Right-Angle Bends in Thin Strip Conductors

Abstract

Current density and resistance expressions are obtained by means of a conformal transformation for a strip conductor which contains a right-angle bend. The approach, similar to that applied by Cockcroft to the problem of rectangular coaxial capacitors, is sufficiently general to take into account the effects arising both from a width change at the bend and from a small radius on the inside corner. It is suggested that the current density expressions can be applied in some cases to superconducting thin film strips, and the effect of a right-angle bend on the supercurrent-carrying capacity of such a strip is discussed. A typical result is that the critical current of a bent superconducting strip may be only 1/6 that of a similar but straight strip if the radius of the inside corner of the bend is 1% of the strip width. A specially shaped right-angle bend is then described, the critical current for which is identical to the corresponding straight strip. Current density nonuniformity somewhat away from the corner is also discussed. For example, a 4% variation across the strip is found two strip widths from the corner. The design of a thin film cryotron gate element is then discussed in the context of these current density results. The resistance expression, which naturally applies only to normal conductors, relates the resistance of the bent film strip to the strip dimensions and the bulk resistivity. It is shown that a radius on the inside corner as large as several percent of the strip width will decrease the resistance by an amount which is generally negligible.