A non-scaling fixed field alternating gradient accelerator includes a racetrack shape including a first straight section connected to a first arc section, the first arc section connected to a second straight section, the second straight section connected to a second arc section, and the second arc section connected to the first straight section; an matching cells configured to match particle orbits between the first straight section, the first arc section, the second straight section, and the second arc section. The accelerator includes the matching cells and an associated matching procedure enabling the particle orbits at varying energies between an arc section and a straight section in the racetrack shape.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
 The present invention was made with government support under Contract Number DE-AC02-98CH10886 awarded to Brookhaven National Laboratory by the Department of Energy (DOE). The U.S. government has certain rights in the invention.