7 Particle Detectors and Detector Systems
323
The basic mathematics can be found in [85, 90, 98]. Computational models can
be found in [100]. The effective final number of transition radiation high energy
photons at the end of the radiator stack is a function of constructive and destructive
effects. See Fig. 7.32b. We will list the main effects here:
• The total radiated energy of a single surface is proportional to the plasma
frequency and thereby proportional to
√
Z of the material. Equation (7.44).
The absorption of these photons is governed by photo-electric effects and the
absorption coefficients in the stack. This goes approximately like Z 5 . The
radiator material should therefore be of low Z.
• The thickness of the radiator material, l 1 in Fig. 7.33a, must be large enough to
contain the formation zone for the required γ , but short enough not to introduce
multiple scattering effects and bremsstrahlung. The gas density will always
introduce a negative effect and should be kept as low as possible.
For a practical transition radiation radiator and following [90], the expression of
the total flux, is then represented by an integration over the emission angle and
a function which represents the incoherent addition of the single foil intensities and
includes the photon absorption in the radiator. The effective number of foils in the
radiator can then be expressed as:
N eff
1 − exp(−Nσ )
1 − exp(−σ )
(7.54)
where σ = (κρt) foil + (κρt) gas and κ, ρ and t are respectively the absorption
coefficient, density and thickness of the material. The self-absorption of the photons
from transition radiation limits the yield and N eff → 1/
1 − exp(−σ )
for N →
∞. A typical mean energy for the photons in a practical radiator is in the range
of 10 keV. See Fig. 7.32b. The spectrum will be softer for foils with lower plasma
frequencies. Since N eff in Eq. (7.54) is depending on the absorption coefficient
through the frequency of the photon, N eff will saturate for high frequencies as shown
in Fig. 7.33b.
7.5.3.3 X-ray Detectors
Any detector which has a sufficiently high efficiency for X-rays of the order of
10 keV can be used. In the design of the detector it should be noted that the number
of transition radiation photons is small and produced very close to the path of
the charged particle which will normally also traverse the detector. The traditional
detector is a MWPC-like detector, Chap. 3, which directly follows the radiator.
In order to enhance the signal-to-noise ratio and efficiently use the space as the
effective number of interfaces in the radiator will saturate, a transition radiation
detector is therefore normally many radiator/detector assemblies.
323
The basic mathematics can be found in [85, 90, 98]. Computational models can
be found in [100]. The effective final number of transition radiation high energy
photons at the end of the radiator stack is a function of constructive and destructive
effects. See Fig. 7.32b. We will list the main effects here:
• The total radiated energy of a single surface is proportional to the plasma
frequency and thereby proportional to
√
Z of the material. Equation (7.44).
The absorption of these photons is governed by photo-electric effects and the
absorption coefficients in the stack. This goes approximately like Z 5 . The
radiator material should therefore be of low Z.
• The thickness of the radiator material, l 1 in Fig. 7.33a, must be large enough to
contain the formation zone for the required γ , but short enough not to introduce
multiple scattering effects and bremsstrahlung. The gas density will always
introduce a negative effect and should be kept as low as possible.
For a practical transition radiation radiator and following [90], the expression of
the total flux, is then represented by an integration over the emission angle and
a function which represents the incoherent addition of the single foil intensities and
includes the photon absorption in the radiator. The effective number of foils in the
radiator can then be expressed as:
N eff
1 − exp(−Nσ )
1 − exp(−σ )
(7.54)
where σ = (κρt) foil + (κρt) gas and κ, ρ and t are respectively the absorption
coefficient, density and thickness of the material. The self-absorption of the photons
from transition radiation limits the yield and N eff → 1/
1 − exp(−σ )
for N →
∞. A typical mean energy for the photons in a practical radiator is in the range
of 10 keV. See Fig. 7.32b. The spectrum will be softer for foils with lower plasma
frequencies. Since N eff in Eq. (7.54) is depending on the absorption coefficient
through the frequency of the photon, N eff will saturate for high frequencies as shown
in Fig. 7.33b.
7.5.3.3 X-ray Detectors
Any detector which has a sufficiently high efficiency for X-rays of the order of
10 keV can be used. In the design of the detector it should be noted that the number
of transition radiation photons is small and produced very close to the path of
the charged particle which will normally also traverse the detector. The traditional
detector is a MWPC-like detector, Chap. 3, which directly follows the radiator.
In order to enhance the signal-to-noise ratio and efficiently use the space as the
effective number of interfaces in the radiator will saturate, a transition radiation
detector is therefore normally many radiator/detector assemblies.