Three-dimensional Magnetic Field Calculation Research Articles

Performance Analysis of a Superconducting Motor for Higher Efficiency Design

The superconducting motor shows several advantages such as smaller size and higher efficiency against conventional motor especially utilized in ship propulsion application. However, this size reduction merit appears in large capacity more than several MW. We are going to develop a 17-MW class synchronous motor with a rotating HTS (high-temperature superconducting) coil that is aimed to be utilized for ship propulsion, therefore it has a slow rotating speed of about 200 rpm. The ship propulsion motor must generate high electromagnetic torque instead of low-speed. Therefore, the rotor (field) coils have to generate large magnetic flux that results in large amounts of expensive HTS conductor for the field coil. In this paper, a 17-MW HTS motor for ship propulsion is designed with smaller manufacturing cost by HTS field coil length reduction because the HTS conductor cost is a critical factor in the construction cost of an HTS motor. Furthermore, the output performance of the machine is simulated based on the equivalent circuit model of the synchronous motor with back electromagnetic field values from three-dimensional magnetic field calculation. The simulation results are used to design higher efficiency motor.

A novel structure of multipole field magnets and their applications in uniformizing beam spot at target

A novel structure of multipole field magnets is proposed, and it can provide any order either symmetric or anti-symmetric field distribution within a good-field region in a flat rectangular shape with relative field errors of about 1%. Some of these field distributions cannot be obtained by standard multipole magnets but are quite useful in some applications, thanks to the decoupling of the two halves of the magnets by a pair of shielding plates. In addition, the simplified structure compared with the standard one makes the magnet fabrication easier and cost effective. Two-dimensional magnetic field calculations for anti-symmetric sextupole, octupole, decapole and dodecapole fields show that the new types of multipole magnets have good field quality. Three-dimensional magnetic field calculations have confirmed the validity of the two-dimensional calculations. Symmetric field distributions by the simplified multipole field magnets have also been confirmed by two-dimensional field calculations. Two application examples by using numerical simulations are also given to show the effectiveness of simplified multipole field magnets in producing uniform-like beam spots at two different targets with different beam inputs. It is also shown that combinations of the lower order anti-symmetric field magnets – a merit of this magnet structure – are more advantageous than the traditional combination of octupole and dodecapole magnets in beam spot uniformization, besides with cheaper construction and operation costs. The applications of non-standard field distributions such as anti-symmetric sextupole and symmetric octupole field distributions in synchrotrons are to be exploited in the future.

Magnetic Field Improvement in End Region of Rectangular Planar DC Magnetron Based on Particle Simulation

For a rectangular planar direct current (DC) magnetron, anomalous target erosion may occur in the curve-out region and inner side of the curved region. One key factor is that the magnetic field in the end region is weaker than that in the straight region, and another important factor may be that there is a circumferential component of the magnetic field in the curved region. Through a calculation of three-dimensional magnetic field for the rectangular magnetron, a magnet structure shimmed by permanent magnet bars and ferromagnetic bars is proposed to solve the above problems. Through a three-dimensional non-self-consistent particle simulation and the Yamamura/Tawara formula, the target erosion profile could be predicted. The simulation results show that for an improved uniformity in magnetic field, the entire target utilization could be much enhanced.

Eddy Current Effects of the J-PARC RCS Sextupole Magnets

Sextupole magnets for the chromaticity correction of the rapid-cycling synchrotron of the Japan Proton Accelerator Research Complex have a large bore of 330 mm and a relatively short length of 320 mm. The end effect, therefore, was not negligible and a three-dimensional magnetic field calculation was necessary to achieve the required field quality of inside the radius of 141.2 mm for the designed maximum field gradient of 18.6 T/m. Eddy current effect on the field quality and temperature rise was considered because the magnets were to be excited with a current pattern of a frequency of 25 Hz. Measurement using harmonic coils confirmed that the required field quality was achieved. Measurement results of the sextupole component and 18-pole component field were reproduced with the magnetic field calculation program OPERA3d/ELEKTRA.

Field interference studies between bump magnets with different coil structures at Chinese Spallation Neutron Source

For magnets arranged so closely that the distance between them is comparable to the magnet apertures, the field interference becomes important. This is the case in the injection region at the China Spallation Neutron Source (CSNS) where several bump magnets are used to create fixed and dynamic local orbit bumps for the beam injection using the H(-) stripping and the phase space painting method. The reduction in the field integral due to the field interference will cause an orbit distortion, and the orbit bumps will be no longer localized. It is found that the end coil structure plays an important role in reducing the fringe field of a magnet. This has been analyzed by using both the image current method and three-dimensional magnetic field calculations. The saddle end coil instead of the compact end coil has been adopted at the CSNS. The relative reduction in the field integration after the optimization can meet the design requirement of about 1% or less.

Proposal for the edge-focusing wiggler for SASE

We are developing a new type of wiggler with a strong focusing force, named the edge-focusing wiggler. It is a Halbach-type wiggler made with permanent magnet blocks with an edge angle φ. An application is given for SASE in the shorter wavelength region. The characteristics of the wiggler are studied in detail using a three-dimensional magnetic field calculation program with the magnetic charge method.

New expressions for calculating the magnetic field created by radial current in massive disks

In this paper, new expressions are presented for three-dimensional magnetic-field calculation for a massive disk currying radial currents. These expressions have been obtained in analytical form as functions of incomplete elliptical integrals (of the first, second, and third kind) and an integral to be solved numerically. This approach enables one to easily calculate the magnetic field everywhere in space at reduced computational cost. In addition, it can be employed to calculate the magnetic field in conductor disk configurations involving complicated geometry as well as to evaluate their self and mutual inductance.

Design and measurement of a combined function magnet intended for a cancer therapy accelerator

A compact proton synchrotron using combined function magnets is proposed to help realize the wider availability of charged particle cancer therapy facilities. This combined function magnet was designed with the help of three-dimensional magnetic field calculations to take account of a realistic fringe and the interference among the magnetic poles. An evaluation scheme for tune values based on particle tracking was developed to improve the magnet design. To verify the magnet design, a model magnet was fabricated and measured. In order to achieve a tune value evaluation from the measured magnetic field, schemes for accurate field mapping and field interpolation were developed. From the tune value evaluation of the measured magnetic field, it was thought that the performance of the model magnet was good enough to construct a synchrotron. In this paper, we report details of the design and the evaluation scheme for the combined function magnet and the results of the field measurements of the model magnet.

An extended magnetic quadrupole lens for a high-resolution nuclear microprobe

This paper describes the design requirements and initial performance of a new style of magnetic quadrupole lens for use in a high-resolution nuclear microprobe, which is presently being constructed in Oxford [1]. Such a microprobe necessitates the use of a small image distance from the exit face of the final quadrupole lens to the image plane in order to produce a large demagnification. This means that the final lens should be as close to the sample chamber as possible. However, with conventional magnetic quadrupoles the current-carrying coils protrude by a typical distance of 10–20 mm beyond the pole face, thereby significantly limiting the minimum image distance. The approach taken here is to recess the coils into the body of the lens, so that they are almost flush with the pole pieces and lens yoke, enabling an image distance of 55 mm. Three-dimensional magnetic field calculations within this lens structure predict that the field in the extended pole piece `nose' region is only slightly less than that in the main lens body. Experimental field profiles, measured using a Hall probe, are used to confirm these calculations.

Surface magnetic charge method combined with spatial harmonic expansion for magnetic field analysis of deflection yokes

The surface magnetic charge method and the Fourier spatial harmonic expansion technique for three-dimensional magnetic field calculations are studied. Spatial harmonic components of the magnetic fields generated by the magnetized ferromagnetic core of deflection yokes were derived by the surface magnetic charge method. Because of the orthogonality of harmonics, a concise and straightforward relation between each harmonic of the fields and that of the surface magnetic charges was obtained. By this method, the two-dimensional integral equations for magnetic charges are reduced to one-dimensional equations, one for each order of charge harmonics. A program was written for the calculation of magnetic fields of the deflection yoke. An example was calculated, and some useful conclusions were obtained from the results.

A cross-type amorphous video head

A cross-type video head composed of cross-shaped amorphous sputtered films and ferrite that can be used with high coercive tapes is described. A three-dimensional magnetic field calculation shows that the cross-type head has a strong recording field and high reproduction efficiency compared to a conventional metal-in-gap head (MIG) or a plate-type head. No large bumps in the output spectrum are observed during recording and reproduction under normal conditions with the cross-type head. The amorphous sputtered film deposited on the inclined plane of the ferrite substrate used for the cross-type head shows a homogeneous structure and high permeability similar to that of a film deposited on a horizontal plane. A cross-type head using a CoNZr amorphous film annealed in a magnetic field under optimum conditions shows excellent recording and reproduction characteristics when used with a high coercivity metal tape.

Construction of a large superconducting spectrometer magnet

A sector-type superconducting spectrometer magnet for nuclear physics experiments has been constructed. The central magnetic field is 3 T with a magnet gap of 50 cm and a stored energy estimated to be 11.2 MJ. Three-dimensional magnetic field calculations and a stress analysis have been performed to design the coil and supporting structures. The magnet has a flexible helium transfer line to measure angular distributions at nuclear physics experiments. To simplify the transfer line, a small-size G-M refrigerator, which is installed on a service port of the helium vessel, is used for thermal insulation at 80 K and 20 K in combination with a medium-size refrigerator for cooling the magnet at 4 K. The heat leak at 4 K is estimated to be 3 W at 4 K. The maximum operation current of 500 A is selected by considering the maximum temperature of the coil at quench. In preliminary cooling tests, the magnet has been cooled within 52 h as expected.

Simulation of a magnetic field correction scheme for a Halbach-type undulator

An electron-beam trajectory in a Halbach-type undulator with simulated magnetization errors in its component magnet blocks has been calculated using a three-dimensional magnetic field calculation program. The errors taken into account were deviations of the magnetization strength from a nominal value and a deviation of the magnetization direction from a nominal axis. Both uniform and Gaussian distributions of the error magnitudes are assumed for the component magnet blocks of an ideal reference undulator. A simple method for rearranging magnet pairs is discovered. The field integrals are reduced by factors of 4–15 on the average with the method, and the local distortion of the trajectory is strongly corrected. It is found that the distortion of the trajectory in the corrected undulator is almost independent of the magnet gap.

Design of a large superconducting spectrometer magnet

A superconducting spectrometer magnet for nuclear physics experiments is currently under construction. The magnet has a sector-type coil. The magnetic field is 3 T with a magnet gap of 50 cm, and the stored energy is 11.8 MJ. Ease of operation and maintenance are taken into consideration in the design. Three-dimensional magnetic field calculations and the stress analysis have been performed. The code QUENCH was applied to determine the operating current and check coil safety. A current of 500 A was selected. Heat leaks were checked and estimated to be <2 W at 4 K. A small refrigerator is to be used for thermal insulations at 80 and 20 K.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The design of deflection coils

The relation between the deflection aberrations and winding distribution of a scanning system is briefly reviewed and the importance of the cosine-distributed coil is pointed out. The winding distribution of the saddle-type deflection coil is completely Fourier-analysed, including the end effect and formulae are given for calculating the Fourier components of an air-core deflection field. A new type of corrector coil is proposed to eliminate the end effect. The equations of motion of Gaussian rays including third-order perturbations are shown. The method developed is applied to evaluating the aberrations of a Vidicon tube printed scanning coil and to designing a new scanning system for microfabrication. The Fourier decomposition technique developed reduces the three-dimensional magnetic field calculation to a two-dimensional one.