Vortex dynamics in temperature gradients: Magnetic flux expulsion in type-II superconductors.

How do vortices in type-II superconductors get expelled as they are cooled down to the Meissner state? Experiments at Fermilab and Cornell on superconducting radio-frequency cavities suggest thermal gradients are the main mechanism behind flux expulsion. Trapped flux significantly contributes to power losses in particle accelerators, thus understanding expulsion is vital to optimizing cavity performance. Here we re-derive the thermal gradient force acting on vortices and study vortex dynamics when this force is offset with pinning forces and vortex-vortex interactions. We show that a thermal gradient acting on interacting vortices is sufficient for flux expulsion in the absence of impurities. We then introduce collective weak pinning and use recent results to obtain analytic expressions for the balance of these forces for isolated vortices. We further explore flux trapping mechanisms by modeling pinning of vortices on strong, but local, pinning centers. By including vortex-vortex interactions in addition to vortex-impurity interactions, we numerically explore their implications on trapped magnetic flux. Finally, we consider the consequences of dendritic inhomogeneity in the cooling temperature-front on flux trapping.