free electron lasers 157
Analysis of a high-gain curve such as the one shown in
Fig. 8.18 helps us to determine an optimal length of the undulator for a particular FEL design.
8.6 FEL designs and properties
We will now review typical accelerator parameters, requirements and radiation characteristics of modern FELs.
8.6.1 FEL beam emittance requirements
As we have determined in Chapter 3, the emittance of a synchrotron radiation photon beam is given by Eq. 3.33 and is
equal to
λ
ε ph = 4π
It is intuitive to assume that efficient generation of FEL radiation (the term, lasing, is often used) requires a fair amount
of overlap between the electron and the photon beam.
The geometrical emittance of an electron beam needed for
efficient lasing, therefore, needs to be smaller than the one for
the photon beam. Thus,
λ
ε ≤
(8.33)
4π
or in terms of the normalized emittance:
λ
ε N ≤ γ
(8.34)
4π
As an example, for λ = 0.2 nm and γ = 3
the required normalized emittance is 0 5 m
· 10 4 (≈ 15 GeV),
.
m mrad, which
results in a necessity to use a very bright
≤
electron
·
source. We
can also note that the requirement for geometrical emittance
can be eased for higher energy electron beams since, during
acceleration, the geometrical emittance decreases in inverse
proportion to the beam energy.
An important clarification of the above emittance requirement relates to the concept of slice emittance. As we discussed
above, radiation slips with respect to the electron beam by λ
for every λ u . Even if the undulator is 100 m long, for any reasonable undulator period (e.g., λ u 1 cm) and wavelength
≈
(assume λ ≈ 0.1 nm), the total slippage will be around 1 μm.
A typical electron bunch is usually much longer. Therefore,
only a small longitudinal fraction of the bunch contributes
to a particular spatial portion of generated radiation. The requirement for the emittance defined above in Eq. 8.33 is thus
applicable to the slice that is generating this portion of the
radiation.
Analysis of a high-gain curve such as the one shown in
Fig. 8.18 helps us to determine an optimal length of the undulator for a particular FEL design.
8.6 FEL designs and properties
We will now review typical accelerator parameters, requirements and radiation characteristics of modern FELs.
8.6.1 FEL beam emittance requirements
As we have determined in Chapter 3, the emittance of a synchrotron radiation photon beam is given by Eq. 3.33 and is
equal to
λ
ε ph = 4π
It is intuitive to assume that efficient generation of FEL radiation (the term, lasing, is often used) requires a fair amount
of overlap between the electron and the photon beam.
The geometrical emittance of an electron beam needed for
efficient lasing, therefore, needs to be smaller than the one for
the photon beam. Thus,
λ
ε ≤
(8.33)
4π
or in terms of the normalized emittance:
λ
ε N ≤ γ
(8.34)
4π
As an example, for λ = 0.2 nm and γ = 3
the required normalized emittance is 0 5 m
· 10 4 (≈ 15 GeV),
.
m mrad, which
results in a necessity to use a very bright
≤
electron
·
source. We
can also note that the requirement for geometrical emittance
can be eased for higher energy electron beams since, during
acceleration, the geometrical emittance decreases in inverse
proportion to the beam energy.
An important clarification of the above emittance requirement relates to the concept of slice emittance. As we discussed
above, radiation slips with respect to the electron beam by λ
for every λ u . Even if the undulator is 100 m long, for any reasonable undulator period (e.g., λ u 1 cm) and wavelength
≈
(assume λ ≈ 0.1 nm), the total slippage will be around 1 μm.
A typical electron bunch is usually much longer. Therefore,
only a small longitudinal fraction of the bunch contributes
to a particular spatial portion of generated radiation. The requirement for the emittance defined above in Eq. 8.33 is thus
applicable to the slice that is generating this portion of the
radiation.