54 unifying physics of accelerators, lasers and plasma
Since the lowest photon emittance depends on the photon
wavelength (Eq. 3.33), the smallest overall emittance will be
obtained when:
ε e = σ e σ e ' ≤ ε ph
(3.38)
which corresponds to a diffraction-limited source.
In modern SR sources, the typical radiation of interest
spans from 100 eV to 100 keV in terms of photon energy. Let’s
o
take an example of 12.4 keV of photon energy which correWavelength λ ≈ 1 A corre sponds to ε
8 pm. For typical third-generation SR light
sponds to 12.4 keV photons.
ph
sources, the horizontal
≈
emittance ε x is usually between 1 and
5 nm and the vertical emittance ε y between 1 and 40 pm.
Thus, such rings are close, in terms of its emittance, to the ultimate performance in the vertical plane. However, they are
many orders of magnitude away from the diffraction-limited
emittance in the horizontal plane. We will discuss the questions of brilliance in closer detail in Chapter 7, which is dedicated to light sources.
3.3.5 Wiggler and undulator radiation
Let’s consider radiation from a sequence of bends, and in particular, let’s assume that the bends are arranged in a sequence
with + − + − +− polarity with a period of λ u , so that the trajectory of the particle wiggles as shown in Fig. 3.9.
FIGURE 3.9
Radiation from sequence of bends.
An external observer will see photons emitted by the particle during its travel along the arc 2R/γ. Let’s now define the
parameter K as the ratio of the wiggling period to the length
of this arc:
K ∼ γ λ u /R
(3.39)
We can qualitatively see that if 2R/γ « λ u /2, then the
radiation emitted at each wiggle is independent. This corresponds to K » 1 and is called the wiggler regime.
On the other hand, if 2R/γ » λ u /2, then we are in a
regime where the entire wiggling trajectory contributes to radiation (therefore interference leads to coherence of radiation,
Since the lowest photon emittance depends on the photon
wavelength (Eq. 3.33), the smallest overall emittance will be
obtained when:
ε e = σ e σ e ' ≤ ε ph
(3.38)
which corresponds to a diffraction-limited source.
In modern SR sources, the typical radiation of interest
spans from 100 eV to 100 keV in terms of photon energy. Let’s
o
take an example of 12.4 keV of photon energy which correWavelength λ ≈ 1 A corre sponds to ε
8 pm. For typical third-generation SR light
sponds to 12.4 keV photons.
ph
sources, the horizontal
≈
emittance ε x is usually between 1 and
5 nm and the vertical emittance ε y between 1 and 40 pm.
Thus, such rings are close, in terms of its emittance, to the ultimate performance in the vertical plane. However, they are
many orders of magnitude away from the diffraction-limited
emittance in the horizontal plane. We will discuss the questions of brilliance in closer detail in Chapter 7, which is dedicated to light sources.
3.3.5 Wiggler and undulator radiation
Let’s consider radiation from a sequence of bends, and in particular, let’s assume that the bends are arranged in a sequence
with + − + − +− polarity with a period of λ u , so that the trajectory of the particle wiggles as shown in Fig. 3.9.
FIGURE 3.9
Radiation from sequence of bends.
An external observer will see photons emitted by the particle during its travel along the arc 2R/γ. Let’s now define the
parameter K as the ratio of the wiggling period to the length
of this arc:
K ∼ γ λ u /R
(3.39)
We can qualitatively see that if 2R/γ « λ u /2, then the
radiation emitted at each wiggle is independent. This corresponds to K » 1 and is called the wiggler regime.
On the other hand, if 2R/γ » λ u /2, then we are in a
regime where the entire wiggling trajectory contributes to radiation (therefore interference leads to coherence of radiation,