AC losses in a finite<i>Z</i>stack using an anisotropic homogeneous-medium approximation

Abstract

A finite stack of thin superconducting tapes, all carrying a fixed current I,\ncan be approximated by an anisotropic superconducting bar with critical current\ndensity Jc=Ic/2aD, where Ic is the critical current of each tape, 2a is the\ntape width, and D is the tape-to-tape periodicity. The current density J must\nobey the constraint \\int J dx = I/D, where the tapes lie parallel to the x axis\nand are stacked along the z axis. We suppose that Jc is independent of field\n(Bean approximation) and look for a solution to the critical state for\narbitrary height 2b of the stack. For c&lt;|x|&lt;a we have J=Jc, and for |x|&lt;c the\ncritical state requires that Bz=0. We show that this implies \\partial\nJ/\\partial x=0 in the central region. Setting c as a constant (independent of\nz) results in field profiles remarkably close to the desired one (Bz=0 for\n|x|&lt;c) as long as the aspect ratio b/a is not too small. We evaluate various\ncriteria for choosing c, and we show that the calculated hysteretic losses\ndepend only weakly on how c is chosen. We argue that for small D/a the\nanisotropic homogeneous-medium approximation gives a reasonably accurate\nestimate of the ac losses in a finite Z stack. The results for a Z stack can be\nused to calculate the transport losses in a pancake coil wound with\nsuperconducting tape.\n