Velocity lens model for longitudinal beam dynamics in inductive linear ion accelerators

Models are presented which facilitate investigation of the longitudinal dynamics of non-relativistic beams in inductive linear accelerators. In the limit that changes in the beam distribution take place during passage through many acceleration gaps, it is shown that the equations governing the response of the beam to the gap voltages are the same as those for the transverse motions of particles passing through an array of thin lenses. The analogy with lenses provides insight into macroscopic beam current profiles, longitudinal emittance growth, beam stability, and velocity bunching