Analysis of the differences and similarities in electromagnetic forces of different equivalent structures of Bi-2212 circular wire

Bi-2212 high-temperature superconducting circular wire exhibit excellent superconducting and electromagnetic properties, making them the preferred material for the next generation of high-temperature superconducting cables, as they can be wound in multiple layers. However, the high stress generated during the transmission of large current by the cable may damage the equipment, and the current density, magnetic field and stress distribution are different in the constant external field and the alternating external field environment. Therefore, it is critical to study the difference between the electromagnetic field distribution and the stress distribution of the circular wire in different forms of external field. In this paper, we focus on Bi-2212 circular wires and establish three types of two-dimensional finite element models using homogenization methods. We emphasize the electromagnetic field, radial stress, and circumferential stress distribution characteristics under constant magnetic field and alternating magnetic field environments. We analyze the similarities and differences among these three equivalent models under the two different external field conditions. When the background magnetic field remains constant, the electromagnetic field, radial stress, and circumferential stress exhibit a center-symmetric distribution. Under an alternating magnetic field, the electromagnetic field and stress exhibit an upper-lower symmetric distribution, with the amplitude being smaller on the left side than on the right side. When the amplitude of the background magnetic field is the same, the electromagnetic field and stress have larger amplitudes under an alternating magnetic field. When the alternating field frequency is large, the current penetration depth in the superconducting region decreases, and a part of the current is driven to Ag and Ag-Mg alloys. The Filament-matrix Homogenized Model accurately reflects the distribution patterns of the electromagnetic field and stress. Under an alternating magnetic field, the Bundle-matrix Homogenized Model has a smaller error in stress amplitude compared to the original structure.