# Distortion maps for Triple 3D GridLeak

(A limited presentation of this topic was given at the 2016-08-10 S&C meeting)

Notes:
• Input for charge sheet widths and relative total charge in sheets taken from Irakli's results:
• Inner sector, inner leak width = 0.81 cm, charge = -42.15 + exp(0.005345*V)
• Inner sector, outer leak width = 0.85 cm, charge = -21.76 + exp(0.005123*V)
• outer sector, inner leak width = 0.99 cm, charge = -16.68 + exp(0.004731*V)
• outer sector, outer leak width = 1.04 cm, charge = -23.38 + exp(0.004751*V)
• Irakli's results for fitting a constant to the regions where voltage wasn't changed imply that there's an uncertainty at the level of ~2-3% on the calculated charges, which I have ignored hereafter.
• Historical middle GridLeak assumed a charge sheet of width 1.595 cm (the spacing between the last inner GG wire and the first outer GG wire), while Irakli finds a total inner + outer width of (0.85+0.99) = 1.84 cm. I will scale charge densities for new calculations by 1.595/1.84 = 0.8668 to preserve same total charge for middle GridLeak.
• Irakli's results were "per incoming electron", so I have scaled them by the radial form we use for SpaceCharge. This has the following impacts:
• The inner leak increases by 276%
• The outer leak decreases by 60%
• The middle leak now varies over its φ span, decreasing by almost 6% at the sector boundaries
• Test maps are created using a timestamp of "2016-04-30 05:17:00" during run 17121001, with SpaceChargeR2 = 0.0343452 C/ε0, EWRatio = 1.096, GL = 9.6, drift velocity 5.570 cm/μsec, BField -4.98975 kGauss.
• Some tests were done with varying the granularity of map on which charge was distributed for distortion calculations: negligible sensitivity was seen.
• Units: all axes on all distortion maps are [cm] except ratios.
• Plots vs. z are calculated at φ=0 (middle of a sector).
• Plots vs. φ are calculated at z=+2.5 cm.
• I calculated one radial bin at r=192.5, which is actually inside the outer charge sheet in the middle of the sectors (I used a local y of 191.49 cm for the inner edge of the outer charge sheet, which crosses r=192.5 cm at φ=±6° from the sector center, and a sector spans ±15° from its center).
• Ratios of maps show large deviations from 1.0 when the distortion is small, so I have included both the ratios of maps and their differences.
Conclusions from the below tests:
1. Effects of both the inner & outer GridLeak are small, but noticeable.
2. Taking into account all typical distortions doesn't change the above conclusion.
3. Increasing inner HV from 1100 V to 1170 V increases middle GridLeak by 12.6%, and the inner GridLeak by 51%, but this is not enough to change the above conclusions.
(click on any plot to see a full size image)

# Test 1:

3D GridLeak distortion only
Inner HV @ 1100 V, Outer HV @ 1390 V (typical of recent operations)

# Test 2:

3D GridLeak distortion only
Inner HV @ 1170 V, Outer HV @ 1390 V (nominal operating voltages)