Predicting the Trapped $B$ Field in Bulk Superconductors Using Critical State Models

Trapped field superconductors hold promise as a potential game changer in a number of electromechanical applications. Predicting the trapped field is integral to their integration in these applications, and by necessity the critical state model is normally used in that regard. This paper offers three contributions towards that end. First, it offers a method to predict the trapped field based on a novel way to break down a mutual coupling matrix one cell at a time. Second, it discusses another predictive scheme based on equivalent column currents in the cell while taking into account the side of the YBCO crystal where seeding occurred. There is an experimental procedure that allows one to predict the equivalent thickness of the YBCO puck. Third, it offers some guidelines for when the simpler critical state Bean model can be employed with some confidence over the more complete Kim model. All the analyses are compared to experimental results on bulk YBCO pre-cooled to 77 ^°K, 20 mm in diameter with an axial length of 8 mm.