In order to develop a compact superconducting machine with high efficiency, the detailed knowledge of flux and eddy current distributions is necessary. Recently, 3-D numerical analysis of magnetic field became possible, due to, for example, the progress of fast and cheap workstations, the introduction of new element and the improvement of algorithms for solving large scale simultaneous equations. In this review, the outlines of the finite element method, features of various formulations, problems in applying the finite element method and recent developments are discussed.
The finite element method (FEM) is one of the most versatile methods of numerically analyzing physical phenomena described by partial differential equation. It is suitable to the analysis of such a complicated region which includes non-linear materials. It has some disadvantages, however, in dealing with the field extending infinitely. The phenomena in the electromagnetic field intrinsically spread over the infinite space. We sometimes have to consider the infinite region rigorously, e.g. in the magnetic stray field of superconducting magnets. The boundary element method (BEM) is useful to analyze very large linear fields. It reduces the domain problem to the boundary problem and is particularly suitable for analyzing the infinite space. Furthermore, the required potentials and those derivatives inside the domain are calculated by using theoretical expressions. Owing to these features, the boundary element method is especially useful for the analysis of electromagnetic phenomena. Taking account of advantages in both the finite element and the boundary element methods, the hybrid utilization of both methods (the hybrid FE-BE method) has been proposed. In this review, the recent development and several analytical results of the three-dimensional boundary element method and the hybrid FE-BE method are described.
Very low boil-off of cryogens is required for cryostats containing superconducting magnets used in various fields. It is important that the thermal insulating efficiency is improved. In order to accurately design the thermal insulating efficiency of components for cryostats, it is necessary to measure the emissivity of the thermal shielding plates and the average thermal conductivity of the multilayer insulation and supports. The boil-off calorimetry method has often been used for measurements of these low temperature heat transfer characteristics. In this review, applications of the boil-off calorimetry method and details of measurement are summarized.
The friction resistance plays an important role to determine the amount of deflection between the wedges of toroidal coil cases of a nuclear fusion magnet under electromagnetic force, and the material combination showing high friction is required to reduce the deflection. In order to obtain the material exhibiting high friction against cryogenic structural steels, JN1 and JN2, at 4K in liquid helium, five copper and its alloys including Cr coated copper were explored under fretting condition, where a peak-to-peak slip amplitude was 100μm, a normal load 20N, a frequency 8.33Hz, and the number of fretting cycles 5×104. Cupronickel showed the highest friction of all, where the coefficient of friction reached 0.8 against JN1 and 1.1 against JN2. However, it took more than 104 fretting cycles to show the high friction. Although the wear damage resulted from adhesive wear, the friction was not so high for other metals. It appeared that the friction was inversely proportional to hardness of the materials.
The reduction of AC losses in ultra-fine multifilamentary superconductors is an important task in their application at power frequencies. Sometimes, hysteresis losses in the superconducting wire are much larger than the design values. In many cases, this is a result of proximity coupling in the normal metal layers between the filaments. Determination of the lowest limit of filament spacing and diameter to which hysteresis losses decrease with decreasing filament diameter is necessary in the design of low-loss superconducting wires for AC use. The authors have investigated the proximity coupling in Cu 10% Ni-matrix superconductors with different filament diameters and spacings by measuring hysteresis loss and initial magnetization. The lowest limit of filament spacing, without proximity coupling problem, was found to be 0.13μm for samples given no heat treatment and 0.09μm for heat-treated samples.
A system with a high sensitivity is developed to measure an ac magnetization curve of superconducting wires for ac uses. A design method of this system is discussed and main points to increase the sensitivity are made clear. As a result, the equation to estimate the error of the designed system is provided and therefore the dependence of some design parameters on the error can be calculated. A system is manufactured as an experiment, and its functions are made certain that the sensitivity is very high as designed. Data of the ac magnetization curve of the superconducting ac wire can be obtained successfully by using this system.
Electrical properties of ethylene propylene rubber (EPR) were studied in the cryogenic temperature region to examine the possibility of its application to the solid electrical insulating material of superconducting power apparatuses and cables. Dissipation factor of EPR sheet under high electric field is rather large even at cryogenic temperatures. Electric strength of EPR film is a little superior to that of PE at liquid helium temperature. The use of EPR as a solid electrical insulation at cryogenic temperatures is discussed based on the results obtained. Furthermore, extruded EPR insulated cable was fabricated as an example of EPR solid insulation. The cable showed fine mechanical and electrical performance in the cryogenic temperature region. EPR is suitable for electrical insulating material of superconducting power apparatuses and cables.
This paper deals with the thermal mechanical response of cracked nonmetallic woven composites with temperature-dependent properties. The composite material in generalized plane strain is assumed. Finite element method is used to study the influence of crack formation, residual thermal stresses and weave curvature on the mechanical performance of G-10CR glass/epoxy laminates at low temperatures. Numerical results on the influence of the crack on the mechanical properties and the distribution of stresses at different temperatures and warp angles are obtained and presented in a graphic form.
Temperature dependence of magnetic relaxation and M-H hysteresis has been measured applying magnetic field parallel to the c-axis of the crystal for Bi2.2Sr1.8Ca1.0Cu2.0Ox single crystal which was grown by the TSFZ method. As for the magnetization decay measurement, distribution of pinning potential was calculated according to the Griessen's formalism, Obtained result shows very narrow distribution centered around 40meV, and does not have intensity at high energy. In case of hysteresis measurement, irreversibility field was obtained as a function of temperature. Irreversibility field increased exponentially at near around 25K with decreasing temperature. These peculiar phenomena may be attributed to the highly two-dimensional character of Bi-based materials.