Fixed field alternating gradient ion accelerator for variable energy extraction

A method and apparatus for use as a compact medical ion accelerator includes a charged particle linear accelerator module and a pair of fixed field magnet assemblies. The linear accelerator module accelerates a pulse of charged particles as a beam aligned along a first ray. The pair of assemblies controls the orbits of the pulse by turning the pulse 360 degrees within a first plane. The magnet assemblies are disposed on opposite sides of the linear accelerator with mirrored symmetry relative to a line that is perpendicular to the first ray and passes through a reference point in the first plane. Each assembly includes a pair of magnets for which a strength of a magnetic field varies non-linearly along a radial direction; and a superconducting magnet for which a strength of a magnetic field varies along a radial direction. The superconducting magnet is disposed between the pair of magnets.