well described by the ideal MHD theory, we find that the growth rate is very high when the decay products have wavelengths of the order of the ion thermal gyroradius or shorter, in which case they must be described by the Hall–MHD equations. The significance of our results to the heating of space and laboratory plasmas as well as for the Solar corona and interstellar media are highlighted.

scholarly journals A resistive extension for ideal magnetohydrodynamics

2019 ◽  
Vol 491 (4) ◽  
pp. 5510-5523
Author(s):  
Alex James Wright ◽  
Ian Hawke
Keyword(s):  
Initial Data ◽  
First Principles ◽  
Source Term ◽  
Mhd Equations ◽  
Fine Tuning ◽  
Additional Source ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Ideal Magnetohydrodynamics ◽  
Ideal Magnetohydrodynamic

ABSTRACT We present an extension to the special relativistic, ideal magnetohydrodynamic (MHD) equations, designed to capture effects due to resistivity. The extension takes the simple form of an additional source term that, when implemented numerically, is shown to emulate the behaviour produced by a fully resistive MHD description for a range of initial data. The extension is developed from first principles arguments, and thus requires no fine-tuning of parameters, meaning it can be applied to a wide range of dynamical systems. Furthermore, our extension does not suffer from the same stiffness issues arising in resistive MHD, and thus can be evolved quickly using explicit methods, with performance benefits of roughly an order of magnitude compared to current methods.

Structures of reconnection layers based on the ideal magnetohydrodynamic equations

1994 ◽  
Vol 51 (3) ◽  
pp. 381-398
Author(s):  
Wenlong Dai ◽  
Paul R. Woodward
Keyword(s):  
Numerical Simulations ◽  
Quantitative Agreement ◽  
Mhd Equations ◽  
Riemann Solver ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
Ideal Mhd ◽  
Ideal Magnetohydrodynamic ◽  
The One ◽  
The Ideal

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.

scholarly journals Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes

2016 ◽  
Vol 19 (4) ◽  
pp. 841-880 ◽  
Author(s):  
Zhiliang Xu ◽  
Dinshaw S. Balsara ◽  
Huijing Du
Keyword(s):  
Magnetic Field ◽  
Finite Volume ◽  
Normal Component ◽  
Mhd Equations ◽  
Finite Volume Scheme ◽  
Reconstruction Method ◽  
Triangular Meshes ◽  
Weno Reconstruction ◽  
Divergence Free ◽  
Ideal Magnetohydrodynamic

AbstractIn this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on two-dimensional triangular meshes. A new divergence-free WENO-based reconstruction method is developed to maintain exactly divergence-free evolution of the numerical magnetic field. In this formulation, the normal component of the magnetic field at each face of a triangle is reconstructed uniquely and with the desired order of accuracy. Additionally, a new weighted flux interpolation approach is also developed to compute the z-component of the electric field at vertices of grid cells. We also present numerical examples to demonstrate the accuracy and robustness of the proposed scheme.

Relaxation of a non-ideal incompressible plasma with mass flow

1999 ◽  
Vol 62 (2) ◽  
pp. 195-202 ◽  
Author(s):  
O. K. CHEREMNYKH ◽  
J. W. EDENSTRASSER ◽  
V. V. GORIN
Keyword(s):  
Mass Flow ◽  
Temporal Structure ◽  
Diffusion Problem ◽  
Hydrostatic Equilibrium ◽  
Mhd Equations ◽  
Nonlinear Vector ◽  
Ideal Magnetohydrodynamic ◽  
Gravitating Systems ◽  
Analytical Time ◽  
The Magnetic Field

The time evolution of an incompressible non-ideal magnetohydrodynamic (MHD), current-carrying plasma with mass flow is investigated. An approach for the reduction of the nonlinear vector MHD equations to a set of scalar partial differential equations is supposed. Analytical time-dependent solutions of this system are presented. They describe kinetic plasma equilibria both with well-defined nested-in magnetic and velocity surfaces and in the form of vortices. The obtained solutions may be called ‘diffusion-like’, since their temporal structure is very similar to the solutions of the diffusion problem. It is shown that the magnetic field and the velocity have different dumping rates. In the asymptotic limit t→∞, the plasma slowly relaxes towards the hydrostatic equilibrium of gravitating systems.

Geometrical shock dynamics for magnetohydrodynamic fast shocks

2016 ◽  
Vol 811 ◽  
Author(s):  
W. Mostert ◽  
D. I. Pullin ◽  
R. Samtaney ◽  
V. Wheatley
Keyword(s):  
Mach Number ◽  
Two Dimensions ◽  
Mhd Equations ◽  
Relative Pressure ◽  
Gas Dynamic ◽  
Shock Dynamics ◽  
Geometrical Shock Dynamics ◽  
Ideal Magnetohydrodynamic ◽  
The Stability ◽  
Spatially Varying

We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as $\unicode[STIX]{x1D716}^{-1}$, where $\unicode[STIX]{x1D716}$ is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock.

On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 1. Fundamental principles

1995 ◽  
Vol 283 ◽  
pp. 125-139 ◽  
Author(s):  
V. A. Vladimirov ◽  
H. K. Moffatt
Keyword(s):  
Alternative Energy ◽  
Variational Principles ◽  
Three Dimensional ◽  
Mhd Flow ◽  
Mhd Equations ◽  
Least Action ◽  
The First Variation ◽  
Ideal Magnetohydrodynamic ◽  
And Variational Principles ◽  
Energy Type

A new frozen-in field w (generalizing vorticity) is constructed for ideal magnetohydrodynamic flow. In conjunction with the frozen-in magnetic field h, this is used to obtain a generalized Weber transformation of the MHD equations, expressing the velocity as a bilinear form in generalized Weber variables. This expression is also obtained from Hamilton's principle of least action, and the canonically conjugate Hamiltonian variables for MHD flow are identified. Two alternative energy-type variational principles for three-dimensional steady MHD flow are established. Both involve a functional R which is the sum of the total energy and another conserved functional, the volume integral of a function Φ of Lagrangian coordinates. It is shown that the first variation δ1R vanishes if Φ is suitably chosen (as minus a generalized Bernoulli integral). Expressions for the second variation δ2R are presented.

Sign in / Sign up

Export Citation Format

Share Document