用各向异性均匀介质近似计算有限Z形叠层的交流损耗
ac Losses in a Finite Z Stack Using an Anisotropic Homogeneous-Medium Approximation
摘要：
有限堆的薄超导带，都承载固定电流I，可以近似为具有临界电流密度Jc=Ic/2aD的各向异性超导棒，其中Ic是每个带的临界电流，2a是带宽度，D是带到带的周期性。电流密度J必须服从约束\int J dx = I/D，其中带平行于x轴放置并且沿着z轴堆叠。我们假设Jc与场无关（Bean近似），并寻找任意堆叠高度2b的临界状态的解决方案。对于c< |x| <a，我们有J=Jc，对于|x| <c，临界状态要求Bz=0。我们表明，这意味着\partial J/ \partial x=0的中心区域。只要纵横比b/a不太小，将c设置为常数（与z无关）会导致场分布非常接近所需的场分布（对于|x| <c，Bz=0）。我们评估各种标准选择C，我们表明，计算的滞后损失只弱依赖于如何选择C。我们认为，对于小的D/a的各向异性介质近似给出了一个合理的准确估计的交流损耗在一个有限的Z堆栈。Z堆的计算结果可用于计算超导带材绕成的扁平线圈中的输运损耗。
英文摘要：
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 Jc=Ic/2aD, where Ic 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 \int 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<|x|<a we have J=Jc, and for |x|<c the critical state requires that Bz=0. We show that this implies \partial J/\partial 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 |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.
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