Absorption of transition radiation photons

 The emission of X-rays from the radiator has to be matched to the absorption method used for the detection. If the ionisation of a gas is used for detection, the frequency response is rather limited with a high Z gas like Xe as the optimal choice. The absorption length for photons in the gas scales is approximately proportional to $\omega^{3}_{}$ in the range below 1 MeV where the photoelectric effect is dominant. Hence it is impossible for a practical gaseous detector to detect X-rays above 20 keV. The absorption length is defined as the length where a factor 1 - e ^{- 1} of the radiation is absorbed.

In fig. 3.7 is shown the absorption length for a pure xenon gas, the gas mixture chosen for the ATLAS TRT, polypropylene and Kapton. The absorption in a polypropylene radiator can be found by scaling the values for solid polypropylene with the air/foil proportion in the radiator.

  

Figure 3.7: The absorption length for photons in xenon, the ATLAS TRT gas, Kapton and a polypropylene (PP) at standard temperature and pressure.

For high photon energies (above 20 keV) the detection efficiency is low as the photons pass straight through the detection gas; for low photon energies (below a few keV) the efficiency is low as well as most transition radiation photons are absorbed inside the radiator or in the walls surrounding the detection gas. Those two constraints define an optimal photon energy, $\omega_{gas}^{}$ , for detection.

The foil thickness l₁ in a N-foil radiator can be adjusted to make the maximal output correspond to $\omega_{gas}^{}$ . In fig. 3.5 is shown that the maximum output is around $\nu$ = 1/$\pi$ . Using (3.18) and (3.21)

 

$${\frac{2 \pi \omega_{gas}}{{\omega_{{P}_1}'}^2}}$$ (65)