Abstract: A FFAG is a particle accelerator having turning magnets with a linear field gradient for confinement and a large edge angle to compensate for acceleration. FODO cells contain focus magnets and defocus magnets that are specified by a number of parameters. A set of seven equations, called the FFAG equations relate the parameters to one another. A set of constraints, call the FFAG constraints, constrain the FFAG equations. Selecting a few parameters, such as injection momentum, extraction momentum, and drift distance reduces the number of unknown parameters to seven. Seven equations with seven unknowns can be solved to yield the values for all the parameters and to thereby fully specify a FFAG.

Abstract: A proton beam radiology system provides cancer treatment and proton radiography. The system includes an accelerator for producing an H.sup.- beam and a laser source for generating a laser beam. A photodetachment module is located proximate the periphery of the accelerator. The photodetachment module combines the H.sup.- beam and laser beam to produce a neutral beam therefrom within a subsection of the H.sup.- beam. The photodetachment module emits the neutral beam along a trajectory defined by the laser beam. The photodetachment module includes a stripping foil which forms a proton beam from the neutral beam. The proton beam is delivered to a conveyance segment which transports the proton beam to a patient treatment station. The photodetachment module further includes a laser scanner which moves the laser beam along a path transverse to the cross-section of the H.sup.- beam in order to form the neutral beam in subsections of the H.sup.- beam. As the scanning laser moves across the H.sup.