The Critical State: Vortex Behavior in Superconductors

This lecture explores the behavior of vortices in superconductors, focusing on their density in equilibrium and the critical state. It discusses the entry of vortices at the surface, their interaction with pinning sites, and the shielding currents that push them inside. The Bean model is introduced to calculate the magnetic response, emphasizing the importance of geometry and the non-linear problem of critical current. Various models of the critical state are compared, highlighting the limitations and advantages of each. Experimental evidence, including magnetic hysteresis loops and vortex avalanches, is presented to illustrate the complex behavior of vortices in superconducting materials.