Surface Magnetic Charge Research Articles

Estimation of Terrestrial Magnetism on High-Gain Electron Synchrotron

Terrestrial magnetism has a significant effect on low-energy electron beam dynamics in a circular accelerator and calculation of the field distribution is neccesary to estimate the COD (closed orbit distortion) and to improve the performance of the accelerator. To overcome the difficulty of the limitation of memory size for the calculation of field distribution in a real synchrotron, the surface magnetic charge method with the iteration technique is developed and the field distribution of the Mitsubishi Electric Corporation synchrotron is calculated. Using this iteration method the equation can be solved with a residual error of less than 1×10-5. The maximum value of COD in the vertical direction caused by the calculated field is 5 mm at the external terrestrial magnetism of 0.1 G. This value is 40% stronger than the simple estimation made under the assumptions that the magnetic field is zero inside the magnets and equal to the external field outside the magnets. This COD, which is twice the expected value by misalignment of the magnets, is caused by the coupling between the perturbation of harmonics 1 by the terrestrial magnetism and the vertical betatron oscillation (νy=1.21) of the model synchrotron.

Surface magnetic charge distributions and demagnetizing factors of circular cylinders

A circular cylinder in which a relative permeability is finite and constant is considered. The surface magnetic charge distributions and the demagnetizing factors are calculated numerically by the surface magnetic charge simulation method and are shown for various cases of different aspect ratios of length to diameter and different relative permeabilities. The results are used to obtain the ballistic demagnetizing factors and to compare them with other available data. >

Nonlinear 3D magnetostatic field calculation by the integral equation method with surface and volume magnetic charges

The authors present a mathematical model for the 3-D nonlinear magnetostatic field based on integral equations with fictitious surface and volume magnetic charges. The solution is performed by the extended boundary element method including surface elements and volume elements. Examples of calculation for both linear and nonlinear magnetic systems are presented. The method has been shown to be accurate and efficient. >

Correlation between normal flux transfer from lamination to lamination during the magnetization process with static domain structures in grain oriented 3% silicon iron

Grain oriented 3% silicon iron is widely used as magnetic core material in power devices. It is usually assessed on the basis of its magnetic losses when magnetized as single strips or in the Epstein square. When material is built into cores and magnetized, some flux passes normal to the plane of the laminations and increases the losses of transformers and rotating machines. Pairs of strips were placed together and magnetized at 50 and 60 Hz at ac longitudinal flux densities from 1.0 to 1.8 T and the normal flux density, BN transferred between them was calculated from the emfs induced in search coils located between the strips. Static domain structures were observed using a colloidal technique. Values of BN have been correlated with the domain structures, grain size, and boundary effects. BN was found to be dependent on the static wall spacing in adjacent grains and varied between 0.5 and 3.0 mT with a repeatability better than ±5%. Most large grains had low surface magnetic charge at their boundaries and BN was low. The opposite was found where the flux was transferred between small, not so well oriented, grains. This large normal flux transfer between poorly oriented small grains causes small additional losses in laminated cores.

Modeling the behavior of the magnetic force microscope

Results of some numerical simulations are presented that model the behavior of the magnetic force microscope under various probe/sample configurations. Analysis is carried out under the assumption of uniform magnetization of an axially symmetric probe of various types including: sphere, cylinder, conical tip, and rounded magnetically coated conical tip. In these cases the analysis can be made by studying the effective magnetic surface charge on the probe. We also consider the case of a spherical probe with magnetization that can rotate in response to the local field. The sample configurations studied are also of the axially symmetric type, which can be used to model the fields generated by arrays of cylindrical samples, e.g., alumite.

Simple analytical expressions for the magnetic field of current coils

Current coils are decomposed in straight segments of rectangular cross section whose sides are trapezoidal in general. For curved coil portions, the appropriate number of straight segments is considered in terms of the desired accuracy. Simple formulas are derived for the contribution of such a coil segment to the resultant magnetic field by modeling the given volume current density in terms of a distribution of fictitious magnetization inside the segment volume and corresponding surface currents and magnetic charges. The expressions obtained contain only elementary functions, and computed results illustrate their efficiency with respect to existing analytical and numerical integration methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The use of modified surface impedance in a minimum-order boundary element method

It has previously been shown that by using both surface electric current and magnetic charge distributions, the equivalence principle provides the basis for a direct boundary-element (BE) method which can be used to give solutions to eddy-current problems in unbounded media. Use of the impedance boundary condition reduces the method to one of minimum order, but the present results show that in the presence of corners inaccurate results are obtained using the simple one-dimensional impedance value. Modification of surface impedance is shown to considerably improve the solution in the corner region. A similar result is obtained when a finite element solution of the conducting region is coupled to the BE method. The improvement in the accuracy of field quantities computed in the region of a corner in a two-dimensional problem is demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Surface source models and formulas for the magnetic field of polygonal cross section conductors

The magnetic field of long, straight conductors of arbitrary polygonal cross section, carrying current of given volume density, is modeled in terms of a distribution of fictitious magnetization inside each conductor and a distribution of fictitious surface current, using the Amperian model for magnetized media. Subsequently, this magnetization is replaced by an equivalent distribution of fictitious magnetic surface charge. As a result, the field calculation is reduced to that of the field due to a long strip of finite width, with simple distributions of surface charge and current. An elementary formula is derived for the field produced by a conductor of arbitrary polygonal cross section carrying a uniformly distributed current. The amount of computation is subsequently reduced compared to that needed for other methods, since a Laplacian scalar potential can be used in the absence of volume current density in these models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Magnetostatics of rods and bars of ideally soft ferromagnetic materials

Surface magnetic charge densities are calculated for circular rods and square bars in a uniform magnetic field applied along the high symmetry axis. Ballistic demagnetizing factors are calculated for the rods and bars and fit to empirical formulae. External midplane magnetic fields are calculated for rods and a global empirical fit is obtained using a simple model. All of the empirical fits are valid for length to diameter ratios from ∼0.05 to 250.

円筒管状磁心の表面磁荷分布

円筒管状磁心の表面磁荷分布

円柱磁心の表面磁荷分布

円柱磁心の表面磁荷分布

く形断面無限長板の表面磁荷分布

く形断面無限長板の表面磁荷分布

An analysis of 3-dimensional magnetic field distributions in a small-sized synchronous motor with a permanent magnet rotor

This paper describes an analysis of 3- dimensional magnetic field distributions in a small-sized synchronous motor with a permanent magnet rotor and a simulation of the rotor behavior. Here, the concept of a surface magnetic charge is introduced, and then the magnetic field distributions are computed by using the integral equation method. Next, the rotor displacement is computed by using Newmark's β-parameter method. By the use of these techniques, simulation of the rotor behavior is performed. The results of the simulation are examined in contrast to those of the experiments.

Measurements and model calculations on the stray-field of permanent magnets

Measurements of the normal component of the stray-field at the surface of small permanent magnets were performed with a vibrating pick-up loop magnetometer with high geometrical resolution. They show a structure which reveals deviations from the desired magnetization configuration. A calculation method originally developed for soft magnetic materials was extended to calculations on permanent magnets. The real demagnetization characteristic of the material is introduced into the calculation using two independent susceptibility components. Thus the magnetic surface charges, the stray-field and the magnetization configuration can be calculated.

Perpendicular stand-still recording in Co-Cr films

Some features of perpendicular recording were investigated by means of stand-still recording experiments. For this purpose several radio frequency (RF)-sputtered Co-Cr layers of two different compositions were used as media while a Permalloy single pole (SP) head was used as a write transducer. A magnetoresistive transducer (MRT) was utilized to read the recorded pattern. Further, an analytical model was developed enabling the magnetization induced by the head field in the recording medium to be calculated. Both calculations and experimental results show a sharpening of the transition, due to the demagnetizing field. For a good approximation it is sufficient to consider only the vertical head field component and vertical magnetization in the recording medium. This is a consequence of the well-developed perpendicular anisotropy and negligible in-plane remanence of the Co-Cr layers. In addition the read-out signal is completely determined by the magnetic surface charges. The remanent magnetization in the recording medium and therefore the read-out amplitude is limited by demagnetization and consequently determined by the coercivity of the Co-Cr layer. The medium noise of a dc-erased medium indicates magnetic structures of much larger dimensions than the size of the individual crystallites. This noise appears to be dependent on the saturation magnetization of the Co-Cr medium. Activation of the single pole head by a homogeneous field results in a nonlinear behavior, caused by head saturation effects. This is supported by simple one-dimensional calculations of the head field.

Potential well of charged-walls

The potential well of the charged-wall in a contiguous disk device has been measured directly by a dynamlc equilibrium method using high speed photography. By applying a bias field gradient perpendicular to the propagation track, a bubble in the potential well of an attracting charged-wall is pulled out of the edge of track. The bubble stays in a dynamic equilibrium position where the pull out force due to the gradient field is equal to the force due to the attracting charged-wall. This equilibrium position depends on the magnitude of the gradient field. The slope of the potential well can be determined by the gradient field. The depth of the potential well is the difference between the collapse field at this position and that of the free bubble far away from the device structure. The width is given by the maximum distance of this equilibrium position. The detailed shape of the potential well can thus be measured directly by the experiments. The experimental results were taken on a 3 μm bubble contiguous disk device chip. This investigation includes various inplane field directions as well as magnitudes and at various bias fields. The results agree with ferrofluid pattern observations as well as the recent analysis of Shir and Lin. We did find, however, that the surface magnetic charges on the edge makes important contributions to the potential well, especially in the repelling charged-wall situation.

Matrices for selective diamagnetic HGMS

Both the diamagnetic and paramagnetic capture forces in HGMS are calculated for infinite arrays of elliptical and circular wires, and sheet matrices. The forces for elliptical wire arrays are obtained by summation of magnetic potentials due to magnetic surface charges. Matrices for selective diamagnetic capture are studied and evidence of capture presented.

Domain wall resonance in magnetic bubble films

Domain wall resonance frequency has been measured as a function of the magnitude and direction of an applied in-plane magnetic field. The effective wall mass determined from this data does not agree with the mass predicted by the usual Bloch wall model for the wall mass. A model that calculates the effect of magnetic surface charges on the mass is found to agree with the data for low fields. A model proposed by Morkowski is found to agree with the data for large values of the in-plane field. The angle dependence of the mass is found to be of the form 1/m = a0+a1 cos (2Θ) where Θ is the angle between the applied in-plane field and the plane of the domain wall.

Comments on "An analysis of tilted magnetic transition in magnetic transitions in magnetic recording media"

Expressions for the demagnetizing field caused by the surface magnetic charge produced by vertical magnetization in a tilted transition are presented. This field should be added to that used by Chang and Perez in their analysis of tilted transitions.

Micromagnetics of curling configurations in magnetically soft cylinders

The response of an ideally soft magnetic cylinder is calculated by approximating magnetostatic interactions while taking into account the exchange energy of curling patterns with point singularities. Detailed calculations of the magnetic surface charge distribution of paramagnetic materials are used as a guide in parameterizing an approximate charge distribution suitable for applying the Ritz method to the micromagnetic problem of ferromagnetic materials without anisotropy or magnetostriction. Numerical results are given for a cylinder with L/D=1 for fields below saturation illustrating how remanence and coercivity depend on the ratio of the exchange length A/M2o to sample dimensions. The role of point singularities in remanence, coercivity, nucleation and irreversibility is outlined.