July2012PosSimulation

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.

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.

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).

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

Y profile (why is the distribution clipped on the left side in the figure)

X divergence profile

Y divergence profile

Momentum distribution

Momentum distribution

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.

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

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).

Step 1: Generated Beam on DQ4

Positrons on detector right before Q4.

X profile

Y profile

X divergence profile

Y divergence profile

Momentum distribution

Momentum distribution

Step 1: Generated Beam on DD1

Positrons on detector right before D1 - first dipole.

X profile

Y profile

X divergence profile

Y divergence profile

Momentum distribution

Momentum distribution

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

Y profile

X divergence profile

Y divergence profile

Momentum distribution

Momentum distribution

Generated Beam on DD1

Positrons on detector right before D1 - first dipole.

X profile

Y profile

X divergence profile

Y divergence profile

Momentum distribution

Momentum distribution

Beam Compare Step1 and Step2

Compare at DD1 of S1 and S2

	Step 1	Step 2
X profile
Y profile
X divergence profile
Y divergence profile
Energy

S3

Counts	DD1UP	DD45	DD2ND	DT2UP	DT2UP (Px>0)	DT2UP (Px>)
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]	300 px	300 px
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]
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]
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]
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]

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

En @ DD45

En @ DD2ND

En @ DT2ND

En @ DT2ND 300 px

En @ DT2ND 300 px

2 MeV

En @ DD1UP

En @ DD45

En @ DD2ND

En @ DT2ND

En @ DT2ND

En @ DT2ND

3 MeV

En @ DD1UP

En @ DD45

En @ DD2ND

En @ DT2ND

En @ DT2ND

En @ DT2ND

4 MeV

En @ DD1UP

En @ DD45

En @ DD2ND

En @ DT2ND

En @ DT2ND

En @ DT2ND

5 MeV

En @ DD1UP

En @ DD45

En @ DD2ND

En @ DT2ND

En @ DT2ND

En @ DT2ND

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

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

Ratio - Positrons reaches T2 to Positrons Detected

The ratio of positrons reaches end of the beamline to the one being detected by NaI detectors in coincidence mode.

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

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
1	[math] ( 1.9 \pm 0.9 )\times 10^{-16} [/math]
2	[math] ( 6.9 \pm 2.4 )\times 10^{-16} [/math]
3	[math] ( 8.3 \pm 1.0 )\times 10^{-15}[/math]
4	[math] ( 4.2 \pm 0.8 )\times 10^{-15}[/math]
5	[math] ( 6.2 \pm 1.6 )\times 10^{-16}[/math]

Estimation

In Run 3735, 100 mA peak current, 300 Hz reprate, 300 ns macro pulse length. positron Rate Detected on NaI detectors are 0.26 for 3 MeV. That means positron rate (reaches T2 location) is 638 per second.

[math] 100 mA * 300 Hz * 300 ns = 9*10^{-6}~C~Hz[/math]

[math] \frac{9*10^{-6}~C}{1.6*10^{-19}~C} = 5.625*10^{13}[/math] electrons per second on HRRL.

Then we have positrons with rate reaches T2 area of beamline

Energy (MeV)	Positron to Electron Ratio
1	[math] ( 1.9 \pm 0.9 )\times 10^{-16} \times 5.625*10^{13}*7718 = 82[/math]
2	[math] ( 6.9 \pm 2.4 )\times 10^{-16} \times 5.625*10^{13}*2008 = 78[/math]
3	[math] ( 8.3 \pm 1.0 )\times 10^{-15} \times 5.625*10^{13}*2454 = 1146[/math]
4	[math] ( 4.2 \pm 0.8 )\times 10^{-15} \times 5.625*10^{13}*2458 = 581 [/math]
5	[math] ( 6.2 \pm 1.6 )\times 10^{-16}\times 5.625*10^{13}*2577 = 86[/math]

Simulation Error

Max = B+Delta_B, Max = B-Delta_B.

D1     Q7             D2
Max    3.5            Max
Min    3.5            Min
Max    3.5            default
Min    3.5            default
Max    3.5+Delta_I    default
Max    3.5-Delta_I    default
Min    3.5+Delta_I    default
Min    3.5-Delta_I    default

Delta_I=0.1 Amp.

Detector	Magnet Settings	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
NaIR && NaIL	D1=Max,Q7=3.5,D2=Max.	25	169	1277	1373	1291	1251	1215	1135	1014	934
NaIR && NaIL	D1=Min,Q7=3.5,D2=Min.	12	156	1255	1320	1306	1271	1061	1118	1031	915
NaIR && NaIL	D1=Max,Q7=3.5,D2=Default.	1	156	1257	1312	1308	1268	1223	1130	1042	923
NaIR && NaIL	D1=Min,Q7=3.5,D2=Default.	6	166	1245	1302	1283	1273	1218	1125	1003	875
NaIR && NaIL	D1=Max,Q7=3.5+Delta_I,D2=Default.	1	143	1158	1333	1268	1244	1197	1098	983	903
NaIR && NaIL	D1=Max,Q7=3.5-Delta_I,D2=Default.	1	190	1363	1321	1366	1257	1220	1135	1026	913
NaIR && NaIL	D1=Min,Q7=3.5-Delta_I,D2=Default.	2	163	1272	1332	1274	1195	1208	1112	975	927
NaIR && NaIL	D1=Min,Q7=3.5+Delta_I,D2=Default.	5	130	1156	1351	1240	1197	1190	1106	1008	904
NaIR && NaIL	D1=Default,Q7=3.5,D2=Default.	12	168	1261	1237	1247	1222	1220	1147	1003	907

After considering detector efficiency 46.24%.

1.015MeV 	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

11.56		78.1456		590.4848	634.8752	596.9584	578.4624	561.816	        524.824	        468.8736	431.8816
5.5488		72.1344		580.312	        610.368	        603.8944	587.7104	490.6064	516.9632	476.7344	423.096
0.4624		72.1344		581.2368	606.6688	604.8192	586.3232	565.5152	522.512	        481.8208	426.7952
2.7744		76.7584		575.688	        602.0448	593.2592	588.6352	563.2032	520.2	        463.7872	404.6
0.4624		66.1232		535.4592	616.3792	586.3232	575.2256	553.4928	507.7152	454.5392	417.5472
0.4624		87.856		630.2512	610.8304	631.6384	581.2368	564.128	        524.824	        474.4224	422.1712
0.9248		75.3712		588.1728	615.9168	589.0976	552.568	        558.5792	514.1888	450.84	        428.6448
2.312		60.112		534.5344	624.7024	573.376	        553.4928	550.256	        511.4144	466.0992	418.0096
5.5488		77.6832		583.0864	571.9888	576.6128	565.0528	564.128	        530.3728	463.7872	419.3968