Interaction of flux tubes in a type I superconductor

The repulsive interaction between multiquantum flux tubes in type I superconducting lead films has been studied magnetooptically. Two or three flux tubes were trapped in a long and narrow region of slightly reduced film thickness, and the flux tube positions were recorded as a function of an applied Lorentz force pressing the tubes against each other. At distances larger than about the flux tube diameter our results agree well with the magnetic monopole model, which only takes into account the magnetic stray field outside the superconducting film. At smaller distances deviations from the monopole model occur due to the influence of the cross-sectional shape of the flux tubes and of the wall of the tubes upon the energy of the flux tube configuration. These influences have been taken into account by means of a subdivision model in which the flux-containing region of each tube is divided into a large number of flux portions each of which is approximated again by a magnetic monopole. For sufficiently high compression due to the Lorentz force, we have observed fusion of two individual flux tubes. Upon reduction of the Lorentz force, the fused flux tubes separate again. The process of fusion and separation shows distinct hysteresis. This behavior is also well explained by our subdivision model.