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.