Magnetic field distributions in a large single crystal of YBa ₂Cu₃O_7-δ with cylindrical non-conducting inclusions

μSR experiments on a large single crystal sample of YBa ₂Cu₃O_7-δ with non-conducting Y ₂BaCuO₅ inclusions show some interesting characteristics, especially the magnetic field distribution in the inclusion regions. This internal magnetic field distribution has been calculated using the London equations for the superconducting regions. In the model we develop here we assume that the inclusions are cylindrical and infinite in length. The interaction energy between an inclusion and an hexagonal array of vortices is also obtained. The difference between the field value in the inclusions and the value at the saddle point is sensitive, in our model, to the penetration depth. Comparing the calculated to observed field differences provides a new alternative method of determining the penetration depth.