FIXED FIELD ALTERNATING GRADIENT PARTICLE ACCELERATORS
D. W. Kerst, K. R. Symon, L. J. Laslett, L. W. Jones, and
K. M. Terwilliger, Midwestern Universities Research Association*
April 26, 1956
I. General Description
. Alternating gradient (AG) focusing1 provides a high degree
of stability for both the radial and vertical modes of betatron
oscillations in circular particle accelerators. This stability
makes possible the construction of many kinds of circular accel-
erators with magnetic guide fields which are constant in time,
called fixed field alternating gradient (hereafter FFAG) accel-
erators. These machines contain stable equilibrium orbits for
all particles from the injection energy to the output energy.
These orbits may all be in an annular ring, as in a synchrotron
or betatron; the magnetic field must then change rapidly with
radius to provide orbits for the different energy particles. If
the guide field gradient were made independent of azimuth, one
of the modes of betatron oscillation would be clearly unstable.
Application of alternating gradient focusing, however, can keep
both modes of betatron oscillation stable even with the rapid
radial change of magnetic field. (1t is interesting to note
that circular particle accelerators can be classified into four
groups according to the type of guide field they use: fixed field