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A finite stack of thin superconducting tapes, all carrying a fixed current I,can be approximated by an anisotropic superconducting bar with critical currentdensity Jc=Ic/2aD, where Ic is the critical current of each tape, 2a is thetape width, and D is the tape-to-tape periodicity. The current density J mustobey the constraint \int J dx = I/D, where the tapes lie parallel to the x axisand 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 forarbitrary height 2b of the stack. For c<|x|<a we have J=Jc, and for |x|<c thecritical state requires that Bz=0. We show that this implies \partialJ/\partial x=0 in the central region. Setting c as a constant (independent ofz) results in field profiles remarkably close to the desired one (Bz=0 for|x|<c) as long as the aspect ratio b/a is not too small. We evaluate variouscriteria for choosing c, and we show that the calculated hysteretic lossesdepend only weakly on how c is chosen. We argue that for small D/a theanisotropic homogeneous-medium approximation gives a reasonably accurateestimate of the ac losses in a finite Z stack. The results for a Z stack can beused to calculate the transport losses in a pancake coil wound withsuperconducting tape.

ac Losses in a Finite Z Stack Using an Anisotropic Homogeneous-Medium Approximation