# FFAG accelerator

A Fixed-Field Alternating Gradient accelerator (FFAG) is a circular particle accelerator concept on which development was started in the early 50s, and that can be characterized by its time-independent magnetic fields (fixed-field, like in a cyclotron) and the use of strong focusing (alternating gradient, like in a synchrotron).[1][2] Thus, FFAG accelerators combine the cyclotron's advantage of continuous, unpulsed operation, with the synchrotron's relatively inexpensive small magnet ring, of narrow bore.

Although the development of FFAGs had not been pursued for over a decade starting from 1967, it has regained interest since the mid-1980s for usage in neutron spallation sources, as a driver for muon colliders [1] and to accelerate muons in a neutrino factory since the mid-1990s.

The revival in FFAG research has been particularly strong in Japan with the construction of several rings. This resurgence has been prompted in part by advances in RF cavities and in magnet design.[3]

## History

### First development phase

The idea of fixed-field alternating-gradient synchrotrons was developed independently in Japan by Tihiro Ohkawa, in the United States by Keith Symon, and in Russia by Andrei Kolomensky. The first prototype, built by Lawrence W. Jones and Kent M. Terwilliger at the University of Michigan used betatron acceleration and was operational in early 1956. That fall, the prototype was moved to the Midwestern Universities Research Association (MURA) lab at University of Wisconsin, where it was converted to a 500 keV electron synchrotron.[4] Symon's patent, filed in early 1956, uses the terms "FFAG accelerator" and "FFAG synchrotron".[5] Ohkawa worked with Symon and the MURA team for several years starting in 1955.[6]

Donald Kerst, working with Symon, filed a patent for the spiral-sector FFAG accelerator at around the same time as Symon's Radial Sector patent.[7] A very small spiral sector machine was built in 1957, and a 50 MeV radial sector machine was operated in 1961. This last machine was based on Ohkawa's patent, filed in 1957, for a symmetrical machine able to simultaneously accelerate identical particles in both clockwise and counterclockwise beams.[8] This was one of the first colliding beam accelerators, although this feature was not used when it was put to practical use as the injector for the Tantalus storage ring at what would become the Synchrotron Radiation Center.[9] The 50MeV machine was finally retired in the early 1970s.[10]

layout of MURA FFAG

MURA designed 10 GeV and 12.5 GeV proton FFAGs that were not funded.[11] Two scaled down designs, one for 720 MeV[12] and one for a 500 MeV injector,[13] were published.

With the shutdown of MURA which began 1963 and ended 1967,[14] the FFAG concept was not in use on an existing accelerator design and thus was not actively discussed for some time.

### Continuing development

In the early 1980s, it was suggested by Tat Khoe[citation needed] and Phil Meads[citation needed] that a FFAG was suitable and advantageous as a proton accelerator for an intense spallation neutron source, starting off projects led by Argonne National Laboratory and Jülich Research Centre.

FFAG conferences exploring this possibility were held starting from 1983;[15] Later, there was an FFAG workshop at CERN (2000) motivated by high energy physics and two at KEK(2000, 2003); these have continued roughly yearly. Articles have appeared in most PAC, EPAC, and cyclotron conferences.[16]

ASPUN ring(scaling FFAG). The first ANL design ASPUN was a spiral machine designed to increase momentum threefold with a modest spiral as compared with the MURA machines.[17]

The successful construction and commissioning of the first proton FFAG by the group of Y. Mori initiated a boom of FFAG activities.[18] The promising application of FFAGs for medical and high energy physics is the main motivation for this. By applying met alloy for the rf cavities the rf acceleration could be increased by an order of magnitude.

16 cell Superconducting FFAG example. Energy: 1.6 GeV, Bmax = 4 T, Bmin = -1.2 T, average radius 26 m

With superconducting magnets, the required length of the FFAG magnets scales roughly as the inverse square of the magnetic field, which was an unexpected result.[19] DFD and FDF triplet magnet designs for FFAGs provided a compact and simplified design that yielded substantially greater drift lengths and which has been used for subsequent scaling FFAGs.[19] This magnet design is specially well suited for radial FFAG machies, leading to a more linear beam dynamic optics. M. Abdelsalam (U. Wisconsin) and R. Kustom (ANL) derived a coil shape to provide the required field with no iron. This magnet design was continued by S. Martin et al. from Jülich.[16][20]

nonscaling FFAG with achromatic insertions

P. Meads invented a nonscaling FFAG where tunes are fixed so no resonances get crossed during acceleration. The design of such a machine starts with two dispersion-free straight sections with a triplet magnet between them. Adjust linear properties to match, then use COSY INFINITY to adjust the fields of the bending magnets, adding nonlinear terms, order by order, to keep the tunes fixed while mapping a reference orbit of arbitrary momentum to go from the center of the first straight section to the center of the second.[citation needed]

## Scaling vs non-scaling types

The magnetic fields needed for an FFAG are quite complex. The computation for the magnets used on the Michigan FFAG Mark Ib, a radial sector 500 keV machine from 1956, were done by Frank Cole at the University of Illinois on a mechanical calculator built by Friden.[4] This was at the limit of what could be reasonably done without computers; the more complex magnet geometries of spiral sector and non-scaling FFAGs require sophisticated computer modeling.

The MURA machines were scaling FFAG synchrotrons meaning that orbits of any momentum are photographic enlargements of those of any other momentum. In such machines the betatron frequencies are constant, thus no resonances, that could lead to beam loss,[21] are crossed. A machine is scaling if the median plane magnetic field satisfies

${\displaystyle B_{r}=0,\quad B_{\theta }=0,\quad B_{z}=ar^{k}~f(\psi )}$,

where

• ${\displaystyle \psi =N~[\tan ~\zeta ~\ln(r/r_{0})~-~\theta ]}$,
• ${\displaystyle k}$ is the field index,
• ${\displaystyle N}$is the periodicity,
• ${\displaystyle \zeta }$ is the spiral angle (which equals zero for a radial machine),
• ${\displaystyle r}$ the average radius, and
• ${\displaystyle f(\psi )}$ is an arbitrary function that enables a stable orbit.

For ${\displaystyle k>>1}$ an FFAG magnet is much smaller than that for a cyclotron of the same energy. The disadvantage is that these machines are highly nonlinear. These and other relationships are developed in the paper by Frank Cole.[22]

The idea of building a non-scaling FFAG first occurred to Kent Terwilliger and Lawrence W. Jones in the late 1950s while thinking about how to increase the beam luminosity in the collision regions of the 2-way colliding beam FFAG they were working on. This idea had immediate applications in designing better focusing magnets for conventional accelerators,[4] but was not applied to FFAG design until several decades later.

If acceleration is fast enough, the particles can pass through the betatron resonances before they have time to build up to a damaging amplitude. In that case the dipole field can be linear with radius, making the magnets smaller and simpler to construct. A proof-of-principle linear, non-scaling FFAG called (EMMA) (Electron Machine with Many Applications) has been successfully operated at Daresbury Laboratory, UK,.[23][24]

## Vertical FFAGs

Vertical Orbit Excursion FFAGs (VFFAGs) are a special type of FFAG arranged so that higher energy orbits occur above (or below) lower energy orbits, rather than radially outward. This is accomplished with skew-focusing fields that push particles with higher beam rigidity vertically into regions with a higher dipole field.[25]

The major advantage offered by a VFFAG design over a FFAG design is that the path-length is held constant between particles with different energies and therefore relativistic particles travel isochronously. Isochronousity of the revolution period enables continuous beam operation, therefore offering the same advantage in power that isochronous cyclotrons have over synchrocyclotrons. Isochronous accelerators have no longitudinal beam focusing, but this is not a strong limitation in accelerators with rapid ramp rates typically used in FFAG designs.

The major disadvantages include the fact that VFFAGs requires unusual magnet designs and currently VFFAG designs have only been simulated rather than tested.

## Applications

FFAG accelerators have potential medical applications in proton therapy for cancer, as proton sources for high intensity neutron production, for non-invasive security inspections of closed cargo containers, for the rapid acceleration of muons to high energies before they have time to decay, and as "energy amplifiers", for Accelerator-Driven Sub-critical Reactors (ADSRs) / Sub-critical Reactors in which a neutron beam derived from a FFAG drives a slightly sub-critical fission reactor. Such ADSRs would be inherently safe, having no danger of accidental exponential runaway, and relatively little production of transuranium waste, with its long life and potential for nuclear weapons proliferation.

Because of their quasi-continuous beam and the resulting minimal acceleration intervals for high energies, FFAGs have also gained interest as possible parts of future muon collider facilities.

## Status

In the 1990s, researchers at the KEK particle physics laboratory near Tokyo began developing the FFAG concept, culminating in a 150 MeV machine in 2003. A non-scaling machine, dubbed PAMELA, to accelerate both protons and carbon nuclei for cancer therapy has been designed.[26] Meanwhile, an ADSR operating at 100 MeV was demonstrated in Japan in March 2009 at the Kyoto University Critical Assembly (KUCA), achieving "sustainable nuclear reactions" with the critical assembly's control rods inserted into the reactor core to damp it below criticality.

## References

1. ^ a b Ruggiero, A.G. (Mar 2006). "Brief History of FFAG Accelerators" (PDF). BNL-75635-2006-CP. Presented at FFAG'05, Osaka, japan.
2. ^ Daniel Clery (4 January 2010). "The Next Big Beam?". Science. 327 (5962): 142–143. Bibcode:2010Sci...327..142C. doi:10.1126/science.327.5962.142.
3. ^ Mori, Y. (2004). "Developments of FFAG Accelerator" (PDF). Proceedings of FFAG04 /.
4. ^ a b c Jones, L. W. (1991). "Kent M. Terwilliger; graduate school at Berkeley and early years at Michigan, 1949–1959". Kent M. Terwilliger memorial symposium, 13−14 Oct 1989. AIP Conference Proceedings. 237. pp. 1–21. doi:10.1063/1.41146.
5. ^ US patent 2932797, Keith R. Symon, "Imparting Energy to Charged Particles", issued 1960-04-12
6. ^ Jones, L. W.; Sessler, A. M.; Symon, K. R. (2007). "A Brief History of the FFAG Accelerator". Science. 316 (5831): 1567. doi:10.1126/science.316.5831.1567.
7. ^ US patent 2932798, Donald William Kerst and Keith R. Symon, "Imparting Energy to Charged Particles", issued 1960-04-12
8. ^ US patent 2890348, Tihiro Ohkawa, "Particle Accelerator", issued 1959-06-09
9. ^ Schopper, Herwig F. (1993). Advances in Accelerator Physics. World Scientific. p. 529. ISBN 9789810209582.
10. ^ E. M. Rowe and F. E. Mills, Tantalus I: A Dedicated Storage Ring Synchrotron Radiation Source, Particle Accelerators, Vol. 4 (1973); pages 211-227.
11. ^ F. C. Cole, Ed., 12.5 GeV FFAG Accelerator, MURA report (1964)
12. ^ Cole, F. T.; Parzen, G.; Rowe, E. M.; Snowdon, S. C.; MacKenzie, K. R.; Wright, B. T. (1963). "Design of a 720 MeV Proton FFAG Accelerator" (PDF). Proc. International Conference on Sector-Focused Cyclotrons and Meson Factories.
13. ^ Snowdon, S.; Christian, R.; Rowe, E.; Curtis, C.; Meier, H. (1985). "Design Study of a 500 MeV FFAG Injector". Proc. 5th International Conference on High Energy Accelerators. Frascati.
14. ^ Jones, L.; Mills, F.; Sessler, A.; Symon, K.; Young, D. (2010). Innovation was not enough: a history of the Midwestern Universities Research Association (MURA). World Scientific. ISBN 9789812832832.
15. ^ Martin, S.; Wüstefeld, G. (ed.) (1983). Seminar on Fixed Field Alternating Gradient accelerators (FFAG), held at Jülich Research Centre. informal collection of contributed talks. KFA report SNQ 2 MZ / BS 001
16. ^ a b Martin, S.; Meads, P.; Wüstefeld, G.; Zaplatin, E.; Ziegler, K. (13–15 Oct 1992). "Study of FFAG Options for a European Pulsed Neutron Source (ESS)". Proc. XIII National Accelerator Conference, Dubna, Russia.
17. ^ R. L. Kustom and T. K. Khoe, IEEE Trans.Nucl. Sci. NS-30, C10 (1983).
18. ^ M. Aiba et al., Development of a FFAG Proton Synchrotron, Proceedings of the European Particle Accelerator Conference, 2000, Vienna (Austria)
19. ^ a b Meads, P. F.; Wüstefeld, G. (1985). "An FFAG Compressor and Accelerator Ring Studied for the German Spallation Neutron Source" (PDF). Proceedings of PAC 1985 / IEEE Trans Nucl. Sci. NS-32 p. 2697.
20. ^ S. A. Martin et al, FFAG Studies for a 5 MW Neutron Source, Presented at ICANS XII, Abington, UK, 24–28 May 1993
21. ^ Livingston, M. S.; Blewett, J. (1962). Particle Accelerators. New York: McGraw-Hill. ISBN 1114443840.
22. ^ Typical Designs of High Energy FFAG Accelerators, International Conference on High Energy Accelerators, CERN-1959, pp 82-88.
23. ^ Edgecock, R.; et al. (2008). "EMMA, The World's First Non-scaling FFAG" (PDF). Proc. European Particle Accelerator Conference 2008.
24. ^ S. Machida et al, Nature Physics vol 8 issue 3 pp 243-247
25. ^ Brooks, S. (2013). "Vertical orbit excursion fixed field alternating gradient accelerators". Physical Review ST: AB. 16. Bibcode:2013PhRvS..16h4001B. doi:10.1103/PhysRevSTAB.16.084001.
26. ^ K. Peach et al, Phys Rev ST Accel. Beams 16 (2013)