synchrotron radiation 51
3.3 SR features
Performance of SR-based light sources depends on spatial
and spectral characteristics of synchrotron radiation. Below
we will introduce basic relevant characteristics, leaving detailed discussion for Chapter 7.
3.3.1 Emittance of single radiated photon
In order to discuss the ultimate brightness of the SR-based
light sources, we require knowledge of the emittance of a single photon radiated from the curved beamline.
To answer this question we must first evaluate the size of
the emitting region seen by the remote observer in the case of
a single electron, as illustrated in Fig. 3.6.
2
2
R
γ
σ ≈
FIGURE 3.6
For illustration of emittance of a single photon.
We first note that the angles of photons coming from the
emitting region are spread over σ ' ≈ 1/γ. The size of the emitting region is given by the height of the arc segment and is
thus equal to σ ≈ R/(2γ 2 ).
The estimate for the emittance of an SR photon emitted
by a single electron can therefore be written as
R
ε ph = σ σ
'
⇒ ε ph ≈ 2γ 3
(3.31)
(In a similar way as above, one can estimate beta function of
photons as β = σ/σ ' .)
Let’s rewrite the photon emittance equation using the expression for photon wavelength
2π c c γ 3
λ c
ω c =
≈
⇒ ε ph ≈
(3.32)
λ c
R
4π
We can see here that the emittance of synchrotron radiation
is directly related to its wavelength. This is not a coincidence
3.3 SR features
Performance of SR-based light sources depends on spatial
and spectral characteristics of synchrotron radiation. Below
we will introduce basic relevant characteristics, leaving detailed discussion for Chapter 7.
3.3.1 Emittance of single radiated photon
In order to discuss the ultimate brightness of the SR-based
light sources, we require knowledge of the emittance of a single photon radiated from the curved beamline.
To answer this question we must first evaluate the size of
the emitting region seen by the remote observer in the case of
a single electron, as illustrated in Fig. 3.6.
2
2
R
γ
σ ≈
FIGURE 3.6
For illustration of emittance of a single photon.
We first note that the angles of photons coming from the
emitting region are spread over σ ' ≈ 1/γ. The size of the emitting region is given by the height of the arc segment and is
thus equal to σ ≈ R/(2γ 2 ).
The estimate for the emittance of an SR photon emitted
by a single electron can therefore be written as
R
ε ph = σ σ
'
⇒ ε ph ≈ 2γ 3
(3.31)
(In a similar way as above, one can estimate beta function of
photons as β = σ/σ ' .)
Let’s rewrite the photon emittance equation using the expression for photon wavelength
2π c c γ 3
λ c
ω c =
≈
⇒ ε ph ≈
(3.32)
λ c
R
4π
We can see here that the emittance of synchrotron radiation
is directly related to its wavelength. This is not a coincidence