Kevin Brown (BNL), Massimo Giovannozzi (CERN) and Thomas Roser (BNL)
1 The origin of alternating-gradient accelerators
A new method of magnetic focusing for accelerators, called alternating-gradient (AG) or strong focusing, started in 1952 leading to a series of accelerators capable of much higher energies than was economically prac-tical with earlier techniques as described in [Livingston and Blewett (1962)].
At the CERN laboratory in Geneva the first of these large accelerators was brought into operation at 28 GeV in late 1959. At Brookhaven National Laboratory (BNL) a machine of similar dimensions became operational in late 1960, with a proton energy of 33 GeV.
The principle of AG focusing originated at BNL in the summer of 1952, at a time when the Cosmotron was nearing completion [Roser and Courant (2015)]. A report of the early concepts was published, describing the possible application to a high-energy proton synchrotron and also discussing the use of magnetic quadrupole lenses in focusing linear beams of particles [Courant et al. (1952)].
The completion in 1952 of the Cosmotron, the first multi-GeV acceler-ator, had attracted to Brookhaven several scientists who were engaged in developing experimental apparatus for research studies. It was the case of a delegation of European scientists, representing the newly established CERN laboratory, with the goal of assessing the Cosmotron as a model for a 10-GeV accelerator. It was known that magnetic saturation effects limited the useful aperture of the C-shaped magnets of the Cosmotron at high fields. A possible technique would have been to retain the C-shape and also expand the useful aperture by alternating the magnets’ return yoke locations from inside to outside the orbit. This would have resulted, at high fields, in a corresponding alternation in magnetic gradients from positive to negative in the successive magnets as a result of saturation. The possibility that
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this alternation in gradients would destroy orbital stability was considered by E. D. Courant who showed that stability was indeed improved rather than damaged. At this time H. S. Snyder joined in the design efforts and helped to develop the general principle of dynamic stability. Stability limits were identified, leading to suitable configurations of positive and negative magnet sectors and field-free straight sections between sectors around the orbit. Mechanical configurations were conceived producing the desired large magnetic gradients. The basic concept was sound, and the use of alternating gradients would allow major reductions in the transverse dimensions, as can be seen in Fig. 1, and the power requirements for magnets. Such a reduction in cost of synchrotron magnets for a given orbit radius would make it possible to design machines with much larger orbits and much higher energies.
By the time the European delegation, O. Dahl, F. Goward, and R. Wider¨oe, arrived at Brookhaven, the concept had been developed suf-ficiently to be presented as a significant improvement over the Cosmotron design. The new concept was very well received, but the CERN group was faced with the very difficult decision of going ahead on proven ground or proceeding with the new and untried idea. The CERN Council approved the latter option at its third session in October 1952 in Amsterdam.1 The benefits of the new approach were perceived to outweigh the risks, but a vigorous plan of studies was launched to probe the critical features of the new invention.A posteriori, this courageous decision has been crucial to the future of CERN.
A number of studies were made in European laboratories to determine whether the orbit stability would be threatened (see, e.g., [Adams et al.
(1953)]). Further work showed that the harmful resonances could be avoided by care in design and by suitable control of the magnetic gradients during the excitation cycle. Another difficult point was reaching and passing the so-called transition energy, but progress in the understanding of the complex physics allowed to gain confidence in the soundness of the new principle, which grew in all laboratories participating in the scientific efforts. The first relatively complete analysis of a practical design for an AG accelerator was for the 15-GeV ring at Massachusetts Institute of Technology (MIT) [MIT (1953)].
It is worth mentioning that the AG concept was developed independently elsewhere. N. C. Christofilos, an electrical engineer of American birth, edu-cated and working in Athens, had been developing several new ideas on accelerator design in the form of private reports and patent applications.
His unpublished report [Christofilos (1950)] presented the concept of AG
1At the same meeting, Geneva had been chosen as the location of the future laboratory.
vacuum chamber outer coils inner coils
2390 2390
1220
240
940
1160
Fig. 1. Comparison between the cross section of the Cosmotron magnet (left, from [Liv-ingston and Blewett (1962)]) and that of the PS main magnet (right). The difference in size is a consequence of the AG principle. The dimensions are in millimetres.
focusing and the possible design of an accelerator using this principle, for which he also applied for United States and European patents. After the Brookhaven publication in 1952, Christofilos came to the United States and claimed his priority, which was recognised in a brief communication [Courant et al.(1953)]. He was then hired by BNL and worked on a small-scale model to test experimentally whether the beam would pass transition energy. The so-called electron analogue had been built in 1954 and remained in operation until 1957. This model had a circumference of 43.1 m, accelerating electrons from 1 to 10 MeV with transition energy at 3.5 MeV. In order to reduce cost, the alternating-gradient, strong focusing was provided by electrostatic lenses and bending by electrostatic fields [Plotkin (1991)]. The test showed that transition energy could be crossed without problems, but the price was a delay in the construction of the BNL ring relative to the CERN one, which was in the end compensated by better preparation of the experimental programme as compared to the CERN machine.
2 The CERN Proton Synchrotron2
The final parameters of the CERN Proton Synchrotron (PS) were adopted on December 1954 [Regenstreif (1959)] and the completion date was set for the end of 1959. By November 1959 transition energy was successfully crossed and the circulating current already exceeded the design value. The flexibility
2Recently, a complete report on the PS machine has been published to celebrate its fiftieth anniver-sary [Gilardoni, Manglunkiet al.(2011)].
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of the AG design has been proven by the different types of ions accelerated, well beyond the original plans: protons for the physics programme at the PS or transfer to the Super Proton Synchrotron (SPS) [Schmidt (2015)] and the Large Hadron Collider (LHC) [Myers (2015)]; antiprotons for the operation of the SPS as a proton–antiproton collider; electrons and positrons for the operation of the Large Electron and Positron collider (LEP); several types of ions (deuterons, alpha particles, oxygen, sulphur, indium, and lead ions) for transfer to the Intersecting Storage Rings (ISR), SPS and the LHC.
The injection energy underwent a number of upgrades, from the origi-nal 50 MeV kinetic injection energy for protons delivered by Linac 1. The first increase to 800 MeV occurred when the PS-Booster was brought into operation in 1973, and since then it is used to fill the PS with a repetition period of 1.2 s, corresponding to about 0.8 Hz; then to 1 GeV since 1987, with the aim of better serving the antiproton production chain [Chohan and Maury (2015)]; finally 1.4 GeV came into operation in 1999 in the framework of the upgrade foreseen to generate the high-brightness beams for the LHC.
A further increase to 2 GeV is planned, as proposed in [Giovannozzi et al.
(2010)] to fully profit from the performance reach of the planned Linac 4. In any upgrade the increase of the PS injection energy was needed to mitigate space charge effects, which have become ever stronger due to the continuous increase of beam intensity.
The overall intensity evolution in the PS is visible in Fig. 2, which clearly shows how in recent years more emphasis is put on the beam brightness, as required by the LHC, than on peak intensity.
The PS lattice is made of combined function magnets, each 4.4 m long, divided into focusing and de-focusing half-units. Each unit consists of five blocks, assembled in a curved structure. The hundred main magnets are separated by a hundred straight sections, twenty of which are longer than the others and house special equipment for, e.g., injection, extraction, and radio-frequency (RF) manipulations. Four types of main magnet are present in the PS ring, depending on the focusing configuration and on whether the magnets’ return yoke is oriented towards the inside or the outside of the ring. In total 35 magnets feature a D-F configuration and yoke outside, 15 a F-D configuration with yoke outside, 35 a F-D configuration, but with yoke inside, and finally 15 a D-F configuration with yoke inside. The lattice has ten super-periods and the optical functions (horizontal and vertical beta-functions and dispersion) for one super-period are shown in Fig. 3.
At low energy the tunes are controlled by means of two families of quadrupoles, the chromaticities being left at their natural values. At higher energies the control of tunes and chromaticities is achieved by means
Fig. 2. Intensity evolution over the years in the PS. The marker indicates the intensity record achieved in 2001.
H V H
Fig. 3. Optical parameters for one super-period of the PS bare lattice. Each super-period contains two long straight sections.
of special circuits that are installed on the magnets’ poles and provide a transverse variation of the magnetic gradient so as to create addi-tional quadrupolar and sextupolar components. These circuits are the so-called pole-face windings (PFW) and figure-of-eight loop. Originally, three independent circuits were used to control three out of the four main global
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Fig. 4. The PS main magnet and its cross section (upper) and the five circuits used to control the tunes and the chromaticities (lower). The dimensions are in millimetres.
optical parameters, namely tunes and chromaticities. A recent upgrade of the system allows control of five physical parameters, four of which are the tunes and the chromaticities. In some applications the second order deriva-tive of the horizontal tune with respect to the momentum deviation is the fifth parameter controlled. The PS magnet together with the layout of the special coils is visible in Fig. 4.
The main RF system consists of 11 cavities (one of which is the hot spare) installed in the long straight sections. They provide power for accelerating the beam. The original choice of the RF harmonic number was 20, but it was changed to 8 in recent years.
The transition energy in the PS machine corresponds to 6.1 GeV and it is crossed by applying the needed RF phase jump and a special manipulation of the beam optics, the so-calledγ-jump [Hardt and M¨ohl (1969)], in order to faster cross transition and hence avoid or mitigate effects that might spoil the beam quality.
The evolution of the PS performance and its flexibility is reflected also in the variety of RF and extraction systems. A large number of longitu-dinal beam manipulations were performed [Garaby (2015)] and some are
Table 1. Basic parameters of the PS machine.
Accelerated particles p±, e±, and several types of ions Maximum particle energy [GeV] 26
Circumference [m] 200π
Magnetic lattice Alternating-gradient focusing, combined-function
Focusing order FOFDOD
Magnetic field index n= 282 Number of main magnets 100
Bending magnetic field [T] 0.101 at injection (1.4 GeV), 1.24 at 26 GeV Betatron oscillations/turn 6.25 (h), 6.25 (v)
Transition energy [GeV] 6.1
Magnetic cycle repetition [s] 1.2 (up to 20 GeV), 2.4 (up to 26 GeV) Straight sections number = 100, 80 of 1.6 m, 20 of 3 m
RF system I (tunable) 10+1 cavities, 2.6 to 9.5 MHz, 200 kV total maximum Auxiliary RF systems [MHz] 13.3, 20, 40, 80, 200
Vacuum chamber [mm2] Inconel, 150×80 in the bending magnets
still routinely used to produce the various beams. Bunch merging and non-adiabatic manipulations, such as bunch rotation, are certainly well-known techniques used in the PS. However, to fulfil the requirements set by the LHC, a longitudinal bunch splitting technique had been developed [Garoby (1998)]. Each bunch injected in the PS is divided into twelve shorter and less intense bunches, but with the longitudinal emittance required for the bunch-to-bucket transfer to the SPS. This is obtained by means of a triple and two double splittings, performed by a number of ancillary RF systems working at different frequencies.
Beam extraction is also performed in several different ways, ranging from fast, single-turn, to slow, and also multi-turn extraction. The last one is per-formed either by slicing the beam on an electrostatic septum and transferring it to the SPS as a continuous ribbon five PS-turn long [Bovet et al.(1973)], or via a new technique based on transverse splitting obtained by an adia-batic crossing of a non-linear, stable betatron resonance [Cappi, Giovannozzi (2002); Gilardoniet al. (2006)].
The key parameters of the PS are listed in Table 1.
3 The BNL Alternating-Gradient Synchrotron3
The construction of the BNL AG (AGS) was approved in 1954 after a deci-sion process of only four months. The construction was led by G. K. Green
3Recently, a complete account on the AGS has been written [H¨ubner (in press)].
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and J. P. Blewett and beam commissioning was completed with the first protons being accelerated to 31 GeV in July 1960 [Green (1961)].
The first injector was a 50-MeV Alvarez-type proton linear accelerator.
The present 200-MeV linear accelerator began operation in 1970. In 1982 H− charge exchange injection into the AGS was introduced [Barton (1983)] and in 1991 a 1.5-GeV booster synchrotron was commissioned [Ahrens (1993)].
The Booster can provide 1.5×1013protons per pulse at 1.9 GeV at the design repetition frequency of 7.5 Hz. The acceleration harmonic schemes (Booster harmonic, AGS harmonic, transfers) evolved from (3, 12, 4) to (2, 8, 4) and finally to (1, 6, 6) in pursuit of higher intensity [Brennan (1999)], thus showing the use of bunch merging in the AGS in past years prior to beam transfer.
Secondary beams from the AGS were initially provided from internal tar-gets, which created high beam loss and activation in the accelerator not com-patible with high-intensity operation. The first fast extraction was installed in the mid 60s, followed by slow extraction in 1967 which served up to six target stations and spilled out protons with repetition periods from 1.8 s to 5.8 s. To cope with the intensity increases, the AGS underwent a series of upgrades including a new main magnet power supply, addition of transverse feed-back, special magnets to provide fast crossing of the transition energy, corresponding to 8.4 GeV, and a high power RF system [Brennan (1995)]. In the early 2000s the AGS provided a slow-extracted beam of 7×1013 protons per pulse at 24 GeV [Brown et al. (2003)], however, such a high-intensity operation was stopped at the end of 2002. The overall intensity evolution in the AGS is visible in Fig. 5. To achieve such a performance required mas-tering the losses induced by intensity-dependent effects. Different methods have been used, e.g., bunch flattening to mitigate space charge effects and octupoles to reduce the slow losses during the injection porch.
With the appropriate source added to the 200-MeV linear accelerator, polarised protons have been produced by the injector chains from 1985 onward for fixed target experiments. To meet injector requirements for the Relativistic Heavy Ion Collider (RHIC) [Fischer (2015)] — intensity and polarisation — the polarised source underwent a major upgrade [Zelenskiet al.(2008)]. The polarisation transmission efficiency in the AGS has been sub-stantially improved with the installation of two partial Siberian snakes [Der-benev and Kondratenko (1976, 1978); Roser (1988)] and a system to rapidly cross weak resonances [Schoefer et al. (2012)]. Polarisation at transfer to RHIC (24 GeV) is 70% (82% at 200 MeV) and with an intensity of 2×1011 protons per bunch [Huanget al. (2009); Schoeferet al. (2011)].
Fig. 5. Intensity evolution over the years in the AGS.
Since 1986 the Booster has also accelerated ions (deuterons to gold) using a Tandem Van de Graaff as the injector. For RHIC operation about 5×109 Au31+ ions at 41.6 MeV/nare injected over 60 turns into the Booster, accelerated to 101 MeV/n, stripped to Au77+ and injected into the AGS. The ions are fully stripped before injection into RHIC [Gardneret al. (2007)]. A new pre-injector is being commissioned based on an EBIS source followed by a new linear accelerator [Pikinet al. (2010)]. The new system adds ura-nium [Alessiet al. (2011)] to the list of ions available to RHIC.
The AGS lattice features some similarities with the PS, but there are also some significant differences that are visible in Fig. 6.
The main magnets are not made of blocks and three variants are avail-able, namely long open (48), long closed (96), short open (96), where the lengths are 2.29 m and 1.91 m for long and short magnets, respectively.
The open magnets have a gap that flares away from the return yoke, while the gap of the closed ones flares towards the return yoke. A sketch of the AGS main magnet is shown in Fig. 7.
The total number of combinations is then six, if the two options for the orientation of the return yoke (inside or outside the ring) are also taken into account. The lattice is made of twelve super-periods, each consisting of 20 main magnets. The two groups of ten combined-function magnets fea-ture an opposite orientation of the return yoke. The straight sections in between main magnets are of three possible lengths, namely 0.61 m (12 in
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Fig. 6. Comparison between the PS (upper) and the AGS (lower) super-period from [Green and Courant (1959)]. The dimensions are in millimetres.
open unit 1000 closed unit
coils
Fig. 7. The AGS long main magnet and its cross section from [Green and Courant (1959)].
The dimensions are in millimetres.
each super-period), 1.52 m (six in each super-period), and 3.05 m (two in each super-period located at the transition between different magnets’ yoke orientation). Unlike the PS, where the tunes and chromaticities are con-trolled by means of pole-face windings, in the AGS tuning quadrupoles and chromaticity sextupoles are located in each super-period, thus enabling more convenient operation of the machine. The optical parameters (horizontal and vertical beta-functions and the horizontal dispersion) are plotted in Fig. 8 for one of the twelve super-periods.
While the minimum and maximum values of the β-functions resemble closely those of the PS, the dispersion values are clearly smaller for the AGS.
The key parameters of the AGS are listed in Table 2.
Fig. 8. Optical parameters for one super-period of the AGS bare lattice.
Table 2. Basic parameters of the AGS machine.
Accelerated particles p, polarised p and heavy ions (up to gold) Particle energy [GeV] 30, 25, and 14.5 GeV/n
Circumference [m] 256.9π
Magnetic lattice Alternating-gradient focusing, combined-function Focusing order (F/2)O(F/2)(D/2)O(D/2)
Magnetic field index n= 365 Number of main magnets 240
Bending magnetic field [T] 0.105 at injection (1.9 GeV), 1.30 at 33 GeV Betatron oscillations/turn 8.75 (h), 8.75 (v)
Transition energy [GeV] 8.4
Rise time/flat top time [s] 0.6/0.5 to 2.5
Straight sections number = 240, 24 of 3.05 m, 72 of 1.52 m, 144 of 0.61 m RF system I (tunable) 10 cavities, 1.8 to 4.5 MHz, 200 kV total maximum Auxiliary RF system [MHz] 92
Vacuum chamber [mm2] Inconel, 173×78 in the bending magnets
Acknowledgements
It is a pleasure to thank K. H¨ubner and E. McIntosh for the excellent com-ments on the original manuscript.
References
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