Synchrotron radiation sources

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Radiat. Phys. Chem. Vol. 45, No. 3, pp. 315-331, 1995 Elsevier Science Ltd. Printed in Great Britain

Pergamon

S Y N C H R O T R O N R A D I A T I O N SOURCES N. MARKS SERC, Daresbury Laboratory, Warrington WA4 4AD, U.K. Abstract--Synchrotrons and storage rings were first built to provide high energy particle beams for nuclear physics. When electrons were accelerated to relativistic energies, they radiated copious quantities of electromagnetic radiation, known as synchrotron radiation; because of the broad spectrum and other properties, it was realised that this radiation was also a valuable research tool for a wide range of disciplines. The paper gives details of the properties of the radiation emitted from different sources and describes the accelerator physics and technology of a modern synchrotron source.

INTRODUCTION

This article is intended as an introduction to synchrotron sources, and the radiation that they generate. In particular, it sets out to describe the nature and characteristics of the radiation and the source properties of the emitting electron beams. This is related to the theoretical and practical issues encountered in the design of the accelerators. The paper commences with a historic review of the development of synchrotron sources; during this section a number of concepts that will be described in greater detail in later sections are introduced. The properties of the radiation are then discussed and the quantitative expressions for the spectral intensities from various types of source are given. Finally, the detailed structure of a synchrotron source is described, together with a description of the dynamics of the electron beam in the accelerator. As the article reviews a subject that has developed over 30 years in many national and international laboratories around the world, it is not practical to cite the original paper for each detailed development mentioned. Reference is therefore made at the end of the chapter to a general review publication that provides greater detail of the subject and which the reader will find useful for more advanced study.

H I S T O R I C A L PERSPECTIVE

The invention of the cyclotron and, subsequently, the synchrotron led, during the middle years of this century, to the rapid development of nuclear and fundamental particle physics. Much of this work was accomplished using beams of high energy protons, and proton synchrotrons of ever increasing diameter and energy were constructed, culminating in the SPS at the CERN Laboratory (Geneva) and other large accelerators in the U.S.A. and U.S.S.R. There was,

however, also a role for electron accelerators to explore the electromagnetic interaction at subatomic dimensions, and in a number of European and American laboratories, rings to accelerate electrons to multi GeV (109 eV) energies were constructed. The same basic principles were behind both the proton and electron synchrotron; radio frequency fields generated in resonant cavity structures located on the fixed particle trajectory provided the means of increasing the particle energy, whilst electromagnets placed around the constant radius orbit defined the trajectory. The strength of the magnetic field was then increased during the acceleration process so as to remain proportional to the momentum of the accelerated particles. There was, however, a fundamental difference in the design of proton and electron machines above about 1 GeV, for, at these higher energies, the electron is ultra relativistic and radiates substantial amounts of power when following a curved path in a magnetic field. This emission, called "synchrotron radiation", is given off tangentially by the electrons and hence is emitted into a 360° fan around the circumference of the synchrotron. The resulting loss of energy was a major problem for the designers of high energy electron machines, for it was the major factor determining the rating o f the radio frequency accelerating system and, for a given project budget, set the limit of achievable energy. In the early 1960s, at a number of European and U.S.A. laboratories that were operating electron synchrotrons for high energy physics, it was realized that the synchrotron radiation itself had the potential for being a valuable research tool. This was due to a number of particular features of the radiation: (1) it has a broad, smooth, spectrum extending from the infrared (IR), through the visible and ultraviolet (UV) and, depending on the energy of the electrons and the dipole field of the source, into the X-ray region;

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(2) its amplitude peaks at the high energy end of this spectrum, where it is highly collimated in the vertical plane, and provides X-ray intensities that are, over a broad spectrum, orders of magnitude greater than those available from conventional sources; (3) the radiation is linearly polarized in the plane of the accelerator, with elliptical polarization off axis; and (4) the radiation has a high frequency time structure imposed by the radio frequency accelerating voltage in the accelerator; in some circumstances, short pulses at lower frequencies can be generated, permitting unique opportunities for time resolved research. Synchrotron radiation therefore attracted scientists from disciplines concerned with what could loosely be termed molecular and atomic rather than sub-nuclear phenomena. This interest rapidly spread from physics based disciplines into chemistry and, later, into materials, life, earth and medical sciences. In response to this demand, facilities to make use of the radiation started to appear world wide at laboratories with electron synchrotrons. Initially, these were added to existing accelerator complexes and the research programmes were parasitic on high energy physics schedules. Later, purpose built, dedicated sources began to be funded and built. These were designed as "storage rings" synchrotron type machines that maintained constant electron energy with static magnetic fields for many hours and kept the same circulating electron beam during that time. During the 1970s, the number of researchers using synchrotron radiation grew rapidly. There was increasing demand for the source to be designed to provide radiation of specified intensity and optical properties in a particular part of the spectrum; the designers of the new dedicated storage ring sources were no longer constrained by the compromises inherent in parasitic sources and hence could work to meet these specific requirements. The radiation spectrum is uniquely determined by the electron energy and the bending magnetic field, higher energies and fields providing spectra extending to shorter wavelengths. Another crucial factor is the design of the "lattice" of bending and focusing magnets in the synchrotron source, for this determines the size and divergence of the circulating electron beam and hence the optical properties of the emitted radiation. The builders of the new dedicated rings could now take account of these considerations during the synchrotron design and the source could be tailored to meet the needs of the proposed experimental programme. A further major development in both parasitic and dedicated sources was the introduction of "insertion device" magnets. These are additional magnetic elements that are placed in the straight sections of sources to stimulate the emission of radiation with particular properties. Whilst there are various types

of insertion magnet, they all have regions of alternating magnetic field giving zero transverse field integral along their full length. This is essential to ensure that the electron beam suffers no net displacement or deflection between entering and leaving the device. They therefore produce an oscillating electron beam trajectory and are known as "wigglers" and "undulators". The former are high field magnets thai generate radiation at wavelengths similar to or shorter than that available from the synchrotron's bending magnets. They usually have a low (odd) number of pole-pairs and their role is to generate photons for experiments working at energies above those served by the bending magnets. In an extreme case, a single central very high field pole with two correcting half poles creates a wiggler known also as a "wavelength shifter" Undulators have large numbers of pole-pairs generating moderate fields; they have the opposite role to wigglers, for. by causing interference between radiation from the different dipoles, they produce narrow band emission at selected wavelengths that are usually within the spectrum generated by the bending magnets; the reward, however, is a substantial increase in intensity at those wavelengths compared with the emission from an ordinary bending magnet. A fuller description of the nature of the radiation emitted by wigglers and undulators is given below. It was soon realized that if the use of insertion devices was to be optimized, the inclusion of such elements placed additional requirements on the design of a dedicated synchrotron source; minimum electron beam cross section was best at the positions of the wigglers, with small electron beam divergence at the undulators. Of great significance to the experimental programme using either bending or insertion magnets was the "brightness" or "brilliance" of the source. The formal definition and significance of these quantities will be covered later; they relate to the number of photons per second, within a given spectral bandwidth, that are emitted into a specified phase space. Brightness and brilliance are maximized by designing for a high electron circulating current with minimal beam cross section and angular divergence. During the 1980s, therefore, storage ring lattice designers developed increasingly well optimised arrangements of bending and focusing magnets to provide high brightness with the required space for wiggler and undulator straights. This work was accompanied by analyses that established realistic goals for electron beam intensities and the theoretical limits to the dimensional optimisations, thus providing criteria against which any synchrotron source design could be judged. The current "state of the art" synchrotron source is therefore a dedicated, high brightness storage ring with a large number of beam lines supplying radiation simultaneously to an extensive complex of experiments. A high percentage of these beam lines will emanate from wigglers and undulators, each

Synchrotron radiation sources

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Fig. 1. Aerial view of the European Synchrotron Radiation Facility (ESRF) complex at Grenoble, France. The storage ring and experimental area are housed in the torroidal shaped building, whilst the smaller booster synchrotron and associated linear accelerator that feed electrons to the main ring a few times a day can be seen inside this ring. device "tuned" to provide the particular wavelength or intensity characteristic required by the experimenter. To house the insertion magnets, the synchrotron will have m a n y long straights between arcs of the dipole

bending magnets, and families of quadrupole and sextupole magnets will be positioned in straight and arc sections to tightly focus and control the electron beam dimensions. Such "third generation" machines

Fig. 2. A schematic diagram showing the layout of the Daresbury Synchrotron Radiation Source (SRS) and its associated experimental area.

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with energies of the order of 1.5-2.0 GeV, to serve the UV and soft X-ray experimental community, are now being constructed in the U.S.A. and elsewhere. More ambitious projects, to build larger sources with energies up to 8 GeV for hard X-ray beams, are underway in the U.S.A. and Japan, whilst in France a 6 GeV source, the European Synchrotron Radiation Facility (ESRF), has been constructed, with successful operation achieved in late 1992. Figure 1 shows an aerial view of the new laboratory at the ESRF, Grenoble, whilst in Fig. 2 a schematic diagram shows the layout of the Synchrotron Radiation Source (SRS) storage ring and experimental area at the Daresbury Laboratory, a facility that has now been operational for over 10 years. In spite of all the present activity, it appears that the demand for synchrotron radiation. for fundamental and applied research across the spectrum from ultra-violet to hard X-rays. still outstrips supply. SYNCHROTRON RADIATION--GENERATION AND PROPERTIES

The radiation emitted by a relativistic electron when traversing a magnetic field can be understood from purely classical considerations. Whilst the ex-

periments will usually analyse the interaction between sample material and radiation in terms of photon effects, and the effect of radiation emission on the circulating electron beam is also partially dependent on quantum processes, the spectrum and intensity of the radiation emitted by both bending magnets and insertion devices are predicted by classical physics. The electron beam in the synchrotron is circulating at a certain orbital frequency, the centripetal acceleration being provided by the fields of the bending magnets. It might therefore be expected that the beam would emit radiation at the orbital frequency, with an instantaneous distribution given by the standard textbook dipole double lobe in the plane of the orbit. If this were the case, radiation would be given off equally in the forward and backward direction. However, because of the relativistic nature of the electron beam, both the frequency and spacial distribution of the emitted radiation are radically altered. The single dipole emission line is strongly broadened, extending to frequencies many orders of magnitude greater than the electron rotational frequency. In principle, the spectrum is made up of a train of lines which are harmonics of the fundamental orbital frequency (usually of the order of a few mega-hertz). At optical frequencies and higher, these are so close that small

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Visible Fig. 3. The radiation spectrum from the 1.2 T dipole bending magnets and the 5 T superconducting wiggler magnet of the Daresbury SRS when operating at 2 GeV with I00 mA of circulating electron beam. The diagram shows the parts of the spectrum in optical nomenclature and indicates the range of wavelengths used by the differenl experimental techniques associated with synchrotron radiation. The SRS normally operates with an electron beam current of between 100 and 250 mA

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Synchrotron radiation sources differences in the energies and orbits of individual electrons result in the spectrum becoming a continuum. The amplitude peak is shifted to the short wavelength end of this spectrum by a factor of the order of 1/7 3, where ~ is the relativistic energy parameter of the circulating electrons:

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where E ' is the total energy of the electron; and E0 is its rest energy (0.511 MeV for electrons). It should be appreciated that in almost all cases of practical synchrotron sources ~ exceeds 10 3, whilst in the largest facilities ~, is greater than 104. A typical spectrum therefore extends from the radio frequencies and peaks in the X-ray region, as shown in Fig. 3. The spatial distribution is also radically modified, with the lobes of the radiation being concentrated into a narrow cone in the forward direction. The angle of this cone is a function of wavelength, but is of the order of 1/7 at short wavelengths. As the electron beam sweeps out the path of the curved orbit, a continuous fan of radiation results in the horizontal plane; the distribution of the radiation in the vertical plane, however, is determined by this narrow cone.

Emission spectrum from dipole and wiggler magnets The exact spectrum from a dipole field is a function of the electron energy, the beam current and the

bending magnetic field in the accelerator. A universal spectrum that describes the radiation from all simple dipole field sources is shown in Fig. 4. This gives the number of photons per s, per mrad (horizontal)/mA/ GeV of the electron beam within an 0.1% wavelength bandwidth, integrated over the complete fan of emission in the vertical plane. In this universal curve, the independent variable is expressed as the ratio of the wavelength 2 to a constant 2c, which is known as the "critical wavelength" and is given by: 2o = (4/3)zR (Eo/E')3,

R is the bending radius in the magnetic field. The critical wavelength is a useful parameter for characterising the emission, for it represents the value of wavelength which equally divides the total integrated photon energy. The spectrum extends for many orders of magnitude into the long wavelengths, but as the photon energy is inversely proportional to wavelength, 2c is near the short wavelength end of the highly asymmetric spectrum. The amplitude maximum lies close to, but somewhat above 2c, at approximately ,t = 3.3 ).c. Below 2c, the intensity falls off very rapidly, and below about 0.1 2 c it is regarded as experimentally unusable. The total radiated power is obtained from the integration of the curve in Fig. 4. It will be seen that in an accelerator of fixed radius, this will lead to an expression that varies as the fourth power of the

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X/x c Fig. 4. Universal Synchrotron Radiation Spectrum giving the photons/s/mrad (horizontal)/mA/GeV of electron beam within an 0.1% wavelength bandwidth at wavelength 2; the emission is integrated over the complete fan of radiation in the vertical plane. By expressing the intensity in these units and plotting it as a function of the ratio of 2 to 2c (the critical wavelength) the curve is valid for electrons of all energies in any simple dipole field.

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electron energy. The expression for the radiated power (in rationalised mks units) is: U = (1/3) e 2fl 3y 4/e0R '

(3)

where U is the total radiated power (W per turn per electron), e is the electronic charge, e0 is the permitivity of free space and fl = v /c.

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= 1/,,/(1-fl~),

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where v is the velocity of the electron; c is the velocity of light. It should be noted that for the ultra relativistic electrons in a synchrotron source, fl is very close to 1, and this is a valid approximation in equation (3). The relationship for the total radiated power has an important bearing on the behaviour of the electrons in a storage ring and will be referred to again at a later stage. The universal curve given in Fig. 4 describes the emission from a single dipole. In the case of insertion magnets, the electron beam passes through a number of successive dipole fields with alternating polarity, so

that the emissions from the successive dipoles are incident on the experiment. The spectrum and intensity of the resulting radiation depends on the type of insertion magnet and the size and number of "wiggles" that are induced in the electron beam. The differences in the emission geometry between wigglers, wavelength shifters and u n d u l a t o r s are summarized in Fig. 5. In the case of wiggler magnets, there are a small number of high field dipoles that produce large angles of bend that do not permit interference effects between the successive radiation fans. Under such circumstances, the radiation from each pole-pair will just add algebraically to the total intensity, with no modification to the simple dipole spectrum. The radiation amplitude is then simply increased by a factor n, where n is the number of dipoles in the insertion device. There are, however, a number of complicating issues; the field distribution in the direction of the electron beam produced by a pole-pair in a wiggler magnet usually does not have the uniformity of a dipole bending magnet in an accelerator, so the nature of the spectrum depends on the azimuthal position of the electron as it passes between each pair of poles. Further, when there are large "wiggles", the emissions from adjacent dipoles will not be co-linear. Hence, whilst the universal curve multiplied by n will provide a rough guide to the spectrum expected from

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Fig. 5. A comparison of the geometry of radiation emission from multipole wigglers, wavelength shifters and undulators. In the case of the first two types of insertion magnet, there are a small number of poles and the deflection angle of the electron beam is large, so that the successive cones of emitted radiation are not co-linear. In undulators the deflection angle is small compared to the cone of emission and interference effects occur.

Synchrotron radiation sources a certain wiggler design, the exact intensity curve must be calculated in each case with the above factors taken into account. Standard wiggler magnet technology uses a small, odd number of dipoles; examples can be found with between 3 and 20 poles. In all cases, the two outer dipoles have half the magnetic length of the main dipoles, so that not only is there zero total field integral and angular deflection through the magnet, but the beam is also returned to its original transverse position when it exits the complete assembly. The highest field wavelength shifting wigglers have only a single central high field dipole with two weaker end pole pairs; these often make use of superconducting technology to provide magnetic fields of 6 T, or more. A photograph of a 5 T superconducting wavelength shifter, installed in the magnet ring of the Daresbury SRS, is shown in Fig. 6; a cut away diagram of the same magnet is given in Fig. 7. The radiation spectrum from this magnet is shown alongside the normal bending magnet spectrum in Fig. 3. Such magnets, together with their cryogenic systems, are very expensive. In compensation, the large bending angles in these devices produce a broad horizontal fan of radiation, which can supply several beam lines

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and multiple experimental stations simultaneously. The "front end" of the beam line conducting radiation from the Daresbury 5 T wiggler to seven different experimental stations is shown in Fig. 8. The optimum electron beam configuration for wigglers is clearly that which provides a minimum beam cross section. This will provide the maximum number of emitted photons per unit area of source and, providing the vertical beam divergence is not too large, high photon fluxes at the experimental sample. The situation is, however, different in the case of radiation from undulator magnets.

Radiation from undulator magnets In an undulator magnet, a large number of low field poles produce co-linear radiation emissions; these strongly interfere, with consequential radical change to the Shape and amplitude of the synchrotron radiation spectrum. Undulator magnets are typified by a factor K: K --- ~

(6)

where c~is the maximum angular deviation of the electron beam in the undulator.

Fig. 6. Photograph of the 5 T superconducting wavelength shifting wiggler shortly after installation in the magnet ring of the Daresbury Laboratory SRS. The wiggler is identified by its large cryostat tank and the services turret which conducts power and liquid helium to the magnet. To the right of the wiggler can be seen (from left to right) a small sextupole/multipole magnet, a focusing quadrupole magnet and one end of a dipole bending magnet, with the stainless steel vacuum vessel installed in the magnet gap.

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Fig. 7. A cut-away diagram of the internal layout of the superconducting magnet shown in Fig. 6. The three sets of coils that produce the single "wiggle" in the circulating electron beam can be seen located about the warm-bore vacuum tube.

It will be recalled that the natural opening angle of the fan of radiation at short wavelength was of the order of 1/7, so it will be seen that K is the ratio of deflection to opening angle. For an undulator, K is less than or of the order of 1 (whilst for a wavelength shifter K is very large). When K is much less than 1, the undulator gives off a single line of radiation with wavelength given by: 2 = (2u/272)(1

+K2/2+TzOZ),

(7)

where 2. is the period of the alternating polarity magnetic poles; 0 is the angle subtended by the observer to the trajectory of the emitting electron. This equation can readily be understood in terms of two Lorentz transformations of the magnet periodicity, each by the factor of 1/7. The first represents the contraction in the magnet dimensions seen from the frame of reference of the relativistic electron beam, whilst the second is the transformation of the radiation back into the frame of reference of the laboratory. The 0 term accounts for the apparent change in periodicity when viewed at that angle. Thus, a simple interference effect is occurring, which is constructive at the transposed periodicity of the magnet. This also

explains the relationship between the number of poles (n) and the line intensity, which varies as n 2 in an undulator. It will be recalled that in the case of the wiggler, the radiation intensity varies directly as n. The additional energy for this enhanced amplitude comes from the "empty" part of the spectrum, for the line width is found to vary as 1/n. As the parameter K is increased from small values to the order of 1, the wavelength of the fundamental line increases, as indicated in equation (7), and harmonics at higher frequencies above the fundamental line appear. If K is further increased, the harmonics acquire greater amplitude and become comparable to the fundamental; line broadening occurs and the harmonics begin to coalesce. Such a situation is shown in Fig. 9, where the radiation spectrum from a K = 3.4 undulator in the Daresbury SRS is compared to the bending magnet spectrum. At higher K, the long train of harmonics becomes continuous and the spectrum tends towards the simple dipole emission spectrum, shown in Fig. 4. Undulators are generally built using permanent magnet material. A diagram of one of the many undulators that will be required in the European Synchrotron Radiation Source (ESRF) at Grenoble is shown in Fig. 10. The upper and lower poles are separately constructed from a large number of

Synchrotron radiation sources

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Fig. 8. A photograph of the beam line conducting synchrotron radiation from the Daresbury 5 T wavelength shifting wiggler magnet to seven different experimental stations. In~he foreground, a wide vacuum chamber provides an acceptance angle of 80 mrad. The radiation is then split into separate channels, each with its own collimator and mask, before passing through the storage ring shield wall into the experimental area. ceramic permanent magnet blocks, which are then assembled into a "carriage". The complete design requires massive mechanical support structures to restrain the magnetic forces between the upper and lower pole assemblies and maintain the pole positions to a very high precision. It is necessary to adjust the

gap between the upper and lower poles, for whilst the periodicity of the magnet poles is fixed, this gap variation allows the field amplitude and hence the parameter K t o be varied. The undulators are designed so that by using the full range of this variation, and choosing an appropriate harmonic, the researcher

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xcA~ Fig. 9. The radiation spectrum produced by a 2 GeV electron beam traversing the K = 3.4, 100 m m period undulator in the Daresbury SRS, compared to the bending magnet spectrum. The spectra are presented as " b r i g h t n e s s " - - t h e n u m b e r of photons/s/A of circulating electrons/mrad horizontal and vertical per 0.1% bandwidth. It can be seen that the undulator produces radiation in the soft X-ray region that is one to one and a half orders of magnitude brighter than that generated by the dipole bending magnet.

Fig. 10. Diagram of an undulator magnet designed for the ESRF, Grenoble. The insert shows how the small ceramic permanent magnet blocks are m o u n t e d to form the upper and lower pole assemblies. U p to three such carriages will be used in a straight section in the storage ring to make a complete undulator magnet.

Synchrotron radiation sources can tune the device to the frequency most appropriate for the experiment in hand and can then enjoy source brilliances that are orders of magnitude greater than those available from a conventional bending magnet. The optimum electron beam configuration for an undulator straight is understood by referring to equation (7). It will be seen that the term in 7 20 2 will result in a significant broadening of the line spectrum if the circulating beam contains electrons with trajectories having angular divergences of the order of 1/7 or more at the position of the undulator. This will result in a significant loss of flux at the desired wavelength and is avoided by placing undulators at positions in the accelerator's magnet lattice where the beam divergence is small. The consequences on the accelerator design will become clearer in the section dealing with the storage ring lattice.

Source brilliance and brightness A number of different parameters are used to describe the photon flux that is radiated by a source, and as these terms are used throughout the relevant literature, they should be defined. The "spectral flux", often abbreviated to "flux", is the number of photons/s/mrad horizontal emitted into an 0.1% bandwidth, the emission being integrated fully in the vertical plane. The universal spectrum given in Fig, 4 is very similar to spectral flux, though this curve has also been normalised per GeV of electron beam energy. The flux is not a very meaningful expression, for few experiments will use the full vertical beam fan. A more useful parameter is the "brightness"; which is the spectral flux per milli-radian vertical. It therefore has units of photons/s/mrad2 per 0.1% bandwidth. Where the incident beam is focused onto a sample, the source area also becomes significant and the concept of "brilliance", which is the brightness per unit source area, is then used. Brilliance has units of photons/s/mrad2/mm2 per 0.1% bandwidth. The appropriate parameter is dependent on the type of experiment that is to be undertaken and how the beam line has been set up to collect the radiation. The values of brightness or brilliance that are achievable for any particular synchrotron source are crucially dependent on the design of the accelerator and particularly its magnet lattice, ACCELERATOR DESIGN FOR STORAGE RING SOURCES

Basic accelerator components The magnet lattice of a modern synchrotron radiation source resembles a complex beam transport system, with different types of magnet at various parts of the circumference. The fundamental components, the dipole magnets, which cause the electron beam to follow the required circular trajectory, are usually split into a relatively large number of individual units, providing many straight sections which are needed RPC 45/3~B

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to accommodate other components. For example, the ESRF, Grenoble has 64 dipoles, each 2.45 m in length. Between the dipoles it is necessary to place quadrupole magnets for beam focusing. Their magnet field is zero at the magnet centre and off axis it varies linearly with position in both the vertical and horizontal plane. Thus, off position particles are deflected. Because of the fundamental laws of electromagnetism, it is not possible to produce a quadrupole field that is focusing in both planes simultaneously; focusing in one transverse plane leads to de-focusing in the other. However, by alternating the polarity of the gradient field in different quadrupoles, it is possible to produce overall focusing in both planes. This concept of alternating gradient focusing led to a great advance in the design of circular particle accelerators and allowed the economic construction of the very high energy machines of the last few decades. In an alternating gradient lattice there are different "families" of quadrupoles. The minimum number is two families, known as "F" and "D" (horizontally focusing and defocusing) quadrupoles, but in an advanced source there will be many families of quadrupoles providing control of the beam dimensions and matching to insertion devices. The magnet lattice will also contain sextupole magnets, which, like the quadrupoles have zero induction at their centres; off axis, they produce a transverse field that varies as the square of the displacement from the magnet centre. The sextupoles are required to adjust the focusing for circulating electrons that have small momentum errors. Sextupoles are also connected into different families, with different strengths and polarities. The distribution of these magnets around the circumference of the storage ring differs to that of the quadrupoles, for there will be tong "dispersion free" straight sections where the circulating beam follows a trajectory that is independent of particle momentum; in these sections sextupoles would be ineffective. This is not so in the arc sections of the lattice, where the bending magnets will produce dispersion effects. The sections including the arcs are therefore referred to as "achromats" and sextupoles will usually be placed in the short straights between bending magnets. The photograph in Fig. 6 shows, in addition to the wiggler magnet, the various types of lattice magnet in the ring of the Daresbury SRS, The other vital dynamic components in the accelerator ring will be a number of radio frequency cavities. These are hollow copper enclosures that are designed and manufactured to very exacting tolerances. The cavities are fed with high frequency radio frequency power, which generates a standing electromagnetic wave. The cavity is designed to ensure that the standing wave has its voltage vector in the direction of the circulating beam. Power is therefore transferred to the beam, to replace the energy lost by synchrotron radiation and, if necessary, to raise its energy after

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injection. The radio frequency will usually be very much higher than the revolution frequency of the electrons, so there will be a number of different azimuthal positions in the circulating beam which correspond to voltage phases in the cavities which will feed energy to the beam. These are referred to as "buckets", for particles at these positions are in a stable potential well; elsewhere, electrons will see incorrect values of accelerating voltage and will quickly be lost from the accelerator. Hence, the beam around the storage ring is bunched at the radio frequency, giving the pulsed structure to the synchrotron radiation that was referred to at the beginning of the paper. The total number of such buckets around the accelerator circumference is referred to as the "harmonic number".

ellipse, divided by 2n, gives the value of emittance, which is invariant around the lattice. However, the ratio of the major and minor axes, and the angle of the ellipse all change as the beam passes through the focusing and de-focusing quadrupoles, implying that the amplitudes of the displacement and angular convergence or divergence vary widely through the lattice. The variation in displacement amplitudes around the lattice are described by beta functions in each plane (fix and /~), as shown in Fig. 11 for the Daresbury SRS. These functions are determined by the strengths and positions of the quadrupoles. The physical size of the beam (neglecting a small contribution from the electron energy distribution) in either plane, and at any position in the lattice is given by:

The oscillations o f the circulating beam in the lattice

where

Ax.z = ,J(/~x~Ex.~) A beam of any nature emitted from a source having non-zero dimensions will have a finite size and angular divergence as it propagates, In the case of the circulating electrons in a storage ring, the lattice quadrupoles will control the beam envelope by applying a focusing force to off-position particles. The resulting oscillations about the central closed orbit are called "betatron oscillations" after an early type of induction accelerator. Betatron oscillations occur in both transverse planes and, as generally an electron can have both a position and an angular error, there are two degrees of freedom in both the vertical and radial plane. Whilst, in some particular situations, it is possible to find populations of particles which all have the same coherent betatron oscillation, in the general case the oscillation amplitudes and phases are random within a beam and the oscillations are incoherent. The number of betatron oscillations per revolution generally differ in the two transverse planes and are important accelerator parameters, referred to as the accelerator "tune", these parameters have major significance in determining the stability of the circulating beam. Whilst the amplitude and phase of the betatron oscillation in one of the transverse planes represent two degrees of freedom, the two parameters are linked through the lattice, for an angular error at one position becomes a displacement error further down the trajectory, and vice versa. Furthermore, there are limits to the maximum displacements, set by the physical and magnetic Farameters of the accelerator. Thus, in each transverse plane, a maximum "beam emittanee" is defined as the product of transverse oscillation amplitude and angle. This parameter has units of metre-radians, with a scale of nano-metreradians in a modern radiation source. It is of major significance in specifying the operational characteristics of a storage ring and for gauging its suitability as a radiation facility, for it is the emittances that determine the brilliance of the source. The emittance in each plane is represented by an ellipse plotted in a 2-D diagram which has axes of positional and angular displacement. The area of the

(8)

A is the beam size; E is the emittance in the radial (x) or vertical (z) plane. These functions have significance when considering the optimum positions for wigglers and undulators. Minimum beta is required in both planes at the position of a wiggler magnet, so as to provide maximum synchrotron radiation brilliance. This point will correspond to the maximum in angular excursion of the electron's oscillations, but as the wiggler itself produces a broad angular fan of radiation, this is of little consequence in the horizontal plane. However, it will be recalled that an undulator must be positioned at a point of minimum beam angular divergence, to prevent the interference effects being corrupted by electron trajectories at widely differing angles. Undulators are therefore positioned at points of maximum beta, to give small angular divergence, so that the interference effects are maximized. The particle beam also has momentum errors, and these are limited by the radio frequency voltage in the cavities. Providing this voltage has sufficient amplitude, the circulating bunches are trapped in the potential well provided by the radio frequency buckets, producing "phase stability", which ensures that off-momentum particles oscillate about the correct momentum as determined by the ring circumference and the imposed dipole field. These longitudinal oscillations, known as "synchrotron oscillations", also have 2 degrees of freedom: particle momentum and phase with respect to the radio frequency voltage. Thus, the electron beam has 6 degrees of freedom of oscillation; depending on the lattice design, these interact in a way that plays a vital role in making the electron storage ring an ideal source of synchrotron radiation.

Radiation damping The summary of electron beam behaviour in an accelerator lattice that i s given above also applies to protons, heavy ions, or any other particle beam

Synchrotron radiation sources

327

131211

I I

10 9

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/

\

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/

E

m. 6 o

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/

/

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'

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Bend. Hag. D-Quad. Hag.

_Oh_ F-Qund.Mag.

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3-

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Fig. 11. The amplitude functions fix and fl: (marked "Beta-h" and "Beta-v" respectively)in the lattice of the Daresbury SRS. The physical beam dimensions are proportional to the square root of these functions. The diagram covers one sixteenth of the total circumference, which contains one bending magnet and a focusing and defocusing quadrupole. The functions repeat with this periodicity.

circulating in a synchrotron. However, only electrons emit significant amounts of synchrotron radiation at GeV energies, and this leads to the unique phenomena of emittance damping in the correctly designed electron lattice. In equation (3) it was indicated that the radiated power from a n electron, circulating in a synchrotron of radius R, was proportional to the fourth power of the electron's energy. This provides a powerful damping mechanism to the synchrotron (energy) oscillations, for it is obvious that a particle with excess energy will rapidly radiate that excess, whilst a low momentum electron will lose energy at a much slower rate. Depending on the design of the lattice, this damping can be shared between the vertical, horizontal and longitudinal planes. Thus, classically, net damping of the oscillations can occur in all three planes and, in a typical multi GeV synchrotron source, the damping time constants are of the order of a few milliseconds, i.e. exceptionally short compared to the storage time of several hours. This implies that during the operation of a radiation source, zero transverse and longitudinal dimensions and emittance of the electron beam should be expected shortly after injection of the beam, with corresponding rewards in spectral brilliance of synchrotron radiation. However, as in

all such situations, quantum mechanical effects determine the real situation. The emission of a photon by a single electron in a magnet located in an achromat section of the lattice, where the lattice dispersion (the variation of orbit with momentum) is non zero, will result in that electron being on an incorrect radial orbit. Consequently, that electron has effectively received an induced radial betatron oscillation, i.e. an anti-damping term. Thus, in the radial plane the final beam emittance is determined by the equilibrium between the damping and anti-damping terms. There is an additional phenomena that should not be neglected. The photons of synchrotron radiation are emitted into a forward cone with angle of the order 1/7 in both transverse planes, so that in addition to losing energy, the electrons also receive some transverse momentum. This produces an additional anti-damping term in both planes, though in the case of the radial direction this effect is small compared to the anti-damping described above. Furthermore, the coupling between the horizontal and vertical betatron oscillations caused by stray magnetic fields and small mis-alignments of the installed magnetic components, produces some transfer of the radial emittance into the vertical plane. This is also the determining factor

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for the small but finite vertical beam size, so the angular spread of photon emission is dominant in neither transverse plane. It should be stressed that radiation damping is a powerful phenomenon in a high energy electron storage ring and, in spite of the anti-damping terms, very small beam emittances result, This is a major factor in the success of electron rings as radiation sources. Much work has now been carried out to establish Criteria for the minimum possible emittance in electron storage rings, and this will be reviewed in the next section.

The quest for minimum emittance Accelerator theorists have, for over 30 years, been developing the magnet lattice in synchrotrons and finding better combinations of bending and focusing magnets. In early machines a frequently used magnet sequence was: "F quadrupole/dipole/D quadrupole/ dipole", with this "FODO" structure repeated around the accelerator. This lattice can still be found in operating synchrotron sources, but has tended to be superseded by later developments that produced lower horizontal emittances and improved flexibility to accommodate wiggler and undulator straights. A significant improvement, that allowed easier matching to the long dispersion free straights, originated at the Brookhaven NSLS source, and was named the

"Chasman-Green" lattice, after the two accelerator physicists who developed the concept. This uses two bending magnets, with a single quadrupole, for dispersion matching, between these dipoles; a quadrupole doublet (F and D quadrupoles separated by a short straight), or some similar focusing scheme, is placed on either side of the central dipole pair. A more recent development used in the large sources is the, double and triple bend achromat ("DBA" and "TBA"), which use a combination of quadrupole doublets between either two or three dipole benders. In Fig. 12, the amplitude functions (beta functions) around one sixteenth of the ESRF lattice are shown. This is a DBA design and provides considerable flexibility for matching to zero dispersion wiggler and undulator straights. Compare the complexity of this lattice with the corresponding functions shown for the SRS in Fig. 11. Theorists have now investigated the lowest achievable horizontal emittance in a lattice and shown that it is given by: (9)

Ex
where C is a constant that depends on the type of lattice; qb is the bending angle in each separate dipole magnet; 7 is the relativistic energy parameter.

~2 t.. E"

--2

" 0

10

20

30

40

50

x (mei-res)

Fig. 12. Amplitude functions fix and fl: around one sixteenth of the ESRF storage ring. The symbols and curve identification follow the nomenclature used in Fig. 11. This advanced, third generation lattice contains 320 quadrupole magnets, giving great flexibilityfor matching to long straights for wigglers (low fl- at the centre of the diagram) and undulators (high fl- at the left and right hand end of the diagram).

Synchrotron radiation sources Thus, as the electron energy is increased to obtain harder radiation, the minimum achievable horizontal emittance increases as the square of the energy. The dependence on qb, however, indicates that high energy sources can obtain small emittances by using large numbers of dipoles. This is readily understood in terms of the contribution of bending magnet radiation to the principal anti-damping term that determines the radial emittance. A large number of separate bending magnets do not, however, guarantee this minimum emittance, and the lattice designer still has to work hard even to approach the optimum value. With the theoretical and engineering developments of the last decades, newly designed storage rings are achieving phenomenally low radial emittances. In medium energy rings (1-2 GeV), figures between 1 x 10-9 and 4 x 10 -9 m.rad are being predicted, with the larger accelerators (6-8 GeV) having designs that will produce emittances 1.5-2 times this figure. Coupling factors of the order of 10% between radial and vertical planes produce vertical emittances of the order of 5 x 10 -1° m.rad. It should be noted that these figures are between one and two orders of magnitude smaller than the emittances that were being obtained in accelerators designed a decade ago.

Sources of beam disturbance There are a number of phenomena in the storage ring, which involve the interaction of the circulating beam with its environment, which can seriously interfere with the stability of the beam and adversely affect the achieved emittances. In the case of "resonance" effects, the particles can interact with small magnetic field errors spatially distributed around the ring, leading to the growth of the betatron oscillations in either plane. This phenomenon is determined by the tune of the accelerator, referred to above. The general condition for a resonance is given by: m Qx + n Qv = p

(10)

where Qx and Qv are respectively the number of horizontal and vertical betatron oscillations per single orbit of the accelerator; and n, m, and p, are any integer. These Q value,~' are a measure of the strength of focusing in the accelerator and the values chosen for a particular synchrotron can be represented as a point (the "working point") on a diagram of horizontal and vertical Q. The resonances are then represented as a series of lines on the diagram, with the value of p being referred to as the order of the resonance. As all integer values of n, m, and p potentially cause beam disturbance, it would be expected that the diagram could be filled with an infinite set of lines and no values of focusing would lead to stable beam conditions. In practice, only the lower orders cause appreciable beam disturbance. This theory is well understood and, to the first order, is not dependent

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on electron beam current. Designers can therefore, with confidence, calculate the sensitivity of the beam to magnetic errors at the chosen working point and specify the field tolerances for the magnet design and the stability of the power supplies; in a third generation light source these are usually very stringent specifications. "Instabilities" are the other major class of phenomena that can lead to beam disturbances and emittance growth. Instabilities are caused by the interaction of the beam with its electromagnetic environment within the vacuum chamber and, more specifically, with its own electromagnetic field. A number of different instability effects are possible; they are proportional to the beam current amplitude and are therefore usually the mechanism that limits the maximum current that can be stacked and held in a storage ring. For this reason, there has been much study of the phenomena and, in spite of their complexity, they are now well documented. One important source of instability is caused by the interaction of the electron beam with the walls of the containing vacuum vessel. The electron beam is bunched at the radio frequency and the resulting electromagnetic field generates image currents in the inner wall of the vacuum chamber. If the vessel presents a significant impedance to these currents, a disturbance of the electron beam in the transverse and longitudinal planes can occur, with potential loss of circailating current. It is therefore vital that if high circul~tting currents are to be achieved, the vacuum charriber has a continuous conducting surface, so that the image currents see a low impedance. Furthermore, as these currents are very high frequency, there must be no sharp discontinuities in the vessel geometry. These would lead to changes in characteristic impedance of the coaxial line created by the inner wall of the chamber, resulting in the partial reflection of the electromagnetic wave at these discontinuities; again, beam disturbance or loss would result. This phenomenon therefore has a major bearing on the complexity and cost of the vacuum chamber for a light source ring. One final important disturbing phenomenon is caused by the positive ions that are generated when electrons collide with molecules of residual gas in the vacuum chamber. The ions can then become trapped in the electrostatic potential well created by the beam. The ion cloud can produce significant changes to the electron beam focusing and causes instabilities generating diverse emittance growth effects. A most irritating feature of positive ions in an accelerator is the non-reproducibility of the phenomenon, for changes in beam current, the closed orbit or the longitudinal distribution of the electrons around the accelerator from one "fill" to the next can produce large variations in the ion effects. These problems can be alleviated by introducing clearing electrodes into the vacuum chamber and generating electric fields of the order of a few tens of V/cm across the chamber.

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This does not disturb the electron beam but generally "sweeps" the ions from the vessel during the gaps between the electron bunches. A more radical approach, that prevents the accumulation of the positive ion cloud, is the use of positrons rather than electrons in the light source. The positrons have identical properties to the electrons with respect to the generation of the synchrotron radiation, but do not provide the potential well for the ions. The generation of the positrons for injection into the storage ring is, however, much more expensive, for the anti-electrons are generated by firing an ultrarelativistic electron beam into a target, collecting the positron and re-accelerating them. This usually involves additional pre-injection and other beam handling equipment. This solution, therefore, tends to be used only for larger projects.

Beam lifetime The beam lifetime that can be achieved in the storage ring is of prime importance to a user of synchrotron radiation. During operation, the stored beam current will decay approximately exponentially: I (t) = I0 exp (t/v)

(11)

where

I ( t ) is the beam current after time t;

must also be minimised in these remote parts of the accelerator aperture. The other major parameter that influences the beam lifetime is the amplitude of the radio frequency voltage in the cavities. As previously explained, the synchrotron radiation is emitted as discrete photons with widely varying energy. An electron with a large energy deviation resulting from the emission of several high energy photons must still be retained in the potential well defined by the r.f. bucket if long fifetimes are to be achieved The level of the r.f. voltage present in the cavities must therefore be many times the value demanded to meet the "average" energy loss per turn. The required factor, called the r.f. overvoltage, depends on the lattice design and the accelerator aperture. It is the principal factor determining the capital cost of the r.f. system and hence contributes significantly to the overall cost of the accelerator. With all these variable factors contributing to the value of the lifetime that will be obtained during operation, synchrotron source designers will usually be conservative in their prediction of the achieved lifetime. Values of the order of 8-10 h are regarded as acceptable, whilst beam lifetimes of 40-50 h have been achieved on some sources; a lifetime of 120 h has been recorded on the "DCI" storage ring at Orsay, near Paris.

z is the "beam lifetime". The beam lifetime parameter (~) is influenced by the design and performance of most of the major systems in the accelerator. Of first importance is the vacuum pressure that is obtained in the vessel. Scrupulous cleanliness is essential during the assembly and installation of the chamber, and this is normally followed by an in-situ bake to achieve ultra-high vacuum performance. This should result in a base pressure of the order of 10-~0 torr, but gas desorption from the chamber walls, caused by the photon and photo-electron bombardment when synchrotron radiation is emitted, raises the pressure appreciably during operation with a beam. The parameter therefore varies with stored beam current, so the decay is not truly exponential, longer lifetimes being obtained at lower currents. The lifetime is also strongly influenced by the relationship between the emittance, vessel aperture and magnetic good field region. To obtain lifetimes of many hours, it is necessary to retain in stable orbit the small percentage of electrons that have, at any instant, suffered large excursions resulting from the random emission of photons. For a brief moment these electrons will have betatron oscillations that are many standard deviations out from the central orbit. The accelerator magnets must provide fields meeting the good-field specification for such electrons and the vacuum chamber aperture should be sufficiently large to still contain 8 10 standard deviations of betatron amplitude. Resonance and instability phenomena

CONCLUSION

Synchrotron sources have now moved through three generations since their inception as a distinct type of accelerator in the 1960s. The demand for radiation for materials and bio-sciences, chemistry and other new areas of exploitation continues to expand and there is sustained pressure on accelerator designers to produce sources with higher brilliance and greater beam stability and lifetime. It is therefore presently difficult to predict what the "fourth generation" source will look like. It is certain that the principal sources of radiation will be insertion devices, and it is likely that these will be of an advanced and exotic nature. It is possible that the free electron laser (f.e.1.), will also become an important experimental tool. This ultra high intensity radiation source uses the interaction of relativistic electrons with transverse electromagnetic fields oscillating in a laser-like longitudinal resonant structure to stimulate the emission of further, highly collimated radiation. However, because of the technical difficulties in reflecting X-rays at angles other than grazing incidence, it is probable that the f.e.1, will have most impact between the IR and the UV region. Ongoing development of the synchrotron source well into the 21st century is therefore foreseen, with consequential growth in the quantity and quality of research and development carried out using these facilities. This is expected to lead to major technical

Synchrotron radiation sources a d v a n c e m e n t s t h a t will result in better u n d e r s t a n d ings a n d perspectives in a wide range o f sciences. W i t h the increased use of s y n c h r o t r o n radiation for industrial research a n d development, this rapidly expanding science also has the potential for radically altering the materials a n d products t h a t we use in o u r everyday life. BIBLIOGRAPHY

As explained in the first chapter, this paper sets out to review a subject of considerable breadth rather than

331

produce an authoritative account of its development. Hence, rather than produce a list of papers and publications dealing with particular features, the reader seeking further information is referred to a single publication which is the record of a two week CERN Accelerator School on synchrotron radiation. The topic is examined in far greater depth than in this short article and can be used as a source of references for further study. CERN Accelerator School: Synchrotron Radiation and Free Electron Lasers, Chester, U.K., April 1989 (S. Turner, Ed.) (CERN 90-03).