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2011-01-29T23:30:45Z

Created page with '[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] ==LINAC parameters used in calculations== 1) pulse width 50 ps 2) pulse current 50…'

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==LINAC parameters used in calculations==
1) pulse width 50 ps 
2) pulse current 50 A 
3) repetition rate 300 Hz 
4) energy 44 MeV 

==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> 

==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> 

<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> 

'''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> 

==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]

← Older revision		Revision as of 23:33, 29 January 2011
Line 1:		Line 1:
−	~~[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]~~
−
−	~~==LINAC parameters used in calculations==~~
−	~~1) pulse width 50 ps <br>~~
−	~~2) pulse current 50 A <br>~~
−	~~3) repetition rate 300 Hz <br>~~
−	~~4) 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]		[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]

Pair Production Rate in Pair Spectrometer - Revision history

Shaproma: Replaced content with '[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]'

Shaproma: Created page with '[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] ==LINAC parameters used in calculations== 1) pulse width 50 ps 2) pulse current 50…'

Shaproma: Created page with '[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] ==LINAC parameters used in calculations== 1) pulse width 50 ps
2) pulse current 50…'