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

Abstract

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 dba/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 dba/dt in ZFC and the maximum radial and hoop stresses are equal and appear at a plateau region by same dba/dt in FC. In ZFC, two cases are considered: Ba > B* and Ba ≤ B*, where Ba is the applied field and B* is the magnetic field where all the body forces point away. When Ba > B*, the flux front r0 is away from the center of the cylinder with increasing dba/dt. However, when Ba ≤ B*, r0 is always at the center with different dba/dt. By discussing the parameter of dba/dt, we find the influence of dba/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.