Critical current density in advanced superconductors

This review paper delves into the concept of critical current density (Jc) in high-temperature superconductors (HTS) across macroscopic, mesoscopic, and microscopic perspectives. Through this exploration, a comprehensive range of connections is unveiled aiming to foster advancements in the physics, materials science, and the engineering of applied superconductors. Beginning with the macroscopic interpretation of Jc as a central material law, the review traces its development from C.P. Bean’s foundational work to modern extensions. Mesoscopic challenges in understanding vortex dynamics and their coherence with thermodynamic anisotropy regimes are addressed, underscoring the importance of understanding the limitations and corrections implicit in the macroscopic measurement of Jc, linked with mesoscopic phenomena such as irradiation effects, defect manipulation, and vortex interactions. The transition to supercritical current densities is also discussed, detailing the superconductor behavior beyond critical thresholds with a focus on flux-flow instability regimes relevant to fault current limiters and fusion energy magnets. Enhancing Jc through tailored material microstructures, engineered pinning centers, grain boundary manipulation, and controlled doping is explored, along with radiation techniques and their impact on large-scale energy systems. Emphasizing the critical role of Jc, this review focuses on its physical optimization and engineering manipulation, highlighting its significance across diverse sectors