Influence of the rate of applied field on the stresses in a long cylindrical superconductor

A cylindrical bulk superconductor that undergoes magnetization processes endures enormous mechanical stresses, which will crack the bulk, especially with the applied field changing at high speed. In this paper, the impact of the relative rate of applied field db_a/dt on both radial and hoop stresses in a long cylindrical superconductor is discussed by solving the Kim model with viscous flux flow. Two magnetization processes are considered during the applied field decreasing: zero-field cooling (ZFC) and field cooling (FC). The radial and hoop stresses increase with increasing db_a/dt in ZFC and the maximum radial and hoop stresses are equal and appear at a plateau region by same db_a/dt in FC. In ZFC, two cases are considered: B_a > B* and B_a ≤ B*, where B_a is the applied field and B* is the magnetic field where all the body forces point away. When B_a > B*, the flux front r₀ is away from the center of the cylinder with increasing db_a/dt. However, when B_a ≤ B*, r₀ is always at the center with different db_a/dt. By discussing the parameter of db_a/dt, we find the influence of db_a/dt on both radial and hoop stresses is appreciable, which can be distinguished from previous works that have discussed the effect of viscous flux flow velocity (υ₀) on the radial and hoop stresses by Bean model with viscous flux flow equation. In addition, we find that the Kim model has a wider applicability than the Bean model.