1 X-Ray Sources at Large-Scale Facilities
11
p’ = p − dp dp
p"
< θ
h/λ
p
radiation
at magnet(s)
dp
θ
RF cavity
Δ
(b)
(a)
reference path
oscillations
initial orbit
for E < 0
photon emission
energy loss
Fig. 1.7 Radiation equilibrium between quantum excitation and radiation damping. a Radiation
damping. An electron traversing a magnet in an insertion device is made to deviate from the central
axis by an angle θ, due to the Lorentz force. Emission of a photon with momentum h/λ =
will be in the direction of the electron at that instant in time. Conservation of momentum dictates
that the electron’s momentum will be reduced to p = p − h/λ. The same electron will regain this
momentum loss d p after travelling through the RF cavity; importantly, this will now be parallel
to the central axis, thus reducing the angle of the electron’s momentum p to the central axis and
hence also the electron beam’s emittance. b Quantum excitation. An electron loses energy due to
the emission of a photon and begins to oscillate around a new reference orbital path with a smaller
radius. These oscillations induce a stochastic distribution of transverse momenta, thereby increasing
the emittance. Reproduced from [3] with permission (Copyright 2019, John Wiley and Sons)
late around a new reference orbit, thus broadening the beam and thereby increasing
the emittance [Fig. 1.7b]. Moreover, the dispersion of the electron beam increases.
Quantum excitation can be reduced by designing the magnet lattice so that the electron energy dispersion is minimized at the main locations of radiation, namely the
bending magnets. This is achieved by horizontal focusing at the bends and the use
of many small deflection angle bends in multibend achromat lattices (see Sect. 1.4)
to limit dispersion growth.
1.2.7 Coherence
We now consider coherence, including both longitudinal and transverse coherence.
The latter depends on the source size and divergence of the photon beam, in other
words, it depends on the emittance; longitudinal coherence depends on the bandwidth. The coherent fraction of a beam is critically important in lensless imaging
techniques and photon correlation spectroscopy, plus also in phase-contrast tomography. Note also that bound up in the figure of merit of brilliance are the above
parameters that quantitatively define coherence: the emittance and the relative spectral BW. Figure 1.8 provides a schematic summary of coherence. Brilliance really
does encompass the most important qualities of synchrotron light; because however,
it combines flux, spatial coherence and longitudinal coherence, it is important to
11
p’ = p − dp dp
p"
< θ
h/λ
p
radiation
at magnet(s)
dp
θ
RF cavity
Δ
(b)
(a)
reference path
oscillations
initial orbit
for E < 0
photon emission
energy loss
Fig. 1.7 Radiation equilibrium between quantum excitation and radiation damping. a Radiation
damping. An electron traversing a magnet in an insertion device is made to deviate from the central
axis by an angle θ, due to the Lorentz force. Emission of a photon with momentum h/λ =
will be in the direction of the electron at that instant in time. Conservation of momentum dictates
that the electron’s momentum will be reduced to p = p − h/λ. The same electron will regain this
momentum loss d p after travelling through the RF cavity; importantly, this will now be parallel
to the central axis, thus reducing the angle of the electron’s momentum p to the central axis and
hence also the electron beam’s emittance. b Quantum excitation. An electron loses energy due to
the emission of a photon and begins to oscillate around a new reference orbital path with a smaller
radius. These oscillations induce a stochastic distribution of transverse momenta, thereby increasing
the emittance. Reproduced from [3] with permission (Copyright 2019, John Wiley and Sons)
late around a new reference orbit, thus broadening the beam and thereby increasing
the emittance [Fig. 1.7b]. Moreover, the dispersion of the electron beam increases.
Quantum excitation can be reduced by designing the magnet lattice so that the electron energy dispersion is minimized at the main locations of radiation, namely the
bending magnets. This is achieved by horizontal focusing at the bends and the use
of many small deflection angle bends in multibend achromat lattices (see Sect. 1.4)
to limit dispersion growth.
1.2.7 Coherence
We now consider coherence, including both longitudinal and transverse coherence.
The latter depends on the source size and divergence of the photon beam, in other
words, it depends on the emittance; longitudinal coherence depends on the bandwidth. The coherent fraction of a beam is critically important in lensless imaging
techniques and photon correlation spectroscopy, plus also in phase-contrast tomography. Note also that bound up in the figure of merit of brilliance are the above
parameters that quantitatively define coherence: the emittance and the relative spectral BW. Figure 1.8 provides a schematic summary of coherence. Brilliance really
does encompass the most important qualities of synchrotron light; because however,
it combines flux, spatial coherence and longitudinal coherence, it is important to