Difference between revisions of "July2012PosSimulation"

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= Efficiency =
 
= Efficiency =
 +
 +
==NaI Efficiency ==
  
 
Detector Efficiency: [[Media:SAINT-GOBAIN_3M33_Efficiency.PDF]]
 
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
 +
 +
This is to say whole simulation started with 13,799,743,800*(21,903,478,000/10,951,790)*(14,359,380,000/5,464,220) = 7.2528135e+16 electrons.
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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
 +
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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
 +
|-
 +
|}
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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 ==
  
−
s1: 13,799,743,800 e- (z=-260 mm) ---> 1105170 e+ Detected at DDNT1 (z=970 mm). R1: 10951790/13,799,743,800 = 0.0007936227
+
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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%
 +
|-
 +
|}
  
−
s2: 21,903,478,000 e+ at DDNT1 --> 5464220 e+ detected at DD1 (entrance of D1.) R2: 5464220/21,903,478,000 = 0.00024946814
+
  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
  
−
R1*R2= (10951790/13,799,743,800)*(5464220/21,903,478,000) =1.97983583e-7=1.98e-7= 2e-7
 
  
−
s3: 8,615,627,800 e+ at DD1 --> 511 gamma detected on (NaIR && NaIL) table below
+
== Transmission Efficiency to DUPT2 ==
  
 +
Bin width is 0.5 MeV. For example for 2.15, the bin is 1.85~2.35.
  
 
{| border="3"  cellpadding="5" cellspacing="0"
 
{| border="3"  cellpadding="5" cellspacing="0"
−
| Q7 = 3.5 A || 1 MeV  || 2 MeV || 3 MeV || 4 MeV || 5 MeV
+
| 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
 
|-  
 
|-  
−
| R3 || 3/8,615,627,800 || 458/8,615,627,800 || 752/8,615,627,800  || 628/8,615,627,800  || 485/8,615,627,800
+
| 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
 
|}
 
|}
 +
  
 
{| border="3"  cellpadding="5" cellspacing="0"
 
{| border="3"  cellpadding="5" cellspacing="0"
−
| Q7 = 3.5 A || 1 MeV  || 2 MeV || 3 MeV || 4 MeV || 5 MeV
+
| 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
 
|-  
 
|-  
−
| R=R1*R2*R3 || 6.9e-17 || 1.05e-14 || 1.73e-14 ||  1.44e-14 ||  1.11e-14
+
| 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
 
|-  
 
|-  
−
| R=R1*R2*R3 || 0.069e-15 || 10.5e-15 || 17.3e-15 ||  14.4e-15 ||  11.1e-15
+
| NaIR && NaIL || 13  || 114      || 1032    ||  1118  ||  1054 || 1025    || 1020  ||  961    ||  848 ||  765
 
|-  
 
|-  
 
|}
 
|}
 +
 +
 +
=== New Run result ===
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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
 +
|-
 +
| NaIR && NaIL || 12  || 168      || 1261    ||  1237  ||  1247 || 1222    || 1220  ||  1147    ||  1003  ||  907
 +
|-
 +
|}
 +
 +
== 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.
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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.
 +
 +
{| border="1" cellpadding="5" cellspacing="0"
 +
| 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>
 +
|-
 +
|}
 +
 +
[[File:HRRL_Jul2012_pos_to_ele_ratio_1.png | 400 px]]
 +
 +
=== 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
 +
 +
{| border="1" cellpadding="5" cellspacing="0"
 +
| 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.
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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.            ||  27  ||  205  ||  1457 ||  1689 || 1599  ||  1541  || 1493  ||  1355  || 1206  ||  1110
 +
|-
 +
| NaIR && NaIL ||D1=Min,Q7=3.5,D2=Min.            ||  5  ||  162  ||  1566 ||  1632 ||  1594 ||  1512  || 1532  ||  1441  || 1287  ||  1159
 +
|-
 +
| NaIR && NaIL ||D1=Max,Q7=3.5,D2=Default.        ||  6  ||  151  ||  1594 ||  1629 ||  1655 ||  1615  || 1547  ||  1371  || 1285  ||  1158
 +
|-
 +
| NaIR && NaIL ||D1=Min,Q7=3.5,D2=Default.        ||  3  ||  186  ||  1662 ||  1642 ||  1626 ||  1540  || 1461  ||  1397  || 1305  ||  1128
 +
|-
 +
| NaIR && NaIL ||D1=Max,Q7=3.5+Delta_I,D2=Default. ||  3  ||  183  ||  1483 ||  1669 ||  1596 ||  1530  || 1522  ||  1373  || 1311  ||  1135
 +
|-
 +
| NaIR && NaIL ||D1=Max,Q7=3.5-Delta_I,D2=Default. ||  6  ||  198  ||  1615 ||  2082 ||  1510 ||  1625  || 1424  ||  1460  || 1487  ||  1156
 +
|-
 +
| NaIR && NaIL ||D1=Min,Q7=3.5-Delta_I,D2=Default. ||  7  ||  280  ||  1736 ||  1718 ||  1596 ||  1553  || 1526  ||  1377  || 1258  ||  1120
 +
|-
 +
| NaIR && NaIL ||D1=Min,Q7=3.5+Delta_I,D2=Default. ||  1  ||  186  ||  1472 ||  1650 ||  1638 ||  1525  || 1546  ||  1413  || 1258  ||  1177
 +
|-
 +
| NaIR && NaIL ||D1=Default,Q7=3.5,D2=Default.    ||  14  ||  209  || 1588  || 1717  || 1563  ||  1549  ||  1517 ||    1396 ||  1223 ||1153
 +
|-
 +
| NaIR && NaIL ||D1=Default,Q7=10,D2=Default.    ||  3    ||  19  || 117  || 226  || 420  ||  678  ||  842  ||    970  ||  842  ||699
 +
|-
 +
| NaIR && NaIL ||D1=Default,Q7= 0,D2=Default.    ||  34  ||  252  || 724  || 889  || 1032  ||  1121  ||  1221 ||    1185 ||  1128 ||1067
 +
|-
 +
 +
|}
 +
 +
After Multiplyed to detector efficiency in coincidense mode: 46.24%
 +
                        Max Min Max Min Max Max Min Min Def
 +
                        Def Def Def Def Max Min Min Max Def percent
 +
                        Max Min Def Def Def Def Def Def Def ave std error
 +
0.765~1.265    MeV 12 2 3 1 1 3 3 0 6 4 4 0.24
 +
1.25~1.75      MeV 95 75 70 86 85 92 129 86 97 90 17 0.15
 +
1.85~2.35      MeV 674 724 737 769 686 747 803 681 734 728 43 0.13
 +
2.25~2.75      MeV 781 755 753 759 772 963 794 763 794 793 66 0.16
 +
2.75~3.25      MeV 739 737 765 752 738 698 738 757 723 739 20 0.04
 +
3.25~3.75      MeV 713 699 747 712 707 751 718 705 716 719 18 0.04
 +
3.77~4.27      MeV 690 708 715 676 704 658 706 715 701 697 19 0.03
 +
4.25~4.75      MeV 627 666 634 646 635 675 637 653 646 646 16 0.03
 +
4.75~5.25      MeV 558 595 594 603 606 688 582 582 566 597 38 0.07
 +
5.25~5.75      MeV 513 536 535 522 525 535 518 544 533 529 10 0.02
 +
 +
 +
 +
== Positron to Electron Ratio Prediction by Simulation ==
 +
 +
Simulation started with 13,799,743,800*(21,903,478,000/10,951,790)*(14,359,380,000/5,464,220) = 7.2528135e+16 electrons. Detected positrons are
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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=Default,Q7=3.5,D2=Default.    ||  14*46.24%  ||  209*46.24%  || 1588*46.24%  || 1717*46.24%  || 1563*46.24%  ||  1549*46.24%  ||  1517*46.24% ||    1396*46.24% ||  1223*46.24% ||1153*46.24%
 +
|-
 +
| NaIR && NaIL ||D1=Default,Q7=3.5,D2=Default.    ||  6.4736|| 96.6416|| 734.2912|| 793.9408|| 722.7312|| 716.2576|| 701.4608|| 645.5104|| 565.5152|| 533.1472
 +
|-
 +
|}
 +
 +
Positron to Electron Ratio Prediction by Simulation is:
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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=Default,Q7=3.5,D2=Default.    ||  14*46.24%  ||  209*46.24%  || 1588*46.24%  || 1717*46.24%  || 1563*46.24%  ||  1549*46.24%  ||  1517*46.24% ||    1396*46.24% ||  1223*46.24% ||1153*46.24%
 +
|-
 +
| NaIR && NaIL ||D1=Default,Q7=3.5,D2=Default.    ||  6.4736|| 96.6416|| 734.2912|| 793.9408|| 722.7312|| 716.2576|| 701.4608|| 645.5104|| 565.5152|| 533.1472
 +
|-
 +
 +
|}
 +
 +
== Wrong NaI Size ==
 +
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
| 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
 +
 +
  D1            Max Min Max Min Max Max Min Min Def
 +
  Q7            Def Def Def Def Max Min Min Def Def
 +
  D2            Max Min Def Def Def Def Def Def Def
 +
Energy
 +
0.765-1.265 MeV 12  6  1  3  5  1  1  2  6
 +
1.25 - 1.75 MeV 78  72  72  77  66  89  75  60  78
 +
1.85 - 2.35 MeV 591 580 581 576 535 630 588 535 583
 +
2.25 - 2.75 MeV 635 610 607 602 616 611 616 625 572
 +
2.75 - 3.25 MeV 597 604 605 593 586 632 589 573 577
 +
3.25 - 3.75 MeV 579 588 586 589 575 582 553 553 565
 +
3.77 - 4.27 MeV 562 491 566 563 553 564 559 550 564
 +
4.25 - 4.75 MeV 525 520 523 520 508 525 514 511 530
 +
4.75 - 5.25 MeV 469 477 482 464 455 474 451 466 464
 +
5.25 - 5.75 MeV 432 423 427 405 418 422 429 418 419
 +
 +
Energy Energy Unit                                                               average std    average std
 +
Min    Max                                                                                            dev            dev
 +
0.77 1.27 MeV 12 6 1 3 5 1 1 2 6 4.11 3.62 4 4
 +
1.25 1.75 MeV 78 72 72 77 66 89 75 60 78 74.11 8.18 74 8
 +
1.85 2.35 MeV 591 580 581 576 535 630 588 535 583 577.67 28.97 578 29
 +
2.25 2.75 MeV 635 610 607 602 616 611 616 625 572 610.44 17.46 610 17
 +
2.75 3.25 MeV 597 604 605 593 586 632 589 573 577 595.11 17.62 595 18
 +
3.25 3.75 MeV 579 588 586 589 575 582 553 553 565 574.44 14.21 574 14
 +
3.77 4.27 MeV 562 491 566 563 553 564 559 550 564 552.44 23.66 552 24
 +
4.25 4.75 MeV 525 520 523 520 508 525 514 511 530 519.56 7.23 520 7
 +
4.75 5.25 MeV 469 477 482 464 455 474 451 466 464 466.89 9.98 467 10
 +
5.25 5.75 MeV 432 423 427 405 418 422 429 418 419 421.44 7.92 421 8

Latest revision as of 07:14, 4 August 2013

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

This is to say whole simulation started with 13,799,743,800*(21,903,478,000/10,951,790)*(14,359,380,000/5,464,220) = 7.2528135e+16 electrons.

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


New Run result

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
NaIR && NaIL 12 168 1261 1237 1247 1222 1220 1147 1003 907

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]

HRRL Jul2012 pos to ele ratio 1.png

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. 27 205 1457 1689 1599 1541 1493 1355 1206 1110
NaIR && NaIL D1=Min,Q7=3.5,D2=Min. 5 162 1566 1632 1594 1512 1532 1441 1287 1159
NaIR && NaIL D1=Max,Q7=3.5,D2=Default. 6 151 1594 1629 1655 1615 1547 1371 1285 1158
NaIR && NaIL D1=Min,Q7=3.5,D2=Default. 3 186 1662 1642 1626 1540 1461 1397 1305 1128
NaIR && NaIL D1=Max,Q7=3.5+Delta_I,D2=Default. 3 183 1483 1669 1596 1530 1522 1373 1311 1135
NaIR && NaIL D1=Max,Q7=3.5-Delta_I,D2=Default. 6 198 1615 2082 1510 1625 1424 1460 1487 1156
NaIR && NaIL D1=Min,Q7=3.5-Delta_I,D2=Default. 7 280 1736 1718 1596 1553 1526 1377 1258 1120
NaIR && NaIL D1=Min,Q7=3.5+Delta_I,D2=Default. 1 186 1472 1650 1638 1525 1546 1413 1258 1177
NaIR && NaIL D1=Default,Q7=3.5,D2=Default. 14 209 1588 1717 1563 1549 1517 1396 1223 1153
NaIR && NaIL D1=Default,Q7=10,D2=Default. 3 19 117 226 420 678 842 970 842 699
NaIR && NaIL D1=Default,Q7= 0,D2=Default. 34 252 724 889 1032 1121 1221 1185 1128 1067 
After Multiplyed to detector efficiency in coincidense mode: 46.24%															
                       Max	Min	Max	Min	Max	Max	Min	Min	Def				
                       Def	Def	Def	Def	Max	Min	Min	Max	Def			percent	
                       Max	Min	Def	Def	Def	Def	Def	Def	Def	ave	std	error	
0.765~1.265     MeV	12	2	3	1	1	3	3	0	6	4	4	0.24	
1.25~1.75       MeV	95	75	70	86	85	92	129	86	97	90	17	0.15	
1.85~2.35       MeV	674	724	737	769	686	747	803	681	734	728	43	0.13	
2.25~2.75       MeV	781	755	753	759	772	963	794	763	794	793	66	0.16	
2.75~3.25       MeV	739	737	765	752	738	698	738	757	723	739	20	0.04	
3.25~3.75       MeV	713	699	747	712	707	751	718	705	716	719	18	0.04	
3.77~4.27       MeV	690	708	715	676	704	658	706	715	701	697	19	0.03	
4.25~4.75       MeV	627	666	634	646	635	675	637	653	646	646	16	0.03		
4.75~5.25       MeV	558	595	594	603	606	688	582	582	566	597	38	0.07		
5.25~5.75       MeV	513	536	535	522	525	535	518	544	533	529	10	0.02


Positron to Electron Ratio Prediction by Simulation

Simulation started with 13,799,743,800*(21,903,478,000/10,951,790)*(14,359,380,000/5,464,220) = 7.2528135e+16 electrons. Detected positrons are

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=Default,Q7=3.5,D2=Default. 14*46.24% 209*46.24% 1588*46.24% 1717*46.24% 1563*46.24% 1549*46.24% 1517*46.24% 1396*46.24% 1223*46.24% 1153*46.24%
NaIR && NaIL D1=Default,Q7=3.5,D2=Default. 6.4736 96.6416 734.2912 793.9408 722.7312 716.2576 701.4608 645.5104 565.5152 533.1472

Positron to Electron Ratio Prediction by Simulation is:

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=Default,Q7=3.5,D2=Default. 14*46.24% 209*46.24% 1588*46.24% 1717*46.24% 1563*46.24% 1549*46.24% 1517*46.24% 1396*46.24% 1223*46.24% 1153*46.24%
NaIR && NaIL D1=Default,Q7=3.5,D2=Default. 6.4736 96.6416 734.2912 793.9408 722.7312 716.2576 701.4608 645.5104 565.5152 533.1472

Wrong NaI Size

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

  D1            Max Min Max Min Max Max Min Min Def
  Q7            Def Def Def Def Max Min Min Def Def
  D2            Max Min Def Def Def Def Def Def Def
Energy
0.765-1.265 MeV 12  6   1   3   5   1   1   2   6
1.25 - 1.75 MeV 78  72  72  77  66  89  75  60  78
1.85 - 2.35 MeV 591 580 581 576 535 630 588 535 583
2.25 - 2.75 MeV 635 610 607 602 616 611 616 625 572
2.75 - 3.25 MeV 597 604 605 593 586 632 589 573 577
3.25 - 3.75 MeV 579 588 586 589 575 582 553 553 565
3.77 - 4.27 MeV 562 491 566 563 553 564 559 550 564
4.25 - 4.75 MeV 525 520 523 520 508 525 514 511 530
4.75 - 5.25 MeV 469 477 482 464 455 474 451 466 464
5.25 - 5.75 MeV 432 423 427 405 418 422 429 418 419

Energy 	Energy 	Unit 		                                                               average	std    average	std 
Min    Max                                                                                             dev             dev
0.77	1.27	MeV	12	6	1	3	5	1	1	2	6	4.11	3.62	4	4
1.25	1.75	MeV	78	72	72	77	66	89	75	60	78	74.11	8.18	74	8
1.85	2.35	MeV	591	580	581	576	535	630	588	535	583	577.67	28.97	578	29
2.25	2.75	MeV	635	610	607	602	616	611	616	625	572	610.44	17.46	610	17
2.75	3.25	MeV	597	604	605	593	586	632	589	573	577	595.11	17.62	595	18
3.25	3.75	MeV	579	588	586	589	575	582	553	553	565	574.44	14.21	574	14
3.77	4.27	MeV	562	491	566	563	553	564	559	550	564	552.44	23.66	552	24
4.25	4.75	MeV	525	520	523	520	508	525	514	511	530	519.56	7.23	520	7
4.75	5.25	MeV	469	477	482	464	455	474	451	466	464	466.89	9.98	467	10
5.25	5.75	MeV	432	423	427	405	418	422	429	418	419	421.44	7.92	421	8
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