Analytical Models for the Magnetic Field Calculation of Racetrack High-Temperature Superconducting Magnet
Gong Tianyong1,2, Ma Guangtong1, Ren Gang1
1. State Key Laboratory of Traction Power Southwest Jiaotong University Chengdu 610031 China; 2. School of Electrical Engineering Southwest Jiaotong University Chengdu 610031 China
Abstract：High-temperature superconducting (HTS) materials have excellent characteristics such as relatively high operating temperature, large critical current density, and strong critical magnetic field. Thus, the HTS magnets wound by HTS tapes have broad application prospects in high-field magnet, medicine, and rail transit. In order to reduce the production cost of HTS magnets, the magnet should be optimized in detail before the practical application, and the magnetic field calculation is significant to the optimization design. In the electromagnetic design of magnets, more attention is paid to the magnetic fields in a specific area of space, which is less dependent on the non-uniform current distribution inside the magnet. As a result, when calculating the magnetic fields of superconducting magnets, the current density inside the superconducting magnet can be fairly treated as a uniform distribution. In this way, the computational efficiency of magnetic fields can be improved, and the optimal superconducting magnet design can be accelerated without compromising the calculation accuracy. In this paper, considering a racetrack structure of superconducting magnets, based on the assumption of uniform current density and Biot-Savart's law, through discretization of both the cross-section and centerline of the magnet, three analytical models, line current model, surface current model, and volume current model, were established to calculate the magnetic fields of racetrack HTS magnets. These analytical models were validated against the finite element method (FEM) model and experiment. It was found that these models improve the computing efficiency at least three times that the FEM model in terms of calculating the magnetic field at any point in space. Afterward, a comprehensive comparison was conducted on the computational accuracy and efficiency of these analytical models. The conclusion is that in terms of the racetrack magnet with an elliptical segment, the linear current analytical model has the highest calculation efficiency, and the surface current analytical model has the highest calculation accuracy. The volume current analytical model has high computational efficiency and accuracy for the racetrack magnet with a circular segment. Furthermore, the magnetic field distribution of racetrack HTS magnets was investigated with these analytical models. When the air gap is small (such as 45 mm), the maximum magnetic field position of the magnet, composed of two magnetic poles connected in series, deviates from the center of the magnet and is closer to the circular segment of one magnetic pole. As the air gap increases, the magnetic field generated by the circular segment in the center of the magnet decreases rapidly, and the maximum magnetic field moves toward the center of one magnetic pole. In addition, when the measuring location of magnetic fields is away from the center of the magnet in 157 mm, the magnetic field component named Bz increases with the increase of the air gap, which is different from the situation when the measuring location is equal to 0 mm or 105 mm. The reason is that the angle β between the Bz and its modulus Bm decreases with the increase of air gap, leading to an increase in cosβ. Moreover, because Bz=Bmcosβ, although Bm decreases with the increase of air gap, the product eventually leads to an increase in Bz. Besides, it was found that, for a racetrack magnet, when the elliptical coefficient is less than 1, the position of the maximum magnetic field will move, providing a valuable reference for the critical current estimate of racetrack HTS magnets. Critical current is a core parameter to evaluate the application performance of the superconducting magnet. This paper established an improved self-consistent model with the help of the above analytical models for estimating the critical current of the racetrack HTS magnet. The modeling efficiency and computing accuracy are improved by the Dirichlet boundary condition that inputs the magnetic fields calculated with the analytical models. A smaller Dirichlet boundary corresponds to a higher computing accuracy, suggesting that a small boundary should be used in the improved self-consistent model.
龚天勇, 马光同, 任刚. 跑道型高温超导磁体的磁场解析计算模型[J]. 电工技术学报, 2023, 38(8): 1991-2003.
Gong Tianyong, Ma Guangtong, Ren Gang. Analytical Models for the Magnetic Field Calculation of Racetrack High-Temperature Superconducting Magnet. Transactions of China Electrotechnical Society, 2023, 38(8): 1991-2003.
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