Nonlinear effects of a beam interacting with a single damped wave

A self-consistent nonlinear theory of the longitudinal dynamics of a low de nsity beam interacting with a single damped wave is developed. In this pape r, the model is applied to the coasting beam-cavity system of accelerator p hysics, but it also applies to beam-plasma systems and traveling wave tubes . Motivating the theory are numerical simulations showing different beam be haviors in the nonlinear regime depending on the amount of wave damping. Fo r highly damped systems, breakoff and energy loss of a self-formed bunch fr om the beam is observed. This bunch breakoff and energy loss is the cause o f the overshoot phenomenon of accelerator physics; furthermore this oversho ot does not contradict the Keil-Schnell criterion, as the beam is far from a Gaussian distribution. An expression for the amount of cavity damping nec essary for bunch breakoff is derived. Finally, using a single-particle mode l, an expression for the rate of energy loss of the bunch in terms of the c avity damping is derived. (C) 2000 American Institute of Physics. [S1070-66 4X(00)04001-5].