Figure 2: Top view of electron envelope in wall "v2.0"
A summary page has also been added here.
General Comments: Unless otherwise specified, the geometry has the three collimators, the concrete collimator vault, QTOR coils, lintels, and beamline. All backgrounds are weighted by cross section, photoelectric efficiency, and asymmetry. The beam is 4x4 mm^2 except for when we were defining the envelope, where 9x9 mm^2 was used.
The maximum allowed space for the upstream wall of the shielding hut is 80 cm from Z=300 to Z=380. The concrete used in the geometry has a density of 2.7 g/cm^3.
14-Feb-2008
The ep elastic profile has been precisely defined through the Z locations of the upstream wall of the shielding hut. The envelope was defined by:
X-Direction
- Plot events accepted at the Cerenkov bar at the different Z locations
- For the purpose of definition, the Cerenkov has an effective height of 22 cm: we consider the optimal radial position +/-2 cm.
- The cutoff point is 0.1% of the peak
Y-Direction
- Same procedure, except that for the purpose of definition, we consider the optimal radial position of the bar +/-2 cm and the actual length +1 cm on each side
We considered BFIL factors of 1.02, 1.04, and 1.06, so that we could figure out how much clearance we could get away with. The actual definition of the aperture comes from BFIL 1.04. Figure 1 shows the upper and lower cutoffs of the envelope radially for the three BFIL's (note that the Cerenkov optimal position is different for each), where the solid black line indicates the aperture. Figure 2 shows the same but for the horizontal direction.
Figure 1: Side view of electron envelope in wall "v2.0"
Figure 2: Top view of electron envelope in wall "v2.0"
For this wall, "v2.0", the aperture is 5 cm of clearance at lower radius, 20 cm clearance at upper radius, and 3 cm clearance on the sides. The clearance is fixed on the bottom due to the dependence of the lower radius on BFIL. The clearance on the sides can be no less than 3 cm due to tolerances.
The top view in Fig. 2 shows that the Y cutoff is independent of BFIL. This is because the bar defines this cutoff. As the BFIL factor increases, we lose part of the profile as it spreads out more. Unfortunately, these are high energy electrons.
With these clearances and an 80 cm thick concrete wall, we get the following backgrounds compared to no wall:
Table 1: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104
Elastic Photons Inelastic Photons Inelastic Electrons Moller Photons Moller Electrons no wall 0.1466% +/- 0.0051% 0.0668% +/- 0.0033% 0.4670% +/- 0.0175% 0.1856% +/- 0.0115% 0.7138% +/- 0.0443% wall v2.0 0.1585% +/- 0.0051% 0.4673% +/- 0.0082% 3.8834% +/- 0.0627% 0.1898% +/- 0.0117% 0.2636% +/- 0.0325% Table 2: Rate, < Q^2 >, FOM for Geometry qweak_gw_7-jan-08_bfil104
Rate < Q^2 > Error no wall 784.535 0.025897 4.1338 wall v2.0 782.705 0.025907 4.1363 Comments: The biggest impact from the wall is seen in the increased rate of photons and electrons from inelastic scattering. The inelastic electrons come from scattering off the top and sides of the window as well as leakage out the back. The next step is to reduce these backgrounds.
6-Mar-2008
Following Dave Mack's suggestion we next wanted to flare the sides at larger radius. To do this involved redefining the opening in GEANT with different volumes, the derivation of which took a little while. Note, as shown in the figure below, that with straight sides with 3 cm clearance the separation between corners of the windows in adjacent octants are as follows:
Figure 3: Upstream Side: Lower Separation = 25.87 cm, Upper Separation = 76.23 cm.We do not want the upper separation to be any less than 25.87 cm. However, this occurs for a side clearance at larger radius of about 30 cm.
In Table 3 we show the backgrounds for
- wallv2.0 - as listed in Table 1 above
- wallv3.0 - same opening as wallv2.0, just defined differently
- wallv3.1 - side clearance of 5 cm at large radius
- wallv3.2 - side clearance of 30 cm at large radius
- wallv3.3 - side clearance of 15 cm at large radius
Table 3: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104
clearance at large r Elastic Photons Inelastic Photons Inelastic Electrons wall v2.0 3 cm 0.1585% +/- 0.0051% ** 0.4673% +/- 0.0082% 3.8834% +/- 0.0627% wall v3.0 3 cm 0.1721% +/- 0.0055% 0.4639% +/- 0.0082% 3.9355% +/- 0.0630% wall v3.1 5 cm 0.1632% +/- 0.0052% 0.4642% +/- 0.0083% 3.8003% +/- 0.0614% wall v3.2 30 cm 0.1655% +/- 0.0054 0.4138% +/- 0.0076% 3.3145% +/- 0.0565% wall v3.3 15 cm 0.1629% +/- 0.0053% 0.4092% +/- 0.0076% 3.2570% +/- 0.0557%
**Random Seed checks have shown that this is a lower estimate of the elastic photon background, so the results for all three geometries agree within statistics.
Here are some images of the inelastic electron background for wallv3.0 (straight sides) and wallv3.3 (flared to give 15 cm side clearance at top compared to 3 cm side clearance at bottom).
Figure 4: Dot plots for wallv3.0
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Figure 5: Dot plots for wallv3.3
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Figure 6: Weighted 1-d plots
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Comments: Flaring the sides at large radius moved the sides away from the inelastic electrons so that they do not scatter into Cerenkov. We get a reduction of about 15%. The ceiling of the window is still a problem.
7-Mar-2008
Starting with wallv3.3 (side clearance of 15 cm on downstream side), I wanted to try increasing the slope of the upper aperture to match the slope of inelastic electrons. The current aperture is parallel to the elastic envelope, which cuts off the inelastic electrons at 26% of the peak at Z=300 and 60% of the peak at Z=380. Increasing the upper clearance on the downstream side to 31 cm (wallv3.4), we get (compared to wall v3.3)
Table 4: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104Comparing the XZ origin of inelastic electrons
Elastic Photons Inelastic Photons Inelastic Electrons wall v3.3 0.1629% +/- 0.0053% 0.4092% +/- 0.0076% 3.2570% +/- 0.0557% wall v3.4 0.1725% +/- 0.0054% 0.3000% +/- 0.0058% 2.7039% +/- 0.0447%
Figure 7: Dot plots for wallv3.3 (left) and wallv3.4 (right)
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Figure 8: Z projection of the above plots, weighted by cross section:
Comments: Raising the ceiling at downstream Z decreased leakage, however there is an increase in slit scattering coming from the upper aperture towards the upstream part of the wall. The overall reduction is about 15%.
10-Mar-2008
While the simulations for wallv3.4 were running, I also defined 'best-case scenario' walls: starting with wallv3.3 aperture, I changed the last 2" or last 4" to lead. These became wallv4.0 and wallv4.1, respectively. All walls are 80 cm thick, just the amount of lead backing is different. Comparing the wallv3.3:
Table 5: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104
amount of lead Elastic Photons Inelastic Photons Inelastic Electrons wall v3.3 0 cm 0.1629% +/- 0.0053% 0.4092% +/- 0.0076% 3.2570% +/- 0.0557% wall v4.0 5.08 cm 0.1590% +/- 0.0051% 0.5630% +/- 0.0089% 1.9106% +/- 0.0416% wall v4.1 10.16 cm 0.1664% +/- 0.0054% 0.4698% +/- 0.0086% 1.7780% +/- 0.0398%
Figure 9: Weighted 1-D plots comparing the inelastic electron (left) and inelastic photon (right) origins in the shielding wall:
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14-Mar-2008
In an attempt to reduce slit scattering we took the 80 cm wall and reduced it to 40 cm. We tried two cases, a Z location of 300-340 cm ('wallv4.2') and a Z location of 340-380 cm ('wallv4.3'). In each case the aperture is the 'wallv3.3' aperture, meaning the upper aperture is parallel to the elastic electrons. The wall is 35 cm concrete + 5 cm lead.
Not surprisingly, the backgrounds are better when the wall is located from Z=300-340 cm (less separation between elastic and inelastics means less scraping), as shown in Table 6.
Table 6: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104We still have the two problematic sources; leakage and slit scattering.
amount of lead Elastic Photons Inelastic Photons Inelastic Electrons wall Z=300-340 5 cm 0.1741% +/- 0.0053% 0.3877% +/- 0.0057% 1.1106% +/- 0.0271% wall Z=340-380 5 cm - 0.6268% +/- 0.0092% 1.7176% +/- 0.0419% Here is the XZ origin plot for the better case, wallv4.2, when the wall is located from Z=300-340:
Figure 10 : XZ origin plot for wallv4.2
In the 80 cm concrete wall case, changing the upper aperture to be parallel to the inelastic electrons helped reduce leakage but increased slit scattering. I now compare:
Figure 11: Z origin comparison of 3 cases listed above
- v4.2: The above case, 35 cm conc + 5 cm lead, upper aperture parallel to elastic electrons
- v4.6: v4.2 but 30 cm conc + 10 cm lead
- v4.4: 35 cm conc + 5 cm lead, upper aperture parallel to inelastic electrons, similiar to wallv3.4
If we can reduce the slit scattering increase in wallv4.4, then the reduction in leakage is the same as having 10 cm of lead instead of 5 cm of lead. Preliminary results suggest that making the aperture parallel to the elastic electrons but having a clearance of 25.5 cm instead of 20 cm give an inelastic electron background of ~0.8%. Need to run more statistics.
20-Mar-2008
The increase in slit scattering when going from 5 cm of lead to 10 cm of lead (wallv4.2 to wallv4.6) seemed questionable (see Fig. 11). Looking more closely at the XZ origin plots of inelastic electrons in the wall for these cases may clear this up.
Figure 12: XZ origin of inelastic electrons, wallv4.2 (left) and wallv4.6 (right)
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It seems as though the inelastic electrons that before were passing through the concrete aperture and exiting the backside of the wall above the opening are now scattering off the lead aperture and hence we see increased slit scattering.
In an update to the last post, if we take wallv4.2 (35 cm concrete + 5 cm lead), and changed the upper clearance from 20 cm to 25.5 cm (wallv4.7), we get:
Table 7: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104The backgrounds for wallv4.6 (30 cm concrete + 10 cm lead, 20 cm upper clearance) are:
upper clearance Elastic Photons Inelastic Photons Inelastic Electrons wallv4.2 20 cm 0.1741% +/- 0.0053% 0.3877% +/- 0.0057% 1.1106% +/- 0.0271% wallv4.7 25.5 cm - 0.2916% +/- 0.0047% 0.8691% +/- 0.0225%
Table 8: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104The inelastic electron backgrounds of wallv4.6 and wallv4.7 are within statistics.
Elastic Photons Inelastic Photons Inelastic Electrons wallv4.6 - 0.2289% +/- 0.0048% 0.9111% +/- 0.0261%
The inelastic generator currently being used is not correct. The weighting is not done properly and therefore the results are not accurate when changing the theta and phi sampling range. Juliette wrote a new inelastic generator that throws flat and theta, phi, and energy, and weights the event properly. The relative comparions presented are still legitimate, but here is the difference between the old and new inelastic generator for the wallv4.2 geometry.
Table 9: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104The results with the new generator are 6 times smaller.
generator Inelastic Photons Inelastic Electrons wallv4.2 old 0.3877% +/- 0.0057% 1.1106% +/- 0.0271% wallv4.2 new 0.0634% +/- 0.0009% 0.1745% +/- 0.0044%
31-Mar-2008
Here are the backgrounds for a 40 cm wall (35 cm concrete + 5 cm lead), where the upper edge is parallel to the elastic electrons with a varying amount of clearance. These results are for the original generator
Table 10: Properly Weighted Backgrounds for Geometry qweak_gw_7-jan-08_bfil104Here are plots of the Z origin of inelastic photons (left) and inelastic electrons (right) in the shielding wall for these cases:
upper clearance Elastic Photons Inelastic Photons Inelastic Electrons 10 cm 0.1860% +/- 0.0053% 0.8690% +/- 0.0108% 2.2902% +/- 0.0489% 15 cm 0.1639% +/- 0.0049% 0.5697% +/- 0.0078% 1.6568% +/- 0.0377% 20 cm 0.1741% +/- 0.0053% 0.3877% +/- 0.0057% 1.1106% +/- 0.0271% 25.5 cm 0.1769% +/- 0.0052% 0.2920% +/- 0.0047% 0.8701% +/- 0.0225% Figure 13: Inelastic background versus Upper Clearance
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