Modeling of the critical state in the granular high-T_c superconductors

Abstract

Considering granular superconductors as the Josephson structures, we study the process of the magnetic flux penetration into the high-T _c superconductor ceramics. We consider the models of the one-, two-, and three-dimensional Josephson lattices, which are formed of the mutually crossed Josephson junctions in a superconductor. In the simplest case of the one dimensional Josephson junction with the dense periodical inhomogeneity the modeling gives the picture of the critical state that is in accordance with the estimations obtained by accounting the pinned vortices interaction. Connections with the stochasticity in the Frenkel-Kontorova model are discussed.

Key Words:

• critical state
• granular superconductors
• high-T _c superconductors
• stochasticity
• Frenkel-Kontorova model