High-temperature superconducting (HTS) wires such as those used for Bi-2223 and REBCO tapes, which are commercially available, are expected to be used in future electric power devices and high-field magnets because of their good criticalcurrent characteristics at high temperatures and in high applied magnetic fields. Therefore, the importance of numerical simulation techniques for HTS applications has increased. Recently, special sessions on numerical simulation of HTS modeling and applications have been held at academic conferences and workshops. Generally, the electromagnetic phenomena including HTS materials use the eddy current problem of Maxwell’s equations together with nonlinear constitutive relationships between the electric field and current density. Until now, the user him/herself had to code a special program in order to manage the modeling of HTS materials and formulations of electromagnetic phenomena including HTS materials. However, recently, the numerical simulation on HTS applications using commercial software has been reported. In this paper, the current status of numerical simulation techniques for HTS applications is reviewed.

A theoretical model is proposed for roughly estimating the screening-current-induced field (SCIF) in hightemperature superconducting coils. The direct relationship between the SCIF and the magnetization of tape wires leads to a scaling law for the SCIF and coil dimensions. A simple analytical expression of the SCIF at the coil center is obtained as functions of the current load factor, tape wire width, and coil dimensions. We verify that the numerical data for the precise simulation of SCIF in the literature are roughly fitted by our theoretical results for flat coils where the height is smaller than the outer diameter.

A no-insulation (NI) winding technique was proposed by Hahn. This technique drastically improves the thermal stability of REBCO pancake coils. Using the technique, a 45.5-T DC field was achieved at the National High Magnetic Field Laboratory in August 2018. Now, Iwasa, of the Plasma Science and Fusion Center, Massachusetts Institute of Technology, is developing an insert NI REBCO magnet for the 1.3-GHz LTS/HTS NMR magnet. However, since the electromagnetic behavior in NI REBCO pancake coils is complicated, it is desirable to evaluate the magnet stability using simulation. Hence, a few simulation methods for NI REBCO pancake coils have been developed and reported, such as a lumped circuit model, a partial element equivalent circuit (PEEC) model, and a distributed network model. In this review paper, we discuss these simulation methods and describe the specifications for each of them. Finally, we compare the simulation results of each method. Accurate simulation of the lumped circuit model and radially-divided circuit model with a small number of elements was not possible because the magnet coupling between elements or coils was not correctly modeled. As a result, we had to use the PEEC model, distributed network model, or a radially-divided circuit model with many elements in order to accurately express the normal zone propagation.

Electromagnetic properties in high temperature superconductor (HTS) wires and coils were numerically evaluated using two kinds of finite element methods. One is the method formulated using a self-magnetic field generated by a current induced in an analysis region. The other is based on current vector potential. First, governing equations for these methods are derived using Maxwell’s equations. After that, electromagnetic responses such as AC loss and screening-current-induced field carried out up to now by several groups including the author are reviewed for one- and two-dimensional HTS wires and coils.

Since high critical-current density can be maintained in a high magnetic field, a multi-coil system composed of REBCO superconducting tape is expected to be applied to MRIs and medical accelerators. We have been developing a REBCO coil system for 9.4-T whole-body MRI. In MRIs, magnetic-field homogeneity with high precision in time and space is required in the imaging space, and in this research and development, the target values are set to 1 ppm/h and 10 ppm, respectively. In REBCO coils, screening currents are remarkably induced in the winding tape by the perpendicular component of the magnetic field to the wide face of the REBCO tape, generating an irregular magnet field that deteriorates the magnetic-field homogeneity. Therefore, in order to realize a coil system satisfying MRI specifications, it is required to accurately predict and reduce this shielding-current magnetic field. In this paper, we report results of detailed analysis and evaluation of the influence of the shielding-current magnetic field, and examine a method and procedure for reducing it. First, in order to improve the temporal stability, we evaluated the effect when the overshoot and the demagnetization methods are applied to control operation current, and optimize current waveform. Next, as a method to enhance the spatial homogeneity, we adopted a tape scribing technique by narrowing the tape width, and evaluated its effect, and optimized the coil-winding region to be scribed. Finally, we confirmed the effect of combining both current control and scribing, and showed that the target values of 1 ppm/h and 10 ppm can be cleared as a result.