## 3 Experiments  
### Instrument, Samples and Field Cooling (FC)  
The motivation for applying an AC field during FC was given in the introduction, i.e., to support the migration of flux-lines over macroscopic distances by superimposing external alternating magnetic fields. The question to be answered is the influence of external AC fields on flux trapping during FC from T \(\geqslant\)\(T_{c}\)\(\to\)\(T<\)\(T_{c}\) and how to measure and to quantize them. Several parameters (purity, crystalline, poly-crystalline, chemically treatment) are relevant in order to associate possible flux trapping to externally applied magnetic AC fields. A high purity (99.999%) polycrystalline crystal Nb sample of cylindrical shape (diameter = 10 mm, height = 5 mm) always underwent the same cooling procedure, i.e., cooling was started at equilibrium T = 15 K and was ended at T = 5 K, well below the critical temperature of Nb (\(T_{c}\) = 9.2 K). The sample first was left 'untreated' (Nb = Nb\({}_{oxid}\)) and after the first series of measurements further treated by buffered chemically polishing (Nb\({}_{bak}\), i.e., annealing at 1400 \({}^{\circ}\)C followed by buffered chemically polishing (BCP), removing 150 \(\upmu\)m of material). Muon spin rotation studies have shown that this treatment is very effective in reducing flux-pinning [33]. During FC different AC fields (B amplitude was \(\pm\)5 mT, f = 0.1 Hz, 0.25 Hz and 0.5 Hz) and B offsets were 0 mT \(\ldots\) 5 mT) were applied to the sample. Reaching T = 5 K, B\({}_{\text{ext}}\) = B + B\({}_{\text{offset}}\) was switched off and neutron images were recorded in 0\({}^{\circ}\) and 90\({}^{\circ}\) sample orientations. Then, the sample was warmed up to 15 K before starting the next series. This procedure was repeated for each parameter set {\(f\), \(B_{\text{ext}}\), \(B_{\text{offset}}\)}. The experiments have been carried out at the instrument PONTO II at the BER II of the Helmholtz Center Berlin, Wannsee (Figure 1). The neutron beam (mean wave length \(\lambda\) = 0.32 nm\(\sim\)8 meV) was collimated horizontally and vertically 0.1\({}^{\circ}\)\(\sim\)1.745 \(\times\) 10\({}^{-3}\) rad, corresponding to a L/D = 573 (i.e., divergence \(\sim\)1.745 \(\times\) 10\({}^{-3}\) rad \(\sim\)0.1\({}^{\circ}\)). The neutron beam was polarized with a super mirror, yielding a 92% beam polarization, the magnetic guide field was parallel to the field direction of the polarizer and the analyzer. In front of the 2D detector (2 k \(\times\) 2 k, pixel size = 13.5 \(\upmu\)m) a spin analyzer acted similar to an optical polarizer with the difference that the opaque orientation for spin down was 180\({}^{\circ}\). Thus, the transparency of the spin analyzer can change from 100% for spin up neutrons (spin parallel to spin analyzer) to 0% for spin down neutrons (spin anti-parallel to spin analyzer), corresponding to a maximum image contrast of 100% and to a minimum contrast of 0%. In the case of unpolarized neutron imaging, the spatial resolution [\(\Delta_{h}\times\Delta_{v}\)] 60 mm apart from the converter screen was 55 \(\upmu\)m \(\times\) 55 \(\upmu\)m; however, in polarized neutrons imaging about 160 \(\upmu\)m \(\times\) 160 \(\upmu\)m for a sample-screen distance of 200 mm [35]. The samples were kept in special Al holder in a conventional cryostat, which was placed between two Helmholtz coils that could generate different external AC magnet fields up to 60 mT and up to 10 Hz. The sample was cooled down from 15 K to 5 K well below T\({}_{c}\) = 9.2 K as described above, with an external applied field B\({}_{\text{ext}}\) always parallel to the rod axis (0\({}^{\circ}\) orientation, (a) in Figure 2). Concerning the cooling rate, a separate series of measurements showed no dependency of flux trapping from cooling speed which was varied using 0.1 K/min, 0.3 K/min and 1 K/min; therefore, the fastest cooling time 1K/min was used. Figure 1: PONTO II Instrument for polarized neutron imaging at the BER II of the University of Applied Sciences Beuth Hochschule fuer Technik Berlin [34].