Point Magnetic Dipole Research Articles

Superconducting Sphere in an External Magnetic Field Revisited

It is the purpose of this article to give the obtainable to undergraduate student’s grasp evidence for the fact that the magnetic field outside the hollow superconducting sphere (superconducting shell) coincides with the field of a point magnetic dipole both when an uniform external magnetic field is applied as when a ferromagnetic sphere is located at the shell’s geometrical center. The evidence is founded on the London’s equation transformation to an integral equation for the vector potential of system. This evidence is alternative to the traditional one, when the London’s equation solution inside a superconductor and the Maxwell’s equation solution outside it are joined on it’s surface. The integral equation may be solved completely for the case of a solid sphere

Distortion of liquid metal flow in a square duct due to the influence of a magnetic point dipole

AbstractWe consider liquid metal flow in a square duct with electrically insulating walls under the influence of a magnetic point dipole using three‐dimensional direct numerical simulations with a finite‐difference method. The dipole acts as a magnetic obstacle. The Lorentz force on the magnet is sensitive to the velocity distribution that is influenced by the magnetic field. The flow transformation by an inhomogeneous local magnetic field is essential for obtaining velocity information from the measured forces. In this paper we present a numerical simulation of a spatially developing flow in a duct with laminar inflow and periodic boundary conditions. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Polarizability Matrix Extraction of a Bianisotropic Metamaterial from the Scattering Parameters of Normally Incident Plane Waves

In this paper, a polarizability matrix retrieval method for bianisotropic metamaterials is presented. Assuming that scatterers can be modeled by electric and magnetic pointdipoles located at their centers, the induced dipole moments are analytically related to the normally incident fields, while the scattered fields are also analytically obtained for two individual cases of normal wave incidence. The latter can be combined with the incident fields, to express the desired polarizabilities, with regard to the measured or simulated scattering parameters. In this way, the polarizability matrix can be extracted by solving the resulting non-linear system of equations. The proposed technique is applied to two different split-ring resonator structures and reveals very good agreement with previously reported techniques.

Unidirectional radiation of a magnetic dipole coupled to an ultracompact nanoantenna at visible wavelengths

The optical radiation of a magnetic dipole coupled to a plasmonic nanoantenna composed of stacked gold nanodisks is investigated. The nanoantenna is fed by a point magnetic dipole properly situated between two nanodisks. It is found that the magnetic dipole efficiently couples to the antenna due to the excitation of an antiphase localized surface plasmon resonance mode. This leads to a remarkable enhancement of the optical radiation at the resonant wavelength associated with the hybridized mode of the nanoantenna. By introducing a slight structural asymmetry in the nanoantenna, the optical radiation is substantially altered. Interestingly, it is shown that the omnidirectional radiation of the magnetic dipole becomes almost unidirectional, further enhanced, and accessible in three-dimensions by the asymmetric nanoantenna. Based on the classical model, quasistatic theory, and electrodynamics calculations, the electromagnetic interaction of the magnetic dipole and the nanoantennas is studied. A remarkable forward-to-backward directionality is achieved by the proposed nanoantenna at visible wavelengths.

Superconducting Sphere and Finite-Size Permanent Magnet: Force, Torque, and Alignment Effect Calculation

Using a local first-order interaction model, previously described, the force and torque between a superconducting sphere in the Meissner state and a finite-size permanent magnet are calculated. These findings are compared to results obtained by other models for the force based on the images method for a point magnetic dipole. It is demonstrated that the first-order calculation is a good approximation. Moreover, the torque between a superconducting sphere and a magnet in different positions and angular orientations is calculated for the first time. We describe the alignment effect that tends to align a magnet tangentially to the superconducting sphere surface. In addition, it is shown that the finiteness of the magnet reduces the magnitude of the repulsive force.

Mechanism Analysis of Induction-Type Coil Target for Velocity Measurement

Induction-type coil target is a common used zone-block device for measuring projectile’s velocity. The magnetized projectile is simplified as the point magnetic dipole, and then the physical model of magnetized projectile passing through the coil target is established, based on these the mathematic model of inductive electromotive force when the magnetized projectile flying through the coil target in a certain speed is deduced with the electromagnetic theory; According to the model, the characteristic parameters such as the zero-crossing point, the slope of zero-crossing point and the extreme value point are discussed, finally the principle and the influence factors of velocity measurement by single-coil target and paired- coil targets are described. All these above provide some foundation and advices for designing and using induction-type coil target.

Micromagnetic Analysis of Effective Magnetic Dipole Position in Magnetic Force Microscope Tip

An accurate micromagnetic model of the magnetic force microscope (MFM) tip has been developed to calculate the effective dipole and its position in a simple point probe model, which are important in the quantitative explanation of MFM images. The pyramid-shaped MFM tips are considered in this paper; so cuboid cells in the body, as well as triangular prism and quadrangle pyramid cells at the edge are included to accurately describe the geometrical shape of the tip. The effective position of the magnetic point dipole and the MFM tip field distribution are analyzed, based on the calculated domain structures in the tips with different materials parameters. The simulated tip fields are compared carefully with that of the point probe model usually utilized in the MFM tips.

Vortex configurations on a thin superconducting spherical shell in the presence of a magnetic dipole

In this work we study vortex configurations on a thin superconducting spherical shell of radius R and thickness d ( R ≫ d ⩾ ξ ) with a magnetic dipole inside it. The point magnetic dipole (with magnetic moment, m z ) is oriented along one of the sphere main axis. It is placed a distance z 0 from the center of the sphere. Due to the symmetry of the sample, there are vortices and antivortices pancakes on the shell resulting in zero total vorticity. The vortex interactions with the shielding currents produced by the external fields – as well as with other vortices – are calculated within the London limit. The vortex configurations are obtained by solving numerically the Bardeen–Stephen equation of motion for the vortices. For z 0 ≈ 0 the most frequent vortex configurations present equal arrangements of vortices and antivortices on the north and south hemispheres. For z 0 ≈ 0.5 R , the diversity of vortex configurations increases, with a higher number of configurations (in comparison to smaller z 0 ) having different vortices and antivortices distributions on each shell hemisphere. We also study the equilibrium states dependence on the magnetic dipole strength and position.

Quantitative imaging of magnetic nanoparticle distributions in organs by a combined multipole-multiple dipoles approach

Event Abstract Back to Event Quantitative imaging of magnetic nanoparticle distributions in organs by a combined multipole-multiple dipoles approach Frank Wiekhorst1*, Daniel Baumgarten2, Wolfgang Haberkorn1, Uwe Steinhoff1, Jens Hauseisen3, Markus Baer1 and Lutz Trahms1 1 Physikalisch-Technische Bundesanstalt, Germany 2 Ilmenau University of Technology, Germany 3 University Hospital, Germany The accurate knowledge of magnetic nanoparticle distributions in biological tissue is an essential prerequisite for the development of novel magnetic nanoparticle based therapeutical applications such as drug targeting and hyperthermia. Measurement techniques like magnetorelaxometry, dc- and ac-susceptometry or remanence so far allow a sensitive as well as robust quantification and localization of focussed (point-like) nanoparticle accumulations in tissue or to reconstruct quantitatively the nanoparticle distibution from individual measurements of a dissected organ. For non-destructive reconstruction an ill-posed inverse problem has to be solved to get underlying nanoparticle distribution from a measured magnetic field pattern. Here, we present a combined approach for the quantitative reconstruction of spatially extended nanoparticle distributions. Within the framework of minimum norm estimates solving the inverse problem we use a multipole expansion to localize the centre and to quantify the total amount of the nanoparticle distribution. Additionally, the principal dimensions of the source distribution are estimated by a second multipole expansion using the afore determined distribution centre as expansion point. Finally, the quantitative distribution is reconstructed modelling the magnetic nanoparticle accumulation by magnetic point dipoles on a planar grid centred at the multipole expansion point. We illustrate this procedure by a simulation of our typical measurement setting comprising extended sources with dimensions up to 20 cm. We find a localization uncertainty below one centimetre. The total magnetic moment can be estimated with an uncertainty of less than 5%. Quantitative images obtained from simulated data as well as from measurement data demonstrate feasibility and performance of our approach. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: Nanoparticles, Biosusceptometry and Effects of Magnetic Fields Citation: Wiekhorst F, Baumgarten D, Haberkorn W, Steinhoff U, Hauseisen J, Baer M and Trahms L (2010). Quantitative imaging of magnetic nanoparticle distributions in organs by a combined multipole-multiple dipoles approach. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00388 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 08 Apr 2010; Published Online: 08 Apr 2010. * Correspondence: Frank Wiekhorst, Physikalisch-Technische Bundesanstalt, Berlin, Germany, frank.wiekhorst@ptb.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Frank Wiekhorst Daniel Baumgarten Wolfgang Haberkorn Uwe Steinhoff Jens Hauseisen Markus Baer Lutz Trahms Google Frank Wiekhorst Daniel Baumgarten Wolfgang Haberkorn Uwe Steinhoff Jens Hauseisen Markus Baer Lutz Trahms Google Scholar Frank Wiekhorst Daniel Baumgarten Wolfgang Haberkorn Uwe Steinhoff Jens Hauseisen Markus Baer Lutz Trahms PubMed Frank Wiekhorst Daniel Baumgarten Wolfgang Haberkorn Uwe Steinhoff Jens Hauseisen Markus Baer Lutz Trahms Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Field induced by an axial magnetic dipole in the presence of two fused superconducting spheres: Analytic solution

An exact solution for a magnetostatic boundary value problem involving two fused (overlapping) spheres placed in a field generated by an axial magnetic point dipole is constructed based on the image method. The basic idea is illustrated for two unequal superconducting spheres intersecting with a vertex angle π/2 and the analytical solution for the scalar magnetic potential satisfying the Neumann boundary condition at the surface is derived. The image solution for a dipole-twin-sphere configuration consists of three image dipoles—one inside each sphere and the third inside a pseudo-/virtual sphere—all located at the respective inverse points inside the superconducting two-sphere assembly. The levitation force acting on the two-sphere superconducting surface is also calculated for the overlapping geometry. These exact results can be used as a benchmark for testing numerical algorithms for overlapping spherical superconductors. Our simple approach also offers clues for solving the Neumann boundary value problem for vertex angles π/n, n is an integer, and other related superconducting geometries.

Interaction between a point magnetic dipole and a high-temperature superconducting sphere

Abstract The interaction between a small magnet and a high-temperature superconducting sphere in the field cooled state is investigated using the frozen image model. Analytical expression of the interaction potential and force between the magnet and the superconductor is derived as function of the geometrical parameters of the system. The angular dependence of the force and energy is analyzed. The interaction between a straight magnetic line and superconducting sphere is investigated.

Magnetic Interaction Force and a Couple on a Superconducting Sphere in an Arbitrary Dipole Field

The calculation of the magnetostatic potential and levitation force due to a point magnetic dipole placed in front of a superconducting sphere in the Meissner state is readdressed. Closed-form analytical expression for the scalar potential function that yields the image system for an arbitrarily oriented magnetic dipole located in the vicinity of a superconducting sphere is given. Analytic expression for the lifting or levitation force acting on the sphere is extracted from the solution for a general dipole. A special case of our expression where the initial magnetic dipole makes an angle with the z-axis is derived. Our expression for the force in this particular case shows that a recently obtained result (J. Supercond. Nov. Magn. 21:93–96, 2008) for an arbitrary dipole is incorrect. A brief discussion of another erroneous result (J. Supercond. Nov. Magn. 15:257–262, 2002) for a transverse/tangential dipole–sphere configuration, corrected elsewhere recently, is reproduced. Correct expressions for the interaction energy with some limiting cases are also provided. The result derived here demonstrates that the value of the levitation force for a dipole that makes an angle with z-axis lies between the values for a radial dipole–sphere and transverse dipole–sphere configurations providing upper and lower bounds. It is found that for a magnetic dipole making an angle with z-axis, there exits a second force component along the negative y-direction, which influences a couple acting on the superconducting sphere. It is also shown that the couple is proportional to the second force component and that both the couple and second force components vanish for a radial dipole–sphere and transverse dipole–sphere configurations, respectively. These results appear to be new and have not had received due attention in the context of superconductivity.

Source localization using electric and magnetic point dipoles with modified genetic algorithm

AbstractA method to reconstruct the source current from far‐field data in terms of electric and magnetic point dipoles is described. The inverse problem of solving the source from a known electromagnetic far‐field pattern is carried out by a combination of genetic algorithm and local optimizers. The source is modelled by a small number of point dipoles, the locations, amplitudes and types of which are determined by minimizing the difference between the field of the ensemble and the targeted pattern. Uniqueness is ensured by limiting the number of dipoles together with an appropriately weighted minimum energy condition. A general description of the method applicable to antenna analysis and synthesis is given and three examples of its practical use are presented. Copyright © 2008 John Wiley & Sons, Ltd.

Levitation Force Between a Small Magnet and Superconducting Sphere

Based on the Meissner effect and the image method, we studied the interaction between a magnetic point dipole and a superconducting sphere. We obtained analytical expressions for the interaction energy and the levitation force when the dipole is in an arbitrary orientation. Our calculations show the validity of using the image method for a antisymmetrical superconducting sphere-magnet system. Results show that the energy and the force are maxima when the magnetic dipole is perpendicular to the surface of superconductor and minima when it is tangent to the surface. Furthermore, the force acting on the tip of a magnetic force microscope above a superconducting sphere was derived as a generalization of the levitation force acts on a point dipole.

Kapteyn series arising in radiation problems

In discussing radiation from multiple point charges or magnetic dipoles, moving in circles or ellipses, a variety of Kapteyn series of the second kind arises. Some of the series have been known in closed form for a hundred years or more, others appear not to be available to analytic persuasion. This paper shows how 12 such generic series can be developed to produce either closed analytic expressions or integrals that are not analytically tractable. In addition, the method presented here may be of benefit when one has other Kapteyn series of the second kind to consider, thereby providing an additional reason to consider such series anew.

Modeling of symmetrical levitation force under different field cooling processes

This paper presents an analytic model of the symmetrical magnetic levitation force between a point magnetic dipole and a flat non-ideally hard superconductor due to different field cooling processes. Yang and Zheng (J. Appl. Phys. 101 (2007) 113922) reported an updated frozen-image model which can give the hysteretic characteristic in the levitation force. But, their model is remarkably influenced by the external parameters and can not give the saturated feature of the maximum levitation force in some situations. We show a model which can give the features both hysteresis and saturation independent from the external parameters.

Magnetic dipole imaging by a scanning magnetic microscope

A reconstruction technique to evaluate residual magnetic fields and simulate magnetic images due to dipole distribution in ferromagnetic samples has been proposed in connection with a scanning magnetic microscope based on a high-Tc superconducting quantum interference device (SQUID). We have extended the expression of a point magnetic dipole to represent spatially extended sources and the generated magnetic field has been compared with experiments. In particular, a recently installed scanning SQUID magnetic microscope (model 770 by Tristan Technology) has been used. Magnetic maps obtained at different sample-to-sensor distances and in several configurations have been compared with simulations. With this aim, ferromagnetic rod samples have been modeled as extended magnetic dipoles close to the sensor. Excellent agreement has been obtained, confirming the efficiency of the proposed technique. Such an imaging technique has been demonstrated to be an easy-to-handle tool to identify dipole configurations producing a specific magnetic image.

Four-component relativistic theory for nuclear magnetic shielding constants: Critical assessments of different approaches

Both formal and numerical analyses have been carried out on various exact and approximate variants of the four-component relativistic theory for nuclear magnetic shielding constants. These include the standard linear response theory (LRT), the full or external field-dependent unitary transformations of the Dirac operator, as well as the orbital decomposition approach. In contrast with LRT, the latter schemes take explicitly into account both the kinetic and magnetic balances between the large and small components of the Dirac spinors, and are therefore much less demanding on the basis sets. In addition, the diamagnetic contributions, which are otherwise "missing" in LRT, appear naturally in the latter schemes. Nevertheless, the definitions of paramagnetic and diamagnetic terms are not the same in the different schemes, but the difference is only of O(c(-2)) and thus vanishes in the nonrelativistic limit. It is shown that, as an operator theory, the full field-dependent unitary transformation approach cannot be applied to singular magnetic fields such as that due to the magnetic point dipole moment of a nucleus. However, the inherent singularities can be avoided by the corresponding matrix formulation (with a partial closed summation). All the schemes are combined with the Dirac-Kohn-Sham ansatz for ground state calculations, and by using virtually complete basis sets a new and more accurate set of absolute nuclear magnetic resonance shielding scales for the rare gases He-Rn have been established.

Method for solution of the interaction between superconductor and permanent magnet

A method for calculating the interaction between a superconductor and a permanent magnet for various initial cooling conditions is proposed. The exact solutions are obtained for the point magnetic dipole over a flat nonideal type-II superconductor. The distinction of the method from the frozen-image method is in the using of the vertical and horizontal movement images that create the same magnetic field distribution outside the superconductor as the trapped fluxes do when the permanent magnet moves vertically and horizontally, respectively. The vertical and lateral forces that are obtained by the method agree with the previous measurements qualitatively. Comparing with the frozen-image method, the method can give the lateral force in zero field cooling and the hysteresis in the vertical and lateral forces. The two characteristics cannot be obtained by the frozen-image method. In this case, the vertical stiffness during vertical traverses and the lateral and cross stiffnesses during lateral traverses are obtained by the analytic expressions of vertical and lateral forces. Those stiffness expressions can reflect the effect of cooling conditions and movement history.

Comment on “London model for the levitation force between a horizontally oriented point magnetic dipole and superconducting sphere”

The levitation force due to a horizontally oriented point magnetic dipole placed in front of a superconducting sphere is calculated and is shown to be different from the result given recently by Coffey [Phys. Rev. B 65, 214524 (2002)]. The present calculation for the levitation force is based on the formulas developed long ago for an equivalent Neumann boundary value problem in hydrodynamics. The result derived here demonstrates that the value of the levitation force for a horizontally oriented dipole lies between one-fourth and one-half the value of the configuration with a radially oriented point dipole, thus providing upper and lower bounds for the levitation force due to a tangentially oriented magnetic dipole.