Modeling of Current Density in Cylindrical Superconductors by Separation of Variables

The distribution of current density in bulk cylindrical superconductors is calculated by the method of separation of variables. The method is applied to conductors with and without the transport current in the transverse, longitudinal, or arbitrary directed magnetic fields. A significant reduction of the matrix equation is achieved due to the decomposition of the solution using the Fourier series over the polar angle. The method is validated on a range of test models comparing the results with the solutions found by the state-of-the-art finite-element analysis (FEA).