AC and heat losses in a superconductor cylinder surrounded by a metallic sheath

In this work, we study numerically the magneto-thermal properties of a composite cylinder made of a superconducting core surrounded by a metallic sheath and subjected to an axial AC magnetic field . The metal is ohmic and non-magnetic while the superconductor is characterized by an E(J) power law. The system is studied in a regime for which the temperature is non uniform (and hence the current density is varying spatially), in order to investigate heat draining by the cryofluid. The magneto-thermal problem is solved by the Brandt method for the magnetic part, associated with a standard discretization of the stationary heat equation. The heat loss in the structure is determined as a function of the external parameters (frequency, amplitude of the applied field and convective exchange coefficient). The influence of the spatial step in the metal and in the superconductor is discussed.