around 10 keV (1.24 Å) for diffraction studies. The light produced is in the form of a
flattened cone at a tangent to the curved path of the electrons and with a fan angle
equal to the angular change in the path of the electrons around the curve. As the
critical energy is proportional to the magnetic field strength, higher photon energies
can be achieved through the use of a ‘superbend’ where a conventional bending
magnet (which will typically have a field of around 1 Tesla) is replaced by a
superconducting magnet (which can have a strength in excess of 4–5 Tesla). In
this manner, the radiated power output can be amplified by a factor of 20 or more
with the critical energy increased by a multiple of about 5 with flux and brightness
gains of around an order of magnitude [31, 32].
The transition from second-generation to third-generation synchrotron light
sources was accomplished once storage rings were designed with long straight
sections to accommodate insertion devices, which are alternating magnetic arrays
placed above and below the electron beam. Some second-generation sources were
later adapted to take ‘insertion devices’; however, it was not until the advent of thirdgeneration sources that most X-ray diffraction beamlines took advantage of insertion
devices, which come in two main flavours: wigglers and undulators. All insertion
devices manipulate the electron beam so that it oscillates in the horizontal plane by
being placed through a periodically alternating magnetic field which is aligned
orthogonally to the path of the beam. If the oscillating excursions of the electron
beam are larger than the radiation cones emitted from each ‘wiggle’, then the
intensities of each period in the oscillation are added, and the device is called a
wiggler. The magnets in a wiggler are often superconducting with field strengths on
the order of 2–5 Tesla. The resulting spectrum is smoothly varying with a high
characteristic energy and with a photon flux commensurate with the number of
magnetic poles used in the device.
In an undulator, the magnetic fields are smaller; hence, the excursions are much
gentler; the radiation cones emitted from each oscillation overlap in such a manner
that there is an interference effect. In this instance, the amplitudes are added (taking
into account the phase difference from each contributing cone), and the sum for each
contribution, or period, along the undulator is squared to produce the intensity. The
intensity peaks at energies where the interference is constructive to produce a
spectrum that is characterised by relatively sharp harmonic peaks. The magnets,
usually powerful permanent magnets (with a strength of about 1 Tesla), are held in
jaws placed parallel either side of the electron beam. The energies of the harmonics
can be tuned by varying the gap between the jaws (that is the strength of the magnetic
field felt by the electron beam) so that a range of energies are available by a
combination of adjusting the undulator gap and hopping to a different harmonic.
As the oscillation of the electron beam within the undulator is relatively shallow, the
X-ray beam has an extremely small divergence in comparison to either a bending
magnet or a wiggler.
With the advent of third-generation synchrotron sources, crystallography
beamlines now tend to be based on undulator sources, as the low divergence, high
flux X-ray beams are ideal for the monochromatic methods of diffraction. The
continuous, smooth, spectrum of a bending magnet or wiggler source can also be
78
S. J. Coles et al.
flattened cone at a tangent to the curved path of the electrons and with a fan angle
equal to the angular change in the path of the electrons around the curve. As the
critical energy is proportional to the magnetic field strength, higher photon energies
can be achieved through the use of a ‘superbend’ where a conventional bending
magnet (which will typically have a field of around 1 Tesla) is replaced by a
superconducting magnet (which can have a strength in excess of 4–5 Tesla). In
this manner, the radiated power output can be amplified by a factor of 20 or more
with the critical energy increased by a multiple of about 5 with flux and brightness
gains of around an order of magnitude [31, 32].
The transition from second-generation to third-generation synchrotron light
sources was accomplished once storage rings were designed with long straight
sections to accommodate insertion devices, which are alternating magnetic arrays
placed above and below the electron beam. Some second-generation sources were
later adapted to take ‘insertion devices’; however, it was not until the advent of thirdgeneration sources that most X-ray diffraction beamlines took advantage of insertion
devices, which come in two main flavours: wigglers and undulators. All insertion
devices manipulate the electron beam so that it oscillates in the horizontal plane by
being placed through a periodically alternating magnetic field which is aligned
orthogonally to the path of the beam. If the oscillating excursions of the electron
beam are larger than the radiation cones emitted from each ‘wiggle’, then the
intensities of each period in the oscillation are added, and the device is called a
wiggler. The magnets in a wiggler are often superconducting with field strengths on
the order of 2–5 Tesla. The resulting spectrum is smoothly varying with a high
characteristic energy and with a photon flux commensurate with the number of
magnetic poles used in the device.
In an undulator, the magnetic fields are smaller; hence, the excursions are much
gentler; the radiation cones emitted from each oscillation overlap in such a manner
that there is an interference effect. In this instance, the amplitudes are added (taking
into account the phase difference from each contributing cone), and the sum for each
contribution, or period, along the undulator is squared to produce the intensity. The
intensity peaks at energies where the interference is constructive to produce a
spectrum that is characterised by relatively sharp harmonic peaks. The magnets,
usually powerful permanent magnets (with a strength of about 1 Tesla), are held in
jaws placed parallel either side of the electron beam. The energies of the harmonics
can be tuned by varying the gap between the jaws (that is the strength of the magnetic
field felt by the electron beam) so that a range of energies are available by a
combination of adjusting the undulator gap and hopping to a different harmonic.
As the oscillation of the electron beam within the undulator is relatively shallow, the
X-ray beam has an extremely small divergence in comparison to either a bending
magnet or a wiggler.
With the advent of third-generation synchrotron sources, crystallography
beamlines now tend to be based on undulator sources, as the low divergence, high
flux X-ray beams are ideal for the monochromatic methods of diffraction. The
continuous, smooth, spectrum of a bending magnet or wiggler source can also be
78
S. J. Coles et al.