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{{short description|Circular particle accelerator concept}}
A '''Fixed-Field alternating gradient Accelerator''' ('''FFA'''; also abbreviated '''FFAG''') is a circular [[particle accelerator]] concept
| last1 = Ruggiero
| first1 = A.G.
| title = Brief History of FFA 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
In all circular accelerators, magnetic fields are used to bend the particle beam. Since the [[Lorentz force|magnetic force]] required to bend the beam increases with particle energy, as the particles accelerate, either their paths will increase in size, or the magnetic field must be increased over time to hold the particles in a constant size orbit. Fixed-field machines, such as cyclotrons and FFAs, use the former approach and allow the particle path to change with acceleration.
Although the development of FFAs 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.▼
In order to keep particles confined to a beam, some type of focusing is required. Small variations in the shape of the magnetic field, while maintaining the same overall field direction, are known as weak focusing. Strong, or alternating gradient focusing, involves magnetic fields which alternately point in opposite directions. The use of alternating gradient focusing allows for more tightly focused beams and smaller accelerator cavities.
FFAs use fixed magnetic fields which include changes in field direction around the circumference of the ring. This means that the beam will change radius over the course of acceleration, as in a cyclotron, but will remain more tightly focused, as in a synchrotron. FFAs therefore combine relatively less expensive fixed magnets with increased beam focus of strong focusing machines.<ref>{{cite arXiv |last=Sheehy |first=S.L. |author-link= Suzie Sheehy |eprint= 1604.05221 |title= Fixed-Field Alternating Gradient Accelerators |class= physics.acc-ph|date= April 18, 2016 }}</ref>
▲
The revival in FFA research has been particularly strong in Japan with the construction of several rings. This resurgence has been prompted in part by advances in [[Radio frequency|RF]] cavities and in magnet design.<ref name=mori2004>{{Cite journal
| first1 = Y.
| last1 = Mori | title = Developments of FFA Accelerator
| journal = Proceedings of FFAG04 /
| year = 2004
| url = http://hadron.kek.jp/FFAG/FFAG04_HP/pdf/mori.pdf
| access-date = 2016-05-04
}}</ref>▼
| archive-url = https://web.archive.org/web/20161220233929/http://hadron.kek.jp/FFAG/FFAG04_HP/pdf/mori.pdf
| archive-date = 2016-12-20
| url-status = dead
▲ }}</ref>
== History ==
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===First development phase===
[[File:MichiganFFAGmark1.jpg|thumb|The Michigan Mark I FFA accelerator. This 400KeV electron accelerator was the first operational FFA accelerator. The large rectangular part on the right is the [[betatron]] transformer core.]]
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.<ref>Lawrence W. Jones, Kent M. Terwilliger, [http://inspirehep.net/record/38999/files/MURA-104.pdf A Small Model Fixed Field Alternating Gradient Radial Sector Accelerator], Technical Report MURA-LWJ/KMT-5 (MURA-104), April 3, 1956; contains photos, scale drawings and design calculations.</ref> 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 book | last1 = Jones | first1 = L. W. | chapter = Kent M. Terwilliger; graduate school at Berkeley and early years at Michigan, 1949–1959| title = Kent M. Terwilliger memorial symposium, 13−14 Oct 1989| series = [[AIP Conference Proceedings]] | doi = 10.1063/1.41146
| number = 2932797
| y = 1960
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| d = 12
| inventor = [[Keith Symon|Keith R. Symon]]
| title = [
}}</ref> Ohkawa worked with Symon and the [[Midwestern Universities Research Association|MURA]] team for several years starting in 1955.<ref>{{Cite journal | last1 = Jones | first1 = L. W. |
[[Donald Kerst]], working with Symon, filed a patent for the spiral-sector FFA accelerator at around the same time as Symon's Radial Sector patent.<ref>{{US patent reference
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| d = 12
| inventor = [[Donald William Kerst]] and [[Keith Symon|Keith R. Symon]]
| title = [
}}</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
| number = 2890348
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| d = 09
| inventor = Tihiro Ohkawa
| title = [
}}</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
| last1 = Schopper | first1 = Herwig F.
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===Continuing development===
[[File:aspun.jpg|thumb|ASPUN ring (scaling FFA). 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|title=ASPUN, Design for an Argonne Super Intense Pulsed Neutron Source|last1=Khoe|first1=T.K.|last2=Kustom|first2=R.L.|volume=30|issue=4|pages=2086–2088|journal=[[IEEE Transactions on Nuclear Science]]|date=August 1983|doi=10.1109/tns.1983.4332724|bibcode=1983ITNS...30.2086K|url=https://digital.library.unt.edu/ark:/67531/metadc1108437/|issn=0891-9356|citeseerx=10.1.1.609.1789|s2cid=31021790 }}</ref>]]
[[File:PhilM3-Gode.pdf|thumb|Example of a 16-cell superconducting FFA. Energy: 1.6 GeV, average radius 26 m.]]
In the early 1980s, it was suggested by Phil Meads that an FFA 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|title=An FFA Compressor and Accelerator Ring Studied for the German Spallation Neutron Source|last1=Meads|first1=P.|last2=Wüstefeld|first2=G.|volume=32|issue=5 (part II)|pages=2697–2699|journal=[[IEEE Transactions on Nuclear Science]]|date=October 1985|bibcode=1985ITNS...32.2697M|doi=10.1109/TNS.1985.4334153|s2cid=41784649 }}</ref> starting off projects like the Argonne Tandem Linear Accelerator at [[Argonne National Laboratory]]<ref>{{cite web |title = Argonne History: Understanding the Physical Universe |publisher = Argonne National Laboratory |url = http://www.anl.gov/Science_and_Technology/History/Anniversary_Frontiers/physhist.html#neutrino|
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 (FFA)|___location=[[Jülich]]|last=Wüstefeld|first=G.|date=14 May 1984|
| first1 = S. | last1 = Martin
| first2 = P. | last2 = Meads
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}}</ref><ref>{{cite journal|title=Fourth Accelerator Meeting for the EPNS|journal=European Particle Accelerator Conference|date=24 March 1992|first=E.|last=Zaplatin}}</ref>
The first proton FFA was successfully construction in 2000,<ref>{{cite journal|author=M. Aiba|display-authors=etal|title= Development of a FFAG Proton Synchrotron|journal=European Particle Accelerator Conference|year=2000
With [[superconducting magnets]], the required length of the FFA 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 =
| volume = 32
| issue = 5
| pages =
| year = 1985
| url = http://accelconf.web.cern.ch/accelconf/p85/pdf/pac1985_2697.pdf
| bibcode = 1985ITNS...32.2697M
| doi = 10.1109/TNS.1985.4334153
| s2cid = 41784649
}}</ref> In 1994, a coil shape which provided the required field with no iron was derived.<ref>{{cite journal|title=Superconducting magnet design for Fixed-Field Alternating-Gradient (FFAG) Accelerator|journal=IEEE Transactions on Magnetics|volume=30|issue=4|pages=2620–2623|date=July 1994|first1=M.|last1= Abdelsalam|first2= R.|last2= Kustom|doi=10.1109/20.305816|bibcode=1994ITM....30.2620A|url=https://digital.library.unt.edu/ark:/67531/metadc1404050/}}</ref> This magnet design was continued by S. Martin ''et al.'' from [[Jülich]].<ref name=FFAGopts/><ref>{{cite journal|author=S. A. Martin|display-authors=etal|title=FFAG Studies for a 5 MW Neutron Source|journal=International Collaboration on Advanced Neutron Sources
In 2010, after the workshop on FFA 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 FFA accelerator. Non-scaling FFAs are often advantageous to scaling FFAs 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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The MURA machines were scaling FFA 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>
{{Cite book
|last1=Livingston |first1=M. S. |
|last2=Blewett |first2=J.
|year=1962
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*<math> \psi=N~[\tan~\zeta~\ln(r/r_0)~ - ~\theta]</math>,
*<math>k</math> is the field index,
*<math>N </math> is the periodicity,
*<math>\zeta</math> is the spiral angle (which equals zero for a radial machine),
*<math>r</math> the average radius, and
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The idea of building a non-scaling FFA 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 FFA 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 FFA 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'' FFA called ([[EMMA (accelerator)|EMMA]]) (Electron Machine with Many Applications) has been successfully operated at Daresbury Laboratory, UK
| title = EMMA, The World's First Non-scaling FFAG
| url = http://cern.ch/AccelConf/e08/papers/thpp004.pdf
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| issue = 8
| pages = 084001
|bibcode = 2013PhRvS..16h4001B | doi-access = free
}}</ref> The major advantage offered by a VFFA design over a FFA design is that the path-length is held constant between particles with different energies and therefore relativistic particles travel [[Cyclotron#Isochronous cyclotron|isochronously]]. Isochronicity 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 FFA designs.
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==Status==
In the 1990s, researchers at the KEK particle physics laboratory near Tokyo began developing the FFA 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=
== See also==
* [[Energy amplifier]] a [[subcritical nuclear reactor]] which might use an FFA as a [[neutron source]]
==Further reading==
* {{
==References==
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