## 3 Experiments
### Experimental Results  
More than 100 polarized neutron images have been recorded and evaluated. As mentioned above, one series was related to the un-treated Nb (\"Nb\({}_{oxid}\)\") sample, the other series when the same sample was further \"treated\" (\"Nb\({}_{back}\)\"). Figure 3 (Nb\({}_{oxid}\)) and Figure 4 (Nb\({}_{back}\)) show two series of each 18 radiograms displaying the two-dimensional neutron spin depolarization images as functions of increasing AC offset field B\({}_{\text{offset}}\) = 1 mT \(\ldots\) 5 mT (horizontal images) and increasing AC-frequency (vertical images), in sample orientation 0\({}^{\circ}\) (for orientation compare Figure 2). The change of color from red to blue in the images corresponds to a spin flip spin up (red color) \(\rightarrow\) spin down (blue color), corresponding to red \(\sim\)0.9 normalized intensity and blue \(\sim\)0.5, and a trapped magnetic field B = 2.1 mT. The results are consistent with other flux trapping experiments with Pb [22; 23; 24]. In Figure 3, (Nb\({}_{\text{oxid}}\)) the trapped field increases simply with increasing B\({}_{\text{offset}}\). If one use Equation (2), and s = 10 mm (s = diameter of the sample) a spin flip for a neutron wavelength \(\lambda\) = 0.32 nm occurs for B = 2.1 mT which indeed was observed for the center of the sample. In all rows in Figure 3 (Nb\({}_{oxid}\)) and  
Figure 2: Examples of a 3D image of a squeezed trapped field in a cylindrical sample (**a**,**c**) and 2D projection images (**b**,**d**), orientation with respect to neutron flight direction (red arrow in (**a**,**c**)) and projected intensities due to neutron spin depolarization (**b**,**d**). Red color = 4.6 mT, blue color = 0 mT. Figure 4 (Nb\({}_{\text{b}ak}\)), AC magnetic fields oscillate between \(\pm\)5 mT with different frequencies (0.1 Hz, 0.25 Hz and 0.5 Hz) and increasing offset of 1 mT...5 mT. Comparing images of a given offset field B in Figure 3, one observes for offset fields 4 mT and 5 mT an increase in field trap with increasing AC field; however, for offset fields 1 mT-3 mT, non-dependency could be measured. A possible frequency dependency of trapped flux, \(\text{B}_{\text{trap}}=\text{B}_{\text{trap}}(f)\) seemed to occur for offset fields larger than 3 mT; however, in contrast to expectations, the trapped field became larger instead of smaller. After the sample was annealed at 1400 \({}^{\circ}\)C and buffered chemically polished (BCP) (Nb\({}_{oxid}\rightarrow\) Nb\({}_{bak}\)), a different behavior of the trapped fields was observed (see Figure 4). Here, one cannot observe a possible frequency dependence for a constant offset field of 4 mT and/or 5 mT. The change (increase) of \(\text{B}_{\text{trap}}\) (color change) is rather observed for different offset fields. The increase of \(\text{B}_{\text{trap}}\) is comprehensible if one keeps in mind that a spin rotation, from, e.g., spin up to spin down due to larger \(\text{B}_{\text{trap}}\), changes the image color (second and third row in Figure 4), or vice versa in the first row of Figure 4.  
In the sample orientation of 90\({}^{\circ}\) yields detailed views of the homogeneity of the trapped fields (see Figures 5 and 6), because once trapped, it rotates with the sample. In the sample orientation of 90\({}^{\circ}\), all neutrons have the same path length in the sample (and in the trapped field, compare Figure 2), so different colors in an image indicate different spin depolarization due to different _strengths_ of magnetic fields and thus different path integrals of B.ds. Note that colors in Figure 3 do not correlate to colors in Figure 5 and colors in Figure 4 not correlate to colors in Figure 6. In the 90\({}^{\circ}\) sample orientation, \(\text{B}_{\text{trap}}\) and its stray field are (nearly) parallel to the neutron flight direction. Its strength increases and decreases slowly for a spin polarized neutron along its path and favor adiabatic change of the spin direction which is much more likely than a spin rotation around \(\vec{B}\).