Self-heating of bulk high temperature superconductors of finite height subjected to a large alternating magnetic field

In this work we study, both experimentally and numerically, the self-heating of a bulk, large YBCO pellet of aspect ratio (thickness / diameter) ~ 0.4 subjected to a large AC magnetic field. To ensure accurate temperature measurements, the sample was placed in an experimental vacuum chamber to achieve a small and reproducible heat transfer coefficient between the superconductor and the cryogenic fluid. The temperature was measured at several locations on the sample surface during the self-heating process. The experimentally determined temperature gradients are found to be very small in this arrangement (< 0.2 K across the radius of the superconductor). The time-dependence of the average temperature T(t) is found to agree well with a theoretical prediction based on the one-dimensional (1-D) Bean model, assuming a uniform temperature in the sample. A 2-D magneto-thermal model was also used to determine the space and time-dependent temperature distribution T(r, z, t) during the application of the AC field. The losses in the bulk pellet were determined using an algorithm based on the numerical method of Brandt, which was combined with a heat diffusion algorithm implemented using a finite-difference method. The model is shown to be able to reproduce the main trends of the observed temperature evolution of the bulk sample during a self-heating process. Finally, the 2-D model is used to study the effect of a non-uniform distribution of critical current density Jc(r, z) on the losses within the bulk superconductor.