1 Historical Developments and Future Perspectives …
11
Fig. 1.2 Schematics of an insertion device. Top panel: side view of the alternating dipole magnets
(red: north pole, blue: south pole) with the electron beam traveling in the center with λ u the magnetic
period and gap the magnetic gap of the undulator. Bottom panel: top view of the sinusoidal electron
movement due to the alternating magnetic field. The amplitude is not to scale and is in the order of
microns
with B 0 the peak magnetic field and λ u the magnetic period. The particle will then
oscillate with the amplitude
y(x) =
K
γ 2π/λ u
cos (
2π
λ u
· x),
(1.20)
with K =
ecB 0 λ u
2πmc 2 the so called deflection or strength parameter. For K 1 the insertion
device is called a wiggler and for K 1 an undulator. The (magnetic field) strength
can be varied by changing the magnetic gap height, which in turn will change the K
value and eventually the wavelengths (energies) of the SR spectrum.
Nowadays, mainly undulators will be used, which allows one to optimize the
photon beam quality such as its brilliance, energy spectrum, signal-to-noise ratio or
to provide special chracteristics such as dedicated (elliptical, circular) polarizations.
For the various harmonics k of an undulator the dependence on K and λ u can be
expressed in photon wavelengths λ as:
λ k =
λ u
2γ 2 k
1 +
1
2
K
2
+ γ
2
Θ
2
,
(1.21)
and in photon energies ε as:
ε k =
4π cγ
2 k
λ u
1 +
1
2
K 2 + γ 2 Θ 2
.
(1.22)
In this paragraph we could only mention those quantities, which are most important with respect to NRS experiments. There exist a waste amount of literature, which
treats all aspects of SR, such as the review work by Wiedemann [24] with references
therein.
11
Fig. 1.2 Schematics of an insertion device. Top panel: side view of the alternating dipole magnets
(red: north pole, blue: south pole) with the electron beam traveling in the center with λ u the magnetic
period and gap the magnetic gap of the undulator. Bottom panel: top view of the sinusoidal electron
movement due to the alternating magnetic field. The amplitude is not to scale and is in the order of
microns
with B 0 the peak magnetic field and λ u the magnetic period. The particle will then
oscillate with the amplitude
y(x) =
K
γ 2π/λ u
cos (
2π
λ u
· x),
(1.20)
with K =
ecB 0 λ u
2πmc 2 the so called deflection or strength parameter. For K 1 the insertion
device is called a wiggler and for K 1 an undulator. The (magnetic field) strength
can be varied by changing the magnetic gap height, which in turn will change the K
value and eventually the wavelengths (energies) of the SR spectrum.
Nowadays, mainly undulators will be used, which allows one to optimize the
photon beam quality such as its brilliance, energy spectrum, signal-to-noise ratio or
to provide special chracteristics such as dedicated (elliptical, circular) polarizations.
For the various harmonics k of an undulator the dependence on K and λ u can be
expressed in photon wavelengths λ as:
λ k =
λ u
2γ 2 k
1 +
1
2
K
2
+ γ
2
Θ
2
,
(1.21)
and in photon energies ε as:
ε k =
4π cγ
2 k
λ u
1 +
1
2
K 2 + γ 2 Θ 2
.
(1.22)
In this paragraph we could only mention those quantities, which are most important with respect to NRS experiments. There exist a waste amount of literature, which
treats all aspects of SR, such as the review work by Wiedemann [24] with references
therein.