Theoretical analysis and numerical calculation of 3D trapped field distribution of single domain SmBCO bulks by Sm+011 TSIG methods

The lower critical temperature Tc and critical current density Jc are serious weaknesses of SmBCO bulk superconductors fabricated in air for practical applications, because of the Sm3+/Ba2+ solid solution in Sm1+xBa2−xCu3Oy crystals. In this paper, high quality single domain SmBCO bulk samples S1 (ϕ20 mm) and S2 (ϕ32 mm) have been fabricated in air by a new Sm+011 TSIG method. The trapped field of the samples is 0.8 T and 1.15 T at liquid nitrogen temperature for the samples S1 and S2 respectively, which is the strongest trapped field of the SmBCO samples fabricated in air today. The theoretical formula for 3D trapped field distribution have been derived for a cylindrical model with uniformly distributed critical current density Jc based on the Biot Savart law; the cylindrical sample is divided into a series of concentric rings with the same width and thickness, the trapped field of the samples is the summation of magnetic field produced by all the rings, while the magnetic field generated by each ring was worked out by trapezoidal numerical integration based on the Biot Savart law with the critical current density Jc of the samples. It is found that the calculated field of the samples is well in agreement with the experimental results if the reasonable Jc of the samples is adopted. The theoretical calculation result also indicates that the larger the diameter and the thickness of the samples, the stronger the trapped flux density, but the optimal diameter/thickness ratio should be of a reasonable value around one, and it is not so good to fabricated samples with too larger diameter or thickness for practical applications.