The critical state and ac losses in long elliptic superconductors with non-uniform transverse critical current density: Applications to Ag sheathed PbBi2223 tapes

Analytical solutions for the critical state of a long elliptic superconductor with a non-uniform transverse critical current J(c) were obtained for both transport current and transverse external fields. The results show that the difference between thin elliptic and thin rectangular conductors can be attributed to the different transverse distribution of J(c) instead of the geometrical differences. It is also found that a particular J, distribution typical of that observed in PbBi2223 tapes with one adjustable parameter, can (1) unify the solutions for both thin elliptic and thin rectangular conductors and (2) cover the range of ac losses between the two cases.