11 Application of Accelerators and Storage Rings
673
Fig. 11.7 Normalized power spectrum see Eq. (11.27) (solid line) and photon number spectrum
(broken line) of synchrotron radiation
Photon Distribution
Sometimes it is necessary to pay attention to the fact that synchrotron radiation is
emitted, as any electromagnetic radiation, in quanta (photons) of energy ε γ =
where is Planck’s constant. The spectral angular photon flux can be obtained from
Eq. (11.24), dividing by
d 2 N γ
dd dε γ /ε γ
=
d 2 W
dd dω
.
(11.28)
Equation (11.28) calculates the number of photons N γ emitted per unit solid
angle into a relative photon energy interval dε γ /ε γ . Again it is noted that this
quantity refers to a single turn in the synchrotron.
The angular-integrated spectral photon spectrum corresponding to Eq. (11.26)
can be expressed in the form
dN γ
dω
=
√
3αγ
ω c
∞
ω/ω c
K 5/3 (x)dx,
(11.29)
with the fine structure constant α = 1/137.036. This spectrum is also depicted in
Fig. 11.7.
Integrating Eq. (11.29) over all frequencies yields the total number N γ of photons
emitted per electron per turn in the synchrotron:
N γ =
5π
√
3
αγ .
(11.30)