Pinning mediated field penetration and complex susceptibility in inhomogeneous superconductors

Abstract

The penetration of the magnetic field in a network consisting of the superconducting grains and intergranular region depends not only on the applied external magnetic field but also on the underlying pinning force density and fraction of the superconducting grains in the sample. Considering the underlying pinning force density in the form of the repetitive Gaussian (RG) nature we have solved the critical state model to get the spatial internal field profile at a particular time instant. The internal magnetic field as a function of the position inside the superconductor exhibits nonlinear, step-like nature. The complicated nature of the penetration of the field gets strongly affected by the size of the granular region and the total pinning force density in the superconductors. We have numerically calculated the real and imaginary parts of the complex susceptibility. The variation of the imaginary part with the temperature has a peak at a temperature which shifts towards the higher temperature with the reduction of the superconducting fraction.