1. Simulations of the double funnel construction for LET. Comparison with a single funnel The aim was to optimise the double funnel configuration to give the best possible flux profile at the sample. After much time with MC simulations (using Ken Andersons program) the following setup was found to be optimal 40 19 10 1100 1119 11 50 350 For various incident energies MC simulations are shown for four situations; 1)the flux profile at the sample position 2)the average flux per unit length v sample size 3)the change of flux on sample v sample position for a 10 mm size sample 4)The change of flux on sample v sample position for a 20mm size sample These results together enable one to determine how stable the flux is relative to a positional variation of the sample or sample size. This is important as it determines to what accuracy one might be able to determine an absolute normalisation.

2. 50 mev (1.3 Angtroms)30 mev (1.65 Angtroms) 10 mm sample 20mm sample Double funnel simulations

3. 20 mev (2.02 Angtroms)10 mev (2.97 Angtroms) 10mm sample 20 mm sample

4. 5 mev (4.04 Angtroms)2 mev (6.4 Angtroms) 10 mm sample 20 mm sample

5. 1 mev (9.04 Angtroms) 10 mm sample 20 mm sample

6. Stability of funnel design In this section we look at how stable this design is to small changes of design parameters. For example the reflectivity profile of the funnels can vary. In the above simulations it assumed a linear reflectivity decrease from m=1 to m=3.8 with a reflectivity of 80% at m=3. In the following we look at the effects a 70% reflectivity would have at 1 and 50 meV. Also we look at the effects of a slight change in funnel separation in going from 21 mm (as in above simulations) to 20 mm. 50 mev (1.3 Angtroms)1 mev (9.04 Angtroms) Reflectivity 80% Funnel sep =21mm Reflectivity 70% Funnel sep =21mm Reflectivity 80% Funnel sep =20mm

7. To test the predictions of Kens program this figure shows a simulation using Vittesse MC code. Using 1.3 Angstroms and a reflectivity of 80 % at m=3 with the same funnel layout as shown in the 1 st figure. The results are the same as for Kens program. See figure on last page. Single Funnel results The MC simulations of a single funnel setup are presented on the following pages. Comparison can then be made with the double funnel setup. The setup used is shown below, all dimensions are in mm. Notice the funnels are twice as long 2.2m as the single funnels of 1.1m. The overall transmission of the double funnel and the single funnel are the same within a few percent. 3502200 40 20 50 Single funnel Single funnel Flux/unit length ratio 40mm/10mmSample Double funnel Double funnel Flux/unit length ratio 40mm/10mmSample Single funnel Flux ratio 10mm sample with a 5mm/0mm position variation Double funnel Flux ratio 10mm sample with a 5mm/0mm position variation 1 mev.94.92.995.99 50 mev.90.99.9751.015 Summary of results comparing single/double funnel

8. 50 mev (1.3 Angtroms) 10 mm sample 20 mm sample Single funnelDouble funnel

9. 1 mev (9 Angtroms) Single funnelDouble funnel

10. Single /double funnel ! Which is best? A number of issues will now be discussed; Beam profile at sample Careful construction of the double funnel design has given a beam profile at the sample which is just as stable to variation in sample position or sample size as a single funnel design. However, the use of SM guides does mean that the flux profile at the sample position is never going to be flat topped (like MAPS, HET etc), so absolute normalisation to better than a couple of percent will prove to be very difficult. Energy resolution The single funnel design has a 20mm opening at the disk chopper compared to 10mm for the double funnel design. This means the chopper opening time is doubled and hence the best achievable resolution is roughly halved. The following gives an ideal of the best resolutions of both designs; double funnelsingle funnel 1 meV 0.6%0.9% 10 meV1.5%2.7% 50 meV3.0% 6.0% These numbers have taken into account the time uncertainty due to detector shape (10 Atms 1” tubes) but have not included sample shape effects. Note that at 1meV the time uncertainties due to detector shape are starting to equal those from the choppers for the double funnel. The single funnel design also has the disadvantage that the funnel needs to be longer, i.e 2.2m long rather than 1.1m for the double funnel. This has a detrimental effect on the resolution and to achieve the resolutions stated above I have to spin the 1 st chopper (controls the moderator width) approx 20% faster than for the 1.1m funnel. This means that the single funnel design has approx 20% less flux than the double funnel design for equal resolutions. You could reduce the second diverging funnel to 1.1m long but then it is not very effective at reducing the beam divergence as seen in the next figures Both figures show the beam divergence on a 40mm wide sample at 50 meV. The one on the left has a 2.2m diverging funnel while the figure on the right is for a 1.1m diverging funnel.

11. Both figures show the beam divergence on a 40mm wide sample at 1 meV. The one on the left has a 2.2m diverging funnel while the figure on the right is for a 1.1m diverging funnel. To improve the best resolution of the single funnel chopper to that of the double funnel a second set of 10mm slits could be put into the chopper (see fig below). This has the clear disadvantage that you immediately lose half of your flux compared to the double funnel design for the same resolution. 3502200 40 20 10 MC simulations of flux across sample position for 20mm (left) and 10mm (right) slits in the disk choppers. Simulations were for 50 meV neutrons. Another disadvantage is the beam profile at the sample position changes with slit width as seen in the above figures.

12. 9 Angtroms 40 mm sampleDF 10 mm sample SF 10 mm sample 6.4 Angtroms 40 mm sampleDF 10 mm sample SF 10 mm sample Single v double funnel Beam divergence Both single and double funnel designs have virtually the same beam divergence profile at the sample position for larger 40mm samples. However, the single funnel design has a slightly small beam divergence for smaller 10mm samples which is also smoother as the following simulations show. This is simple to understand from comparing the geometry of the funnels. The following simulations show the beam divergence at the sample position for; 1)40mm sample (done for the double funnel but is almost the same as the single funnel) 2)10mm sample with double funnel, DF 3)10mm sample with single funnel, SF

13. 2 Angtroms 40 mm sampleDF 10 mm sample SF10 mm sample 1.3 Angtroms 40 mm sampleDF 10 mm sample SF 10 mm sample 4 Angtroms 40 mm sampleDF 10 mm sample SF 10 mm sample

14. Conclusions The initial concern was that the beam profile at the sample position from the DF design has too much structure in it. This would make absolute calibration very difficult. With careful design the DF structure can be made such that the beam profile is fairly smooth over the whole energy range of interest. In fact the simulations show that the SF has no advantage over the double funnel in terms of beam profile and flux stability with sample position etc. The big advantage of the DF design is it can achieve up to double the energy resolution of the SF design. Although a second set of smaller 10mm slits in the SF design will allow it to reach the same energy resolution, there are two large penalties; you lose half your flux and the beam profile at the sample changes with slit configuration. The SF design also suffers as the diverging funnel needs to be 2.2m long to do the same job (remove the same amount of divergence) as the 1.1m funnel of the DF design. Lengthening the distance from the chopper to the detector degrades the resolution and to regain this means spinning the monochromating chopper approximately 20% faster which loses you 20% of your flux compared to the DF design. The SF design does have one advantage over the DF design. It has a smoother beam divergence profile for small samples (10mm used in simulation). The beam divergence profile for larger samples was the same for both funnel designs.