On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 2. Stability criteria for two-dimensional flows

1996 ◽  
Vol 329 ◽  
pp. 187-205 ◽  
Author(s):  
V. A. Vladimirov ◽  
H. K. Moffatt ◽  
K. I. Ilin
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Variational Principles ◽  
Two Dimensional ◽  
Ideal Fluids ◽  
The Mean ◽  
And Variational Principles ◽  
The Second Variation ◽  
The Magnetic Field ◽  
Standard Techniques

The techniques developed in Part 1 of the present series are here applied to two-dimensional solutions of the equations governing the magnetohydrodynamics of ideal incompressible fluids. We first demonstrate an isomorphism between such flows and the flow of a stratified fluid subjected to a field of force that we describe as ‘pseudo-gravitational’. We then construct a general Casimir as an integral of an arbitrary function of two conserved fields, namely the vector potential of the magnetic field, and the analogous potential of the ‘modified vorticity field’, the additional frozen field introduced in Part 1. Using this Casimir, a linear stability criterion is obtained by standard techniques. In §4, the (Arnold) techniques of nonlinear stability are developed, and bounds are placed on the second variation of the sum of the energy and the Casimir of the problem. This leads to criteria for nonlinear (Lyapunov) stability of the MHD flows considered. The appropriate norm is a sum of the magnetic and kinetic energies and the mean-square vector potential of the magnetic field.

On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part III. Stability criteria for axisymmetric flows

1997 ◽  
Vol 57 (1) ◽  
pp. 89-120 ◽  
Author(s):  
V. A. VLADIMIROV ◽  
H. K. MOFFATT ◽  
K. I. ILIN
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Variational Principles ◽  
Sufficient Conditions ◽  
Boussinesq Approximation ◽  
Mhd Flows ◽  
Ideal Fluids ◽  
Axisymmetric Solutions ◽  
And Variational Principles ◽  
The Magnetic Field

The general theory developed in Part I of the present series is here applied to axisymmetric solutions of the equations governing the magnetohydrodynamics of ideal incompressible fluids. We first show a helpful analogy between axisymmetric MHD flows and flows of a stratified fluid in the Boussinesq approximation. We then construct a general Casimir as an integral of an arbitrary function of two conserved fields, namely the vector potential of the magnetic field and the scalar field associated with the ‘modified vorticity field’, the additional frozen-in field introduced in Part I. Using this Casimir, sufficient conditions for linear stability to axisymmetric perturbations are obtained by standard Arnold techniques. We exploit Arnold's method to obtain sufficient conditions for nonlinear (Lyapunov) stability of the MHD flows considered. The appropriate norm is a sum of the magnetic and kinetic energies and the mean square vector potential of the magnetic field.

On the stability of parallel flows with parallel magnetic fields

1966 ◽  
Vol 293 (1434) ◽  
pp. 342-358 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Parallel Magnetic Field ◽  
Parallel Flows ◽  
The Mean ◽  
The Stability ◽  
The Magnetic Field ◽  
Parallel Magnetic Fields

The first part of the paper is a physical discussion of the way in which a magnetic field affects the stability of a fluid in motion. Particular emphasis is given to how the magnetic field affects the interaction of the disturbance with the mean motion. The second part is an analysis of the stability of plane parallel flows of fluids with finite viscosity and conductivity under the action of uniform parallel magnetic fields. We show that, in general, three-dimensional disturbances are the most unstable, thus disagreeing with the conclusion of Michael (1953) and Stuart (1954). We show how results obtained for two-dimensional disturbances can be used to calculate the most unstable three-dimensional disturbances and thence we prove that a parallel magnetic field can never completely stabilize a parallel flow.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

scholarly journals Modelling of the Magnetic Configuration of CP Stars from Polarimetric Observations

1998 ◽  
Vol 11 (2) ◽  
pp. 679-681
Author(s):  
M. Landolfi
Keyword(s):  
Magnetic Field ◽  
Stokes Parameter ◽  
Quadratic Field ◽  
Mean Field ◽  
Longitudinal Component ◽  
Stokes Parameters ◽  
Longitudinal Field ◽  
The Mean ◽  
The Magnetic Field ◽  
Polarized Radiation

The observational quantities commonly used to study the magnetic field of CP stars – the mean field modulus and the mean longitudinal field, as well as the ‘mean asymmetry of the longitudinal field’ and the ‘mean quadratic field’ recently introduced by Mathys (1995a,b) – are based either on the Stokes parameter / or on the Stokes parameter V. However, a complete description of polarized radiation requires the knowledge of the full Stokes vector: in other words, we should expect that useful information is also contained in linear polarization (the Stokes parameters Q and U); or rather we should expect the information contained in (Q, U) and in V to be complementary, since linear and circular polarization are basically related to the transverse and the longitudinal component of the magnetic field, respectively.

scholarly journals Simulating Solar Global Magnetism in 3-D

2012 ◽  
Vol 10 (H16) ◽  
pp. 101-103
Author(s):  
A. S. Brun ◽  
A. Strugarek
Keyword(s):  
Magnetic Field ◽  
Recent Progress ◽  
Convection Zone ◽  
Thermal Structure ◽  
Solar Convection ◽  
Self Consistent ◽  
The Mean ◽  
The Magnetic Field

AbstractWe briefly present recent progress using the ASH code to model in 3-D the solar convection, dynamo and its coupling to the deep radiative interior. We show how the presence of a self-consistent tachocline influences greatly the organization of the magnetic field and modifies the thermal structure of the convection zone leading to realistic profiles of the mean flows as deduced by helioseismology.

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

scholarly journals A case study of the plasma in the magneto-sheath using the numerical magnetosheath-magnetosphere model and THEMIS measure-ments

2018 ◽  
Vol 145 ◽  
pp. 03004
Author(s):  
Polya Dobreva ◽  
Olga Nitcheva ◽  
Monio Kartalev
Keyword(s):  
Magnetic Field ◽  
Field Model ◽  
Specific Aspect ◽  
Plasma Parameters ◽  
Ion Density ◽  
Magnetic Field Model ◽  
Wind Spacecraft ◽  
The Mean ◽  
The Magnetic Field

This paper presents a case study of the plasma parameters in the magnetosheath, based on THEMIS measurements. As a theoretical tool we apply the self-consistent magnetosheath-magnetosphere model. A specific aspect of the model is that the positions of the bow shock and the magnetopause are self-consistently determined. In the magnetosheath the distribution of the velocity, density and temperature is calculated, based on the gas-dynamic theory. The magnetosphere module allows for the calculation of the magnetopause currents, confining the magnetic field into an arbitrary non-axisymmetric magnetopause. The variant of the Tsyganenko magnetic field model is applied as an internal magnetic field model. As solar wind monitor we use measurements from the WIND spacecraft. The results show that the model quite well reproduces the values of the ion density and velocity in the magnetosheath. The simlicity of the model allows calulations to be perforemed on a personal computer, which is one of the mean advantages of our model.

scholarly journals INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

2021 ◽  
Author(s):  
Jasim Mohmed Jasim Jasim ◽  
Iryna Shvedchykova ◽  
Igor Panasiuk ◽  
Julia Romanchenko ◽  
Inna Melkonova
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Three Dimensional ◽  
Magnetic Potential ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Air Gaps ◽  
Vector Magnetic Potential ◽  
Electromagnetic Separator ◽  
The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

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