Magnetic flux penetration into a non-uniform Josephson junction

The extreme profile of a magnetic field penetrating into a non-uniform Josephson junction is computed in the case of periodically arranged pinning centres by use of a numerical solution of a chain of the sine-Gordon equations with boundary conditions at the pinning centres. It is found that the extreme profile obtained is approximately described by the Bean critical-state theory. At sufficiently small spacings the authors find no stochastic regime for a Josephson junction of a finite length. This shows two possibilities: either the front of the profile is extremely extended or at magnetic fields larger than Hcl, only a uniform vortex distribution is realized.