nsepol20000121

The polarizer on the NG-5 NSE is a Mezei cavity: a 1500 mm section of ⁵⁸Ni-equivalent guide that contains a polarizing supermirror “V” 1253 mm long. The polarizing “V” is made from 1 mm thick Si wafers that are coated on one side with 3 $\theta_{c}^{}$ Fe/Si supermirror (see top of Figure 1).

The polarizing elements have been installed by Cilas so that the supermirror is on the outside of the “V” (on the side closest to the guide section walls), with no overlap of the two arms at the tip of the “V”. As a result, the center of the beam is only slightly polarized, as can be seen in Figure 1.

**Figure 1:** Measurement of the flipping ratio of the direct “polarized” beam with a 2mm gap in the supermirror coverage at the tip of the “V”, using a slit at the end of the guide, 1125mm past the tip of the “V” and the detector in its normal position. The simulation line includes the effect of the reflectivity dip discussed in the text.
$\resizebox {\textwidth}{!}{\includegraphics{mezeiGD0p8deg.slitout.eps}}$

We removed this gap by placing a piece of B-loaded Al at the tip of the “V”, thereby removing the worst of the effect, with only a slight decrease in the flipping ratio toward the center of the guide, as shown in Figure 2.

**Figure 2:** Measurement of the flipping ratio of the direct “polarized” beam with the 2mm gap in the supermirror coverage at the tip of the “V” masked by a 2mm wide by 1.75mm thick piece of ¹⁰B_0.05Al_0.95 , using a slit at the end of the guide, 1125mm past the tip of the “V” and the detector in its normal position. The simulation line includes the effect of the reflectivity dip discussed in the text.
$\resizebox {\textwidth}{!}{\includegraphics{mezeiFD0p8deg.slitout.eps}}$

In testing a piece of ILL Co/Ti polarizer on the spectrometer (located in place of the analyzer), I found that the flipping ratio of an elastically scattered beam was much larger (R =12-13) than that of the direct beam (R = 9). I started to do some Monte Carlo simulations of the polarizing cavity to see if I could reproduce this behavior by mispositioning the mask.

I performed the simulations with two different image planes. In the first, I placed the image plane at the sample position. This, after integrating over the sample area, corresponds to simulating the behavior of the scattered beam, since in the actual measurement, the sample coherently scatters into a single detector. The direct beam measurement (with no sample) is modeled when the image plane is placed at the analyzer. In our tests with the ILL supermirror, only the polarization at the center of the detector is measured, since the supermirror subtends a width of only about 2mm.

The original simulations of the Mezei cavity had the polarizing supermirror on the inside of the “V”, but simulations with the supermirror on the outside of the “V” and the neutrons first incident on the Si, showed that there were many low-divergence neutrons with the wrong spin state passing through the polarizing cavity. These are apparently due to a dip in the + (parallel) spin state reflectivity at around the Si critical edge when the neutrons impinge on the supermirror through the Si substrate (see Figure 3).

**Figure 3:** Measurement of the spin-dependent reflectivity for a “typical” Fe/Si supermirror with the neutron beam impinging on the supermirror from air and through the Si substrate. Note the dip near the Si critical edge for neutrons impinging throug the Si. The simulations described elsewhere in this report use a dip that is 45% the size of the dip shown here.
$\resizebox {\textwidth}{!}{\includegraphics{fs218001n2.eps}}$

**Figure 4:** Simulation of masked gapped-“V” with dip in supermirror reflectivity. The top images, taken at the sample position, indicate the parallel (left) and anti-parallel (right) spin states. The image shows in color the polarization of the entire beam, while the line indicates the 1d-integration of the polarization along the vertical height of the sample. The rectangle indicates the position and dimensions of a typical 3×3cm² sample.
$\resizebox {0.8\textwidth}{!}{\includegraphics{mezeiE0p8deg.out.eps}}$

**Figure 5:** Simulation of masked gapped-“V” with dip in supermirror reflectivity. Image at Analyzer position. The top images, taken at the analyzer position, indicate the parallel (left) and anti-parallel (right) spin states. The image shows in color the polarization of the entire beam, while the line indicates the 1d-integration of the polarization along the vertical height of the image.
$\resizebox {0.8\textwidth}{!}{\includegraphics{mezeiED0p8deg.out.eps}}$

If we assume that the flipping ratio is 24 (P = 0.92) for the ILL test piece (as Ian Anderson reported) we then expect to observe flipping ratios of 12.1 (P = 0.847) for the scattered beam and 9.2 (P = 0.803) for the direct beam with the test piece, in good agreement with experiment.

We can then use the observed flipping ratio with the Fe/Si analyzer (in a too-small field) to determine that the analyzer polarization is 0.77, giving our observed flipping ratio of 6 in the scattered beam and 5.4 in the direct beam. If the Mezei cavity is flipped to remove this problem, we should get a cavity polarization of 0.97 and so a final polarization of 0.747, increasing the flipping ratio to 6.9. With the new analyzer polarization of 0.92, R = 17.6.

**Table 1:** Comparison of observations and simulations of polarization for direct and scattered beams in various polarizer/analyzer configurations
	Direct beam		Scattered beam
	Sim	Obs.	Sim	Obs.
Fe/Si pol. w/dip (0.873,0.920)
Co/Ti analyzer (P = 0.92)	0.803	0.8	0.847	0.852
Fe/Si analyzer (P = 0.77)	0.672	0.666	0.708	0.714
Fe/Si pol. no dip (0.97)
Co/Ti analyzer (P = 0.92)	0.892		0.892
Fe/Si analyzer (P = 0.77)	0.747		0.747

Polarizer and analyzer efficiencies on NG-5 NSE