Provided is a long-lived fission product (LLFP) processing method using neutrons that enables generation of high-intensity neutrons using only an accelerator without a fast-neutron reactor or an accelerator-driven nuclear reactor and thereby enables efficient nuclear transmutation of long-lived fission products. In the processing method, neutron-containing primary particles such as deuterons are accelerated under specific conditions inside an FFAG accelerator (10) and are caused to collide with a plate-shaped target (18) to generate high-energy first neutrons that form a beam in a single direction through the break-up of the primary particles and low-energy diffuse second neutrons through excitation of atomic nuclei in the plate-shaped target. A first LLFP (20) is located in the direction of travel of the beam of the first neutrons and a second LLFP (24) is located in proximity to the plate-shaped target (18).

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.

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.