Calculations using the circuit equation for current and field distributions of type II superconductors

Abstract

The current distributions of untwisted infinitely long superconductors have been studied during the current sweep and under an external field, using the inductance matrix among superconducting finite elements which are generated from a superconductor. The self-and mutual inductances of general polygonal conductors with a uniform current density over each cross section are precisely calculated from the analytical expressions for the geometrical mean distances. The current distributions among each superconducting element are obtained by solving the circuit equation with the Bean model and a nonlinear E-J relation based on the power law. In addition, the magnetic field and vector potential distributions of an untwisted superconducting composite are also obtained, using the analytical expressions for the magnetic field and vector potential due to polygonal conductors.

Self- and mutual inductances of long coaxial helical conductors

“…For the circuit system consisting of a superconducting composite and a return conductor, the circuit equation for the transport current or the shielding current under the external field in a long superconductor is generally described without the length dependence due to the cancellation of the common term [1,4,13].…”

Current and field distributions of a superconducting power transmission cable composed of helical tape conductors

“…The current distribution among whole divided segments of a superconductor during a current sweep can be calculated fundamentally due to the electric circuit theory under the Bean model [4][5][6]. The vector potential and mutual inductance of the right-handed and left-handed thin helical conductors are shown in appendix A.…”