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| {{Expand Russian|FFAG|date=May 2012}}
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| A '''Fixed-Field Alternating Gradient accelerator''' (FFAG) is a circular [[particle accelerator]] concept 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]]).<ref name=briefhistory>{{Cite journal
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| | last1 = Ruggiero
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| | first1 = A.G.
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| | title = Brief History of FFAG Accelerators
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| | journal = [[Brookhaven National Laboratory|BNL]]-75635-2006-CP
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| | location = Presented at FFAG'05, Osaka, japan
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| | date = Mar 2006
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| | url = http://www.bnl.gov/isd/documents/31130.pdf
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| }}</ref><ref>{{Cite doi|10.1126/science.327.5962.142}}</ref> Thus, FFAG accelerators combine the cyclotron's advantage of continuous, unpulsed operation, with the synchrotron's relatively inexpensive small magnet ring, of narrow bore.
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| Although the development of FFAGs had not been pursued for over a decade starting from 1967, it has gained interest since the mid-1980s for usage in [[neutron]] [[spallation]] sources, and as driver for [[muon]] colliders since the mid-1990s.<ref name=briefhistory />
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| == History ==
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| ===First development phase===
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| 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]].<ref name=JonesTerwilliger>{{Cite doi|10.1063/1.41146}}</ref> Symon's patent, filed in early 1956, uses the terms "FFAG accelerator" and "FFAG synchrotron".<ref>{{US patent reference | |
| | number = 2932797
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| | y = 1960
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| | m = 04
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| | d = 12
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| | inventor = [[Keith Symon|Keith R. Symon]]
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| | title = [http://www.google.com/patents?id=ZGZVAAAAEBAJ Imparting Energy to Charged Particles]
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| }}</ref> Ohkawa worked with Symon and the [[Midwestern Universities Research Association|MURA]] team for several years starting in 1955.<ref>{{Cite doi|10.1126/science.316.5831.1567}}</ref>
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| [[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.<ref>{{US patent reference
| |
| | number = 2932798
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| | y = 1960
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| | m = 04
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| | d = 12
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| | inventor = [[Donald William Kerst]] and [[Keith Symon|Keith R. Symon]]
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| | title = [http://www.google.com/patents?id=ZWZVAAAAEBAJ Imparting Energy to Charged Particles]
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| }}</ref> 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.<ref>{{US patent reference
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| | number = 2890348
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| | y = 1959
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| | m = 06
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| | d = 09
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| | inventor = [[Tihiro Ohkawa]]
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| | title = [http://www.google.com/patents?id=4aEBAAAAEBAJ Particle Accelerator]
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| }}</ref> This was one of the first [[Collider|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]].<ref>{{Cite book
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| | last1 = Schopper | first1 = Herwig F.
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| | title = Advances in Accelerator Physics
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| | publisher = World Scientific
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| | year = 1993
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| | page = 529
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| | url = http://books.google.com/books?id=v9SoaCWFgigC&pg=PA529
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| | isbn = 9789810209582
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| }}</ref> The 50MeV machine was finally retired in the early 1970s.<ref>E. M. Rowe and F. E. Mills, Tantalus I: A Dedicated Storage Ring Synchrotron Radiation Source, [http://cdsweb.cern.ch/record/1107919/files/p211.pdf Particle Accelerators], Vol. 4 (1973); pages 211-227.</ref>
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| [[File:mura ring.jpg|thumb|layout of MURA FFAG]]
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| [[Midwestern Universities Research Association|MURA]] designed 10 GeV and 12.5 GeV proton FFAGs that were not funded.<ref>F. C. Cole, Ed., 12.5 GeV FFAG Accelerator, MURA report (1964)</ref> Two scaled down designs, one for 720 MeV<ref>{{Cite journal
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| | title = Design of a 720 MeV Proton FFAG Accelerator
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| | year = 1963
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| | first1 = F. T. | last1 = Cole
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| | first2 = G. | last2 = Parzen
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| | first3 = E. M. | last3 = Rowe
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| | first4 = S. C. | last4 = Snowdon
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| | first5 = K. R. | last5 = MacKenzie
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| | first6 = B. T. | last6 = Wright
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| | url = http://accelconf.web.cern.ch/AccelConf/c63/papers/cyc63g05.pdf
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| | journal = Proc. International Conference on Sector-Focused Cyclotrons and Meson Factories
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| }}</ref> and one for a 500 MeV injector,<ref>{{Cite journal
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| | first1 = S. | last1= Snowdon
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| | first2 = R. | last2 = Christian
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| | first3 = E. | last3 = Rowe
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| | first4 = C. | last4 = Curtis
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| | first5 = H. | last5 = Meier
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| | title = Design Study of a 500 MeV FFAG Injector
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| | journal = Proc. 5th International Conference on High Energy Accelerators
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| | year = 1985
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| | location = Frascati
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| | url = http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4453496
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| }}</ref> were published.
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| With the shutdown of MURA which began 1963 and ended 1967,<ref>{{Cite book
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| | title = Innovation was not enough: a history of the Midwestern Universities Research Association (MURA)
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| | isbn = 9789812832832
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| | year = 2010
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| | first1 = L. | last1 = Jones
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| | first2 = F. | last2 = Mills
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| | first3 = A. | last3 = Sessler
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| | first4 = K. | last4 = Symon
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| | first5 = D. | last5 = Young
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| | url = http://books.google.com/books?id=Bn7Z4VVB9uUC&pg=PP1
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| | publisher = World Scientific
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| }}</ref> the FFAG concept was not in use on an existing accelerator design and thus was not actively discussed for some time.
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| ===Continuing development===
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| {{Cleanup|section|reason=need for more context and compression of present content|date=May 2012}}
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| In the early 1980s, it was suggested by Tat Khoe{{Citation needed|date=May 2012}} and Phil Meads{{Citation needed|date=May 2012}} 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]].
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| FFAG conferences exploring this possibility were held starting from 1983;<ref>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</ref> 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.<ref name=FFAGopts>{{Cite journal
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| | first1 = S. | last1 = Martin
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| | first2 = P. | last2 = Meads
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| | first3 = G. | last3 = Wüstefeld
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| | first4 = E. | last4 =Zaplatin
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| | first5 = K. |last5 = Ziegler
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| | title = Study of FFAG Options for a European Pulsed Neutron Source (ESS)
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| | journal = Proc. XIII National Accelerator Conference, Dubna, Russia
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| | date = 13-15 Oct 1992
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| }}</ref>
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| [[File:aspun.jpg|thumb|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.<ref>R. L. Kustom and T. K. Khoe, IEEE Trans.Nucl. Sci. NS-30, C10 (1983).</ref>]]
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| The successful construction and commissioning of the first proton FFAG by the group of Y. Mori initiated a boom of FFAG activities.<ref>M. Aiba et al., Development of a FFAG Proton Synchrotron, Proceedings of the European Particle Accelerator Conference, 2000, Vienna (Austria)</ref> 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.
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| [[File:PhilM3-Gode.pdf|thumb|16 cell Superconducting FFAG example. Energy: 1.6 GeV, B<sub>max</sub> = 4 T, B<sub>min</sub> = -1.2 T, average radius 26 m]]
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| Wth superconducting magnets, the required length of the FFAG magnets scales roughly as the inverse square of the magnetic field, which was an unexpected result.<ref name=mewu>{{Cite journal
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| | first1 = P. F. | last1 = Meads
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| | first2 = G. | last2 = Wüstefeld
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| | title = An FFAG Compressor and Accelerator Ring Studied for the German Spallation Neutron Source
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| | journal = Proceedings of PAC 1985 / IEEE Trans Nucl. Sci. NS-32 p. 2697
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| | year = 1985
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| | url = http://accelconf.web.cern.ch/accelconf/p85/pdf/pac1985_2697.pdf
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| }}</ref> 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
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| subsequent scaling FFAGs.<ref name=mewu /> 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.<ref name=FFAGopts /><ref>S. A. Martin et al, FFAG Studies for a 5 MW Neutron Source, Presented at ICANS XII, Abington, UK, 24–28 May 1993</ref>
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| [[File:Meads ring.jpg|thumb|nonscaling FFAG with achromatic insertions]]
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| 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|date=March 2012}}
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| ==Scaling vs non-scaling types==
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| 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, Inc.|Friden]].<ref name=JonesTerwilliger /> 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.
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| 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,<ref>
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| {{Cite book
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| |last1=Livingston |first1=M. S. | authorlink1 = Milton Stanley Livingston
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| |last2=Blewett |first2=J.
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| |year=1962
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| |title=Particle Accelerators
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| |publisher=[[McGraw-Hill]]
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| |location=New York
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| |isbn=1114443840
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| }}</ref> are crossed. A machine is scaling if the median plane magnetic field satisfies
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| :<math> B_r =0 , \quad B_{\theta} =0 , \quad B_z=a r^k ~f(\psi)</math>,
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| where
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| *<math> \psi=N~[\tan~\zeta~\ln(r/r_0)~ - ~\theta]</math>,
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| *<math>k</math> is the field index,
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| *<math>N </math>is the periodicity,
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| *<math>\zeta</math> is the spiral angle (which equals zero for a radial machine),
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| *<math>r</math> the average radius, and
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| *<math>f(\psi)</math> is an arbitrary function that enables a stable orbit.
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| For <math>k>>1</math> 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.<ref>Typical Designs of High Energy FFAG Accelerators, International Conference on High Energy Accelerators, CERN-1959, pp 82-88.</ref>
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| 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,<ref name=JonesTerwilliger /> but was not applied to FFAG design until several decades later.
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| 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 (accelerator)|EMMA]]) (Electron Machine with Many Applications) has been successfully operated at Daresbury Laboratory, UK,.<ref>{{Cite journal
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| | title = EMMA, The World's First Non-scaling FFAG
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| | url = http://cern.ch/AccelConf/e08/papers/thpp004.pdf
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| | last1 = Edgecock | first1 = R.
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| | author2 = et al.
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| | journal = Proc. European Particle Accelerator Conference 2008
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| | year = 2008}}</ref><ref>S. Machida et al, Nature Physics vol 8 issue 3 pp 243-247</ref>
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| ==Applications==
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| FFAG accelerators have potential medical applications in [[proton therapy]] for cancer [[PAMELA project]], as proton sources for high intensity neutron production, for non-invasive security inspections of closed cargo containers, for the rapid acceleration of [[muon]]s to high energies before they have time to decay, and as "energy amplifiers", for Accelerator-Driven [[Subcritical reactor|Sub-critical Reactors]] (ADSRs) 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 [[non-proliferation|nuclear weapons proliferation]].
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| 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|muon collider]] facilities.
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| ==Status==
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| 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.<ref>K. Peach et al, Phys Rev ST Accel. Beams 16 (2013)</ref> 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.
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| ==Further reading==
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| * {{Cite journal | publisher = CERN Courier | title = The rebirth of the FFAG | url = http://cerncourier.com/cws/article/cern/29119 | date = Jul 28, 2004 | accessdate = Apr 11, 2012 }}
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| ==References==
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| {{reflist}}
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| [[Category:Accelerator physics]]
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