Transverse particle motion in radio-frequency linear accelerators

The transverse motion of a relativistic charged particle in a radio-frequency linear accelerator (rf linac) is examined. The spatially averaged equations of motion are derived for a particle in a periodic accelerating cavity system, and solved exactly in the ultrarelativistic limit. These solutions, along with an impulse treatment of the transients at the entrance and exit of the linac cavities, allow derivation of a linear transport matrix through the cavity. This generalized matrix is improved over previously derived results in that it is applicable to both traveling- and standing-wave structures, allows for arbitrary injection phase and spatial-harmonic content of the rf fields, and is more accurate in approximating the exact charged-particle motion.