Concentric superconducting shells with weak links in an external magnetic field

A model calculation for a system of concentric superconducting shells with one weak link in each shell is considered to help understand the behavior of granular high-temperature superconductors. In this type of superconducting material the contacts between grains often resemble the weak links in classical superconductors. The behavior of a system of concentric superconducting shells, containing weak links, in an external magnetic field is studied. The dependence of inner magnetic flux on external magnetic flux is calculated, as well as the distribution of magnetic field in the space between the shells. An additional modulation appears in the φ_i vs. φ_ex curve. The modulation period depends on the spacing between the shells but not on the number of shells. The cooperative behavior of the system of shells is considered as well