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