Flux penetration in thin elliptic superconducting cylinders subjected to transverse magnetic fields

Abstract

We solve for the flux penetration in thin superconducting strips of elliptic cross-section subjected to an external magnetic field. We consider general solutions of current distributions J(r) that allow B to vanish identically within the flux front. From those solutions that violate the requirement J(r) ≤ J_c at some r, we reproduce the line current densities that match results being currently presented in the literature for thin strips. We derive new solutions for line current densities with the constraint that the corresponding J(r) macroscopically averages to J_c. We present results for the M-H curve, and the magnetic-field distributions. These are then compared with earlier results when J(r) ≤ J_c is never transgressed.