Abstract: The demand for higher performing, cost-effective superconducting cables continues to grow with emerging applications in high-field magnets, electricity grid, lightweight motors, and generators.  Moreover, very recently, high-temperature superconductors have been identified as the enabling technology for generating 12T-scale confinement magnetic fields in compact tokamak fusion reactors. Ultimately, the performance of a superconductor is determined by its ability to immobilize vortex lines by defects. Therefore, the generation of effective vortex-pinning potentials is an essential part of the development process for high-performance superconductors.

Two main approaches to achieve this goal are the creation of self-assembled inclusions during synthesis and post-processing particle irradiation. Purely empirical approaches, however, are not able to establish achievable ultimate limits of critical currents. We explored these limits by using large-scale numerical simulations of time-dependent Ginzburg-Landau equations.

In particular, we considered pinning by identical spherical inclusions and computed their optimal size and density giving the maximum critical current at fixed magnetic field. We also explored in detail multiple pinning regimes by such inclusions with the increasing magnetic field. To find the best pinning potential at the fixed magnetic field and current direction, we employed the targeted-evolution algorithm amounting to ​“mutating” the existing defect structures and selecting ones giving the highest critical current.   This process produced a series of planar defects parallel to the current with definite width and separation, which gives the highest critical current significantly higher than for other possible candidate defect structures, such as an array of parallel columnar defects.  In general, the optimal pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales, operation temperatures, and sensitivity to current and field orientations. Numerical simulations are established as a valuable tool in this design process.