Suzanne Sheehy, University of Oxford, United Kingdom, and University of Melbourne, Australia
The Fixed Field Alternating Gradient accelerator is a flexible accelerator type, which can be used for leptons or hadrons over a wide energy range. To understand where FFAs fit in the landscape of applications, we first need to look at how accelerators are used worldwide and which properties are required in terms of particle type, energy, intensity, size, flexibility and so on. Then, we can identify areas where FFAs may have advantages over existing cyclotron, synchrotron, LINAC and electrostatic accelerator technologies.
Of course, the applications of particle accelerators are incredibly broad. There are estimated to be between 35,000 and 45,000 of them in the world and their use can be roughly divided into 50% industrial application and 50% medical, with just a few large machines for scientific applications and particle physics . Some of these applications are well established, with machines produced and developed almost exclusively in industry. These include machines in the medical domain including radioisotope production cyclotrons and short 3GHz linacs for electron and X-ray radiotherapy (radiotherapy alone accounts for around 15,000 accelerators worldwide, although a shortage exists in low and middle-income countries ).
Machines for ion implantation in the semiconductor industry, electron beam processing and irradiation are key commercial applications. Other commercial applications are rapidly growing. These include proton and ion (hadron) therapy machines, neutron generators, accelerators for security applications, inspection using ion beam analysis, non-destructive testing and compact synchrotron radiation sources. Other applications cross over into cultural and heritage areas, such as the established techniques of ion beam analysis in art and ceramics, accelerator mass spectrometry in radiocarbon dating, through to the much newer muon tomography currently performed using cosmic rays.
A revival of interest since the 1990s has seen a number of FFAs constructed, including scaling and linear non-scaling variants for protons [3, 4] and electrons  respectively. Since this time, the range of FFA designs has rapidly diversified and there are now designs with non-linear field profiles and non-radial edge angles, racetrack shapes and other super-periodic structures, dispersion suppression sections, vertical orbit movement and other innovations. While it would be impossible to give an exhaustive review of such developments here, I will highlight some examples to outline general direction of travel in this constantly evolving field. The purpose of this article is to outline which applications FFAs have been used for, which areas are active in R&D but have not yet been realised and which may have potential in the future.
FFA accelerators have been considered in particle physics projects for their large energy and dynamic acceptance. The primary work in this application was undertaken in the context of the muon collider and neutrino factory programmes [5–7]. That work has now evolved into potential nearer-term muon and neutrino projects. For instance, the NuSTORM project which aims to create a high flux of neutrinos in order to measure neutrino couplings precisely, an FFA option may be able to store an enhanced number of muons compared to a conventional storage ring . The PRISM project (Phase Rotated Intense Slow Muon source) , aims to study charged lepton flavour violation by creating a facility which reduces the muon beam energy spread by phase rotation and purifies the muon beam in the storage ring. A 6-cell FFA ring was constructed and tested using alpha particles in Osaka, demonstrating phase rotation. The PRISM task force continues to address the challenges in realising an FFA based muon-to-electron conversion experiment .
A large amount of R&D work has also gone into the development of recirculating non-scaling FFA arcs for the eRHIC project . The most recently developed, constructed and commissioned FFA is the non-scaling FFA arcs of the CBETA project at Cornell, demonstrating the capacity of one FFA arc to enable a 4-turn Energy Recovery Linac (ERL with superconducting injector LINAC [13, 14]. The layout and magnet girder are shown in Fig. 1.
Looking forward, one current R&D project which is pushing forward the development of high intensity hadron FFAs is the consideration of this technology for a novel short pulse spallation neutron source, under the auspices of the ISIS-II study . In the present design, a novel ‘FD Spiral’ configuration  is employed. Advantages of the FFA method over the alternative rapid cycling synchrotron option include; flexibility in the pulse rate up to 100 Hz, lower power requirements for DC operation of magnets, and potential for high intensity operation. However, the technology is less mature than the rapid cycling synchrotron, so detailed studies and ideas for prototyping are currently underway.
A number of projects are looking to combine the large energy-acceptance capability of FFA optics with novel accelerator techniques which (at present) produce beams with a large energy spread. One such application, discussed at the 2018 FFA workshop, was the idea of a FFA-based Free Electron Laser system with a laser-plasma wakefield injector. The challenge of course would be to utilise all of the beam created in a LPWA source to generate radiation at a single wavelength in a relatively compact setup. Meanwhile, the Centre for Clinical Application of Particles (CCAP) at Imperial College, London, are discussing ideas for a laser-plasma injected beamline for radiobiology facility, with long term plans for an FFA as part of the facility .
FFAs are considered a promising future option for medical applications due to their capability of high repetition rate and variable energy extraction operation with no limitation on top energy. This appears to be an advantage over synchrotrons in terms of repetition rate and achievable intensity, and also over cyclotrons as FFAs should be able to accelerate heavier ions for therapy, with clean variable energy fast extraction and no need for a degrader system.
FFAs in the right energy range for hadron therapy have been designed and realised in Japan with a 150 MeV radial sector scaling FFA  for protons, with versions at Kyoto University (shown in Fig. 2) and Kyushu University. Prototype magnets were also produced for the spiral scaling machine RACCAM (Recherche en ACCélérateurs et Applications Médicales) which took a multi-room delivery approach to optimise treatment time [21, 22]1.
A review of accelerators for hadron therapy in 2014  gives a convenient overview of the many different approaches and designs of FFA accelerators for hadron therapy facilities, which was a very active research area particulary from around 2004 - 2012. Designs for linear non-scaling FFA based hadron therapy facilities  emerged in the early 2000’s. However, integer resonance crossing was highlighted as a potential issue in a hadron ns-FFA accelerator with realistic acceleration over thousands of turns . Note that this is due to the limited acceleration rate achievable in a hadron machine of this type, whereas there was no beam degradation observed in the fast-accelerating EMMA demonstrator machine , where serpentine acceleration is used.
To overcome the resonance crossing issue, non-scaling variants with small orbit excursion and incorporating non-linear magnetic fields emerged, primarily as part of the PAMELA (Particle Accelerators for MEdicaL Applications) project  shown in Fig. 3. The fields were configured to stabilise the betatron tune and ensure that no integer or half-integer resonances were crossed during acceleration .
An alternative method to stabilise tunes using magnet edge angles and arbitrary functions of field with radius was also developed . Continued work in this direction for non-scaling arbitrary field FFA designs now includes a concept for ions including helium and carbon from 70/90 to 430 MeV/u [29, 30]. The design is based on a racetrack configuration which allows long straight sections, where an extraction system based on a bipolar field is located. While this has not yet been demonstrated in an operating machine, it would allow a fast variable energy extraction system with no degrader. The design is near to isochronous for CW operation, which leads to a large cyclotron-like radial aperture for both the magnets and rf system.
In recent years, the PAMELA work was taken forward to develop normal-conducting designs in a racetrack configuration , removing the seemingly complicated superconducting magnets of the PAMELA design and increasing the energy range in one ring to 350 MeV with proton CT in mind. A microtron-like FFA has also been proposed for Carbon Ions, and a patent application is in process . At the time of writing, none of these designs have been realised in operating facilities.
1 A full facility based on this design was not part of the original funded project.
In addition to the accelerator, a clinical hadron therapy centre also requires transport lines and gantries which can focus, scan and deliver the beam to the patient at any angle. The potential advantage of FFA optics in this domain is the large energy acceptance with relatively compact magnets to enable fast variable energy delivery all the way to the patient, and the potential to use permanent or superconducting magnets to reduce the size and weight of existing gantries. The key R&D work on non-scaling FFA gantries has been carried out by Trbojevic et al. , and a number of patents now exist in this area although no clinical gantries of this type have yet been realised.
With the advent of linear accelerators such as that made by ADAM/AVO  which can change energy at a high repetition rate around 100 Hz, interest may well emerge in the use of FFA optics to deliver beams in a large energy acceptance design, even if the accelerator itself is not an FFA. Further work toward this including approaches using adiabatic matching have recently been studied .
A major step toward the realisation of permanent magnet beamlines applicable to hadron therapy gantries was made recently at Brookhaven National Laboratory (Fig. 4), where a linear non-scaling permanent magnet arc bending through 40 degrees was demonstrated with electrons over the energy range of 17-80 MeV kinetic energy, highlighting the efficacy of using ns-FFA technology over a factor of 4 in momentum .
Compact high current FFAs may be applied to radio-isotope production. One such design is the Proton Isotope Production (PIP) design  shown in Fig.5. This is a cyclotron-like FFA being studied for proton energies up to 26 MeV for the production of radioisotopes, in particular Tc. The magnetic field varies from 0.99 to 1.03 T up to a 1.5 m radius and the gradient is optimised by adjusting the magnet geometry to stabilise the tunes and enhance beam focusing whilst maintaining isochronicity. The use of a thin internal target and recycled beam is being investigated as it could greatly improve production efficiency. At present, simulations with a 20 mA beam in OPAL show good transmission through the acceleration cycle of over 98%.
The design and implementation of an electron FFA with serpentine acceleration for industrial applications has now been realised with NHV Corp in Japan . The primary requirements were for fixed frequency RF and fixed magnetic field, providing roughly 10 MeV electrons at a high current. The design built on earlier work on serpentine acceleration in a scaling FFA .
A substantial amount of work has been undertaken in designing and understanding how an FFA could act as a high power proton driver for ADS. Of paramount importance here is providing a CW beam; fixed field and fixed rf frequency at the same time. This was achieved in the lower energy electron machines in the previous section, but is substantially more challenging when taking protons up to the 1 GeV energy range required for accelerator driven transmutation systems.
Designs have included a scaling racetrack FFA , which requires challenging levels of RF to open up the serpentine acceleration channel at 20 MV/turn. Similar studies were carried out on a ‘nearly’ isochronous ring using a non-scaling approach , which were again found to be challenging in terms of high RF voltage requirements, although a further iteration toward better isochronicity would be needed to progress the design. Further questions remain in terms of the effect of space charge in an accelerator which uses serpentine acceleration, as there is no longitudinal focusing of the bunch in the serpentine channel. However, a lot of progress has been made on simulation tools, particularly OPAL , which will help answer these questions.
Additional ideas include a vertical excursion FFA with harmonic number jump, the ‘harmonytron’ concept . Machine parameters have been studied for this type of vertical scaling FFA which accelerates proton from 50 MeV to 500 MeV. This concept aims to accelerate protons or ions over a wide range of non-relativistic energies with a fixed frequency rf acceleration and fixed magnetic field, while overcoming the lack of longitudinal focusing in normal isochronous rings (such as cyclotrons).
At Kyoto University (KURNS), an experimental programme is underway which has modified the existing Energy Recovery Internal Target FFA (ERIT) to a demonstrator for muon production, MERIT. The primary changes include a lower energy injection, the introduction of a wedge-shaped target for muon production, and the reduction in k-value of the focusing system of the accelerator. The long-term idea is to create an intense negative muon source for muon nuclear transformation, which is aimed at the mitigation of long lived fission products in existing nuclear waste. MERIT stands for Multiplex Energy Recovery Internal Target. Studies estimate that roughly /sec could be achieved .
The recent developments in FFA accelerators have moved on from just paper design studies to the realisation of FFAs for real world use. Of particular note is the compact electron FFA for electron processing. A number of different types of FFA are now in prototype and commissioning stage for applications ranging from fundamental science through to medical and industrial use. Many design studies have now been completed, particularly in the medical domain. The practical realisation and then commercialisation of medical FFAs, particularly in the domain of beam delivery systems and gantries, is now needed. In all domains but particularly in high power proton applications, creative and novel FFA designs and ideas continue to emerge and evolve. This dynamic activity in the field makes this a particularly exciting time to review the rapid pace of progress. A positive and exciting future lies ahead for the applications of FFAs.
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