AC losses in a finite Z stack using an anisotropic homogeneous-medium approximation

A finite stack of thin superconducting tapes, all carrying a fixed current I, can be approximated by an anisotropic superconducting bar with critical current density J(c) = I-c/2aD, where I-c is the critical current of each tape, 2a is the tape width, and D is the tape-to-tape periodicity. The current density J must obey the constraint integral J dx = I/D, where the tapes lie parallel to the x axis and are stacked along the z axis. We suppose that Jc is independent of field (Bean approximation) and look for a solution to the critical state for arbitrary height 2b of the stack. For c < vertical bar x vertical bar < a we have J = J(c), and for vertical bar x vertical bar < c the critical state requires that B-z = 0. We show that this implies. partial derivative J/partial derivative x = 0 in the central region. Setting c as a constant (independent of z) results in field profiles remarkably close to the desired one (Bz = 0 for vertical bar x vertical bar < c) as long as the aspect ratio b/a is not too small. We evaluate various criteria for choosing c, and we show that the calculated hysteretic losses depend only weakly on how c is chosen. We argue that for small D/a the anisotropic homogeneous-medium approximation gives a reasonably accurate estimate of the ac losses in a finite Z stack. The results for a Z stack can be used to calculate the transport losses in a pancake coil wound with superconducting tape.