Computation of Current Distribution on Superconducting Parallel Wire Using an Analytic Approach

This article proposes an analytical solution for finding the current density distribution in superconducting parallel wire transmission lines. As usual, for this type of transmission line, the operation wavelength is much larger than the structure cross-section. Therefore, a static solution can describe the electromagnetic behavior of the structure. In this regard, using London's second equation, the magnetic field within the superconductor is described through the Helmholtz equation. By defining the proper boundary condition, the magnetic field within the wire is obtained as a series of Bessel and Sine functions. Finally, through the Ampere's Law, the current distribution of the wire is determined. Apart from the proposed analytical approach, a numerical solution is presented to verify the analytical approach. The numerical solution is performed by forming an integral equation based on London's second equation and then solving it through the powerful moment method. The agreement between the analytical approach and the presented numerical solution shows that the proposed analytical approach gives an efficient way in analyzing superconducting parallel wires. Through the proposed analytical approach, for several parallel wire structures with different aspect ratios, the curret distribution is evaluated and discussed. Results show that as the aspect ratio is decreased, the wires experience much more current density at the internal edges.