Number of electron-positron pairs/sec out of Al converte
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]\displaystyle{ 50\ \frac{Coulomb}{sec} \times \frac{1\cdot e^-}{1.6\cdot 10^{-19}C} \times 50ps \times 300Hz = 4.68 \cdot 10^{12} \frac{e^-}{sec} }[/math]
Number of photons/sec out of radiator
[math]\displaystyle{ \sigma_{brems}=0.1 photons/electrons/MeV/r.l }[/math]
r.l.(Ti) = 3.59 cm
radiator thickness = 12.5 [math]\displaystyle{ \mu m }[/math]
[math]\displaystyle{ \frac{12.5\ \mu m}{3.59\ cm} = 3.48 \cdot 10^{-4} \ r.l. }[/math]
[math]\displaystyle{ 0.1\ \frac{\gamma 's}{(e^- \cdot MeV \cdot r.l.)} \times 3.48 \cdot 10^{-4} r.l. \times 10\ MeV \times 0.47 \cdot 10^{13} \frac{e^-}{sec}=1.63 \cdot 10^{9} \frac{\gamma}{sec} }[/math]
Alex factor is 6.85 %
[math]\displaystyle{ 1.64 \cdot 10^{9} \frac{\gamma}{sec} \cdot 6.85\ % = 1.12 \cdot 10^{8} \frac{\gamma}{sec} }[/math]
Number of electron/positron pairs/sec out of Al converter
[math]\displaystyle{ \sigma_{pairs} = 0.5 }[/math]
[math]\displaystyle{ l = 0.01 \mu m }[/math] (by varying width we can vary the yield)
[math]\displaystyle{ N_{Al} = \frac{2.375 \frac{g}{cm^3} \times 6.02 \cdot 10^{23} \frac{1}{mol} \times l} {26.98 \frac{g}{mol}} = 5.30 \cdot 10^{20} \frac{atoms}{m^2} }[/math]
[math]\displaystyle{ \frac {1.12 \cdot 10^{8} \frac{\gamma}{sec} \times \sigma_{pairs} \times N_{Al}} {f} = 2.96 \blank \frac{pairs}{pulse} }[/math]