|
}}</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. | authorlink1 = Lawrence W. Jones| last2 = Sessler | first2 = A. M. | last3 = Symon | first3 = K. R. | doi = 10.1126/science.316.5831.1567 | title = A Brief History of the FFAG Accelerator | journal = [[Science (journal)|Science]] | volume = 316 | issue = 5831 | pages = 1567 | year = 2007 | pmid = 17569845| pmc = }}</ref>
[[Donald Kerst]], working with Symon, filed a patent for the spiral-sector FFAGFFA accelerator at around the same time as Symon's Radial Sector patent.<ref>{{US patent reference
| number = 2932798
| y = 1960
}}</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>
[[File:mura ring.jpg|thumb|Layout of MURA FFAGFFA]]
[[Midwestern Universities Research Association|MURA]] designed 10 GeV and 12.5 GeV proton FFAGsFFAs that were not funded.<ref>F. C. Cole, Ed., 12.5 GeV FFAGFFA Accelerator, MURA report (1964)</ref> Two scaled down designs, one for 720 MeV<ref>{{Cite journal
| title = Design of a 720 MeV Proton FFAGFFA Accelerator
| year = 1963
| first1 = F. T. | last1 = Cole
| first4 = C. | last4 = Curtis
| first5 = H. | last5 = Meier
| title = Design Study of a 500 MeV FFAGFFA Injector
| journal = Proc. 5th International Conference on High Energy Accelerators
| year = 1985
| publisher = World Scientific
| bibcode = 2010ine..book.....J
}}</ref> the FFAGFFA concept was not in use on an existing accelerator design and thus was not actively discussed for some time.
===Continuing development===
[[File:aspun.jpg|thumb|ASPUN ring (scaling FFAGFFA). 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}}</ref>]]
[[File:PhilM3-Gode.pdf|thumb|Example of a 16-cell superconducting FFAGFFA. Energy: 1.6 GeV, average radius 26 m.]]
In the early 1980s, it was suggested by Phil Meads that an FFAGFFA 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 FFAGFFA 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}}</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|deadurl=yes|archiveurl=https://web.archive.org/web/20040909173546/http://www.anl.gov/Science_and_Technology/History/Anniversary_Frontiers/physhist.html|archivedate=9 September 2004}}</ref> and the Cooler [[Synchrotron]] at [[Jülich Research Centre]].<ref>{{cite web|url=http://www.fz-juelich.de/ikp/EN/Forschung/Beschleuniger/_doc/COSY.html|title=COSY - Fundamental research in the field of hadron, particle, and nuclear physics|publisher= Institute for Nuclear Physics|accessdate=12 February 2017}}</ref>
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 (FFAGFFA)|___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 FFAGFFA accelerators<ref>{{cite journal|url=http://accelconf.web.cern.ch/AccelConf/p05/papers/foac003.pdf|title=New Concepts in FFAG Design for Secondary Beam Facilities and Other Applications|journal=21St Particle Accelerator Conference (Pac 05)|pages=261|first=M.K.|last=Craddock|year=2005|accessdate=12 February 2012|bibcode=2005pac..conf..261C}}</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 FFAGFFA accelerators.<ref name=FFAGopts>{{Cite journal
| first1 = S. | last1 = Martin
| first2 = P. | last2 = Meads
}}</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 FFAGFFA 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|access-date=}}</ref> initiating a boom of FFAG activities in [[Particle physics|high-energy physics]] and [[medicine]].
With [[superconducting magnets]], the required length of the FFAGFFA magnets scales roughly as the inverse square of the magnetic field.<ref name=mewu>{{Cite journal
| first1 = P. F. | last1 = Meads
| first2 = G. | last2 = Wüstefeld
}}</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}}</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 (ICANS)|date=24 May 1993}}</ref>
In 2010, after the workshop on FFAGFFA 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 FFAGFFA accelerator. Non-scaling FFAGsFFAs are often advantageous to scaling FFAGsFFAs 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>
==Scaling vs non-scaling types==
The magnetic fields needed for an FFAGFFA are quite complex. The computation for the magnets used on the Michigan FFAGFFA 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.
The MURA machines were scaling FFAGFFA 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. | authorlink1 = Milton Stanley Livingston
*<math>f(\psi)</math> is an arbitrary function that enables a stable orbit.
For <math>k>>1</math> an FFAGFFA 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 FFAGFFA Accelerators, International Conference on High Energy Accelerators, CERN-1959, pp 82-88.</ref>
The idea of building a non-scaling FFAGFFA 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 FFAGFFA 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 FFAGFFA 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'' FFAGFFA called ([[EMMA (accelerator)|EMMA]]) (Electron Machine with Many Applications) has been successfully operated at Daresbury Laboratory, UK,.<ref>{{Cite journal
| title = EMMA, The World's First Non-scaling FFAG
| url = http://cern.ch/AccelConf/e08/papers/thpp004.pdf
|bibcode = 2013PhRvS..16h4001B }}</ref>
The major advantage offered by a VFFAGVFFA design over a FFAGFFA 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 FFAGFFA designs.
The major disadvantages include the fact that VFFAGsVFFAs requires unusual magnet designs and currently VFFAGVFFA designs have only been [[Dynamical simulation|simulated]] rather than tested.
==Applications==
FFAGFFA 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 [[muon]]s to high energies before they have time to decay, and as "energy amplifiers", for [[Accelerator-driven sub-critical reactor|Accelerator-Driven Sub-critical Reactors]] (ADSRs) / [[Subcritical reactor|Sub-critical Reactors]] in which a [[neutron]] beam derived from a FFAGFFA 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]].
Because of their quasi-continuous beam and the resulting minimal acceleration intervals for high energies, FFAGsFFAs have also gained interest as possible parts of future [[Muon Collider|muon collider]] facilities.
==Status==
In the 1990s, researchers at the KEK particle physics laboratory near Tokyo began developing the FFAGFFA 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|issue=3|pages=030101|doi=10.1103/PhysRevSTAB.16.030101|bibcode=2013PhRvS..16c0101P}}</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.
==Further reading==
| 