GridLeak Distortion
I recommend using tabbed browsing to view these plots, whereby you open a series of plots in a series of tabs, and then move through the tabs to see the variations/dependencies.

• Original distortion
• Files used
• No space charge distortion corrections
• Determining a good GLS
• Validity of first solution
• Radial shift of first solution
• Allowing for inner/outer leaks
• Different Volume SC shapes
• Different luminosities with volume SC=1/r^3
• Trying to make inner leaks work

Original distortion

Yuri's discussion of the problem and explanation of these plots: here

EbyE volume space charge is running in the following plots: Yuri's plot showing luminosity and B-field dependence
One of my first plots: Half field

The proposed location for GridLeaks can be seen by the gaps in the gating grid seen on the schematic diagrams found in this postscript file.

Files used

• Half Field: st_physics_adc_5057050_raw_1060007 (productionHalfHigh)
• Low luminosity Full Field: st_physics_adc_5030048_raw_4050008 (productionMinBias)
• Mid luminosity Full Field: st_physics_adc_5029044_raw_4060001 (productionMinBias)
• High luminosity Reverse Full Field: st_physics_5067038_raw_1040001 (productionHigh)

No space charge distortion corrections

Other distortion corrections in place (no GridLeak, no volume SC):

• half field
• low
• mid
• high (RFF)

Determining a good GLS

Attempting to remove residual gap by varying GLS on half field run:

• 30
• 40
• 50
• 75
• 100
• 125

GLS (GridLeakageStrength) is a multiplier which defines how strong the grid leak charge is relative to the volume SpaceCharge. Tying the two together like this allows the charges/distortions/corrections to fluctuate along with the luminosity (as defined via the volume SpaceCharge correction).

The EbyE SpaceCharge correction is left running to bring the mean physical signed DCAs of global tracks to zero. The prepass must also be run because the GridLeak distortion changes DCAs, so a different guess of the necessary SpaceCharge magnitude is necessary (NOTE: StMagUtilities::PredictSpaceCharge() must call the function to undo the GridLeak distortion as well as the SpaceCharge).

During this process, I learned that I needed to reduce the InnerOuterRatio in StMagUtilities::PredictSpaceCharge() down to 0.5 (from 1.3) in order to get the prepass to work.

Validity of first solution

Application of GLS from half field solution to other luminosities and fields using the azimuthally symmetric GridLeak correction. There appears to be some luminosity-dependent issues still:

• (half field)
• low
• mid
• high (RFF)

Radial shift of first solution

First attempt at moving the radius of the azimuthally symmetric GridLeak to higher radii using high luminosity run. This moved significant distortions into the outer sector. Using high luminosity run with GLS=65.

• 1.0cm shift
• 1.25
• 1.5

Allowing for inner/outer leaks

Now using sector-faceted GridLeak (no longer azimuthally symmetric, and GLS magnitude scale changed by a factor of ~4-5 to a value of ~15 to remove the gap) and allowing for inner/outer leaks. iGLS is the fraction of GLS for the strength of the inner sector leak, and oGLS for the outer. Inner sheet is at radius 55 +/- 3, and outer is at 195 +/- 3. Varying iGLS and oGLS together using high luminosity run:

• 0.0
• 0.25
• 0.5
• 1.0
• 2.0
• 4.0

Since the outer leak did not seem to help, now setting oGLS=0 and varying only iGLS:

• 50.0
• 25.0
• 10.0
• 1.0
• 0.5
• 0.25
• 0.1
• 0.0
• -0.25
• -1.0
• -4.0 (BAD: space charge fits failed)

Different Volume SC shapes

SC = SpaceCharge. Had used only the Wieman (~1/r^2) shape until this point.

High luminosity, RFF run, GLS=15, no inner or outer grid leaks:

• 1/r^0.5
• 1/r
• 1/r^1.65
• Wieman (~1/r^2)
• 1/r^3

Change GLS to compensate for different volume SC necessary to bring DCAs to zero:

• 1/r^0.5 GLS=20
• 1/r GLS=18
• 1/r^1.65 GLS=15
• Wieman (~1/r^2) GLS=15
• 1/r^3 GLS=15

Different luminosities with volume SC=1/r^3

SpaceCharge shape = 1/r^3, GLS=15, no inner or outer grid leaks:

• high (RFF)
• med
• low
• half field

Looks pretty good! So the charge distributions must be something similar to this (1/r^3 moves more charge to small radii).

Trying to make inner leaks work

Following the hypothesis that an inner leak plus Wieman volume SC might be able to create similar distortions to the 1/r^3 volume space charge field, we started looking more closely at really large inner leaks (large iGLS). In the inner/outer leaks section above, iGLS of 25.0 and 50.0 changed the DCAs so much that the volume SC magnitude changed, thereby affecting the inner/outer gap because GLS (essentially the ratio of gap charge density to volume charge density) stayed constant at 15.0. Here, we try changing GLS while holding iGLS constant (and large) to see what happens.

iGLS=50:

• 15.0
• 10.0
• 5.0

iGLS=25:

• 15.0
• 10.0
• 5.0

From that data, it looks like the optimum relation for keeping the gap zero may be approximately:
GLS = 15.0 - iGLS/10.0:

• iGLS=20, GLS=13.0
• iGLS=25, GLS=12.5
• iGLS=30, GLS=12.0
• iGLS=35, GLS=11.5
• iGLS=40, GLS=11.0

Not perfect, so the above relation is likely inexact. And some structure between padrows 2 and 7 remains. A little tweaking of parameters:

• iGLS=30, GLS=11.5
• iGLS=35, GLS=11.0
• iGLS=40, GLS=10.5

Looking at those last two vesus luminosity: iGLS=35, GLS=11.0:

• high (RFF)
• med
• half field

iGLS=40, GLS=10.5:

• high (RFF)
• med
• half field

Gene Van Buren (gene@bnl.gov)