Achieving optimal magnetic flux expulsion of a Nb3Sn superconducting radio-frequency cavity via spatial temperature gradient

The trapped magnetic flux leads to residual resistance, thereby reducing the quality factor of the superconducting cavity and affecting its power consumption. It has been experimentally shown that the trapped magnetic flux of the superconducting radio-frequency cavity can be expelled during cooldown under a spatial temperature gradient. In the present paper, we simulate the magnetic flux expulsion behavior during the cooling process of a Nb3Sn superconducting cavity using time-dependent Ginzburg-Landau (TDGL) theory. In order to achieve optimal magnetic flux expulsion, the effect of grain size, grain boundary strength |ψ|GB, and cooling time on flux expulsion ratio ε for different temperature gradients are studied theoretically. The results show that ε first increases rapidly and then varies slightly to a steady value with increasing temperature gradient, which is in good agreement with the experimental results. In general, for larger |ψ|GB, ε decreases with increasing grain size. While for smaller |ψ|GB, ε first increases to the maximum then decreases with increasing grain size. Moreover, It is found that a larger cooling time is more beneficial for the expulsion of the flux vortices from the sample. The results of this paper The vortex dynamics behavior can give an insight into the mechanism of magnetic flux expulsion, which can provide a theoretical basis for further enhancing the performance of superconducting cavities.