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 modula ted Josephson contact has been calculated with account of the pinning due t o inhomogeneity of the medium for the case of a monotonically growing exter nal 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(c) demarcating tw o regimes with different types of critical state. The obtained value g(c) = 3.369 differs from the value 0.9716 suggested by other researchers. The sl ope of the magnetic held profile near the boundary is obtained as a functio n of g.