A Fixed-Field Alternating Gradient accelerator (FFAG) is a type of circular  particle accelerator  that has features of cyclotron and synchrotrons.  FFAG accelerators combine the cyclotron's advantage of continuous, unpulsed operation, with the synchrotron's relatively inexpensive small magnet ring, of narrow bore.

FFAG accelerators were invented about half a century ago independently by K. Symon. and T. Ohkawa in 1956.  Two. electron prototypes were built and operated at the end of the 50's and the beginning of the 60's to demonstrate the principles of operation at MUM, Madison, Wisconsin

The magnet configuration is a mixture of dipoles and quadrupoles that combines fixed field magnets with the alternating gradient field variation technique, which provides the strong focusing without which the bunch would diverge and be lost.  The  FFAG requires complicated magnetic field configurations which have to be very precisely attained, and the variation in path length requires a matching change in the frequency of the RF used to supply the acceleration.

There are 2 type of FFAGs, Scaling and Non Scaling.

In scaling FFAGs, the bending field increases at a high power of the radius, such that the higher energy orbits move outwards but without changing shape. This is useful to avoid so-called betatron oscillations, resonances in transverse beam stability that have long plagued the designers of cyclic accelerators. If however the acceleration is fast enough, the particles can pass through the 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. These newer, non-scaling FFAGs are under development.

The first FFAG ever built, a 400 keV electron machine first operated at MURA in 1956. The visitors include Niels Bohr and Subrahmanyan Chandrasekhar