Influence of field penetration ratios and filamentation on end-effect related hysteretic loss reductions for superconducting strips

There are a few key conductor-specific factors which influence the power loss of superconductors; these include critical current, geometry, and normal metal resistivity. This paper focuses on the influence of sample geometry on the power loss of superconducting strips and the effect of filamentation and sample length as a function of the field penetration state of the superconductor. We start with the analytical equations for infinite slabs and strips and then consider the influence of end effects for both unstriated and striated conductor. The loss is then calculated and compared as a function of applied field for striated and unstriated conductors. These results are much more general than they might seem at first glance, since they will be important building blocks for analytic loss calculations for twisted geometries for coated conductors, including helical (Conductor on Round Core, CORC), and twisted (e.g., twist stack cables) geometries. We show that for relatively low field penetration, end effects and reduced field penetration both reduce loss. In addition, for filamentary samples the relevant ratio of length scales becomes the filament width to sample length, thus modifying the loss ratios.