Study on the electromagnetic characteristics and AC loss of a spherical superconductor based on London equations

A spherical superconductor is fixed in a vacuum and surrounded by a harmonic magnetic field. In this paper, we analyze the electromagnetic characteristics and ac loss of the rough sphere by two steps. Firstly, we regard a superconductor as a good conductor and determine the distribution of the magnetic flux density on the surface of a rough sphere. Then, regarding the surface of the sphere as an infinite plane relative to the penetration depth of niobium, we solve the electromagnetic field in a thin layer in which the magnetic field penetrates. By integrating the inner product of electric field and normal current we calculate the ac loss of the rough sphere basing on Maxwell equations and London equations. The results indicate that the superconductor produces ac loss when it is affected by the outside alternating magnetic field, even if it is in the Meissner state.