A Fixed-Field alternating gradient Accelerator (FFA; also abbreviated FFAG) is a circular
particle accelerator
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.
Large accelerators are used for fundamental research in particle ...
concept that can be characterized by its time-independent magnetic fields (''fixed-field'', like in a
cyclotron
A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: Janu ...
) and the use of alternating gradient
strong focusing
In accelerator physics strong focusing or alternating-gradient focusing is the principle that, using sets of multiple electromagnets, it is possible to make a particle beam simultaneously converge in both directions perpendicular to the direction ...
(as in a
synchrotron
A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed p ...
).
In all circular accelerators, magnetic fields are used to bend the particle beam. Since the
magnetic force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
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.
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.
The initial concept of the FFA was developed in the 1950's, but was not actively explored beyond a few test machines until the mid-1980s, for usage in
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
spallation
Spallation is a process in which fragments of material (spall) are ejected from a body due to impact or stress. In the context of impact mechanics it describes ejection of material from a target during impact by a projectile. In planetary p ...
sources, as a driver for
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wi ...
colliders
and to accelerate muons in a
neutrino factory The Neutrino Factory is a proposed particle accelerator complex intended to measure in detail the properties of neutrinos, which are extremely weakly interacting fundamental particles that can travel in straight lines through normal matter for thous ...
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
RF cavities and in magnet design.
History
First development phase
The idea of fixed-field alternating-gradient synchrotrons was developed independently in Japan by
Tihiro Ohkawa
was a Japanese people, Japanese physicist whose field of work was in Plasma (physics), plasma physics and fusion power. He was a pioneer in developing ways to generate electricity by nuclear fusion when he worked at General Atomics. Ohkawa died S ...
, in the United States by
Keith Symon Keith Randolph Symon (March 25, 1920 – December 16, 2013) was an American physicist working in the fields of accelerator physics and plasma physics.
Symon graduated summa cum laude, Phi Beta Kappa, from Harvard in 1942 with a BA in Philosophy a ...
, and in Russia by
Andrei Kolomensky
Andrei, Andrey or Andrej (in Cyrillic script: Андрэй , Андрей or Андреј) is a form of Andreas/ Ἀνδρέας in Slavic languages and Romanian. People with the name include:
*Andrei of Polotsk (–1399), Lithuanian nobleman
*An ...
. The first prototype, built by
Lawrence W. Jones
Lawrence William Jones (born 1925) is an American academic and professor emeritus in the Physics Department at the University of Michigan. His field of interest is high energy particle physics.
Early life and education
Lawrence W. Jones was ...
and
Kent M. Terwilliger at the
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
used
betatron
A betatron is a type of cyclic particle accelerator. It is essentially a transformer with a torus-shaped vacuum tube as its secondary coil. An alternating current in the primary coils accelerates electrons in the vacuum around a circular path. Th ...
acceleration and was operational in early 1956. That fall, the prototype was moved to the
Midwestern Universities Research Association The Midwestern Universities Research Association (MURA) was a collaboration between 15 universities with the goal of designing and building a particle accelerator for the Midwestern United States. It existed between 1953–1967, but could not achiev ...
(MURA) lab at
University of Wisconsin
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...
, where it was converted to a 500 keV electron
synchrotron
A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed p ...
.
Symon's patent, filed in early 1956, uses the terms "FFAG accelerator" and "FFAG synchrotron". Ohkawa worked with Symon and the
MURA team for several years starting in 1955.
Donald Kerst
Donald William Kerst (November 1, 1911 – August 19, 1993) was an American physicist who worked on advanced particle accelerator concepts (accelerator physics) and plasma physics. He is most notable for his development of the betatron, a novel ...
, working with Symon, filed a patent for the spiral-sector FFA accelerator at around the same time as Symon's Radial Sector patent. 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. This was one of the first
colliding beam accelerators, although this feature was not used when it was put to practical use as the injector for the Tantalus
storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating typically for many hours. Storage of a particular particle depends upon the mass, momentum and usually the charge of th ...
at what would become the
Synchrotron Radiation Center. The 50MeV machine was finally retired in the early 1970s.
MURA designed 10 GeV and 12.5 GeV proton FFAs that were not funded. Two scaled down designs, one for 720 MeV and one for a 500 MeV injector, were published.
With the shutdown of MURA which began 1963 and ended 1967, the FFA concept was not in use on an existing accelerator design and thus was not actively discussed for some time.
Continuing development
In the early 1980s, it was suggested by Phil Meads that an FFA was suitable and advantageous as a proton accelerator for an
intense spallation neutron source, starting off projects like the Argonne Tandem Linear Accelerator at
Argonne National Laboratory
Argonne National Laboratory is a science and engineering research United States Department of Energy National Labs, national laboratory operated by University of Chicago, UChicago Argonne LLC for the United States Department of Energy. The facil ...
and the Cooler
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed p ...
at
Jülich Research Centre
Jülich (; in old spellings also known as ''Guelich'' or ''Gülich'', nl, Gulik, french: Juliers, Ripuarian: ''Jöllesch'') is a town in the district of Düren, in the federal state of North Rhine-Westphalia, Germany. As a border region betwe ...
.
Conferences exploring this possibility were held at Jülich Research Centre, starting from 1984. There have also been numerous annual
workshops
Beginning with the Industrial Revolution era, a workshop may be a room, rooms or building which provides both the area and tools (or machinery) that may be required for the manufacture or repair of manufactured goods. Workshops were the only ...
focusing on FFA accelerators at
CERN
The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Gene ...
,
KEK
, known as KEK, is a Japanese organization whose purpose is to operate the largest particle physics laboratory in Japan, situated in Tsukuba, Ibaraki prefecture. It was established in 1997. The term "KEK" is also used to refer to the laboratory ...
,
BNL,
TRIUMF
TRIUMF is Canada's national particle accelerator centre. It is considered Canada's premier physics laboratory, and consistently regarded as one of the world's leading subatomic physics research centers. Owned and operated by a consortium of uni ...
,
Fermilab
Fermi National Accelerator Laboratory (Fermilab), located just outside Batavia, Illinois, near Chicago, is a United States Department of Energy national laboratory specializing in high-energy particle physics. Since 2007, Fermilab has been operat ...
, and the Reactor Research Institute at
Kyoto University
, mottoeng = Freedom of academic culture
, established =
, type = National university, Public (National)
, endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD)
, faculty = 3,480 (Teaching Staff)
, administrative_staff ...
. In 1992, the European Particle Accelerator Conference at CERN was about FFA accelerators.
The first proton FFA was successfully construction in 2000, initiating a boom of FFA activities in
high-energy physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and b ...
and
medicine
Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pract ...
.
With
superconducting magnets
A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled to cryogenic temperatures during operation. In its superconducting state the wire has no electrical resistance and therefore can conduct much ...
, the required length of the FFA magnets scales roughly as the inverse square of the magnetic field.
In 1994, a coil shape which provided the required field with no iron was derived. This magnet design was continued by S. Martin ''et al.'' from
Jülich
Jülich (; in old spellings also known as ''Guelich'' or ''Gülich'', nl, Gulik, french: Juliers, Ripuarian: ''Jöllesch'') is a town in the district of Düren, in the federal state of North Rhine-Westphalia, Germany. As a border region betwe ...
.
[
In 2010, after the workshop on FFA accelerators in ]Kyoto
Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ci ...
, the construction of the Electron Machine with Many Applications (EMMA) was completed at Daresbury Laboratory
Daresbury Laboratory is a scientific research laboratory based at Sci-Tech Daresbury campus near Daresbury in Halton, Cheshire, England. The laboratory began operations in 1962 and was officially opened on 16 June 1967 as the Daresbury Nuclear ...
, 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.
Scaling vs non-scaling types
The magnetic fields needed for an FFA are quite complex. The computation for the magnets used on the Michigan FFA Mark Ib, a radial sector 500 keV machine from 1956, were done by Frank Cole at the University of Illinois
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...
on a mechanical calculator
A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators wer ...
built by Friden. This was at the limit of what could be reasonably done without computers; the more complex magnet geometries of spiral sector and non-scaling FFAs require sophisticated computer modeling.
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, are crossed. A machine is scaling if the median plane magnetic field satisfies
:,
where
*