674
M. Dohlus et al.
It is interesting to note that N γ is typically about 100, i.e. it is a rather small
number, although the photon number spectrum diverges for ω → 0, see Eq. (11.29)
and Fig. 11.7.
The mean photon energy is given by
ε γ
=
8
15
√
3
c .
(11.31)
The considerable granularity in the emission process has quite some impact on
the electron beam parameters in electron storage rings [5].
11.1.1.3 Simple Means of Changing the Emission Spectrum
Users often don’t appreciate the spectrum of synchrotron radiation, either because
of its large frequency width or because it might not contain sufficiently high
frequencies for the particular application. In the latter case, the most straight forward
solution would be making use of the strong γ -dependence of Eqs. (11.24) and
(11.26) and increasing the electron energy. However, there are often considerable
technical limitations in this respect, in particular at electron storage rings operating
in the GeV regime.
Wavelength Shifters
As the synchrotron radiation spectrum is normalized to the critical frequency
ω c , according to Eq. (11.18) the spectrum can also be hardened by increasing
the magnetic field strength, thus reducing the bending radius ρ. To this end,
often superconducting magnets are applied. In order to restrict the subsequent
modification of the electron beam’s design orbit to a small section of the storage
ring, a sequence of dipole magnets is frequently used with zero net deflection
angle. Such an arrangement is called wavelength shifter. The radiation properties
are determined in the same way as for ordinary synchrotron radiation. Beyond
hardening the spectrum and increasing the flux, there is also some advantage in
terms of flexibility in the geometrical arrangement of radiation beam lines.
Short-Magnet Radiation, Edge Radiation
When discussing the characteristic time profile of synchrotron radiation it was
assumed in the context of Figs. 11.4 and 11.5 that the electron would propagate in
the magnetic field for sufficiently long time such that the radiation cone passes the
observer’s aperture in its entire angular extension of ±1/γ . To this end, the dipole
magnet must have a length of at least
Δl c ≈ cΔt
≈
2ρ
γ
≈
2m 0 c
eB
.
(11.32)
For electrons and magnetic fields in the B ≈ 1 T range, this results in a few
millimeters, which would be of little relevance in most cases. However, if B is
M. Dohlus et al.
It is interesting to note that N γ is typically about 100, i.e. it is a rather small
number, although the photon number spectrum diverges for ω → 0, see Eq. (11.29)
and Fig. 11.7.
The mean photon energy is given by
ε γ
=
8
15
√
3
c .
(11.31)
The considerable granularity in the emission process has quite some impact on
the electron beam parameters in electron storage rings [5].
11.1.1.3 Simple Means of Changing the Emission Spectrum
Users often don’t appreciate the spectrum of synchrotron radiation, either because
of its large frequency width or because it might not contain sufficiently high
frequencies for the particular application. In the latter case, the most straight forward
solution would be making use of the strong γ -dependence of Eqs. (11.24) and
(11.26) and increasing the electron energy. However, there are often considerable
technical limitations in this respect, in particular at electron storage rings operating
in the GeV regime.
Wavelength Shifters
As the synchrotron radiation spectrum is normalized to the critical frequency
ω c , according to Eq. (11.18) the spectrum can also be hardened by increasing
the magnetic field strength, thus reducing the bending radius ρ. To this end,
often superconducting magnets are applied. In order to restrict the subsequent
modification of the electron beam’s design orbit to a small section of the storage
ring, a sequence of dipole magnets is frequently used with zero net deflection
angle. Such an arrangement is called wavelength shifter. The radiation properties
are determined in the same way as for ordinary synchrotron radiation. Beyond
hardening the spectrum and increasing the flux, there is also some advantage in
terms of flexibility in the geometrical arrangement of radiation beam lines.
Short-Magnet Radiation, Edge Radiation
When discussing the characteristic time profile of synchrotron radiation it was
assumed in the context of Figs. 11.4 and 11.5 that the electron would propagate in
the magnetic field for sufficiently long time such that the radiation cone passes the
observer’s aperture in its entire angular extension of ±1/γ . To this end, the dipole
magnet must have a length of at least
Δl c ≈ cΔt
≈
2ρ
γ
≈
2m 0 c
eB
.
(11.32)
For electrons and magnetic fields in the B ≈ 1 T range, this results in a few
millimeters, which would be of little relevance in most cases. However, if B is