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| first1 = A.G.
| title = Brief History of FFAG Accelerators
| journal =
| date = Mar 2006
| url = http://www.bnl.gov/isd/documents/31130.pdf
}}</ref><ref>{{cite journal | author=Daniel Clery | date=4 January 2010 | title=The Next Big Beam? | journal=[[Science (journal)|Science]] | volume=327 |pages=142–143 | doi=10.1126/science.327.5962.142 | pmid=20056871 | bibcode = 2010Sci...327..142C | issue=5962 | url = | format = | accessdate = }}</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.
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 <ref name=briefhistory /> and to accelerate muons in a [[Neutrino Factory|neutrino factory]] since the mid-1990s.
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| journal = Proc. 5th International Conference on High Energy Accelerators
| year = 1985
|
}}</ref> were published.▼
▲}}</ref> were published.
With the shutdown of MURA which began 1963 and ended 1967,<ref>{{Cite book
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===Continuing development===
[[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>{{cite journal
[[File:PhilM3-Gode.pdf|thumb|Example of a 16-cell superconducting FFAG. Energy: 1.6 GeV, average radius 26 m.]]
In the early 1980s, it was suggested by Phil Meads that an FFAG was suitable and advantageous as a proton accelerator for an [[Spallation#Production of neutrons at a spallation neutron source|intense spallation neutron source]],<ref>{{cite journal
Conferences exploring this possibility were held at Jülich Research Centre, starting from 1984.<ref>{{cite web|url=http://jdsweb.jinr.ru/record/38097|title= 2nd Jülich Seminar on Fixed Field Alternating Gradient Accelerators (FFAG)|___location=[[Jülich]]|last=Wüstefeld|first=G.|date=14 May 1984|accessdate=12 February 2017}}</ref> There have also been numerous annual [[Academic conference|workshops]] focusing on FFAG accelerators<ref>{{cite web|url=http://accelconf.web.cern.ch/AccelConf/p05/papers/foac003.pdf|title=New Concepts in FFAG Design for Secondary Beam Facilities and Other Applications|first=M.K.|last=Craddock|year=2005|accessdate=12 February 2012}}</ref> at [[CERN]], [[The High Energy Accelerator Research Organization|KEK]], [[Brookhaven National Laboratory|BNL]], [[TRIUMF]], [[Fermilab]], and the Reactor Research Institute at [[Kyoto University]].<ref>{{cite web|url=https://www.bnl.gov/ffag14/pastWorkshops.php|title=Previous Workshops|publisher=[[Brookhaven National Laboratory|BNL]]|accessdate=12 February 2017}}</ref> In 1992, the European Particle Accelerator Conference at CERN was about FFAG accelerators.<ref name=FFAGopts>{{Cite journal
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| date = 13 October 1992
| url = https://accelconf.web.cern.ch/accelconf/c92/papers/xii-02.pdf
}}</ref><ref>{{cite journal|title=Fourth Accelerator Meeting for the EPNS|journal=European Particle Accelerator Conference
The first proton FFAG was successfully construction in 2000,<ref>{{cite journal|author=M. Aiba et al.|title= Development of a FFAG Proton Synchrotron|journal=European Particle Accelerator Conference|year=2000
With [[superconducting magnets]], the required length of the FFAG magnets scales roughly as the inverse square of the magnetic field.<ref name=mewu>{{Cite journal
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| first2 = G. | last2 = Wüstefeld
| title = An FFAG Compressor and Accelerator Ring Studied for the German Spallation Neutron Source
| journal = Proceedings of PAC 1985 / IEEE Trans Nucl. Sci. NS-32
| year = 1985
| url = http://accelconf.web.cern.ch/accelconf/p85/pdf/pac1985_2697.pdf
}}</ref> In 1994, a coil shape which provided the required field with no iron was derived.<ref>{{cite journal
In 2010, after the workshop on FFAG accelerators in [[Kyoto]], the construction of the [[EMMA (accelerator)|Electron Machine with Many Applications]] (EMMA) was completed at [[Daresbury Laboratory]], [[UK]]. This was the first non-scaling FFAG accelerator. Non-scaling FFAGs are often advantageous to scaling FFAGs because large and heavy magnets are avoided and the beam is much better controlled.<ref>{{cite web|url=http://www-pub.iaea.org/MTCD/Publications/PDF/P1251-cd/papers/65.pdf|title=Non-Scaling Fixed Field Gradient Accelerator (FFAG) Design for the Proton and Carbon Therapy|author=D. Trbojevic, E. Keil, A. Sessler|access-date=12 February 2017}}</ref>
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|publisher=[[McGraw-Hill]]
|___location=New York
|isbn=
}}</ref> are crossed. A machine is scaling if the median plane magnetic field satisfies
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| year = 2013
| first1 = S. | last1 = Brooks
| journal = Physical Review Special Topics: Accelerators and Beams
| doi=10.1103/PhysRevSTAB.16.084001
| volume=16
| issue = 8
|bibcode = 2013PhRvS..16h4001B }}</ref>▼
| pages = 084001
▲ |bibcode = 2013PhRvS..16h4001B }}</ref>
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 [[Cyclotron#Isochronous cyclotron|isochronously]]. Isochronousity of the revolution period enables continuous beam operation, therefore offering the same advantage in power that isochronous cyclotrons have over [[synchrocyclotron]]s. Isochronous accelerators have no [[longitudinal focusing|longitudinal beam focusing]], but this is not a strong limitation in accelerators with rapid ramp rates typically used in FFAG designs.
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==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.<ref>{{cite journal|last1=Peach|first1=K|title=Conceptual design of a nonscaling fixed field alternating gradient accelerator for protons and carbon ions for charged particle therapy|journal=Phys Rev ST Accel Beams|date=11 March 2013|volume=16|
==Further reading==
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