Investigation of the effect of conformal pinning array on critical current density in infinitely long superconductors

In this study, the influence of conformal pinning centers on enhancing the critical current density in superconductors has been investigated. To increase the critical current density, a square-pinned array with dimensions of 10λ by 10λ under two appropriate conformal transformations is considered. Initially, by specifying the forces acting on the vortices, the relevant Langevin equation for the vortices is solved. By solving this equation, the vortex positions versus time are determined, and using this information, the critical current density is calculated as a function of the magnetic field. Then, the critical current density is calculated for various conformal function parameters in a superconductor tape. The results indicate that after applying two conformal transformations with appropriate parameters, the critical current density could be increased at higher magnetic fields. Simulations demonstrate a 25% increase in critical current density in the optimal case.