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

TL;DR

This paper models ac losses in a finite stack of superconducting tapes using an anisotropic homogeneous-medium approximation, providing insights into critical state behavior and loss estimation for practical coil applications.

Contribution

It introduces an analytical approximation for ac losses in finite Z stacks of superconducting tapes, simplifying complex geometries for practical loss calculations.

Findings

The approximation closely matches detailed models for certain aspect ratios.

Hysteretic losses depend weakly on the choice of the critical region boundary.

The method is effective for small tape-to-tape spacing D relative to tape width a.

Abstract

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.