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Extra resources for Granular gas dynamics
The magnetic field from the vortices in the superconductor penetrates into the ferrimagnetic garnet film and there causes a rotation of the plane of polarization of the light. An analyzer located in front of the CCD camera only transmits light whose polarization is rotated away from the original direction. In this way the vortices appear as bright dots, as shown in Fig. 7) This method yields a spatial resolution of better than 1 mm. Presently, one can take about 10 images per second, allowing the observation also of dynamic processes.
Hence, we can say that the flux line has a magnetic radius of lL. Now we can estimate also the lower critical field Bc1. Each flux line carries a flux quantum F0, and one needs at least a magnetic field Bc1 ≈ F0/(cross-sectional area of the flux line) ≈ F0/(pl2L) to generate this amount of flux. With a value of lL = 100 nm, one finds Bc1 ≈ 25 G. For increasing magnetic field the flux lines are packed closer and closer to each other, until near Bc2 their distance is about equal to the Ginzburg-Landau coherence length xGL.
However, in the superconducting state the pairs are correlated with respect to the center of the Fermi sphere. They can only scatter around the sphere, without affecting the center of the sphere. Hence, the circulating current does not decay, and we have a permanent current. The simplest possibility for slowing down the circulating current in a ring containing many electrons arises by briefly eliminating the pair correlation in the smallest possible volume element of the ring by means of a fluctuation.