Difference between revisions of "Calculation of radiation yield"

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<math>\eta = \rho/(\rho+2)</math>;
 
<math>\eta = \rho/(\rho+2)</math>;
  
<math>L = 2 ln(\frac{(E_0-1)^{\frac{1}{2}}+[\eta(E_0+1)^{\frac{1}{2}}}{(E_0-1)^{\frac{1}{2}}-[\eta(E_0+1)^{\frac{1}{2}}]})</math>
+
<math>L = 2 ln(\frac{(E_0-1)^{\frac{1}{2}}+[\eta(E_0+1)^{\frac{1}{2}}]}{(E_0-1)^{\frac{1}{2}}-[\eta(E_0+1)^{\frac{1}{2}}]})</math>

Revision as of 20:04, 8 May 2008

The number of photons per MeV per incident electron per [math]g/cm^2[/math] of radiator (Z,A) is given by [*]:

[math]\frac{d^2n}{d\kappa dt} = \frac{3.495 \times 10^{-4}}{A\kappa}[Z^2\Phi_n(Z,E_0,k)+Z\Phi_e(Z,E_0,k)](MeV^{-1}g^{-1}cm^2)[/math],

where [math]\kappa[/math] - photon kinetic energy in MeV;

[math]E_0[/math] - incident electron total energy (in units of the electron rest mass);

[math]k[/math] - incident photon energy (in units of the electron rest mass);

[math]\Phi_e(Z,E_0,k) = C_B\{2[1-\frac{2E}{3E_0}+(\frac{E}{E})^2][L-\sqrt{\eta}]+\sqrt{\eta}[1-\frac{L^2}{2\rho}-\frac{1}{\rho^2}(\frac{1}{2}L-[\frac{\rho(\rho+2)(E_0+1)}{E_0-1}]^{\frac{1}{2}})^2]\}[/math];

[math]E = E_0 - k[/math];

[math]\rho = E_0 -k(1+E_0-\sqrt{E^2 - 1})[/math];

[math]\eta = \rho/(\rho+2)[/math];

[math]L = 2 ln(\frac{(E_0-1)^{\frac{1}{2}}+[\eta(E_0+1)^{\frac{1}{2}}]}{(E_0-1)^{\frac{1}{2}}-[\eta(E_0+1)^{\frac{1}{2}}]})[/math]