Mlr Summ TF

VanWasshenova_Thesis#Mlr_Summ_TF

Moller Summary

Scattering Xsect

As derived earlier, in the Differential_Cross-Section section

In the Ultra-relativistic limit as [math] E \approx p[/math]

[math]\frac{d\sigma}{d\Omega}=\frac{\alpha ^2}{4E^{*2}\sin^4{\theta}}\left( \cos^4{\theta}+6\cos^2{\theta}+9\right)=\frac{\alpha ^2\left(3+\cos^2{\theta}\right)^2}{4E^{*2}\sin^4{\theta}} [/math]

Figure 3a: A plot of the number of Moller scattering angle theta in the center of mass frame versus the theoretical differential cross section. The width of the bins is 0.001 degrees for the angles in the center of mass frame corresponding to angles of 5 to 40 degrees in the lab frame. A weight has been assigned for each value in theta which will give the theoretical differential cross section when applied.

Figure 3b: A plot of the number of Moller scattering angle theta in the lab frame versus the theoretical differential cross section. The width of the bins is 0.5 degrees for the angles in the lab frame. A weight has been assigned for each value in theta which will give the theoretical differential cross section when applied.

Weight the E-vs-Theta plot with Xsect

Figure 2: Using the theoretical differential cross section, the distribution of Moller electrons for a CM energy of approximately 53Mev can be distributed through the CM scattering angle Theta. Using Lorentz transformations, these distributions can be transformed to the lab frame. At around 60 degrees in the lab the Moller electron has an energy of close to 1 MeV. Such a low energy does not allow the Moller electron to leave the constrains of the target where they are created.

Moller electron radius -vs- Momentum (Full solenoid and relativistic)

Moller events using an lH2 target geometry No Raster

DC hits -vs- Solenoid

Starting the clas12 Moller simulation with a simple configuration, most components downstream with respect to the drift chambers are taken out of the gcard file. The remaining components, the Drift Chamber (DC), the Solenoid, and the Magnetic Components (CAD) are all that remain as shown below. The Torus field is held at zero Tesla, and the Solenoid field strength is increased from 0 to it's max of 5T.

Figure 2: With the Torus strength at zero Telsa, the solenoid is varied to show the hits within the DC moving off the faces of R1. These hits consist of primary Moller electrons, as well as secondary electrons and photons created by the Moller electrons.

As the Solenoid field strength increases, the Moller electrons are forced to into a helical path of decreasing radius, effectively "rotating" off the DC face. The relative value of the field changes the direction field, which in turn causes slightly more hits to be deposited on one side versus the other. This effect is only noticeable in that the neighboring sectors to S1 were not simulated.

Figure 2: The effect of the sign of the solenoid magnetic field is apparent when neighboring sectors are not simulated.

However, as the field reaches maximum, there are still particles which are found at higher values of [math]\theta[/math] that would have been expected to have remained after the effects of the Solenoid. To understand the causes of this phenomena, the hits on Region 1 can be broken into the most common types of particles that are detected; Primary Moller electrons and secondary electrons and photons caused by the Moller electron. Looking more closely at this particle makeup as the solenoid field is increased, we can see that the ratio of primary electrons to total hits decreases while the ratio of photons to total hits increases.

Figure 2: The rate of primary Moller electron traversing S1R1 decreases as the solenoid field strength is increased.

Without Magnet Components

To examine the possibility that scattering is the cause of the noise, the simulation is further simplified by removing the magnetic components stored in the CAD directory.

Figure 2: With the Torus strength at zero Telsa, the solenoid is at full strength and the magnet components in the CAD directory are removed. Due to scattering effects, the rate for 50nA is reduced by a factor of almost 20.

To effectively determine the cause of the remaining particles in S1R1 the hit particles' vertex points can be recorded producing a tomography plot.  A changing field is still useful in that the lack of number of hits at high solenoid field strength would make determining the physical cause difficult.

Photons Hits in R1

Merging background hits

Primary Moller Electron Hits in R1

CLAS12 Conditions

 Summarize with picture photo rates -vs- change and location of photons

  Summarize secondary moller electron rate location

FTOn ShieldIn

For the Moller electron,

For the scattered electron, there are no secondary hits.

FTOff ShieldIn

For secondary hits from the Moller electron

FTOn ShieldOut

FTOff ShieldOut

New Cone

FTOn

From beamline text file

1589.27-238.8=1350.47

PbCylinder  |                root  |         Pb pipe on beamline  |                           0*mm 0.0*mm 1350.47*mm  |                                   0 0 0  | 999966   |                Cons  |                          34*mm 36*mm 111.2*mm 113.2*mm 441.3*mm 0.0*deg 360*deg  |          beamline_w  |                  no  |     1   |     1   |     1   |   1   |   1   |                  no  |                  no  |                                      no 

At Standard Vertex Position:

High Cone Position:

[math]1350.47+441.3=1791.77\ mm[/math]

[math]\theta_{high}=\arctan \left( \frac{113.2}{1791.77} \right)=3.61^{\circ}[/math]

Low Cone Position:

[math]1350.47-441.3=909.17\ mm[/math]

[math]\theta_{low}=\arctan \left( \frac{113.2}{909.17} \right)=2.39^{\circ}[/math]

standard_R1_36_38_R2_111_113

At forward Vertex Position: (subtract 40mm from standard vertex distance)

High Cone Position:

[math]1791.77-40=1751.77\ mm[/math]

[math]\theta_{high}=\arctan \left( \frac{113.2}{1751.77} \right)=3.69^{\circ}[/math]

Low Cone Position:

[math]909.17-40=869.17\ mm[/math]

[math]\theta_{low}=\arctan \left( \frac{113.2}{869.17} \right)=2.5^{\circ}[/math]

[math]\rightarrow \theta_{high}=5^{\circ} \rightarrow 1751.77 \arctan 5^{\circ} = 153.26\ mm [/math]

[math]\rightarrow \theta_{low}=5^{\circ} \rightarrow 869.17 \arctan 5^{\circ} = 76.04\ mm [/math]

Summary Tables

FTOn from 0,0,0 Vertex

50nA	S1R1 2ndryMoller e- rate	S1R1 2ndryMoller gamma rate	S1R1 2ndryMoller particle rate	Effective Shield Rate
R1_36_38_R2_36_38	405 Hz	15480 Hz	160 Hz	?
R1_36_38_R2_50_52	470 Hz	15227 Hz	146 Hz	?
R1_36_38_R2_70_72	461 Hz	15045 Hz	150 Hz	?
R1_36_38_R2_75_77	372 Hz	14916 Hz	130 Hz	?
R1_36_38_R2_80_82	376 Hz	14995 Hz	109 Hz	?
R1_36_38_R2_90_92	413 Hz	14580 Hz	119 Hz	?
R1_36_38_R2_95_97	383 Hz	14186 Hz	117 Hz	?
R1_36_38_R2_111_113	447 Hz	14196 Hz	109 Hz	?
R1_36_38_R2_116_118	420 Hz	14167 Hz	144 Hz	?
R1_36_38_R2_121_123	389 Hz	14251 Hz	117 Hz	?
R1_74_76_R2_151_153	492 Hz	14280 Hz	110 Hz	?
R1_36_38_R2_500_503	1000 Hz	18363 Hz	120 Hz	?

FTOn from (0,0,0) Vertex w/o FT

50nA	S1R1 2ndryMoller e- rate	S1R1 2ndryMoller gamma rate	S1R1 2ndryMoller particle rate	Effective Shield Rate
R1_0_524.0_R2_0_1034.47	?	?	?	?

FTOn from Forward Vertex

50nA	S1R1 2ndryMoller e- rate	S1R1 2ndryMoller gamma rate	S1R1 2ndryMoller particle rate	Effective Shield Rate
R1_36_38_R2_36_38	?	?	?	?

Moller Electrons below 5 degrees

CLAS12_MollerDataTable_12-16-2018

Moller rate -vs- length of a single taerget

0.5 cm radius -vs- Z

Target is a one 0.5 cm radius cylinder of length Z.

By how much does the moller rate change at full field ?

Latest Stuff

VanWasshenova_Thesis#Mlr_Summ_TF

References

CLASNOTE 2016-06 Moller shield simulations: comparison of the GEMC-optimized layout and the engineering design