Vortex pinning and magnetic field penetration into a long periodically modulated Josephson contact

A system of vortices formed near the boundary of a long periodically modulated Josephson contact has been calculated with account of the pinning due to inhomogeneity of the medium for the case of a monotonically growing external magnetic field at different values of the pinning parameter g which is proportional to the critical current and the spatial modulation period. It is shown that there exists a critical pinning parameter g sub(c) demarcating two regimes with different types of critical state. The obtained value g sub(c) identical with 3.369 differs from the value 0.9716 suggested by other researchers. The slope of the magnetic field profile near the boundary is obtained as a function of g.