Magnetic-field calculation for a high-temperature superconducting cryogenic current comparator

Abstract

The problem considered in this paper arises in the design of a high-temperature superconducting cryogenic current comparator (CCC). The CCC consists of two currents flowing in opposite directions inside a toroidal superconducting shield. The shield has a radial cut, necessary for the measurement of the current ratio, but causing an error in the obtained ratio. The problem of interest is the dependence of the error on the geometric parameters of the device: the major and minor radii of the shield, the cut width, the material thickness, and the location of the currents. In the first part of the paper, a toroidal shield with an infinitesimal cut is considered and analytic expressions are derived for the magnetic field and the surface-current distribution. In the second part, a cut of finite width is introduced. Since all the perturbing currents are present in the narrow region around the cut, a shield of cylindrical shape is assumed. Expressions are derived for the flux through the cut and the magnetic field around the cut. Analytical results are in good agreement with the numerical results obtained by a finite-element method. In the final part, the expression for the ratio error is derived, which shows that in order to minimize the error, currents should be concentrated around the shield axis, the major radius of the shield should be maximized and the bore radius minimized. The error depends logarithmically on the cut width.