## 4 Conclusions  
Within an extended series of measurements, the influence of external magnetic AC fields with different offset fields on magnetic flux trapping during field cooling (FC) was investigated for a polycrystalline, heat-treated Nb sample of cylindrical shape (radius = 5 mm, length = 10 mm). Close to the transition temperature T \(\longrightarrow\) Tc the mobility of flux lines should be enhanced by AC fields with different frequencies and offset amplitudes. The cooling time was chosen 1 K/min, which should be long enough around T\({}_{c}\) to influence the mobility of flux lines and thus flux trapping. Further cooling fixed this state in order to determine the trapped flux with polarized neutron imaging. AC fields with different frequencies and amplitudes \(\pm\)5 mT have been applied to the Nb sample during cooling from T = 15 K down to T = 5 K (T\({}_{c}\) = 9.2 K) and at T = 5 K and after switching off the external magnetic field, the size of flux trapping was measured with polarized neutron imaging. When the Nb sample is left 'untreated' (Nb\({}_{oxid}\)), different offset AC fields of 1 mT \(\ldots\)5 mT increases flux trapping and, therefore, amplifies this unwanted impact instead of reducing it; this happens much less when the Nb sample is 'treated' (Nb\({}_{buk}\)). Here, one observes a small flux trapping symmetrically and centered around the rod axis. Due to increasing AC fields, the trapped flux appears more and more homogeneously distributed in the sample, especially in the case of Nb\({}_{buk}\) where, starting from the rod axis, the trapped flux dissipates to the whole volume. This remarkable behavior could be well observed with polarized neutrons; no other technique yields such position resolved (real) information about magnetic flux trapping in the bulk sample in the superconducting state, and these observations underline again the commonly known importance of a careful surface treatment in order to suppress magnetic field trapping during field cooling. The  
Figure 12: Nb\({}_{buk}\) (Nb sample “treated”): the integrated intensity of central part of each image of Figure 6 (1024 pixel) was plotted as a function of offset field for frequencies f = 0.1 Hz, 0.25 Hz and 0.5 Hz (see text). calculation of images of trapped flux under different conditions and comparison of these experimental ones yields good agreement for nearly all images. As far as measurement technology (neutron imaging) is concerned, the result of the spin detection by the spin analyzer in this experiment is the same for both spin rotations, thus in this experiment one could not distinguish whether the trapped field showed in +y or -y direction, one only could determine a certain increase or decrease in flux trapping. For our measurement, it was not important to know which orientation the trapped field had rather than to measure its size in the sample. A comparison with results of publications on magnetic fields in Nb, using neutron diffraction and neutron small angle scattering [9; 10; 36; 37; 38], shows the different approaches to obtain information about the bulk magnetism in superconductors. From the flux line densities, absolute values of the form factors were obtained, which allows us to determine local magnetic field distribution. The results of diffraction and small angle scattering are usually in the nm size range, about three orders of magnitude smaller than the spatial resolution of a current neutron image, and one obtains detailed (nm-large) local information, about the flux line density. In the measurements presented in this paper trapped magnetic fields are determined directly, i.e., visualized and quantified as functions of AC fields, applied during field cooling. A spatial resolution of nm is not useful at this point, since one is interested in a significant reduction of the flux lines and thus the trapped magnetic fields for the entire sample.