Difference between revisions of "Pair Production Rate in Pair Spectrometer"

Latest revision as of 23:33, 29 January 2011

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-==LINAC parameters used in calculations==
-) pulse width 50 ps <br>
-) pulse current 50 A <br>
-) repetition rate 300 Hz <br>
-) energy 44 MeV <br><br>
-==Number of electrons/sec on radiator==
-<math> 50\ \frac{C}{sec} \times \frac{1\cdot e^-}{1.6\cdot 10^{-19}\ C} \times 50\ \mbox{ps} \times  300\ \mbox{Hz} = 0.47 \cdot 10^{13}\ \frac{e^-}{sec}</math><br><br>
-==Number of photons/sec out of radiator==
-#<math>\sigma_{brems}=0.1\ \mbox{photons/electrons/MeV/r.l}</math>
-#<math>\mbox{r.l.(Ti)} = 3.59\ \mbox{cm}</math>
-#<math>\mbox{radiator}\ \mbox{thickness} = 12.5\ \mu m</math>
- <math>\frac{12.5\ \mu m}{3.59\ cm} = 3.48 \cdot 10^{-4}\ r.l.</math><br>
- <math>0.47 \cdot 10^{13} \frac{e^-}{sec} \times 0.1\ \frac{\gamma 's}{(e^- \cdot MeV \cdot r.l.)} \times 3.48 \cdot 10^{-4}\ r.l. \times 10\ MeV =1.63 \cdot 10^{9} \frac{\gamma}{sec}</math><br><br>
-'''Alex factor is 6.85 %'''
- <math>1.63 \cdot 10^{9} \frac{\gamma}{sec} \cdot 6.85\ % = 1.12 \cdot 10^{8} \frac{\gamma}{sec}</math><br><br>
-==Pair production rate==
-===out of Al converter===
- <math>\sigma_{pairs} = 0.5\ \frac{\mbox{barns}}{\mbox{atom}}</math>
- <math>l = 3.0\ \mu m</math> (by varying width we can vary the yield)
- <math>N_{Al} = \frac{2.70\ \frac{g}{cm^3} \times 6.02 \cdot 10^{23}\ \frac{atoms}{mol} \times 3.0\ \mu m} {26.98\ \frac{g}{mol}} = 1.81 \cdot 10^{23}\ \frac{\mbox{atoms}}{m^2}</math>
- <math>\frac {1.12 \cdot 10^{8}\ \frac{\gamma}{sec} \times \sigma_{pairs} \times N_{Al}} {f} = 3.38\ \frac{\mbox{pairs}}{\mbox{pulse}} </math>
-===through 1 m of air ===
-Assume air consists entirely from Nitrogen:
- <math>\sigma_{pairs}\ (\mbox{Nitrogen}) = 0.15\ \frac{\mbox{barns}}{\mbox{atom}}</math>
- <math>l = 1.0\ \mbox{m}</math>
- <math>N_{\mbox{Nitrogen}} = \frac{0.00125\ \frac{g}{cm^3} \times 6.02 \cdot 10^{23}\ \frac{atoms}{mol} \times 1.0\ \mbox{m}} {14.01\ \frac{g}{mol}} = 5.37 \cdot 10^{25}\ \frac{\mbox{atoms}}{m^2}</math>
- <math>\frac {1.12 \cdot 10^{8}\ \frac{\gamma}{sec} \times \sigma_{pairs} \times N_{Al}} {f} = 300\ \frac{\mbox{pairs}}{\mbox{pulse}} </math>
-==Appendix==
-===pair production cross sections in an Al target===
-'''Ref.''' ''Geant4 and Theoretical Pair Production Cross Sections for 1 MeV - 100 GeV photons in Aluminum. Vakho Makarashvili, December 18, 2007''
-[[File:pair_production_Al.png | 800 px]]
-===pair production cross sections in a Nitrogen===
-'''Ref.''' ''Photon Cross Section, Attenuation Coefficients, and Energy Absorption Coefficients From 10 keV to 100 Gev. J.H.Hubbell. Center for Radiation Research.National Bureau of Standards. Washington, D.C. 20234''
-[[File:pair_prodiction_nitrogen.png | 800 px]]
-Here I just plotted the table above for pair production cross section in (0, 40) MeV energy region
-[[File:Sigma nitrogen fitted m2.png | 800 px]]
 [http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]

Difference between revisions of "Pair Production Rate in Pair Spectrometer"

Latest revision as of 23:33, 29 January 2011

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