AC losses in a finiteZstack 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 /2 aD , where I c is the critical current of each tape, 2 a is the tape width, and D is the tape-to-tape periodicity. The current density J must obey the constraint , where the tapes lie parallel to the x axis and are stacked along the z axis. We suppose that J c is independent of field (Bean approximation) and look for a solution to the critical state for arbitrary height 2 b of the stack. For c <| x |< a we have J = J c , and for | x |< c the critical state requires that B z = 0. We show that this implies in the central region. Setting c as a constant (independent of z ) results in field profiles remarkably close to the desired one ( B z = 0 for | x |< 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.