1 X-Ray Sources at Large-Scale Facilities
9
While the electron contribution can be minimized by sophisticated electron optics
(see Sect. 1.4), the photon emittance is an intrinsic property defined by Heisenberg’s
uncertainty principle, and is equal to λ/4π in both the x- and y-plane. In thirdgeneration storage rings, the electron emittance in the orbital plane
e
x dominates the
total emittance and is thus the limiting factor for the brilliance. In fourth-generation
DLSRs, the benchmark for modern storage ring designs,
e
x has been reduced to values
close to or even below (in the case of soft X-rays) the intrinsic photon emittance,
which we consider in detail in Sect. 1.4. In other words, the emittance is no longer
limited by the electron optics, but by the fundamental optical diffraction limit. This
is the meaning of the moniker ‘diffraction-limited storage ring’ defining the fourthgeneration synchrotron facilities now coming online.
Synchrotrons have brilliances using modern undulators of approximately 10
22 photons s
−1 mrad
2 mm
−2 0.1% bandwidth
−1 . This is some 12 orders of magnitude higher
than that of a standard laboratory-based Cu K α source and less than a factor of 100
lower than high-quality visible laser sources. The main reasons for this are the size
of the radiation source, of the order of ten micrometres at fourth-generation DLSRs,
the high collimation of the beams, being of the order of 10 µrad in the orbital plane
and the fact that synchrotrons emit an enormous amount of light. The power emitted
by an electron is proportional to the square of the electron’s centripetal acceleration
a, and the fourth power of the storage ring energy.
1.2.5 The Radio-Frequency Power Supply
Conservation of energy dictates that the kinetic energy of the electrons is dissipated
due to emission of radiation at the bending magnets and insertion devices. This
energy must be replenished, or otherwise, the electrons would spiral into the inner
wall of the storage ring. This is achieved by boosting the electrons’ energy at one or
more positions along the storage ring as they pass through RF cavities [Fig. 1.6a].
This requires that the electrons enter the cavity at a certain point of the RF cycle.
Because the electrons can only receive the correct amount of energy at very
specific and narrowly defined values in the RF cycle, they are separated into a series
of packets, or ‘bunches’. The energy loss of the electrons for each cycle around the
ring is given by the total power loss of the storage ring divided by the storage ring
current and is equal to approximately 0.2–1 MeV, or of the order of 0.05% of the
nominal electron energy. Depending on the size of the facility, most storage rings
host between two and eight RF cavities. Between them, they must be able to replenish
this loss.
Consider Fig. 1.6b. On average, the electrons require a certain energy boost in
order to keep them on a stable path, given by an amount eV ref . If an electron loses
more than this amount of energy, it will enter the RF cavity somewhat earlier at
point A. This might sound counterintuitive—surely if the electron has less energy, it
will be slower and enter the cavity later. But because it takes a shorter path in the bends
according to the linear dependence of the bending radius and the electron energy it
9
While the electron contribution can be minimized by sophisticated electron optics
(see Sect. 1.4), the photon emittance is an intrinsic property defined by Heisenberg’s
uncertainty principle, and is equal to λ/4π in both the x- and y-plane. In thirdgeneration storage rings, the electron emittance in the orbital plane
e
x dominates the
total emittance and is thus the limiting factor for the brilliance. In fourth-generation
DLSRs, the benchmark for modern storage ring designs,
e
x has been reduced to values
close to or even below (in the case of soft X-rays) the intrinsic photon emittance,
which we consider in detail in Sect. 1.4. In other words, the emittance is no longer
limited by the electron optics, but by the fundamental optical diffraction limit. This
is the meaning of the moniker ‘diffraction-limited storage ring’ defining the fourthgeneration synchrotron facilities now coming online.
Synchrotrons have brilliances using modern undulators of approximately 10
22 photons s
−1 mrad
2 mm
−2 0.1% bandwidth
−1 . This is some 12 orders of magnitude higher
than that of a standard laboratory-based Cu K α source and less than a factor of 100
lower than high-quality visible laser sources. The main reasons for this are the size
of the radiation source, of the order of ten micrometres at fourth-generation DLSRs,
the high collimation of the beams, being of the order of 10 µrad in the orbital plane
and the fact that synchrotrons emit an enormous amount of light. The power emitted
by an electron is proportional to the square of the electron’s centripetal acceleration
a, and the fourth power of the storage ring energy.
1.2.5 The Radio-Frequency Power Supply
Conservation of energy dictates that the kinetic energy of the electrons is dissipated
due to emission of radiation at the bending magnets and insertion devices. This
energy must be replenished, or otherwise, the electrons would spiral into the inner
wall of the storage ring. This is achieved by boosting the electrons’ energy at one or
more positions along the storage ring as they pass through RF cavities [Fig. 1.6a].
This requires that the electrons enter the cavity at a certain point of the RF cycle.
Because the electrons can only receive the correct amount of energy at very
specific and narrowly defined values in the RF cycle, they are separated into a series
of packets, or ‘bunches’. The energy loss of the electrons for each cycle around the
ring is given by the total power loss of the storage ring divided by the storage ring
current and is equal to approximately 0.2–1 MeV, or of the order of 0.05% of the
nominal electron energy. Depending on the size of the facility, most storage rings
host between two and eight RF cavities. Between them, they must be able to replenish
this loss.
Consider Fig. 1.6b. On average, the electrons require a certain energy boost in
order to keep them on a stable path, given by an amount eV ref . If an electron loses
more than this amount of energy, it will enter the RF cavity somewhat earlier at
point A. This might sound counterintuitive—surely if the electron has less energy, it
will be slower and enter the cavity later. But because it takes a shorter path in the bends
according to the linear dependence of the bending radius and the electron energy it