Benchmark Solutions for Magnetic Fields in the Presence of Two Superconducting Spheres

2012 ◽  
Vol 721 ◽  
pp. 21-26 ◽  
Author(s):  
Ioan R. Ciric ◽  
Kumara S.C.M. Kotuwage
Keyword(s):  
Magnetic Field ◽  
Numerical Methods ◽  
Magnetic Fields ◽  
Boundary Value Problem ◽  
Uniform Magnetic Field ◽  
Complete Solution ◽  
Perfect Conductor ◽  
Arbitrary Orientation ◽  
Scalar Magnetic Potential ◽  
Benchmark Solutions

A complete solution is presented for the boundary value problem of two perfect conductor spheres in a uniform magnetic field of arbitrary orientation. Expressions are given for the scalar magnetic potential and for the field intensity. They can readily be applied for calculating the forces between the spheres. Benchmark numerical results of specified accuracy are generated, which are also useful for validating various approximate numerical methods.

Torsional oscillations of a fluid sphere with a rigid boundary in a uniform magnetic field

1966 ◽  
Vol 24 (2) ◽  
pp. 275-284
Author(s):  
R. A. Wentzell
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Uniform Magnetic Field ◽  
Perfect Conductor ◽  
Rigid Boundary ◽  
Torsional Oscillations ◽  
Magnetic Viscosity ◽  
Eigen Values ◽  
Infinite Conductivity ◽  
Axis Of Symmetry

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).

Theoretical Optimization of Cascading Magnets’ Structure for Oxygen Enrichment by Gradient Magnetic Fields

2009 ◽  
Author(s):  
Fengchao Li ◽  
Li Wang ◽  
Ping Wu ◽  
Shiping Zhang
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Oxygen Concentration ◽  
Uniform Magnetic Field ◽  
Oxygen Enrichment ◽  
Gradient Magnetic Field ◽  
Length Direction

Oxygen molecules are paramagnetic while nitrogen molecules are diamagnetic. In the same gradient magnetic field, the magnetizing forces on oxygen molecules are stronger than those on nitrogen molecules, which in opposite directions. The intercepting effect on oxygen molecules by gradient magnetic field can be used for oxygen enrichment from air. The structure, which is called multi-channel cascading magnets array frame in the paper, are optimized by additional yokes. By comparison of distributions of magnetic field in multi-channel array without yokes and that with yokes, the additional yokes can eliminate the differences among different magnetic spaces in multi-channel cascading magnets’ arrays and enhances the magnetic flux densities in spaces. Joining magnets together in the length direction can make the air stay longer in the ‘magnetic sieve’ and raise the oxygen concentration of air flowing out from the optimized multi-channel cascading magnets’ arrays. The inside additional yoke can used to avoid the gradient magnetic field at the joints of the magnets and get near uniform magnetic field along length direction. The optimized multi-channel cascading magnets’ array frames can effectively promote the development of oxygen enrichment from air by “magnetic sieve”.

scholarly journals Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 467
Author(s):  
Fayçal Hammad ◽  
Alexandre Landry ◽  
Parvaneh Sadeghi
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Total Mass ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Schwarzschild Solution ◽  
Relativistic Regime ◽  
The Magnetic Field

The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the particles are derived as functions of the magnetic field, the radius of the massive sphere and the total mass of the latter. As no assumption is made on the relative strengths of the particles’ interaction with the gravitational and magnetic fields, the relevance of our results to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense, is discussed.

scholarly journals Influence of uniform magnetic field on physicochemical properties of freeze-thawed avocado puree

RSC Advances ◽  
2019 ◽  
Vol 9 (68) ◽  
pp. 39595-39603
Author(s):  
Yinying Tan ◽  
Yamei Jin ◽  
Na Yang ◽  
Zhe Wang ◽  
Zhengjun Xie ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Physicochemical Properties ◽  
Uniform Magnetic Field ◽  
Quality Of Food

3D magnetic fields have the potential to improve the quality of food after freeze-thawing.

scholarly journals Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
E. Hirvijoki ◽  
J. Decker ◽  
A. J. Brizard ◽  
O. Embréus
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Uniform Magnetic Field ◽  
Reaction Force ◽  
Charged Particles ◽  
Collision Operator ◽  
Radiation Reaction ◽  
Transform Method ◽  
Lie Transform ◽  
Radiation Reaction Force

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

scholarly journals Experiments and Numerical Implementation of a Boundary Value Problem Involving a Magnetorheological Elastomer Layer Subjected to a Nonuniform Magnetic Field

2021 ◽  
Vol 88 (7) ◽  
Author(s):  
Charles Dorn ◽  
Laurence Bodelot ◽  
Kostas Danas
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Boundary Value Problem ◽  
Magnetic Particles ◽  
Boundary Value ◽  
Energetic Efficiency ◽  
Iron Core ◽  
Isotropic Layer ◽  
Magnetorheological Elastomer ◽  
Electromagnetic Coil

Abstract This study investigates experimentally and numerically the response of a magnetorheological elastomer (MRE) layer placed atop an electromagnetic coil. The MRE layer is deflected upon application of a current in the coil, which creates highly nonuniform magnetic fields. Isotropic and transversely isotropic layers (i.e., containing chains of magnetic particles) are tested experimentally, and the isotropic layer exhibits the largest deflection. To enhance the energetic efficiency of the model device, an iron core is introduced inside the electromagnetic coil, thereby leading to an increase in the resulting magnetic field near the center of the MRE layer. In parallel, the boundary value problem —including the MRE layer, the coil, the core (if present) and the surrounding air—is modeled numerically. For this, a magneto-mechanical, vector potential-based variational formulation is implemented in a standard three-dimensional finite element model at finite strains. For the material description, a recently proposed analytical homogenization-guided model is used to analyze the MRE in the “coil-only” configuration. It is then employed to predict the response of the layer in the “coil plus core” configuration, thus circumventing the need for a separate material characterization procedure. The proposed numerical simulation strategy provides a deeper understanding of the underlying complexity of the magnetic fields and of their interaction with the MRE layer. This study also reveals the importance of modeling the entire setup for predicting the response of MRE materials and, as a result, constitutes a step toward designing more efficient MRE-based devices.

scholarly journals Equatorial Geodesics Around the Magnetars

2017 ◽  
Vol 45 ◽  
pp. 1760050
Author(s):  
Viviane A. P. Alfradique ◽  
Orlenys N. Troconis ◽  
Rodrigo P. Negreiros
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Neutron Stars ◽  
Complete Solution ◽  
Compact Object ◽  
Relativistic Effects ◽  
Schwarzschild Solution ◽  
Soft Gamma Repeaters ◽  
Definition Of ◽  
The Magnetic Field

Neutron stars manifest themselves as different classes of astrophysical sources that are associated to distinct phenomenology. Here we focus our attention on magnetars (or strongly magnetized neutron stars) that are associated to Soft Gamma Repeaters and Anomalous X-ray Pulsars. The magnetic field on surface of these objects, reaches values greater than [Formula: see text] G. Under intense magnetic fields, relativistic effects begin to be decisive for the definition of the structure and evolution of these objects. We are tempted to question ourselves to how strengths fields affect the structure of neutron star. In this work, our objective is study and compare two solutions of Einstein-Maxwell equations: the Bonnor solution, which is an analytical solution that describe the exterior spacetime for a massive compact object which has a magnetic field that is characterize as a dipole field and a complete solution that describe the interior and exterior spacetime for the same source found by numerical methods). For this, we describe the geodesic equations generated by such solutions. Our results show that the orbits generated by the Bonnor solution are the same as described by numerical solution. Also, show that the inclusion of magnetic fields with values up to [Formula: see text]G in the center of the star does not modify sharply the particle orbits described around this star, so the use of Schwarzschild solution for the description of these orbits is a reasonable approximation.

Linear Buckling and Vibration Behavior of Piezoelectric/Piezomagnetic Beam under Uniform Magnetic Field

2014 ◽  
Vol 592-594 ◽  
pp. 2071-2075 ◽  
Author(s):  
A. Kumaravel ◽  
J. Jones Praveen ◽  
Raju Sethuraman ◽  
A. Arockiarajan
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Fields ◽  
Boundary Conditions ◽  
Constitutive Equations ◽  
Uniform Magnetic Field ◽  
Vibration Behavior ◽  
Linear Buckling ◽  
Piezoelectric Coupling

The constitutive equations of MEE materials are used to derive the finite element equations involving the coupling between mechanical, electrical and magnetic fields. The candidate materials for this study are piezoelectric (BaTiO3) and magnetostrictive (CoFe2O4) material. The linear buckling and vibration behavior of layered MEE beam under uniform magnetic field is carried out using finite element method. The present study is limited to clamped-clamped boundary conditions. The influence of stacking sequences and piezoelectric coupling on critical buckling magnetic field and vibration behaviour is investigated.

E-layer precession in a plasma

1971 ◽  
Vol 6 (2) ◽  
pp. 413-424 ◽  
Author(s):  
H. L. Berk ◽  
R. N. Sudan
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Rigid Body ◽  
Plasma Density ◽  
Uniform Magnetic Field ◽  
Alfven Wave ◽  
Background Plasma ◽  
Low Density ◽  
High Background ◽  
Plasma Background

A weak E layer in a non-uniform magnetic field will tend to precess as a rigid body in response to the radial focusing of external magnetic fields and fields due to wall currents. We study the interaction of this precessional mode with a background plasma, and we explicitly include dissipation mechanisms in the plasma, walls and external resistors. When the plasma background is treated in the MHD approximation, we find that the mode changes character from a precessional mode at low density to a compressional Alfvén wave at high density. For a very weak E layer, instability is found, even without dissipation, when a sufficiently high background plasma density is present. However, for moderate E-layer strengths, the modes are found to be stable, even with dissipation.

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