5 Interactions of Beams with Surroundings
195
Table 5.2 Numerical values
for σ eN for an energy loss of
at least 1% and for σ pN , the
pN cross section at high
energy (p lab = 0.01–10 TeV)
Gas σ eN
σ pN
b
b
H 2
0.28 0.08
He
0.39 0.19
CH 4
3.02 0.43
H 2 O
4.38 0.40
N 2
6.47 0.56
CO
6.56 0.56
CO 2 10.7
0.87
Ar
17.8
0.60
beam pipe
γ
e
Compton
scattering
Fig. 5.3 Schematic view of the inverse Compton scattering with thermal photons. A high energy
beam particle collides and loses energy to a low energy photon radiated from the beam pipe by
black body radiation
ρ γ = 8π
kT
hc
3 ∞
0
x 2
e x − 1
dx
= 2.404
(5.5)
where T is the absolute temperature, and k,h,c the Boltzmann, Planck constants and
the speed of light. For a beam pipe at room temperature (23 ◦ C), we get a photon
density of ρ γ = 5.3 × 10 14 m −3 which is an order of magnitude higher than the
typical residual gas molecular densities ρ m , considered in this chapter for beam gas
estimates (Fig. 5.3).
The lifetime from thermal photon scattering is
τ t =
1
ρ γ c σ C
∼26 h
1
f loss
(5.6)
where ρ γ is the photon density, σ C the Compton cross section (at high energy ∼
0.665 barn) and f loss the fraction of the e ± lost after collision. Numerical values
calculated using the program described in [16] are given in Table 5.3. We can see that
thermal photon scattering at room temperature becomes only relevant for electron
beam energies above 10 GeV.