Issue 76

Beam Dynamics Newsletter

3.2 Overview of Fixed Field Alternating Gradient Accelerators

Grahame H. Rees (RAL, U.K., retired)

Non-linear magnetic field FFAs were invented by Ohkawa  [1] in 1953 and subsequently prototyped at MURA (Mid-western Universities Research Association), Wisconsin  [2]. The combined function gradient magnets had either spiral edges, or formed F(+) O D(-) O type lattice cells, where (\( \pm \)) indicates magnet bend directions. Field profiles were defined by \( B_{y=0}=B=B_0(1+x/r_0)^K \), where \( K \) is the constant field index, \( x \) is the radial offset from a \( B_0 \) reference orbit, at a distance \( r_0 \) from the FFA ring’s centre, and \( r=r_0+x \). Local, normalized field gradients are: \( B^\prime /B\rho =K_v=K/\rho r \), where \( \rho _0 \) and \( \rho \) are the local magnet bend radii. Beam orbits are said to be scaling if different momenta orbits are scaled replicas of one another. Conditions for F D lattice scaling are that the beam orbits follow arcs at a constant field level and magnet edges are aligned with radial lines drawn to the ring centre \( (\rho /\rho _0=r/r_0) \). In most practical cases, these conditions are not met.

Interest in FFAs returned in the 1990s  [3], mainly in Japan, employing spiral or {D(-) o F(+) o D(-) O} triplet cell designs (with short o and longer O drift lengths). A 150 MeV proton triplet FFA was built at KEK  [4]. A chain of three proton FFAs was built at KURRI1  [5], to allow ADSR studies at KURRI’s research reactor. There is a 0.1-2.5 MeV spiral ring and 2.5-20 MeV and 20-150 MeV triplet rings. The output energy of the first ring is adjustable and fields may be lowered in the other rings to provide scaled momentum ranges. The first ring uses induction acceleration, while the other two use broadband magnetic alloy (MA) Ohmori-type cavities  [6] for the acceleration.

A FFA may use an internal emittance recovery target (ERIT) for an intense source of secondary particles (neutrons, pions etc.)  [7]. A 10 MeV proton FFA has been developed for a KURRI neutron source since 2005, using a 5 micron thick beryllium target and a 200 kV, ionisation cooling cavity. Cooling limits transverse and longitudinal emittance growth due to multiple scattering and energy loss in the target. ERIT has been modified recently into a POP-MERIT (multiplex energy recovery internal target), with a reduction of the field index to allow simultaneous fixed frequency acceleration and storage  [8], and the studies are to continue.

Traditional doublet or triplet FFAs have wide magnets and so are costly for higher intensities; studies at ANL, Chicago and Jülich, Germany were discontinued after low loss H\( ^- \) injection proved to be a problem area. Scaling pumplet cells  [9], {O d(-) o F(+) o D(-) o F(+) o d(-) O} and {O f(+) o D(-) o F(+) o D(-) o f(+) O} both allow reduced apertures, but H\( ^- \) injection remains a problem for high powers. An alternative of direct, two plane multi-turn injection of protons  [10] allows a higher current, lower emittance injector linac and an insertion-free FFA ring. A novel proposal is that of a vertical orbit excursion, superconducting magnet FFA  [11], using a vertical field component to yield a skew quadrupole focusing action.

FFA rings may operate at a high repetition rate or, possibly, in a cw mode, to reach high power. Schemes appeared in the late 1990s to reduce the orbit separations and hence the radial apertures. Different arrangements of magnets were considered which were far removed from the scaling designs. Orbit bend radii were allowed to alter for each orbit, with continuously changing orbit beam dynamics. Designs were obtained for non-isochronous or nearly, or fully isochronous rings. A design using linear focusing magnets was proposed in 1999 for the rapid acceleration of high energy, \( \mu ^\pm \) beams  [12].

Another type of non-scaling FFA accelerator  [13] was proposed in 2004 by A.G. Ruggiero (BNL), for use in proton or heavy ion, high power driver applications. It again employed linear focusing gradient magnets  [14]. Beam dynamics is different from that of the muons, however, as the normalised beam emittances are smaller, space charge issues are involved, acceleration is always in the stable region, and operation is far away from isochronism. Both designs are similar, though, in that the negative chromaticities give large variations of tune with momentum, so that integer and half integer, betatron resonances are crossed in the ten to a hundred turns of acceleration and yet give only a small growth of the emittances.

An electron ring, EMMA, was built and commissioned at Daresbury Laboratory to study beam dynamic issues that occur in accelerators similar to those of references  [12–14]. EMMA operated over the energy range 10 to 20 MeV and had 42 F D doublet cells and 19 rf cavities operating at 1.3 GHz. Studies were made of rapid acceleration, with large variations of the ring tunes, and the machine was able to demonstrate a new type of out-of-bucket acceleration called serpentine  [15]. EMMA was the only FFA to have been built in Europe and the world’s first non-scaling fixed field alternating gradient accelerator; however, it has since been dismantled. Despite all the studies that have been made, no high power FFA has yet been built.

Some of the design issues listed were previously reviewed in reference  [16].

1 Kyoto University Research Reactor Institute. The name has recently been changed to the Kyoto University Institute of Integrated Radiation and Nuclear Science, KURNS.

  • [1]  T. Ohkawa, Proceedings of the annual meeting of the JPS, Japanese Physical Society (1953).

  • [2]  K.R. Syman et al., (MURA), Phys. Rev., p. 1837, 103 (1956).

  • [3]  M.K. Craddock, The Rebirth of the FFAG, CERN Courier, 44-6, (2004).

  • [4]  M. Aiba et al., Status of 150 MeV Proton FFAG, Proceedings of International Workshop on FFAG Accelerators, KURRI (2005).

  • [5]  Y. Mori, Development of FFAG Accelerators at KURRI, Proceedings of International Workshop on FFAG Accelerators, KURRI (2006).

  • [6]  C. Ohmori et al., High Field-gradient Cavities Loaded With Magnetic Alloys for Synchrotrons, Proceedings of PAC99, p413-417, New York (1999).

  • [7]  Y. Mori, Secondary source by FFAG–ERIT scheme, Proceedings of International Workshop on FFAG Accelerators, KURRI (2005).

  • [8]  Y. Mori, Beam study of MERIT-FFAG, Proceedings of International Workshop on FFAG Accelerators, KURRI (2018).

  • [9]  G.H. Rees, FFAG Studies for Neutrino Factory Accelerators, Neutrino Factory Workshop, (2005).

  • [10]  G.H. Rees, Direct Proton Injection for Spallation Source Rings, RAL internal note GHR1/ASTeC/Nov. (2016).

  • [11]  S.J. Brooks, Vertical orbit excursion, fixed field alternating gradient accelerators, Phys. Rev. Vol. 16, Issue 8, Aug (2013).

  • [12]  C.J. Johnstone et al., Fixed field circular accelerator designs, Proceedings of PAC99, p3068-3070 (1999).

  • [13]  A.G. Ruggiero, FFAG-based high intensity proton drivers, Proceedings of ICFA-HB2004, 324 (2004).

  • [14]  A.G. Ruggiero, FFAG-based proton and ion drivers, ICFA Beam Dynamics Newsletter No. 43, 84 (2007)

  • [15]  S. Machida, et al., Nature Physics 8, 243 (2012).

  • [16]  C.R. Prior, issue editor, FFAG accelerators, ICFA Beam Dynamics Newsletter No. 43, p12-126 (2007).