Multi-bunch dynamics in accelerating structures including interaction with higher order modes

The case of interaction of not fully relativistic multi-bunch beams with the fundamental and higher order modes of a cavity is not yet covered by existing codes, nevertheless it is a fundamental problem in the design of RF guns and/or collider cavities. A simple model that couples Newton and Maxwell equations, taking into account also space charge, beam loading and build-up effects of higher order modes under beam-tube cutoff frequency, is presented. This approach is intended to fill that gap, avoiding relativistic approximation. It uses a current density description of the beam and a slowly varying envelope approximation for the time evolution of the modes amplitude. A fast running code (HOMDYN), based on this model has been developed and the application to a few typical examples is illustrated