An accurate method of calculating multilayer, multimaterial cylindrical magnetic shields

The basic concepts of shielding theory have existed since the last century [1,2]. There have been many publications on the subject of magnetic shielding, treating the case of shielding apparatus from static fields by means of multiple concentric shields and deriving several principles of fundamental importance. Unfortunately, however, theory has been applied to only the most ideal shield configurations, for the case of constant permeability [3-5]. This paper covers the analysis of shielding effectiveness of variable Permeability cylindrical shielded enclosures for the DC magnetic field case. When the permeability is a function of magnetic induction, the simple boundary solution for spherical or cylindrical shields can no longer be applied since the induction, through the permeability, is caused to vary as much as two orders of magnitude, causing nonuniformity in the field in the cavity and inside the shield. Thus, the permeability of the shielding material is considered as a function of the induction, and a significantly improved method of estimating the induction and permeability of the shield is presented. The effects of a multiple-shell geometry are treated in the equations of this analysis. This method gives fast, accurate results and can be run on a small computer for shielding optimization. Results of these magnetic field calculations allowed the selection of optimization criteria and showed how system requirements could be met by choosing a suitable shell structure arrangement. Experimental measurements on real materials for various shell structures confirmed the accuracy of this method.     

Magnetic-field calculation for a high-temperature superconducting cryogenic current comparator

The problem considered in this paper arises in the design of a high-temperature superconducting cryogenic current comparator (CCC). The CCC consists of two currents flowing in opposite directions inside a toroidal superconducting shield. The shield has a radial cut, necessary for the measurement of the current ratio, but causing an error in the obtained ratio. The problem of interest is the dependence of the error on the geometric parameters of the device: the major and minor radii of the shield, the cut width, the material thickness, and the location of the currents. In the first part of the paper, a toroidal shield with an infinitesimal cut is considered and analytic expressions are derived for the magnetic field and the surface-current distribution. In the second part, a cut of finite width is introduced. Since all the perturbing currents are present in the narrow region around the cut, a shield of cylindrical shape is assumed. Expressions are derived for the flux through the cut and the magnetic field around the cut. Analytical results are in good agreement with the numerical results obtained by a finite-element method. In the final part, the expression for the ratio error is derived, which shows that in order to minimize the error, currents should be concentrated around the shield axis, the major radius of the shield should be maximized and the bore radius minimized. The error depends logarithmically on the cut width.     

Comparison of deterministic and Monte Carlo methods in shielding design

In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions.     

应用于铯喷泉钟的磁屏蔽系统的设计

高质量磁屏蔽系统是铯喷泉钟的重要部件之一。首先给出评定磁屏蔽效果的3个指标,即磁场均匀区长度、磁场均匀区起点位置和磁屏蔽效率。在此基础上,讨论了利用有限元计算3层磁屏蔽系统的层间径向间距、轴向间距、端盖孔套管长度和端盖连接方式对磁屏蔽的影响,给出了相应的优化参数,并对比了按优化参数设计的3层磁屏蔽与原有4层磁屏蔽系统用有限元计算的磁屏蔽效果。有限元计算结果为中国计量科学研究院新铯喷泉钟磁屏蔽系统的技术设计提供了理论指导。     

Analysis of perforated magnetic shields for electric power applications

The shielding performance of perforated magnetic shields for electric power applications is described. The shielding of an axisymmetric induction heating device is studied as a function of frequency, number of perforations and dimensions of the perforations. From the numerical point of view, the perforations cause the numerical model to be 3D. A numerical optimisation is carried out to find the optimal geometry with respect to the shielding factor and the volume of the shield. For the optimisation, two approaches are presented. The first approach is fast and easy-to-implement, but has limited accuracy. It uses a classical 2D axisymmetric model where the perforations are approximated by 'axisymmetric air gaps' resulting in a segmented shield. It is shown how to modify the 2D model to obtain results that are similar to the ones of a 3D model. The second approach is more accurate although quite fast, but more difficult to implement. It combines a 3D thinshell finite element model with the unmodified 2D model in a space mapping optimisation algorithm. The validation of both models is based on experimental work for an unperforated shield and for the optimised perforated shield.     

Dynamic magnetic shield for the CLAS12 central TOF detector photomultiplier tubes

The Central Time-of-Flight detector for the Jefferson Laboratory 12-GeV upgrade is being designed with linear-focused photomultiplier tubes that require a robust magnetic shield against the CLAS12 main 5-T solenoid fringe fields of 100 mT (1 kG). Theoretical consideration of a ferromagnetic cylinder in an axial field has demonstrated that its shielding capability decreases with increasing length. This observation has been confirmed with finite element analysis using POISSON model software. Several shields composed of coaxial ferromagnetic cylinders have been studied. All difficulties caused by saturation effects were overcome with a novel dynamical shield, which utilizes a demagnetizing solenoid between the shielding cylinders. Basic dynamical shields for ordinary linear-focused 2-in. photomultiplier tubes were designed and tested both with models and experimental prototypes at different external field and demagnetizing current values. Our shield design reduces the 1 kG external axial field by a factor of 5000.     

Improvement of YBCO Superconductor Magnetic Shielding by Using Multiple Bulks

HTS bulks present a high critical current density which can be used as magnetic shields. Previous works showed that BSCCO bulks can screen magnetic fields up to 0.1 T. For large scale applications like electrical machines, stronger magnetic field is usually needed. In so doing, (RE)BCO materials are more suitable since they can shield much higher magnetic fields. Another key issue concerns the size of the bulks. Nowadays, it is possible to manufacture 150-mm diameter class cylindrical YBCO bulk. In order to get larger magnetic shielding areas, multiple bulk superconductors should be arrayed and stacked in layers. This paper presents experimental results on screening performances of layered YBCO pellets. These results are compared with 2D simulations. The experiments are carried out at 77 K under external magnetic fields of 150 mT. Different topologies are considered: single-layer configuration with 9 square pellets and double-layer configuration with respectively 9 and 4 square pellets. Experimental and simulation results show that a checkerboard of one layer configuration does not fully shield the external magnetic field. Improved shielding properties are obtained when the double-layer configuration is used.     

Inductance of magnetically shielded air-core coils of circular cross section

An expression for the inductance of shielded cylindrical air-core solenoids of arbitrary diameter to length ratio is developed. Three shielding configurations are investigated: 1) the use of a coaxial-concentric magnetic shield, 2) the coaxial magnetic shield with conducting end plates, 3) the coaxial magnetic shield with conducting end rings. Case 2) is solved in closed form by separation of variables, and from this result a method is given for predicting the length of the coaxial magnetic shield required to contain the field for the three cases.     

Optimized configurations for passively shielded magnetic resonanceimaging magnets

A design approach is presented for the development of passive shields for coil configurations, with particular emphasis on those used for magnetic resonance imaging (MRI). The approach is based on minimizing the weight of the shield by ensuring that the shield material is everywhere near saturation. A mathematical model is developed to describe the shielding efficiency of a cylindrical shield as a function of shield geometry and type of shield material. The model is used to develop a possible multiple-shield configuration for a 1.5-T MRI magnet     

Transform method for calculating low-frequency shieldingeffectiveness of planar linear multilayered shields

A two-dimensional analytical solution for quasistatic magnetic field shielding with planar infinite multilayered shields is presented. The magnetic field source is a system of long straight wires parallel to the shield, carrying sinusoidal currents. The analysis assumes that material media can be considered linear under the applied source fields. The spatial Fourier cosine and sine transforms are applied to the analytical expressions of the magnetic field intensity and flux density is obtained by solving the diffusion equation in each layer. Using transfer relations for every layer in terms of transformed variables allows one to obtain the shielded field, and thus the shielding effectiveness, with no need to determine the integration functions explicitly. The results obtained with both this approach and a finite-element computer code are in good agreement. The method seems to be also suited for the analysis of problems with more complex geometries and source distributions     

A numerical and experimental study of crack tip shielding in presence of overloads

The mechanism underlying plasticity-induced shielding of a crack tip under fatigue loading has been already experimentally investigated by means of photoelasticity using a recently-developed mathematical model which considers stress field near the crack tip and along the flanks. Stress intensification factors have also been defined to describe shielding effects on the applied elastic field. In this paper a new application of this model is developed through a numerical simulation of the experimental tests, which were previously performed.The study is aimed to analyze the shielding effect related to constant amplitude cycling loading and a single overload peak, considering numerical simulation. By means of the models developed by XFEM technique, the plastic region is reproduced finding a good agreement with the experimental data, and a systematic procedure is proposed to evaluate the stress intensity factors.A good correspondence is found by comparing the numerical with the experimental parameters, obtained from the mathematical model.     

Analysis and improvement of cyclotron thallium target room shield

Because of high neutron and gamma-ray intensities generated during bombardment of a thallium-203 target, a thallium target-room shield and different ways of improving it have been investigated. Leakage of neutron and gamma ray dose rates at various points behind the shield are calculated by simulating the transport of neutrons and photons using the Monte Carlo N Particle transport computer code. By considering target-room geometry, its associated shield and neutron and gamma ray source strengths and spectra, three designs for enhancing shield performance have been analysed: a shielding door at the maze entrance, covering maze walls with layers of some effective materials and adding a shadow-shield in the target room in front of the radiation source. Dose calculations were carried out separately for different materials and dimensions for all the shielding scenarios considered. The shadow-shield has been demonstrated to be one suitable for neutron and gamma dose equivalent reduction. A 7.5-cm thick polyethylene shadow-shield reduces both dose equivalent rate at maze entrance door and leakage from the shield by a factor of 3.     

The effect of shaking on magnetic shields

The increase of the shielding factor due to shaking was measured in a scale model for a magnetically shielded room. The increase was found to be 7 dB for a single-layer square cylinder biased by the Earth's magnetic field. The shielding factor of a large-volume three-layer Mumetal^®room was estimated to increase by a factor of 30, thus confirming the feasibility of shaking in magnetic shields. The shaking parameters, amplitude, and frequency are not critical according to the experiments. Winding the shaking coils along the edges of the cubic shield leads to minimum disturbances inside the cube, and the winding can also be applied to demagnetize the shield by an alternating field of 25 A/m, 50 Hz. The relative incremental permeability of Mumetal was studied as a function of the shaking and biasing fields. The permeability was found to increase considerably by shaking and by decreasing the biasing field. With zero biasing and with shaking field of Hs= 5 A/m root mean square (rms), 50 Hz, the permeability reached its maximum value of 89 000, which is sevenfold the value without shaking.     

Near-tip microcrack shielding in advanced ceramics

Recent manufacturing of advanced ceramics has developed phase transformation and cracks tilted or bridged to enhance ceramic‐inherent toughness. However, main crack and near‐tip microcracks interaction is another prominent means in toughening of the ceramic materials. In this study, mechanics of discrete model combined with alternative iterating numerical technique is developed and applied in assessment of main–microcrack interaction. Consequences of main–microcrack interaction can either shield or amplify the resulting main crack stress intensity factor, which accounts for the increase or decrease of ceramic toughness. Numerical outcomes show good agreement with the available solutions in the literatures; in addition results also reveal that the toughness shielding or amplification is dependent on the type of loadings as well as location/orientation of the microcrack. Nevertheless, residual normal stress plays an important role in shielding/amplification region trade‐off. This work may provide a useful quantitative tool in ceramic design and a valuable insight into main–micro interaction phenomenon.     

Multipole shaking field for magnetic shielding

The authors propose a novel method of magnetic shaking for enhancing the performance of ferromagnetic shielding. The method employs a new type of planar coil which generates higher-order multipole fields. Ferromagnetic shielding walls placed close to the planar coil can be suitably shaken by its field, whereas unwanted leakage of the shaking field into the shielded space can be avoided due to the highly localized nature of the multipole field. The configuration of the novel planar coil is similar to a square mesh in which alternating cells are clockwise or counterclockwise current loops. The shaking effect on the shielding performance and the leakage of the shaking field are evaluated using cylindrical shields and compared with results obtained with toroidal shaking coils     

Magnetic field shielding concepts for power transmission lines

High current carrying cables used in power transmission lines create strong magnetic fields in their vicinity. For ac lines at 50-60 Hz, the magnetic field is quasi-static and hence uncoupled from the electric field. Shielding of such low frequency magnetic fields is a challenge. In this paper, finite element modeling is used to study the effect of various shield geometries and shield materials around a current carrying wire. Two-dimensional analysis is sufficient for this problem because the cables are very long compared to the wire diameters. Shielding effectiveness, defined as the difference in the magnetic field intensity with and without the shield, is presented. It is concluded that a partial shield is the optimal design for shielding the region below the cable. To achieve this, the shield gap must be oriented above the high current wire     

Magnetic Characterization of MgB2 Bulk Superconductor for Magnetic Field Mitigation Solutions

Magnetic shielding properties of MgB₂ bulk samples synthesized by the SPS (Spark?CPlasma?CSintering) technique were characterized in low applied magnetic fields at temperatures ranging from 20 to 37 K. The used growth technique allows one to produce this compound in different shapes and sizes required for shielding applications. In this framework, shielding magnetic-induction field profiles generated by MgB₂-based shield components, shaped as planar thick disks, were measured by means of a suitable Hall probe in-plane array. The magnetic field distribution at different vertical distances above the sample was also obtained by a micrometric motion of the probe ensemble. Magnetic field profiles were then analyzed in the framework of the critical state model and the critical current density, J _c , was evaluated. The J _c magnitude indicates that the material under test is a good candidate for passive magnetic shield manufacturing up to temperatures close to the transition one.     

Arrangement of high-energy neutron irradiation field and shielding experiment using 4 m concrete at KENS

An irradiation field of high-energy neutrons produced in the forward direction from a thick tungsten target bombarded by 500 MeV protons was arranged at the KENS spallation neutron source facility. In this facility, shielding experiment was performed with an ordinary concrete shield of 4 m thickness assembled in the irradiation room, 2.5 m downstream from the target centre. Activation detectors of bismuth, aluminium, indium and gold were inserted into eight slots inside the shield and attenuations of neutron reaction rates were obtained by measurements of gamma-rays from the activation detectors. A MARS14 Monte Carlo simulation was also performed down to thermal energy, and comparisons between the calculations and measurements show agreements within a factor of 3. This neutron field is useful for studies of shielding, activation and radiation damage of materials for high-energy neutrons, and experimental data are useful to check the accuracies of the transmission and activation calculation codes.     

Thermal analysis of magnetic shields for induction heating

For the design of magnetic shields for induction heating, it is useful to analyse not only the magnetic field reduction but also the temperature behaviour of the shield. The latter is heated by its electromagnetic losses and by thermal radiation from the workpiece. A coupled thermal-electromagnetic axisymmetric finite element model is used to study the temperature of a shield for an axisymmetric induction heater, highlighting the effect of the radius, length, thickness and material of the shield on its temperature and magnetic shielding factor. Also the effect of frequency and workpiece dimensions is investigated. The model is validated by measuring magnetic induction, induced currents in the shield and temperature of the shield on the experimental setup. The temperature is unacceptably high for shields close to the excitation coil, especially if the shield length is lower than the workpiece length. Although the study is carried out for one specific induction heater geometry, the paper indicates the effect of parameters such as geometry, material and frequency on shield temperature so that the results are also useful for other induction heating configurations.     

Shielding Effectiveness Measurements for Ferromagnetic Shields

This paper proposes a new way to measure the shielding effectiveness of ferromagnetic shields. The procedure combines an experimental characterization of the shielding material and numerical simulations. In a first case, magnetic hysteresis is reduced to a series of equivalent $B$ –$H$ linear relations through an optimization procedure that is applied to a measured set of symmetric minor loops, and an equivalent multilayer linear medium is defined through a subsequent iterative procedure. In a second case, magnetic hysteresis is reduced to a simple $B$–$H$ nonlinear relation, obtaining an equivalent nonlinear shield. In both cases, the obtained results are compared with the direct measurements of the shielding effectiveness at different operating frequencies, showing good agreement and the validity of the proposed method. A comparison and a discussion on the harmonic content of the attenuated field for the investigated shield geometry are reported. The same analysis is carried out for a basic diffusion problem, comparing the results with those obtained by the use of a Preisach model.