52 unifying physics of accelerators, lasers and plasma
in a single example, but is actually an inherent property of
photon radiation:
λ
ε ph =
(3.33)
4π
This, together with information about the SR spectrum in the
next section, will bring us to discuss the brightness of SR light
sources.
3.3.2 SR spectrum
In all the estimations above, we assumed that the photons
emitted are monoenergetic. It is not exactly the case, and in
reality the energy of the photons will be distributed around
the characteristic frequency of the SR photons ω c .
Accurate mathematics, which we do not show here, predicts that the SR spectrum looks like the one shown in
Fig. 3.7.
FIGURE 3.7
SR spectrum and its approximations for low (curve a — behaves
as 4/3 · x 1/3 ) and high (curve b — behaves as 7/9 · x 1/2 e −x )
energies.
We can indeed see that a large fraction of the photons will
have energies close to ω c . However, there is also a lower energy tail, as well as some fraction of higher energy photons.
It is also natural to expect that the photons’ angular distribution will deviate from the 1/γ rule, and indeed, the lower
energy photons typically have larger angular spread.
3.3.3 Brightness or brilliance
Following discussion of the SR spectrum, we can introduce
the notion of bandwidth — the interval of interest in the spectrum of photon frequencies. This bandwidth is denoted here
BW and is expressed, typically, in %.
Let’s assume that our photon beam is emitted from the
in a single example, but is actually an inherent property of
photon radiation:
λ
ε ph =
(3.33)
4π
This, together with information about the SR spectrum in the
next section, will bring us to discuss the brightness of SR light
sources.
3.3.2 SR spectrum
In all the estimations above, we assumed that the photons
emitted are monoenergetic. It is not exactly the case, and in
reality the energy of the photons will be distributed around
the characteristic frequency of the SR photons ω c .
Accurate mathematics, which we do not show here, predicts that the SR spectrum looks like the one shown in
Fig. 3.7.
FIGURE 3.7
SR spectrum and its approximations for low (curve a — behaves
as 4/3 · x 1/3 ) and high (curve b — behaves as 7/9 · x 1/2 e −x )
energies.
We can indeed see that a large fraction of the photons will
have energies close to ω c . However, there is also a lower energy tail, as well as some fraction of higher energy photons.
It is also natural to expect that the photons’ angular distribution will deviate from the 1/γ rule, and indeed, the lower
energy photons typically have larger angular spread.
3.3.3 Brightness or brilliance
Following discussion of the SR spectrum, we can introduce
the notion of bandwidth — the interval of interest in the spectrum of photon frequencies. This bandwidth is denoted here
BW and is expressed, typically, in %.
Let’s assume that our photon beam is emitted from the