Radiation emitted from charged particles travelling at relativistic speeds (v ≃ c, the speed of light) in circular orbits was first observed from a 70 MeV synchrotron at General Electric's Research Laboratory in Schenectady, New York, in 1947. The observed radiation was called synchrotron radiation (SR) due to the source. However, today this term has been generalized to be applied to radiation emitted by accelerating ultra-relativistic charged particles regardless of the actual source (synchrotron, storage ring, linear accelerator or linac etc.). There are many excellent summaries of the history of synchrotron radiation, including those found in the first chapters of the books Synchrotron Radiation – Techniques and Applications (Kunz, 1979) and Synchrotron Radiation Research (Winick & Doniach, 1980), and in a special issue of Synchrotron Radiation News (Williams & Winick, 2015). One of the more colourful summaries is the overview given at a US National Synchrotron Radiation Instrumentation Meeting in 1981 by Paul Hartman (Hartman, 1982), who along with Diron Tomboulian performed some of the pioneering work characterizing the spectral and angular properties of synchrotron radiation in the 60–450 Å range from the 300 MeV synchrotron at Cornell in 1955 (Tomboulian & Hartman, 1956).

The use of synchrotrons as a source of radiation began slowly, primarily due to the fact that the radiation from synchrotrons was particularly difficult to use because the energy of the electrons in a synchrotron is continuously varying. This situation changed in the mid-to-late 1970s when storage rings – accelerators in which the energy of the particles remains constant – began to be used as light sources. A constant electron energy means that the spectral and angular properties of the emitted radiation do not vary in time as in a synchrotron. Initially, storage-ring sources operated in a parasitic mode to high-energy physics programs (so-called first-generation sources), but soon dedicated storage-ring light sources were constructed, first using bending magnets as the source of the radiation (second-generation sources) and then being further optimized for insertion devices (third-generation sources). Third-generation sources have been superb sources of X-rays for the scientific community for the last 20 years, but there is always a demand for even better and brighter sources.

Today, accelerator physicists are developing two important concepts that will lead light sources into the 21st century, namely the design of higher brightness storage rings based on so-called multiple-bend achromat (MBA) lattices (Borland, 2014; Eriksson et al., 2014; Farvacque et al., 2013) and X-ray free-electron laser (FEL) sources using linacs (Schlichting et al., 2015; Pellegrini et al., 2016).

Before getting into the specific characterization of radiation from various sources (bending magnets, wigglers, undulators), it is useful to define the beam brightness. Brightness, an important parameter of synchrotron radiation, is defined as the number of photons radiated per second within some energy bandwidth divided by the source size and source solid angle. Knowledge of the beam brightness is important for predicting the X-ray optical performance. However, one needs to know the contributions from both the electron and photon beam to accurately calculate the X-ray beam brightness.

Brightness is often written with the following units,where Σ_x and Σ_y and Σ_x′ and Σ_y′ are the (one-sigma) source size and source divergence in the x and y transverse directions, respectively, and (ΔE/E) is the X-ray bandwidth. Here, Σ and Σ_′ have contributions from the particle beam and photon beam, i.e.

The size and divergence transverse to the propagation direction of the electron beam can be characterized by a four-dimensional phase space with coordinates x, y, x′ and y′, where x and y are the position coordinates and x′ and y′ are the angular coordinates in the horizontal and vertical planes, respectively. A phase-space representation is often used to describe the source properties.

Mono-energetic electrons, which are a good approximation for particles in a storage ring, trace a contour in phase space that is an ellipse (Banford, 1966; Wiedemann, 2015). In general, the equation for this ellipse iswhere x = x(s) and x′ = x′(s) are the transverse position and angle, respectively, in the x direction at some position s around the storage-ring circumference. There is a similar equation for y. The emittance ɛ_x and ɛ_y in the x and y directions is constant, i.e. it is not a function of the position around the storage ring. The coefficients α, β and γ are called the Twiss parameters and it is conventional to define the relations between them as follows,where . The equation for y is similar. The beta function, β(s), is a periodic function of s with a period equal to the repeat distance (i.e. the super-period) of the magnetic lattice guiding the electron beam around the storage ring. The area of an ellipse given by equation (3) is(where we have omitted the subscripts) and with the relationships between α, β and γ given above, the emittance ɛ is related to the area of the phase-space ellipse simply byWhen the β function is at a minimum [dβ_x,y(s)/ds = 0] then the one-sigma beam size and divergence can be written as(and similarly for y). This discussion is for storage rings and does not apply to free-electron lasers.

The product of the size and divergence of a photon beam is ultimately limited by the Heisenberg uncertainty principle and can be expressed aswhere λ is the radiation wavelength of interest. When X-ray sources satisfy equation (8) exactly, i.e. when Σ_xΣ_x′ = λ/4π, they are called diffraction-limited sources. Storage rings based on MBA magnetic lattices can approach the diffraction limit at vacuum ultraviolet and soft X-ray wavelengths, but in the X-ray wavelength regime the full diffraction-limit condition cannot currently be attained. Nonetheless, MBA-based lattices will be able to boost the X-ray beam brightness two to three orders of magnitude over current third-generation sources. X-ray free-electron lasers, which can be fully coherent at X-ray wavelengths, have a similar average brightness as MBA-based storage rings but with a peak brightness that is ten orders of magnitude higher due to the very short pulses (in some cases less than 10 fs) that can be realized in FELs.

Another important characterization of synchrotron radiation is its temporal properties. The electrons circulating in a storage ring are not uniformly distributed around the ring, but are grouped in packets by the radio-frequency (rf) cavities that maintain the energy of the electrons, i.e. supply the electrons with the energy that is lost through the emission of radiation. The time between packets depends on the circumference of the storage ring and the number of stable orbit points (called rf buckets) populated with electrons. Since most synchrotrons currently operate with 350–500 MHz rf systems, the minimum time between X-ray bursts is a few nanoseconds, while at large storage rings with circumferences of the order of a kilometre the time between X-ray bursts can be up to several microseconds, depending on the specific fill pattern that is being used (see chapter 9 of Brown & Moncton, 1991; Winick, 1994). The length of the packets (divided by the speed of light) determines the duration of the X-ray bursts. For storage rings this is typically of the order of 100 ps and is determined by the equilibrium length of the stored particle beam. Free-electron lasers have a much different time structure. Pulse lengths from FELs can be as short as a few femtoseconds and are derived from the short pulses that can be generated by the linac (and not lengthened by the action of a storage ring); they can be further shortened by bunch compressors. FELs based on room-temperature linacs can produce repetition rates up to about 100 Hz, while superconducting linacs can approach a MHz repetition rate. Thus, the two sources are complementary: FELs have short pulses and low(er) repetition rates, while storage-ring sources have longer pulses and typically higher repetition rates (many MHz).

Bending magnets are the magnets that keep the particles circulating in a closed orbit in a storage ring. The instantaneous horizontal and vertical divergence (or opening angle) of radiation emitted from a relativistic electron is approximately 1/γ, where γ is the ratio of the rest mass energy of the electron (m_oc²) to its total energy (E), i.e. γ = E/m_oc². (Note that this γ is not the same as the Twiss parameter.) The horizontal deflection of the electron by the bending magnet smears out the horizontal divergence, but the vertical X-ray divergence () is preserved. The emitted radiation covers a wide range of photon energies and can be characterized by the critical energy E_c, which is approximately the energy at which half of the power is emitted in photons with energies less than E_c and half above. In practical units, one can write the critical energy (in keV) aswhere E is the electron beam energy (in GeV) and B is the magnetic field in the bending magnet in Tesla.

The flux from bending magnets has traditionally been given in units of photons per second per bandwidth (usually ΔE/E = 10⁻³) per horizontal milliradian (integrated over the vertical direction). Fig. 1 shows the flux from a bending magnet at the Advanced Photon Source (APS) located at Argonne National Laboratory.

Figure 1 Vertically integrated photon flux of an APS bending magnet for a beam energy of 7 GeV, a beam current of 100 mA and a magnetic field of 0.599 T (critical energy Ec = 19.5 keV).

The on-axis radiation from a bending magnet is linearly polarized in the plane of the orbit. Elliptically polarized radiation can be obtained from a bending-magnet source by using narrow slits set slightly above or below the plane of the orbit; the radiation has opposite helicities above and below the orbit. This approach was employed early on at second-generation sources but, with the advent of third-generation sources, insertion devices specially designed to produce circular polarized X-rays are now routinely used (see Section 8).

Insertion devices (IDs), both wigglers and undulators, are composed of periodic magnetic fields that deflect the particle beam back and forth with ideally no net change in the orbital trajectory (or angle) of the beam. They are inserted in straight sections of the storage ring (see Fig. 2).

Figure 2 Top view of a portion of a typical storage ring. The bending magnets (red) and focusing magnets (quadrupoles in blue and sextupoles in yellow) are shown. Two insertion devices are located in the straight section at the far right. The light-grey walls indicate the storage-ring tunnel. The beamlines exit through the walls. The beamline in the centre is from an ID out of the picture on the left; the beamline on the right side is from the bending magnet that is shown to the right.

IDs are characterized by a parameter K, which is sometimes called the deflection parameter or field index, which is defined aswhere B₀ is the peak magnetic field in Tesla and λ_ID is the magnetic period of the insertion device in centimetres. K characterizes the motion of the particle beam in the ID. For an insertion device with the magnetic field oriented in the vertical direction, the maximum deflection x_max and maximum angular excursion of a particle passing through the ID are given bywhere γ = E/m_oc². When K ≫ 1 the insertion device is called a wiggler, and when K ≃ 1 it is called an undulator. For the vast majority of IDs today the magnetic field is oriented vertically and the Lorentz force seen by the particles causes them to undulate (wiggle) in the horizontal plane, producing only linear polarization in a narrow cone, as illustrated in Fig. 3. Insertion devices can also be nonplanar (see Section 8), in which case there will be two values of K (K_x and K_y) corresponding to the two transverse coordinates of the motion of the particle.

Figure 3 Illustration of radiation from a planar insertion device with a vertical magnetic field (the electrons oscillate in the horizontal plane). When permanent magnets are used, the strength of the peak magnetic field B0 is varied by changing the vertical gap between the magnetic arrays.

Most undulators (K ≃ 1) are made from arrays of permanent magnets, although there is a growing trend to develop superconducting magnets for short-period (<2 cm) devices. Wigglers (K ≫ 1), on the other hand, with longer magnetic periods can be fabricated with permanent-magnet or electromagnet arrays. More on the properties of radiation from insertion devices can be found in Winick & Doniach (1980), Walker (1998), Duke (2000), Onuki & Elleaume (2003), Clarke (2004) and Hofmann (2004). Experimental methods and applications are also described in Mobilio et al. (2015).

For K ≫ 1 the spectrum looks much like the continuous spectrum of a bending-magnet source with an intensity increase of 2N, where N is the number of magnetic periods in the wiggler. The spectrum from the wiggler can be characterized by the critical energy of the wiggler, which is calculated as for the bending-magnet source but replacing the magnetic field of the bending magnet with that of the wiggler. Today wigglers are primarily used as `wavelength shifters', i.e. to provide a bending-magnet-like source but with a different critical energy (or wavelength) to the bending magnets. As storage rings have steadily decreased their emittance, undulators have become the preferred IDs for high-brightness applications, since wigglers, with their large K values, substantially increase the horizontal divergence of the beam and thus reduce the beam brightness.

The characteristics of radiation from undulators have been documented by many authors. Some of the most elucidatory articles were published by K.-J. Kim (Kim, 1989, 1995). When K ≃ 1, radiation from different undulator periods will interfere coherently and produce sharp peaks at harmonics of the fundamental radiated photon energy. The energy of the nth harmonic E_n (in keV) for a planar insertion device is given bywhere E is the beam energy in GeV, θ is the observation angle away from the forward direction, n is the harmonic number and γ is the relativistic γ. Only odd harmonics are produced in the on-axis direction, whereas both even and odd harmonics are produced off-axis (the particle beam emittance will cause even harmonics in the forward observation direction, but these are much weaker and are generally not used unless n is very large).

The spectral line width (full-width at half-maximum) is approximatelywhere N is the number of undulator periods and n is the harmonic number.

The one-sigma angular size of the central cone of radiation at the harmonic energy E_n is approximately given bywhere λ_n = λ₁/n is the corresponding wavelength and L = Nλ_ID is the undulator length. Additional rings of radiation appear from higher harmonics at larger angles (from the angular dependence of the harmonic energy; equation 12), giving rise to complicated spectral angular distributions. It should be noted that the central cone is smaller by a factor of 1/(nN^1/2) compared with the characteristic bending-magnet radiation opening angle 1/γ.

Since undulators produce highly collimated X-ray beams at the harmonics, they dominate the types of IDs installed in storage rings. Fig. 4 shows an example of the angular distribution of the first harmonic of a typical undulator installed at the APS storage ring. The electron beam emittance and energy spread broaden the central cone and reduce the peak flux, which is illustrated in Fig. 4(b). This broadening becomes substantially less with the new low-emittance MBA lattices that are being developed and constructed around the world.

Figure 4 (a) Zero-emittance calculated first-harmonic angular flux density at 2.9 keV for a typical undulator with a 3.3 cm period length installed on the APS 7 GeV storage ring. (b) The same but with the APS 2.5 nm rad emittance applied using the same vertical scale. The central cone of radiation is seen in the centre, with the second- and third-order harmonics seen off-axis at large angles.

Circular or elliptical polarization can be produced by arranging magnets in both the x and y planes (with corresponding K_x and K_y values) so that the particles undulate in both planes and traverse the IDs along a circular or elliptical helical path. The first-harmonic energy is still given by equation (12) but with K²/2 replaced by K² for circular polarization when K_x = K_y. Only the first harmonic is produced in the forward direction for circular polarization, and the on-axis power density will be substantially reduced compared with that of planar IDs (high power densities are produced off-axis but can be masked off from reaching the sample and the first optical elements). This is a very attractive feature of helical undulators because the power density generated by IDs on high-energy storage rings typically exceeds hundreds of kilowatts per mrad². Although a very challenging task, current-day beamlines are constructed routinely around the world to handle such high heat loads.

Because the spectrum peaks at specific energies with much lower flux and brightness between the peaks, it is important to be able to tune (change) the peak photon energy. This is performed by changing the undulator magnetic field, i.e. changing the K value (i.e. B₀), or less commonly by changing the undulator period length (see equation 12). Typical K values in the range 0.5–3 are desirable to give a sufficient tuning range and flux/brightness. Fig. 5 shows an example of brightness-tuning curves of the first few odd harmonics for two undulators installed on the APS storage ring (superimposed on spectra computed at their minimum gaps).

Figure 5 Typical brightness spectra of two undulators with 3.3 and 2.3 cm period lengths installed on the APS 7 GeV storage ring, calculated for a gap setting of 11 mm (with K values of 2.7 and 1.2 for the U3.3 cm and U2.3 cm undulators, respectively). The dashed curves indicate the tuning curves of the (first) odd harmonics when the undulator gaps open.

For permanent magnet IDs, the K value is typically varied by changing the undulator gap (for a fixed period). Typical minimum gap values are a few millimetres for so-called in-vacuum undulators (IVUs) and are about 10 mm for in-air undulators, when space must be allowed for the particle beam vacuum chamber. For electromagnetic undulators (including superconducting undulators; SCUs), the K value is changed by changing the current in the main coil windings.

The accessible range of K values is of the utmost importance since it determines the photon energy tuning range (for a fixed undulator period length and beam energy). Generally, one wants to make the period length as short as possible and yet maintain sufficiently large K values to reach the desired harmonic energies. The photon flux increases linearly with the number of periods N, so the shorter the period, the higher the flux (for a fixed undulator length). It is helpful to keep this in mind because newer technologies such as cryogenically cooled magnets and superconducting undulators push towards shorter and shorter period lengths.

The majority of research at high-energy storage rings (above 6 GeV) uses photon energies in the range ∼1–100 keV. At medium-energy storage rings (3 GeV), energies are typically in the range ∼0.1–20 keV. However, there has been a remarkable amount of progress in improving the undulator magnetic field quality (through very precise mechanical designs and magnetic shimming and advancements in magnet and pole materials), so very high harmonics are frequently used to extend the photon energy range coverage at medium-energy storage rings. Undulator period lengths are typically ∼15–40 mm and lengths are usually between 2 and 5 m. Conventional electromagnetic IDs extend the commonly used period lengths to ∼10 cm and above.

Beyond planar IDs, the most common undulators are the elliptically polarizing undulators for the generation of X-rays with a variety of polarizations (left- and right-handed circular polarization, elliptical and linear in any inclination). The most commonly used device around the world is the so-called APPLE undulator with four moveable magnet arrays invented by Sasaki. A few different variations of the original design have been developed, but the most common type is the second version, APPLE-II (Sasaki, 1994). A newer variation, in which the magnetization direction of the magnet blocks is inclined by 45° relative to the vertical, can accommodate round beam-vacuum chambers, which may be important for MBA-based or FEL light sources (Bahrdt et al., 2004).

Another more recent development for full polarization control and small round beam-vacuum chambers is the DELTA undulator, which also consists of four moveable arrays made of pure permanent magnets (PPMs). It was installed and successfully commissioned as the last undulator segment at the Linac Coherent Light Source at the SLAC National Accelerator Laboratory at Stanford (Nuhn et al., 2015).

Fast helicity switching of circularly polarized X-rays is important for probing electronic and magnetic phenomena in materials using the technique of magnetic circular dichroism. However, fast switching is not feasible for large mechanical moving parts; instead, it may be achieved by fast switching of the magnetic field in an electromagnetic undulator (Jaski et al., 2013) or by switching of the particle beam trajectory through two end-to-end undulators with different helicities so that the photons traveling down the beamline are produced alternately by each undulator (Matsuba et al., 2009). Research and development are still ongoing in this area.

Revolver undulators have been built in which each jaw is equipped with two or three magnet arrays with different period lengths on a revolving mechanism. The user can select whichever period length is most suitable for their experiment of the moment and have it revolve into the `beam' position. This is a very cost-effective and practical way to extend the range of energy coverage within the footprint of a single undulator.

As mentioned earlier, the quest for short-period undulators for higher brightness has continued. Two recent developments have emerged: (i) the cryogenic cooling of permanent magnets and (ii) the use of superconducting magnet technology. The cryogenic technology takes advantage of the enhancement of the remanent field and the increase in the intrinsic coercivity of commonly used permanent-magnet materials at low temperatures. A higher remanent field correlates directly with a higher K value and hence a larger photon energy tuning range, and a higher intrinsic coercivity is associated with higher resistance to radiation-induced demagnetization (a very important factor for cryogenic permanent-magnet undulators and in-vacuum undulators operating at very small gaps of a few millimetres). For articles on recent technologies, see Moog (2011), Tanaka (2015), Bahrdt & Ivanyushenkov (2013), Couprie (2013) and Huang et al. (2016).

The advancement of superconducting undulator technology has paved the way for the development and installation of superconducting undulators (SCUs) in storage rings (Ivanyushenkov et al., 2015; Ivanyushenkov, Harkay et al., 2017; Casalbuoni et al., 2016). It has been demonstrated that stable storage-ring operation without quenching the SCUs is feasible. To date these SCUs have been planar devices, with the exception of one helical SCU, which is now operational in a storage ring (Kasa et al., 2018). The development of superconducting devices with full polarization control is also ongoing and will open up the possibility of rapid helicity switching by using two end-to-end helical SCUs (Ivanyushenkov et al., 2016; Ivanyushenkov, Fuerst et al., 2017). All currently operating SCUs installed at storage rings have been fabricated with NbTi superconducting wires. There is a push for even higher on-axis magnetic fields for enhanced brightness and X-ray energy tuning range. Substantial progress in the realization of such devices has recently been made at different laboratories using Nb₃Sn superconducting wires for enhanced performance (Kesgin et al., 2019).

Traditionally, IDs installed in storage rings have had the main magnetic field oriented vertically. For future light sources with ultra-small emittances, the particle beam-vacuum chamber may be nearly round and an ID with a horizontal main magnetic field is feasible. Such a device has been built and tested (Strelnikov et al., 2017) for use on a hard X-ray beamline at the upgraded Linac Coherent Light Source (LCLS-II). The polarization direction of the emitted radiation is in the vertical plane, which simplifies the experimental setup (monochromators bounce the photon beam in the horizontal plane instead of the vertical plane). Further, the ID drive mechanism can become more compact by using dynamic spring compensation of the attractive forces between magnet arrays instead of relying on a massive strongback. Series production of these devices is now ongoing for the LCLS-II project (Leitner et al., 2019).

Another special device is the quasiperiodic undulator. It is common practice to use higher harmonics to extend the available photon energy range; thus, higher harmonics are desirable. However, in certain experiments harmonics will cause degradation of the signal. It is not feasible to completely eliminate the higher harmonics from an undulator (including helical undulators), but one can shift the energies of the higher harmonics either up or down by manipulating the magnetic field of some of the poles in a quasiperiodic pattern (Onuki & Elleaume, 2003). This idea was extended to the development of the so-called `APPLE-Knot' undulator, which also has the additional feature of reducing the on-axis power density in linear polarization modes (Ji et al., 2015).

A summary of novel undulator designs with enhanced radiation performance and capabilities can be found in a special issue of Synchrotron Radiation News (Schlueter, 2018).

Synchrotron radiation from third-generation light sources has flourished due to significant advances in the technology of insertion devices during the past 20 years. However, looking forwards, the next big leap will come from advances in accelerator magnet technology, paving the way for the next-generation storage rings: MBA-based storage rings with ultra-small emittance. Although the effect of the beam emittance and beam energy spread on the spectral angular radiation distributions is not important for bending-magnet sources, it has a strong impact for undulator sources.

The radiation will approach the diffraction limit in the X-ray regime (1 Å) for the proposed upgrades of high-energy storage rings, in both horizontal and vertical planes, resulting in an increase in brightness and coherent flux by two to three orders of magnitude. The flux increase is less impressive (∼2–3 times), but for an X-ray beam focused to a very small spot size the brightness helps to increase the flux.

For an overview of the next-generation sources and their potential impact on science, see Weckert (2015). As an example, Fig. 6 shows a brightness comparison of the proposed MBA-lattice-based storage ring (APS Upgrade, APS-U) to the present-day APS. Similar impressive brightness gains are expected at other MBA storage rings around the world.

Figure 6 Brightness tuning-curve comparisons of the present APS and the APS-U after upgrade to a fourth-generation storage ring. The brightness envelope of all currently installed IDs of the present APS are shown. A special 1.72 cm period undulator (4.8 m long) gives rise to the sharp increase at 23.7 keV and SCUs (1.8 cm period, 1.1 m long) dominate above 60 keV. The gap in energy coverage between the first and third harmonics for the APS-U can be closed by choosing an undulator with a slightly larger period length. U2.5 cm indicates a permanent-magnet undulator with a period length of 2.5 cm (4.8 m long) and SCU1.7 cm an undulator with a period length of 1.7 cm (3.6 m long). (All future APS-U storage-ring and device parameters are subject to change.)