July2012PosSimulation

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In G4beamline manual "The electromagnetic processes of these physics lists are advertised to be valid above a few hundred electron Volts; Geant4 has a set of low energy electromagnetic processes, indicated by a suffix “_EMX” in the physics list name."

2 MeV Positrons

Measured Electron energy distribution at 10 MeV on 1.mm target

Simulation steps

1.) GEANT4 Simulated Beam energy distribution


2.) GEANT4 Simulated Positrons emitted from 1.x mm thick target


3.) Now use above Positron distribution as the particle source for G4beamline

Positrons hitting Tungsten Converter target

4.) Use GEANT4 to determine 511s from the positrons distribution impinging converter target

Oct 16th 2012 BenchMark

stages:

1. Program to input emittance, output beamsize, beam, divergence and beam energy.

2. e- on W, outcome e+. Incident electron distribution on T1. with general particle source with step 1 histogram. check graph x, y, z theta, En_dis out_put is the input. (directory for each).

3. insert T1 and generate positron distribution.

4. Acceleractor code to transport positron along the beamline. Out put positron theta, beamsize (x,y), energy distribution, out puts transported positron.

5. Geant4 takes step 4 output generates gamma (and other e+,e-) and look at those goes to detectors. beamline, plus shielding, and detectors.

HRRL pos sim benchmark Oct 16th 2012 update.jpg

Simulations

Partical Data Ground ID: PDGid=11 is electron. PDGid=-11 is positron. PDGid=22 is photon.

Parameters

Dipole vacuum chamber width is [math] 17 \pm 0.5 [/math] mm

The cavity exit diameter is about 7.3 mm.


Energy Spread Two Skewed Gaussian Fit

Energy spread fitted with two skewed Gaussian.

Hrrl 17May2012 12MeV En Spread2.png

Beam Distributions Beyond RMS: Media:Beam_Distributions_Beyond_RMS.pdf 


Amplitude = 2.13894, mean = 12.07181, sigma_L = 4.46986, sigma_R = 1.20046 

Sigma = 2.83516, Skewness = -0.57658 

Amplitude2 = 10.88318, mean2 = 12.32332, sigma_L2 = 0.69709, sigma_R2 = 0.45170 

Sigma2 = 0.57440, Skewness2 = -0.21360

Electron Distribution Upstream and Positron Distribution Downstream of Target1

simulation: Electron Distribution Upstream and Positron Distribution Downstream of Target1

3067274 Electrons fired.

T1_s=943.5

FDT1_s=$T1_s-26.52

BDT1_s=$T1_s+26.52

Thickness of T1 is 1.016 mm, radius of T1 is 15.875 mm (0.625 inches).

HRRL pos Jul2012 sim FDT1 BDT1 T1.png

HRRL pos Jul2012 sim FDT1 BDT1 Oerlay.png


Step 1: Generating positron from electron beam

Detector is after T1 to saple positron distribution. 13,799,743,800 electrons shot at the tungsten target to generate positrons.

step 1: ratio

DDNT1 = Detector DowN from T1

DQ4 = Detector at entrance Quad 4 located right after T1

DD1 = Detector at entrance of the first Dipole.

e-(DUPT1) = 13,799,743,800

e+(DDNT1) = [math]1.095179 \times 10^7[/math]

e+(DQ4) = [math]62780[/math]

e+(DQ4) = [math]6742[/math]


e-(DUPT1)/e+(DDNT1) = 1260

e-(DUPT1)/e+(DQ4) = 219811 = [math]2.2 \times 10^5[/math]

e-(DUPT1)/e+(DD1) = 2046832 = [math]2.0 \times 10^6[/math]


e+(DDNT1)/e+(DQ4) = 174

e+(DDNT1)/e+(DD1) = 1624


e+(DQ4)/e+(DD1) = 9.3

Step 1: Generated Beam on DDNT1

Detector down T1:

Positrons on detector right before Q4.

X profile Hrrl pos sim s2 beam DDNT1 x s1.png

Y profile (why is the distribution clipped on the left side in the figure) Hrrl pos sim s2 beam DDNT1 y s1.png


X divergence profile Hrrl pos sim s2 beam DDNT1 xp s1.png

Y divergence profile Hrrl pos sim s2 beam DDNT1 yp s1.png

Momentum distribution Hrrl pos sim s2 beam DDNT1 mom s1.png

Momentum distribution Hrrl pos sim s2 beam DDNT1 En s1.png

Sharp drop issue

The Y-position distribution of the beam shown in Figure ~\ref{sim-DDNT1-y-vs-x} has a sharp drop in the region between -25.8 mm and -27.2 mm that corresponds to the boundary of the target T1. Figure ~\ref{sim-DDNT1-T1-geo} shows the geometry of the target T1 and the sensitive detector DDNT1. If the target size was increased, it would eventually intersected the detector DDNT1 at a distance of 25.8 mm from the beam center. A 1.4 mm wide stripe of low counts is visible on DDNT1 that is a result of the target's thickness of 1.016 mm and the 45 degree angle of intersection. ([math]1.016 \sqrt{2}=1.44[/math]). The edge of the target does not produce many positrons compared to the face of the target, and as a result you see the stripe.

As shown in figures ~\ref{sim-DDNT1-theta-vs-y} and ~\ref{sim-DDNT1-theta-vs-y-zoom} (zoomed figure) the positron distribution decrease occures at [math]\theta = 45^o[/math]. Positrons are emitted from both the downstream and upstream side of the target. As shown in the figure, positrons from the downstream side of the target intersect the detector at angles below 45 degrees while positrons from the upstream side of the target begin to hit the detector at angles beyond 45 degrees. The 1.4 mm gap represents the transition of positrons between these two extremes.

Hrrl pos sim pos sharp drop geometry2.png

Hrrl pos sim s2 beam DDNT1 xy zoom s1.png Hrrl pos sim s2 beam DDNT1 xy zoom2 s1.png

Cut off line is around 26.5 mm corresponding to the large angle.

Hrrl pos sim beam DDNT1 y yp s1.png Hrrl pos sim beam DDNT1 y yp zoom s1.png


Hrrl pos sim s2 beam DDNT1 y s1.png Hrrl pos sim s2 beam DDNT1 xy s1.png

Hrrl pos sim s2 beam DDNT1 yp s1.png Hrrl pos sim s2 beam DDNT1 xpyp s1.png


DDNT1 is at 26.52 mm (53.04 mm)downstream of T1.

T1 radius is 25.4 mm (d=50.8 mm)

DDNT1 radius is 31.75 mm (d=63.5 mm).


Hrrl pos sim s2 beam DDNT1 xy zoom s1.png


Hrrl pos sim pos sharp drop geometry.png

Step 1: Generated Beam on DQ4

Positrons on detector right before Q4.

X profile Hrrl pos sim s2 beam DQ4 x s1.png

Y profile Hrrl pos sim s2 beam DQ4 y s1.png

X divergence profile Hrrl pos sim s2 beam DQ4 xp s1.png

Y divergence profile Hrrl pos sim s2 beam DQ4 yp s1.png

Momentum distribution Hrrl pos sim s2 beam DQ4 mom s1.png

Momentum distribution Hrrl pos sim s2 beam DQ4 En s1.png

Step 1: Generated Beam on DD1

Positrons on detector right before D1 - first dipole.

X profile Hrrl pos sim s2 beam DD1 x s1.png

Y profile Hrrl pos sim s2 beam DD1 y s1.png

X divergence profile Hrrl pos sim s2 beam DD1 xp s1.png

Y divergence profile Hrrl pos sim s2 beam DD1 yp s1.png

Momentum distribution Hrrl pos sim s2 beam DD1 mom s1.png

Momentum distribution Hrrl pos sim s2 beam DD1 En s1.png

Step 2: generate positron

The positrons after T1 is detected on a virtual detector. The positrons beam size, divergence and momentum distributions are extracted and created new positron beam.

Generate positron beam from the detector after T1 and transport it to right before D1.

219034780*100=21,903,478,000 positrons generated.


step 2: ratio

e+(DDNT1)/e+(DQ4) = 3536518400/47788670 = 74

e+(DDNT1)/e+(DD1) = 3536518400/5464220 = 647

e+(DQ4)/e+(DD1) = 8.7

Generated Beam on DQ4

Positrons on detector right before Q4.

X profile Hrrl pos sim s2 beam DQ4 x.png

Y profile Hrrl pos sim s2 beam DQ4 y.png

X divergence profile Hrrl pos sim s2 beam DQ4 xp.png

Y divergence profile Hrrl pos sim s2 beam DQ4 yp.png

Momentum distribution Hrrl pos sim s2 beam DQ4 mom.png

Momentum distribution Hrrl pos sim s2 beam DQ4 En.png


Generated Beam on DD1

Positrons on detector right before D1 - first dipole.

X profile Hrrl pos sim s2 beam DD1 x.png

Y profile Hrrl pos sim s2 beam DD1 y.png

X divergence profile Hrrl pos sim s2 beam DD1 xp.png

Y divergence profile Hrrl pos sim s2 beam DD1 yp.png

Momentum distribution Hrrl pos sim s2 beam DD1 mom.png

Momentum distribution Hrrl pos sim s2 beam DD1 En.png

Beam Compare Step1 and Step2

Compare at DD1 of S1 and S2


Step 1 Step 2
X profile Hrrl pos sim s2 beam DD1 x s1.png Hrrl pos sim s2 beam DD1 x.png
Y profile Hrrl pos sim s2 beam DD1 y s1.png Hrrl pos sim s2 beam DD1 y.png
X divergence profile Hrrl pos sim s2 beam DD1 xp s1.png Hrrl pos sim s2 beam DD1 xp.png
Y divergence profile Hrrl pos sim s2 beam DD1 yp s1.png Hrrl pos sim s2 beam DD1 yp.png
Energy Hrrl pos sim s2 beam DD1 En s1.png Hrrl pos sim s2 beam DD1 En.png

S3

Counts DD1UP DD45 DD2ND DT2UP DT2UP (Px>0) DT2UP (Px>)
1 MeV [math]1.4\times10^8[/math] ST sim s3 1Mev En D1UP.png [math]3.8 \times 10^5[/math]ST sim s3 1Mev En D45.png [math]1.8 \times 10^3[/math] ST sim s3 1Mev En DD2ND.png [math]1.2 \times 10^1[/math] ST sim s3 1Mev En DT2ND.png 300 px 300 px
2 MeV [math]1.4\times10^8[/math] ST sim s3 2Mev En D1UP.png [math]2.6 \times 10^6[/math]ST sim s3 2Mev En D45.png [math]6.1 \times 10^4[/math]ST sim s3 2Mev En DD2ND.png [math]4.3 \times 10^2[/math] ST sim s3 2Mev En DT2ND.png [math]4.2 \times 10^2[/math]ST sim s3 2Mev En DT2ND BT 0.png [math]1.1 \times 10^2[/math]ST sim s3 2Mev En DT2ND BT A.png
3 MeV [math]1.4\times10^8[/math] ST sim s3 3Mev En D1UP.png [math]5.9 \times 10^6[/math]ST sim s3 3Mev En D45.png [math]4.2 \times 10^5[/math]ST sim s3 3Mev En DD2ND.png [math]2.3 \times 10^3[/math]ST sim s3 3Mev En DT2ND.png [math]2.1 \times 10^3[/math]ST sim s3 3Mev En DT2ND BT 0.png [math]1.5 \times 10^3[/math]ST sim s3 3Mev En DT2ND BT A.png
4 MeV [math]1.4\times10^8[/math] ST sim s3 4Mev En D1UP.png [math]5.1 \times 10^6[/math]ST sim s3 4Mev En D45.png [math]5.9 \times 10^5[/math]ST sim s3 4Mev En DD2ND.png [math]4.4 \times 10^3[/math] ST sim s3 4Mev En DT2ND.png [math]4.0 \times 10^3[/math]ST sim s3 4Mev En DT2ND BT 0.png [math]2.9 \times 10^3[/math]ST sim s3 4Mev En DT2ND BT A.png
5 MeV [math]1.4\times10^8[/math] ST sim s3 5Mev En D1UP.png [math]4.8 \times 10^6[/math]ST sim s3 5Mev En D45.png [math]7.4 \times 10^5[/math]ST sim s3 5Mev En DD2ND.png [math]5.0 \times 10^3[/math] ST sim s3 5Mev En DT2ND.png [math]4.6 \times 10^3[/math]ST sim s3 5Mev En DT2ND BT 0.png [math]3.2 \times 10^3[/math]ST sim s3 5Mev En DT2ND BT A.png


Counts DD1UP DD45 DD2ND DT2UP DT2UP (Px>0) DT2UP (Px>) dE/E
1 MeV [math]1.4\times10^8[/math] [math]3.8 \times 10^5[/math] [math]1.8 \times 10^3[/math] [math]1.2 \times 10^1[/math]
2 MeV [math]1.4\times10^8[/math] [math]2.6 \times 10^6[/math] [math]6.1 \times 10^4[/math] [math]4.3 \times 10^2[/math] [math]4.2 \times 10^2[/math] [math]1.1 \times 10^2[/math] 0.3/2 = 15%
3 MeV [math]1.4\times10^8[/math] [math]5.9 \times 10^6[/math] [math]4.2 \times 10^5[/math] [math]2.3 \times 10^3[/math] [math]2.1 \times 10^3[/math] [math]1.5 \times 10^3[/math] 0.22/3 = 7%
4 MeV [math]1.4\times10^8[/math] [math]5.1 \times 10^6[/math] [math]5.9 \times 10^5[/math] [math]4.4 \times 10^3[/math] [math]4.0 \times 10^3[/math] [math]2.9 \times 10^3[/math] 4.42-3.64 = 20%
5 MeV [math]1.4\times10^8[/math] [math]4.8 \times 10^6[/math] [math]7.4 \times 10^5[/math] [math]5.0 \times 10^3[/math] [math]4.6 \times 10^3[/math] [math]3.2 \times 10^3[/math] 5.43-4.59 = 17%



Checks

  1. Make delta function incident beams, does the dipole transport 100% of them
  2. Increase Delta E(1,3,5,10,20,40% of E), incident positrons are at 0 degrees, centered on dipole, plot loss as function of Delta E for 1,3,5 meV incident beam
  3. Next consider incident angle of positrons on the Quad

1 MeV

En @ DD1UP ST sim s3 1Mev En D1UP.png

En @ DD45 ST sim s3 1Mev En D45.png

En @ DD2ND ST sim s3 1Mev En DD2ND.png

En @ DT2ND ST sim s3 1Mev En DT2ND.png

En @ DT2ND 300 px

En @ DT2ND 300 px

2 MeV

En @ DD1UP ST sim s3 2Mev En D1UP.png

En @ DD45 ST sim s3 2Mev En D45.png

En @ DD2ND ST sim s3 2Mev En DD2ND.png

En @ DT2ND ST sim s3 2Mev En DT2ND.png

En @ DT2ND ST sim s3 2Mev En DT2ND BT 0.png

En @ DT2ND ST sim s3 2Mev En DT2ND BT A.png

3 MeV

En @ DD1UP ST sim s3 3Mev En D1UP.png

En @ DD45 ST sim s3 3Mev En D45.png

En @ DD2ND ST sim s3 3Mev En DD2ND.png

En @ DT2ND ST sim s3 3Mev En DT2ND.png

En @ DT2ND ST sim s3 3Mev En DT2ND BT 0.png

En @ DT2ND ST sim s3 3Mev En DT2ND BT A.png

4 MeV

En @ DD1UP ST sim s3 4Mev En D1UP.png

En @ DD45 ST sim s3 4Mev En D45.png

En @ DD2ND ST sim s3 4Mev En DD2ND.png

En @ DT2ND ST sim s3 4Mev En DT2ND.png

En @ DT2ND ST sim s3 4Mev En DT2ND BT 0.png

En @ DT2ND ST sim s3 4Mev En DT2ND BT A.png

5 MeV

En @ DD1UP ST sim s3 5Mev En D1UP.png

En @ DD45 ST sim s3 5Mev En D45.png

En @ DD2ND ST sim s3 5Mev En DD2ND.png

En @ DT2ND ST sim s3 5Mev En DT2ND.png

En @ DT2ND ST sim s3 5Mev En DT2ND BT 0.png

En @ DT2ND ST sim s3 5Mev En DT2ND BT A.png

Dipole test

100 e+ shot to the entrance of D1.

Following table shows the number of e+ detected on each detectors.

Detector order is DD1UP->D45->DD2DN->DT2UP.

[math]dE=En_{Max}-En_{mean}[/math]

Q7 is off

dE/E 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100
0.001 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100
0.003 100->100->81->81 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100
0.005 100->100->56->56 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->88
0.01 100->100->100->28 100->100->100->90 100->100->100->78 100->100->100->54 100->100->100->44
0.03 100->100->58->10 100->100->66->30 100->100->67->27 100->100->67->18 100->100->67->15
0.05 100->77->34->5 100->94->40->18 100->96->40->15 100->97->40->10 100->97->40->8
0.1 100->39->17->2 100->48->20->9 100->50->20->8 100->52->20->5 100->52->20->4
0.2 100->19->8->1 100->24->10->5 100->25->10->4 100->26->10->3 100->26->10->2
0.4 100->10->4->1 100->12->5->3 100->12->5->2 100->13->5->1 100->13->5->1
0.495 100->8->3->1
0.5 - 100->10->4->1 100->10->4->1 100->10->4->1 100->10->4->1
0.6 - 100->8->3->1 100->8->3->1 100->8->3->1 100->8->3->1
0.7 - 100->7->3->1 100->7->3->1 100->8->3->1 100->8->3->1


Search Q7 for max MeV Transmission

Find Q7 current so transmission max is like experiment (3 meV)


Q7 Current dE/E 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 A 0.01 100->100->100->28 100->100->100->90 100->100->100->78 100->100->100->54 100->100->100->44
0.5 A 0.01 100->100->100->51 100->100->100->100 100->100->100->89 100->100->100->59 100->100->100->47
1 A 0.01 100->100->100->100 100->100->100->100 100->100->100->99 100->100->100->65 100->100->100->51
2 A 0.01 100->100->100->41 100->100->100->100 100->100->100->100 100->100->100->82 100->100->100->61
Q7 Current dE/E 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 A 0.03 100->100->58->10 100->100->66->30 100->100->67->27 100->100->67->18 100->100->67->15
1 A 0.03 100->100->100->84 100->100->100->48 100->100->89->34 100->100->82->22 100->100->79->17
Q7 Current dE/E 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 A 0.1 100->39->17->2 100->48->20->9 100->50->20->8 100->52->20->5 100->52->20->4
1 A 0.1 100->39->37->27 100->49->32->14 100->50->27->10 100->52->25->7 100->52->23->5
2 A 0.1 100->39->24->4 100->49->46->34 100->50->39->14 100->52->31->8 100->52->28->7
3 A 0.1 100->39->12->3 100->49->48->48 100->50->47->25 100->52->44->10 100->52->35->7
4 A 0.1 100->39->9->1 100->50->44->24 100->50->49->45 100->52->48->16 100->52->45->10
5 A 0.1 100->39->7->1 100->50->27->13 100->51->50->46 100->52->49->34 100->52->49->14
6 A 0.1 100->39->5->1 100->50->19->10 100->52->48->27 100->52->50->50 100->52->49->23
Q7 Current dE/E 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 A 0.2 100->19->8->1 100->24->10->5 100->25->10->4 100->26->10->3 100->26->10->2
1 A 0.2 100->19->19->14 100->25->16->7 100->25->14->5 100->26->12->3 100->26->12->3
2 A 0.2 100->19->12->2 100->25->23->17 100->25->20->7 100->26->16->4 100->26->14->3
3 A 0.2 100->19->6->2 100->25->24->24 100->25->23->13 100->26->22->5 100->26->18->3
4 A 0.2 100->19->4->0 100->25->22->12 100->25->23->23 100->26->24->8 100->26->22->5
5 A 0.2 100->19->4->0 100->25->14->7 100->26->25->23 100->26->25->17 100->26->25->7
6 A 0.2 100->19->2->0 100->25->9->5 100->26->24->14 100->26->25->25 100->26->25->12

X' effect on transmission

Set dE/E = 0 and change x-prime

Q7 Current=0

X'(rad) 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0.001 100->100->100->96 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100
0.003 100->100->100->60 100->100->100-> 88 100->100->100->99 100->100->100->98 100->100->100->98
0.005 100->94->94->39 100->94->92-> 67 100->94->92->87 100->95->91->84 100->95->91->84
0.01 93->69->69->21 91->67->64-> 36 91->68->64->59 91->68->62->54 91->66->61->50
0.03 41->25->25->8 41->24->22-> 12 43->25->24->20 43->25->22->19 41->24->21->18
0.05 27->16->16->5 26->15->14-> 8 27->18->16->14 26->16->14->11 24->13->12->9

Q7 is at 10 A

dE/E 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 100->100->100->0 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100
0.001 100->100->100->7 100->100->100->100 100->100->100->100 100->100->100->100 100->100->100->100
0.003 100->100->86->24 100->100->100->87 100->100->100->100 100->100->100->100 100->100->100->100
0.005 100->100->72->15 100->100->100->72 100->100->100->95 100->100->100->100 100->100->100->100
0.01 100->100->37->7 100->100->85->45 100->100->100->73 100->100->100->76 100->100->100->95
0.03 100->100->12->2 100->100->31->15 100->100->58->26 100->100->92->32 100->100->100->55
0.05 100->79->8->2 100->95->18->9 100->96->35->15 100->97->64->20 100->97->94->33
0.1 100->39->4->1 100->50->9->5 100->51->18->8 100->52->32->10 100->52->49->17
0.2 100->19->2->0 100->25->4->2 100->26->9->4 100->26->16->5 100->26->24->9
0.4 100->10->1->0 100->12->2->1 100->13->4->2 100->13->8->2 100->13->12->5

S3: transmission efficiency

Q7 effects on transmission efficiency

287,187,580 e+ started on the entrance of D1.

287,187,580 e+ ->DD1UP->D45->DD2DN->DT2UP

Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
3.5 A 1.397606e+8 ->372,799->14,023->211 1.397651e+8 ->2,565,113 ->423,855 -> 15,880 1.396887e+8 ->5,875,882 -> 1,229,176 -> 29,033 1.398474e+8 -> 5,136,409-> 925,689-> 24,525 1.399909e+8 -> 4,829,786 -> 842527->24,270
4 A 1.39766 e+8 -> 372,822 -> 10,489 -> 144 1.397609 e+8 -> 2,562,350 -> 376,893 -> 11,395 1.396925 e+8 -> 5,878,246 -> 1,236,380 -> 28,788 1.398244 e+8 -> 5,134,603 -> 943,772 -> 24,351 1.399884 e+8 -> 4,831,365 -> 862,823 -> 21,619
4.5 A 1.397694e+8 ->371,717->8,133->122 1.397624e+8 ->2,568,162->328,002->8,340 1.396864e+8 ->5,879,573->1,215,941->28060 1.39825e+8 ->5,133,561->955,976->23,687 1.399705e+8 ->4,835,046->877,511->21,117
5 A 1.397738 e+8 -> 373,758 -> 6,682 -> 102 1.397676 e+8 -> 2,569,453 -> 276,527 -> 6,133 1.396864 e+8 -> 5,880,665 -> 1,160,296 -> 26,523 1.398232 e+8 -> 5,134,971 -> 962,467 -> 23,238 1.399815 e+8 -> 4,837,973 -> 890,292 -> 20,894
5.5 A 1.397576 e+8 -> 373106 -> 5635 -> 91 1.397755 e+8 -> 2569892 -> 231582 -> 4816 1.396929 e+8 -> 5882742 -> -> 25479 1.398403 e+8 -> 514112 -> 961255 -> 22746 1.399873 e+8 -> 4834026 -> 899850 -> 20798

511 keV photons at NaI Left and NaI Right. NaIL:NaIR.

Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 A 4:4 22:20 42:51 62:60 57:42
1 A 2:5 24:26 53:50 54:50 61:49
2 A 0:3 50:57 50:66 68:46 72:46
3 A 0:0 38:57 49:54 70:51 53:26
3.5 A 1:1 31:36 56:67 53:45 52:30
4 A 0:0 25:22 55:83 67:51 68:49
4.5 A 0:0 17:16 54:68 60:59 59:49
5 A 0:0 19:15 54:63 59:53 55:44
5.5 A 1:1 16:12 51:66 70:41 66:39
10 A 0:0 14:4 20:15 57:34 68:39
15 A 1:1 9:1 17:7 34:7 48:39
20 A 1:1 5:5 23:6 29:9 39:13
A : : : : :

Normalized

Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
3.5 A 0.007268 0.546964 1 0.844728 0.835945
4 A 0.005002 0.395825 1 0.845873 0.750973
4.5 A 0.004348 0.297220 1 0.844155 0.752566
5 A 0.003846 0.231233 1 0.876145 0.787769
5.5 A 0.003572 0.189018 1 0.892735 0.816280

e+ Annihilation Efficiency

S5 test 1

(100,000 e+ shot)->(photons on NaI Left):(photons on NaI Right)-> (e+ at DT2ND)

dispersion=10/1000 sigX=0.1 sigY=0.1 sigXp=0 sigYp=0 XP=0 YP=0

Runs 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
1 100000->6581:10135->575 100000->6841:10575->577 100000->7891:11389->636 100000->8849:12159->640 100000->10191:12699->647
1 1000->66:101->5.75 1000->68:106->5.77 1000->79:114->6.36 1000->89:122->6.4 1000->102:127->6.47


Runs 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
1 6581:10135 6841:10575 7891:11389 8849:12159 10191:12699
NaI Right 0.79809 0.83274 0.89684 0.95745 1
NaI Left 0.64577 0.67128 0.77431 0.86832 1

S5 test 2

dispersion=0/1000 sigX=0 sigY=0 sigXp=0 sigYp=0 XP=0 YP=0

Runs 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
2 100000->6567:10164->572 100000->7014:10575->536 100000->7752:11162->601 100000->8984:11995-> 630 100000->10018:12518->677
2 1000->65.77:101.64->5.72 1000->70.14:105.75->5.36 1000->77.52:111.62->6.01 1000->89.84:119.95-> 6.30 1000->100.18:125.18->6.77

Which Q7 Current to Chose

Ratio of Positron Rate to Electron Rata

The measured ratio of positron to electron ratio is given the following table and figure.

Energy (MeV) Positron to Electron Ratio Normalize to the peak
1 [math] ( 1.9 \pm 0.9 )\times 10^{-16} [/math] 0.02289
2 [math] ( 6.9 \pm 2.4 )\times 10^{-16} [/math] 0.08313
3 [math] ( 8.3 \pm 1.0 )\times 10^{-15}[/math] 1
4 [math] ( 4.2 \pm 0.8 )\times 10^{-15}[/math] 0.50602
5 [math] ( 6.2 \pm 1.6 )\times 10^{-16}[/math] 0.07470

HRRL Jul2012 pos to ele ratio 1.png

Compounding Q7 and Annihilation Efficiency

Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
3.5 A 0.007268 0.546964 1 0.844728 0.835945
4 A 0.005002 0.395825 1 0.845873 0.750973
4.5 A 0.004348 0.297220 1 0.844155 0.752566
5 A 0.003846 0.231233 1 0.876145 0.787769
5.5 A 0.003572 0.189018 1 0.892735 0.816280


Runs 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
NaI Left 0.64577 0.67128 0.77431 0.86832 1


Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
3.5 A 0.007268*0.64577 0.546964*0.67128 1*0.77431 0.844728*0.86832 0.835945*1
4 A 0.005002*0.64577 0.395825*0.67128 1*0.77431 0.845873*0.86832 0.750973*1
4.5 A 0.004348*0.64577 0.297220*0.67128 1*0.77431 0.844155*0.86832 0.752566*1
5 A 0.003846*0.64577 0.231233*0.67128 1*0.77431 0.876145*0.86832 0.787769*1
5.5 A 0.003572*0.64577 0.189018*0.67128 1*0.77431 0.892735*0.86832 0.816280*1
Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
3.5 A 0.004693 0.367166 0.77431 0.733494 0.835945
4 A 0.003230 0.265709 0.77431 0.734488 0.750973
4.5 A 0.002808 0.199518 0.77431 0.732997 0.752566
5 A 0.002484 0.199518 0.77431 0.760774 0.787769
5.5 A 0.002307 0.126884 0.77431 0.775180 0.816280

Require Same Event Number

Energy (MeV) Positron to Electron Ratio Normalize to the peak
1 [math] ( 1.9 \pm 0.9 )\times 10^{-16} [/math] 0.02289
2 [math] ( 6.9 \pm 2.4 )\times 10^{-16} [/math] 0.08313
3 [math] ( 8.3 \pm 1.0 )\times 10^{-15}[/math] 1
4 [math] ( 4.2 \pm 0.8 )\times 10^{-15}[/math] 0.50602
5 [math] ( 6.2 \pm 1.6 )\times 10^{-16}[/math] 0.07470


Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
3.5 A ３ 458 752 628 485
3.5 A 0.004 0.61 1 0.83 0.64
Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
0 A 19 233 483 484 474
0 A 0.04 0.48 1 1 0.98
Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
10 A 0 34 197 400 436
10 A 0 0.08 0.45 0.92 1
Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
5 A 3 155 695 545 502
5 A 0.004 0.22 1 0.78 0.72
Q7 1 MeV 2 MeV 3 MeV 4 MeV 5 MeV
5 A 1 66 508 555 489
5 A 0.002 0.12 0.92 1 0.88 
overlay positron energy distribution at T1 with what is seen at T2 for several values of Q7

Efficiency

NaI Efficiency

Detector Efficiency: Media:SAINT-GOBAIN_3M33_Efficiency.PDF

Detector Efficiency: Media:SAINT-GOBAIN_Efficiency.PDF

At 511 keV, NaI crystals has 68% efficiency. If they are in coincidence, their efficiency is 68% * 68% =46.24%.

Siumlated results

s1: 13,799,743,800 e- (z=-260 mm) ---> 10951790 e+ Detected at DDNT1 (z=970 mm).

s2: 21,903,478,000 e+ at DDNT1 --> 5464220 e+ detected at DD1 (entrance of D1.)

s3: 14,359,380,000 e+ at DD1 --> 511 gamma detected on (NaIR && NaIL) table below


step generated particle detected x times more e+ generated than previous step
s1 13,799,743,800 e- 10,951,790 e+ @ DDNT1 62,780 e+ @ DQ4 and 6742 e+ @ DD1
s2 21,903,478,000 e+ @ DDNT1 5,464,220 e+ @ DD1 143,039,300 e+ @ DQ4 21,903,478,000/10,951,790 = 1999.99068645
s3 14,359,380,000 e+ @ DD1 e+ @ DT2DN 14,359,380,000/5,464,220 = 2627.89199556
s2*s3 (21,903,478,000/10,951,790)*(14,359,380,000/5,464,220) = 5255759.51613

DDNT1:21,903,478,000*14,359,380,000/5,464,220 ->DQ4:143,039,300*14,359,380,000/5,464,220 -> DD1:14,359,380,000

DDNT1:57,559,974,511,209.3->DQ4:375,891,831,521 ->DD1:14,359,380,000


Q7 = 3.5 A 1.015 MeV 1.5 MeV 2.15 MeV 2.5 MeV 3 MeV 3.5 MeV 4.02 MeV 4.5 MeV 5 MeV 5.5 MeV
NaIR && NaIL 13 114 1032 1118 1054 1025 1020 961 848 765
NaIR && NaIL,B_D2*0.95 3 33 48 132 397 411 483 430 426 360
NaIR && NaIL,B_D2*1.05 6 219 192 483 666 658 638 540 600 520
NaIR && NaIL,B_D2*1.05 2 30 64 290 464 503 497 462 448 463
Q7 = 3.5 A 1.015 MeV 1.5 MeV 2.15 MeV 2.5 MeV 3 MeV 3.5 MeV 4.02 MeV 4.5 MeV 5 MeV 5.5 MeV
R 1.7924079e-16 1.5718038e-15 1.4228961e-14 1.5414708e-14 1.4532292e-14 1.4132447e-14 1.4063508e-14 1.3250031e-14 1.1692014e-14 1.0547631e-14
R 0.18e-15 1.57-15 14.23e-15 15.41e-15 14.53e-15 14.13e-15 14.06e-15 13.25e-15 11.69e-15 10.54e-15

simulation after considering detector efficiency

Q7 = 3.5 A 1.015 MeV 1.5 MeV 2.15 MeV 2.5 MeV 3 MeV 3.5 MeV 4.02 MeV 4.5 MeV 5 MeV 5.5 MeV
NaIR && NaIL 13*46.24% 114*46.24% 1032*46.24% 1118*46.24% 1054*46.24% 1025*46.24% 1020*46.24% 961*46.24% 848*46.24% 765*46.24%
NaIR && NaIL,B_D2*0.95 3*46.24% 33*46.24% 48*46.24% 132*46.24% 397*46.24% 411*46.24% 483*46.24% 430*46.24% 426*46.24% 360*46.24%
NaIR && NaIL,B_D2*1.05 6*46.24% 219*46.24% 192*46.24% 483*46.24% 666*46.24% 658*46.24% 638*46.24% 540*46.24% 600*46.24% 520*46.24% 
 Q7 = 3.5 A                || 1.015 MeV || 1.5 MeV  || 2.15 MeV || 2.5 MeV || 3 MeV    || 3.5 MeV  || 4.02 MeV || 4.5 MeV || 5 MeV    ||  5.5 MeV
 NaIR && NaIL              || 6.0112    || 52.7136  || 477.1968 || 516.9632|| 487.3696 || 473.96   || 471.648  || 444.3664|| 392.1152 ||  353.736
 NaIR && NaIL,B_D2*0.95    || 1.3872    || 15.2592  || 22.1952  || 61.0368 || 183.5728 || 190.0464 || 223.3392 || 198.832 || 196.9824 ||  166.464  
 NaIR && NaIL,B_D2*1.05    || 2.7744    || 101.2656 || 88.7808  || 223.3392|| 307.9584 || 304.2592 || 295.0112 || 249.696 || 277.44   ||  240.448


Transmission Efficiency to DUPT2

Bin width is 0.5 MeV. For example for 2.15, the bin is 1.85~2.35.

Detector 1.015 MeV 1.5 MeV 2.15 MeV 2.5 MeV 3 MeV 3.5 MeV 4.02 MeV 4.5 MeV 5 MeV 5.5 MeV
Detector 0.765~1.265 MeV 1.25~1.75 MeV 1.85~2.35 MeV 2.25~2.75 MeV 2.75~3.25 MeV 3.25~3.75 MeV 3.77~4.27 MeV 4.25~4.75 MeV 4.75~5.25 MeV 5.25~5.75 MeV
DT2UP (s3) 10707 140228 958080 1190199 1196043 1193796 1159452 1095487 1010286 906707
DDNT1 (s1) should be multiplyed *(21903478000/10951790)*(14359380000/5464220) 481565 936192 1232531 1294501 1262790 1163914 1016908 871468 717717 573574
DQ4 (s2) should be multiplyed *(14359380000/5464220) 5195306 10459770 14297460 15433380 15490470 14792460 13346730 11796010 10101670 8394400
DD1 (s2) should be multiplyed *(14359380000/5464220) 520593 1050496 1435086 1549003 1555254 1484034 1340350 1183247 1015548 842818


Detector 1.015 MeV 1.5 MeV 2.15 MeV 2.5 MeV 3 MeV 3.5 MeV 4.02 MeV 4.5 MeV 5 MeV 5.5 MeV
Detector 0.765~1.265 MeV 1.25~1.75 MeV 1.85~2.35 MeV 2.25~2.75 MeV 2.75~3.25 MeV 3.25~3.75 MeV 3.77~4.27 MeV 4.25~4.75 MeV 4.75~5.25 MeV 5.25~5.75 MeV
DT2UP (s3) 10707 140228 958080 1190199 1196043 1193796 1159452 1095487 1010286 906707
DDNT1 (s1) 481565 936192 1232531 1294501 1262790 1163914 1016908 871468 717717 573574
DQ4 (s2) 5195306 10459770 14297460 15433380 15490470 14792460 13346730 11796010 10101670 8394400
DD1 (s2) 520593 1050496 1435086 1549003 1555254 1484034 1340350 1183247 1015548 842818
NaIR && NaIL 13 114 1032 1118 1054 1025 1020 961 848 765

back tracking

Detector 1.015 MeV 1.5 MeV 2.15 MeV 2.5 MeV 3 MeV 3.5 MeV 4.02 MeV 4.5 MeV 5 MeV 5.5 MeV
Detector 0.765~1.265 MeV 1.25~1.75 MeV 1.85~2.35 MeV 2.25~2.75 MeV 2.75~3.25 MeV 3.25~3.75 MeV 3.77~4.27 MeV 4.25~4.75 MeV 4.75~5.25 MeV 5.25~5.75 MeV
DT2UP (s3) 10707 140228 958080 1190199 1196043 1193796 1159452 1095487 1010286 906707
NaIR && NaIL 13 114 1032 1118 1054 1025 1020 961 848 765
(DT2UP)/(NaIR && NaIL) 3569 1230.07017544 928.372093023 1064.57871199 1134.76565465 1164.67902439 1136.71764706 1139.94484912 1191.375 1185.2379085
(DT2UP)/(NaIR && NaIL) 3569 1230 928 1065 1135 1165 1137 1140 1191 1185
Include Detector efficiency (DT2UP)/(NaIR && NaIL) 7718.42560554 2660.18636557 2007.72511467 2454.07797286 2454.07797286 2518.76951641 2458.29940973 2465.27865294 2576.50302768 2563.23077098
Include Detector efficiency (DT2UP)/(NaIR && NaIL) 7718 2660 2008 2454 2454 2519 2458 2465 2577 2563
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