Fixed-field alternating gradient accelerator: Difference between revisions

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| 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 }}</ref>

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.

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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 initial concept of the FFA was developed in the 1950's1950s, but was not actively explored beyond a few test machines until 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.

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

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| d = 12

| inventor = [[Keith Symon|Keith R. Symon]]

| title = [httphttps://wwwpatents.google.com/patents?id=ZGZVAAAAEBAJpatent/US2932797 Imparting Energy to Charged Particles]

}}</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. | author-link1 = 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| s2cid = 5201822 }}</ref>

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| d = 12

| inventor = [[Donald William Kerst]] and [[Keith Symon|Keith R. Symon]]

| title = [httphttps://wwwpatents.google.com/patents?id=ZWZVAAAAEBAJpatent/US2932798 Imparting Energy to Charged Particles]

}}</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 = [httphttps://wwwpatents.google.com/patents?id=4aEBAAAAEBAJpatent/US2890348 Particle Accelerator]

}}</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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| 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 (ICANS)|date=24 May 1993}}</ref>

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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*<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,.<ref>{{Cite journal

| title = EMMA, The World's First Non-scaling FFAG

| url = http://cern.ch/AccelConf/e08/papers/thpp004.pdf

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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=Physical Review Special Topics - Accelerators and Beams|date=11 March 2013|volume=16|issue=3|pages=030101|doi=10.1103/PhysRevSTAB.16.030101|bibcode=2013PhRvS..16c0101P|doi-access=free}}</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.

== See also==

* [[Energy amplifier]] a [[subcritical nuclear reactor]] which might use an FFA as a [[neutron source]]