Numerical calculation of the inductances of a multi-superconductor transmission line system

A variational numerical method is described in this paper to calculate the inductances of a multi-superconductor transmission line system. We show that the currents in the superconductors are distributed in a way that the sum of the total magnetostatic energy and the total kinetic energy of the system is a minimum. Using this principle, a variational technique is formulated to calculate the current distribution in the conductors and to calculate the inductances of the conductor system, in particular, we subdivide the conductor into small rectangular sub-conductors and assume a uniform trial current in each of the sub-conductor. The total energy of the system is obtained through Green's function and is minimized by applying the Lagrange multiplier technique. Once the current distribution is obtained, the inductances can be obtained easily. The method is implemented numerically and proved to be fast and accurate.