Notes on Simulations Below are some preliminary results from the simulations. Still there is more benchmarking work to do against experiment, but I thought it worth getting some results now with things pretty close. Perhaps this will generate more ideas about how to use the codes. The simulation codes now incorporate isotropic scattering from Al windows and air in air gaps. The target chambers can be "filled" with liquid He at various temperatures, air, or 4He gas. The empty target chambers are normally filled with 4He gas, unless one is running with air in the main chambers, in which case air also fills the empty chambers. Cross sections for 4He gas and air (actually 14N) are were obtained from ENDF's interpreted data, which contains little actual data at the relevant energies. In the end, each of the 0.1cm Al windows scatter about 1.5% of the beam and the air gaps scatter ~0.5% or less of the beam; the 4He empty target scatters about 0.1% of the beam. These neutrons can change energies significantly, but virtually none of them reach the detector since the scattering is treated as isotropic in the CM (e.g., of the 1.5% that scatter in the first Al window, only <1E-4 of those reach the detector). The simulation starts AFTER the PSM and runs trought the ASM, but does NOT fully simulate the supermirror, only the geometry and index of refraction (3mrad/ang). Rotations are calculated assuming a longitudinal field of 0.1mGauss starting at the 10cm air gap before the target, including several Al windows, and ending after the 13 cm air gap after the targets. In the middle of the air gap between the upsream and downstream targets the rotaion angle is reversed, playing the role of the pi-coil. So, before the pi-coil the neutrons have 55.8 cm of beam length in which to rotate, and 58.8 cm after the pi coil. The neutrons starting positions are chosen with equal probability in the x-y directions and with isotropic trajectories within a given critical angle. The input critical angle was set to 3.35mrad/ang. This is much bigger than the NG6 value of 2mrad/ang, but closer to the increased divergence from the PSM. All x-y openings of guides and targets, etc. are the most recent from Kangfei. The value of 3.35mrad/ang was chosen to give rough agreement with the experimental results of the beam attenuation. I get the following beam attenuation compared with the experimental results in Anna's paper, in which either air or 4He gas filled the target. Target material --> Air Air 4He gas 2.1K He 4.25K He Exp. Results Simulation Simulation Simulation Simulation after PSM 100% 100% 100% 100% 100% after Input coil 48% 50.8% 50.7% 50.8% 50.8% into Up-stream target (W) 22% 22% 22% 22% into Dn-stream target (E) 17% 17% 17% 17% after Output coil 16% 14.5% 15.7% 10.9% 10.9% So, there is a bit of an difference between the simulated attenuation with air target and experiment, but we're within a couple %. So, moving on, the above cases were run with 1E9 neutrons to look at West vs. East count rate, average energy loss, rotations, etc. These runs each took about 12 hours of CPU time. So, increasing the statistics by a factor of 10 is possible but a little tough (e.g., run for 10 days on 10 machines). COUNT RATE COMPARISON Comparing West and East count rates, shows the effect of solid angle from scattering from the upstream target (West side) and downstream target (East side). Note that the "detector" counts are counts at the downstream end of the ASM, but the losses due to scattering or absorption in the ASM are not being accounted for. In the simulation neutrons leave the beam in the ASM only if they have too big an angle when they hit a wall or are outside the x-y acceptance. Target material --> 4He gas 2.1K He 4.25K He all neutrons all neutrons all neutrons West (Up-target) 6.761890E7 4.705054E7 4.703383E7 East (Dn-target) 6.761869E7 4.705106E7 4.704131E7 West (Up) - East (Dn) (0.2 +- 1.2)E3 (-0.5 +- 9.7)E3 (-7.5 +- 9.7)E3 Target material --> 4He gas 2.1K He 4.25K He only neutrons that have scattered West (Up-target) 1.7990E3 7.7380E4 2.7948E5 East (Dn-target) 1.8630E3 7.8903E4 2.8574E5 West (Up) - East (Dn) (-64 +- 61) (-1.5 +- 0.4)E3 (-6.3 +- 0.8)E3 %diff (W-E)/W 0% 2.0% 2.3% Frac. hits from scatters 2.6E-5 1.7E-3 6.0E-3 We notice from the above that there is not a statistical difference in the number of counts reaching the left and right sides from the fact that the detector solid angle differs for the two target positions. This is because we have so few scatters that reach the detector. Looking just at scattered neutrons, we see the East side (with target in downstream position) getting only 2% more counts. While the detector solid angle is bigger from the down-stream (East) side, there is about 35% more beam reaching the upstream target (West), and thus producing 35% more scatters. These competing effects apparently almost balance. We also see about 4 times more scattered neurtrons from 4K He reaching the detector than from 2K He. ENERGY LOSS The average energy losses for neutrons that reach the detector is about 0.03meV. Avg. energy loss for scattered neutrons reaching detector: Target material --> 4He gas 2.1K He 4.25K He West (Up-target) 0.024(1)meV 0.0296(4)meV 0.0232(1)meV East (Dn-target) 0.023(1)meV 0.0314(4)meV 0.0245(1)meV So, we see a slightly lower energy loss on the West (UP) side. This is consistent with the idea that the larger solid angle of the East side (Dn-target) would allow larger scattering angles and thus larger energy loss. This energy change is quite small, however. Thinking about the rotation with the pi-coil OFF and assuming the neutrons scatter in the middle of the target, there is aobut 50cm between the center of UP and the center of DN, over which the neutrons would travel with different energies. So, assuming a mean energy of 2meV, this is about a 1.5% decrease in energy, which corresponds to a 0.75% increase in rotation angle. So, a neutrons starting a 2meV would see a difference in rotation between Up and Down targets of about 1E-2 mrad over that 50cm. Coupled with the 0.17% contribution from the scattered neutrons, we could estimate an increase in measured rotation of 1.7E-5mrad or 1.7E-8rad. With the pi-coil ON things there are basically two pieces to the difference in rotation from UP targets and DOWN targets 1. The different energies in the region between scattering in the UP target and scattering in the DOWN target, where the rotation angle is reversed part way through. 2. the very slightly different energies in the region after the scattering in the second target. Again, assuming scattering is in the middle of each target, then since in the code the pi-coil is exactly in the middle of this region, the part of the rotation difference due to 1. is zero. For part 2. we see above that the DOWN target does cause a slightly more energy loss that the UP target on average, so we can estimate the pi-coil ON rotation difference from the different energies in the roughly 25cm after the middle of the DOWN target. This gives 2.5E-4mrad. Combining the 0.17% contribution from scatters, we get 4E-7mrad or <1E-9rad. ROTATION COMPARISON The rotation values are small: a 2meV neutron rotates about ~1.63mrad the first 55.8cm, flips sign at the pi coil, and rotates another 1.71mrad during the 58.8cm, leaving 0.08mrad of net rotation. Average Rotation values in milliradians Target material --> 4He gas 2.1K He 4.25K He all neutrons all neutrons all neutrons West (Up-target) 6.7783E-2 7.4100E-2 7.0281E-2 East (Dn-target) 6.7794E-2 7.4103E-2 7.0285E-2 West (Up) - East (Dn) (-10 +- 6)E-7 (-3.4 +- 7.8)E-6 (-3.8 +- 7.7)E-6 Target material --> 4He gas 2.1K He 4.25K He only scattered neutrons West (Up-target) 1.8392E-1 1.4213E-1 1.3784E-1 East (Dn-target) 1.7300E-1 1.4139E-1 1.3767E-1 West (Up) - East (Dn) (11 +- 7)E-3 (7.3 +- 9.3)E-4 (1.8 +- 4.3)E-4 Looking at the 4He gas, 2K, and 4K He runs, we do not see a statistically significant difference in rotation between West and East above the 1E-5mrad or 1E-8 rad level. Neither do the scattered neutrons produce a significant difference at the 1E-3mrad or 1E-6 rad level. Even if the neutrons scattered from 2K He contribute at a few times 1E-6 rad effect, since they contribute only 0.17% to the total, the rotation difference from all neutrons would be below 5E-9 rad (3E-6 rad * 0.17%). This all seems consistent with the estimates above from energy loss. FUTURE Some more things to try/update: -- benchmark beam attenuation against more varied experiments (e.g., different targets, different beam conditions) -- include Kangfei's correction to pathlength from wall scatter -- include new S(q) and omega(q) calculations from Mike and Murad -- sensitivity of rotation asymmetry to beam divergence -- sensitivity of rotation asymmetry to beam alignment (add small angle to initial theta) -- Number of detector hits that come from wall scatters