InternationalCrystallography of biological macromoleculesTables for Crystallography Volume F Edited by E. Arnold, D. M. Himmel and M. G. Rossmann © International Union of Crystallography 2012 |
International Tables for Crystallography (2012). Vol. F, ch. 8.1, pp. 189-190
## Section 8.1.2. The physics of SR |

The physics of the SR source spectral emission was predicted by Iwanenko & Pomeranchuk (1944) and Blewett (1946), and was fully described by Schwinger (1949). It is `universal' to all machines of this type, *i.e.*, wherever charged particles such as electrons (or positrons) travel in a curved orbit under the influence of a magnetic field, and are therefore subject to centripetal acceleration. At a speed very near the speed of light, the relativistic particle emission is concentrated into a tight, forward radiation cone angle. There is a continuum of Doppler-shifted frequencies from the orbital frequency up to a cutoff. The radiation is also essentially plane-polarized in the orbit plane. However, in high-energy physics machines, the beam used in target or colliding-beam experiments would be somewhat unstable; thus, while pioneering experiments ensued through the 1970s, a considerable appetite was stimulated for machines dedicated to SR with stable source position, for fine focusing onto small samples such as crystals and single fibres, and with a long beam lifetime for more challenging data collection. Crystallography has been both an instigator and major beneficiary of these developments through the 1970s and 1980s onwards. An example of a machine lattice (the ESRF) is shown in Fig. 8.1.2.1.

The properties of synchrotron radiation can be described in terms of the well defined quantities of high flux (a large number of photons), high angular brightness (also well collimated), high spectral brightness (also a small source size and well collimated), tunable, polarized, defined time structure (fine time resolution) and exactly calculable spectra. The precise definition of the spectral brightness isCare needs to be exercised to check precisely the definition in use (Mills *et al.*, 2005). The mrad^{2} term refers to the radiation solid angle delivered from the source, and the mm^{2} term to the source cross-sectional area. Mills *et al*. (2005) concluded that the units given in equation (8.1.2.1), which do not follow the SI code for units, are so ensconced in the field `that a drive to change this would only lead to more confusion rather than more clarity in the descriptions of synchrotron-radiation sources'. At the ESRF the term brilliance is firmly ensconced in house and with its large user community, and so is the label for the *y* axes used in Fig 8.1.2.2.

Another useful term is the machine emittance, . This is an invariant for a given machine lattice and electron/positron machine energy. It is the product of the divergence angle, σ′, and the source size, σ: The horizontal and vertical emittances need to be considered separately.

The total radiated power, *Q* (kW), is expressed in terms of the machine energy, *E* (GeV), the radius of curvature of the orbiting electron/positron beam, ρ (m), and the circulating current, *I* (A), as The opening half-angle of the synchrotron radiation is and is determined by the electron rest energy, , and the machine energy, *E*: The basic spectral distribution is characterized by the universal curve of synchrotron radiation, which is the number of photons per s per A per GeV per horizontal opening in mrad per 1% integrated over the vertical opening angle, plotted versus . Here the critical wavelength, , is given by again with ρ in m and *E* in GeV. Examples of SR spectral curves are shown in Fig. 8.1.2.2(*a*). The peak photon flux occurs close to , the useful flux extends to about , and exactly half of the total power radiated is above the critical wavelength and half is below this value.

In the plane of the orbit, the beam is essentially 100% plane polarized. This is what one would expect if the electron orbit was visualized edge-on. Away from the plane of the orbit there is a significant (several per cent) perpendicular component of polarization. Schiltz & Bricogne (2009) advocated definitions to use in the analysis of polarization-dependent phenomena that are instrument-independent and completely general. They have implemented these methods in the macromolecular phasing program *SHARP* for exploiting the polarization anisotropy of anomalous scattering in protein crystals.

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