Magnetostatic Solutions Research Articles

On the Magnetic Field Orientation and Plasma Flows in Solar Filament Barbs

Speeds of vertical flows in quiescent solar filaments are typically much less than the local Alfven speed. This is why the flows in filament barbs can be modeled by perturbing a magnetostatic solution describing a balance between the Lorentz force, gravity, and gas pressure in a barb. This approach explains why some of the flows are neither aligned with the magnetic field nor controlled by gravity. Both the observed upflows and the magnetic field dips in barbs are likely to be caused by photospheric magnetic reconnection.

Coupled magnetostatic/microwave solver for ferrite edge-mode phase shifters

A linked static/microwave finite element solver for the analysis of ferrite-loaded waveguides with arbitrary geometry and magnetization is described. The magnetostatic solution of the DC bias circuit and ferrite magnetization curve are used to construct the tensor permeability for the microwave solver. This avoids using normalized tensor entries or demagnetizing fields and it caters for non-uniform bias fields. Split phase constants and a higher-order mode diagram are presented for the case of a quasi-planar stripline edge mode phase shifter. Field plots illustrate the edge mode phenomena. Copyright © 1999 John Wiley & Sons, Ltd.

Modified scalar potential solution for three-dimensional magnetostatic problems

A novel three-dimensional magnetostatic solution based on a modified scalar potential method has been developed. This method has significant advantages over the traditional total scalar, reduced scalar, or vector potential methods. The new method was successfully applied to a three-dimensional geometry of an iron core inductor and a permanent magnet motor. The results obtained are in close agreement with those obtained from traditional methods.

Algorithms of data processing for distributed multychannel SQUID-gradiometer system in the case of magnetic field source localization

Algorithms of magnetostatic inverse problem solution for dipole and multipole layer of unidirected dipole are examined. Inverse problems are solved by analytical methods. By the numerical examples practical realizability of data processing methods is shown.

Coupled elements for problems involving movement (switched reluctance motor)

A novel technique for use in finite-element models of devices which move is proposed. Independence meshes are coupled together with a suitable interface, such as the air gap of a conventional electrical machine, using Lagrange multipliers. The proposed approach allows a finite-element mesh to move with respect to an adjacent mesh without any need for remeshing. At different positions, only the terms which couple the meshes together at the interface are altered. While only the problem of producing many different magnetostatic solutions or 'snapshots' of the rotor at different instants in time is addressed here, the authors expect that treating velocity-induced eddy currents in a time-transient situation should be possible by extending the same basic techniques.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On two-dimensional magnetostatic equilibria and their stability

A class of analytic solutions is presented to study two-dimensional magnetostatic equlibria and their stability, ignoring the energy equation. A magnetostatic equilibrium solution is constructed for an arbitrary potential magnetic field by introducing two functions of its magnetic flux function to vary the magnetic field strength on the fixed field lines, changing the thermodynamic structure of the plasma so that the mechanical equilibrium in the presence of an external gravity is satisfied. It is found that the instabilities of such equilibria are associated with gas pressure gradients parallel to the magnetic field and electric currents. Some general criteria are given for these instabilities, and their application is illustrated by examples. 16 references.

On a family of solutions of the Einstein-Maxwell equations

A family of axisymmetric asymptotically flat solutions of the Einstein-Maxwell field equations is presented. In a particular case we obtain a magnetostatic solution which reduces to the well-known Schwarzschild metric in the absence of a magnetic field and describes the exterior gravitational field of a massive magnetic dipole moment.

Edge effects on foil fuses

We investigate the edge effect on foil fuses in a cylindrical enclosure containing a tamping medium. This type of fuse is being considered for use in microsecond switching of high power electromagnetic pulses. By using the exact magnetostatic solution for axial current lines in a cylindrical enclosure, we find a circuitlike model for the foil fuse and the driving external circuit. The foil resistivity is a function of the joule heat per unit volume dissipated at each position along the width of the foil. In the extreme example given in this letter, we find that the strong edge effects observed at the beginning of the pulses ‘‘heal’’ faster than the time it takes for the foil to switch and hence, edge effects, even in such cases are not important.

Stationary solutions in five-dimensional general relativity

Asymptotically Minkowskian stationary axisymmetric solutions of the five-dimensional Einstein equations are generated from particular classes of stationary axisymmetric solutions of the four-dimensional Einstein-Maxwell equations. First, the five-dimensional electrostatic and magnetostatic solutions are generated from the four-dimensional electrostatic solutions and a harmonic scalar field. Then, a new class of five-dimensional nonstatic solutions are generated from the four-dimensional class ℰ=+1. As an example, a three-parameter family of regular asymptotically flat rotating solutions is constructed. These solutions can be interpreted, after dimensional reduction to four dimensions, as extended elementary particles with mass, spin, electric charge, and magnetic dipole moment.

Stationary axisymmetric fields in Generalized Theory of Gravitation

The problem of stationary axisymmetric gravitational fields is formulated within the framework of Generalized Theory of Gravitation. It is shown that solutions of the problem mentioned above may be found, if analogous solutions in General Relativity are obtained. As an illustration a Kerr-like solution is offered. A generation theorem for finding magnetostatic solution from stationary vacuum solutions is proposed.

Generator Simulation-Model Constants by Finite Elements: Comparison with Test Results

This paper describes the development and validation of a process combining finite element techniques and improved equivalent circuit analysis methods to find circuit data for a generator directly from the generator design. This work was accomplished under EPRI Research Projects RP1288 and RP1513. The process uses non-linear magnetostatic methods to find a steady-state two-dimension flux pattern and next, a linear diffusion method to find the small-signal frequency response of the generator in terms of frequency-dependent operational inductances, such as lfd(s) and lddo(s). Correspondence of the small signal inductances to small perturbations around the given load point is ensured through the use of incremental permeabilities. The incremental permeabilities are assigned to match the local steady-state flux density, obtained from the initial magnetostatic load-point solution. The equivalent circuit model data are found by multi-variable curve fitting techniques, simultaneously fitting the rotor, stator, and field circuit constants to the operational inductance data.

The rotation axis for stationary and axisymmetric space-times

A set of 'extended' regularity conditions is discussed which have to be satisfied on the rotation axis if the latter is assumed to be also an axis of symmetry. For a wide class of energy-momentum tensors these conditions can hold at the origin of the Weyl canonical coordinate. For static and cylindrically symmetric space-times the conditions can be derived from the regularity of the Riemann tetrad coefficients on the axis. For stationary space-times, however, the extended conditions do not necessarily hold, even when 'elementary flatness' is satisfied and when there are no curvature singularities on the axis. The authors generalise the result by Davies and Caplan (1971) for cylindrically symmetric stationary Einstein-Maxwell fields, by proving that only Minkowski space-time and a particular magnetostatic solution possess a regular axis of rotation. Further, several sets of solutions for neutral and charged, rigidly and differentially rotating dust are discussed. In most cases only very narrow classes of solutions satisfy the extended requirements.

Finite element postprocessing for direct current machines

A stand-alone microcomputer workstation uses finite element methods to solve for the vector potential of dc machines. Vector potential solutions result in calculation of dc machine design parameters such as volts/bar, losses, inductances and flux densities using postprocessing design programs. The design parameters are calculated for two-dimensional, non-linear magnetostatic and linear eddy current vector potential solutions.

Poisson finite difference boundary equations for the magnetic potentials

Magnetostatic solutions may be obtained by using Laplace's equation in finite difference form. The boundary equations are of primary importance and even these have been put forward as special forms of Laplace's equation. They can be derived in what appears to be a simpler and more flexible manner by assuming that Poisson's equation applies at the interface for both scalar and vector potentials.

Nonlinear periodic solutions for the isothermal magnetostatic atmosphere

A set of analytical, periodic magnetostatic solutions is presented describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field. The magnetic field has no component along the filament, and the temperature is uniform in space. The problem is two dimensional and reduces to solving the magnetostatic equation of Dungey in a nonlinear form. Different field topologies are associated with the same basic plasma structure, depending on the sign and strength of the field far above and below the array of parallel filaments. These equilibria are shown to be locally unstable against ideal magnetohydrodynamic perturbations having large wavenumbers along the plasma filaments. It is suggested that the system may be stabilized if there is a component of the magnetic field parallel to the plasma filaments.

Self-induced magnetic force of a toroidal current

A class of magnetostatic solutions is obtained for the magnetic field and current in a toroid. The solutions are characterized by nested toroidal flux surfaces whose cross-sections are concentric circles. The model distribution of the magnetic field and current allows a correct calculation of the typical self-induced magnetic force exerted by a current interacting with its own magnetic field in a toroidal configuration.

Detailed toroidal effects on the force free magnetostatic solution for toroidal reversed field pinches

Detailed toroidal effects on the force free magnetostatic solution for toroidal reversed field pinches

Dielectrically induced surface wave on a YIG substrate

Exchange-free surface waves on a tangentially magnetized YIG substrate are treated for the case of propagation at right angles to the bias field. In addition to a modified magnetostatic solution, a new dielectrically induced surface wave is found to exist.

On the Possibility of Generating Solutions to Electromagnetic Problems from known Solutions of Corresponding Static Problems

This paper coordinates and formalizes previous ideas on the possibility of creating solutions to electromagnetic wave (i.e. dynamic) problems in three dimensions from the electrostatic and magnetostatic solutions for the corresponding zero-frequency (i.e. static) problems in the same geometry. Extension of the method to the conical coordinate system is shown to be possible. Previous workers had included the rectangular, circular cylindrical, elliptic cylindrical, parabolic cylindrical, and spherical coordinate systems. It is further reported that it is impossible to extend the method to the other five coordinate systems in which the Laplace and Helmholtz equations, in three dimensions, are separable.

Magnetostatic Modes in Antiferromagnets and Canted Antiferromagnets

The resonance frequencies of the magnetostatic modes are calculated for an antiferromagnetic sphere with a dc magnetic field applied along the direction of easy magnetization. For resonance at a fixed frequency, the separations between the various modes are of order 0.2 (2HexHA)½4πM/Hex Oe. The magnetostatic modes of canted antiferromagnets of the α-Fe2O3 type are also investigated. Application of the magnetostatic conditions and solution of the differential equation for the magnetic scalar potential for a spherical sample reveals separations between modes of order 0.1 (H0+HDM) 4πM/Hex Oe. These modes are associated with the low-frequency resonance near ω1=γ[2HexHA′ + H0+HDM)]½.