Geometric Arrangements for Maximizing Power-Transmission Capability in Superconducting Transmission Cables

Abstract

An analysis is given of the power carrying capability of several geometric arrangements of superconducting transmission cables for use in dc, single‐phase ac, and three‐phase ac applications. The integrated Poynting vector is maximized with respect to internal geometric variations under the restrictions that E and H remain below fixed maximum values. The discussion includes calculations of maximum energy densities for several three‐phase ac geometric arrangements. For a type‐I material, the single‐phase or dc energy density achievable with optimized multiple concentric cylinders is found to be approximately three times that available by an intermixed wire geometry using the same materials. A theoretical upper limit is given for the energy per cm² which may be sent down a superconducting cable of given type‐I material and given dielectric, independent of the geometry adopted. It is shown that attempts to use flux‐canceling geometries to uniformly reduce H are based on misconceptions of the nature of the problem, for both type‐I and type‐II lines. Use of fine filaments of type‐II material to counterlace currents and reduce H are found to be of negative benefit. For niobium ac lines, the dielectric is found to be the limiting material when helium is used as the dielectric.