A Dynamic Feedback Model for High Repetition Rate LINAC-Driven FELS

One of the concepts for the next generation of linacdriven FELs is a CW superconducting linac driving an electron beam with MHz repetition rates. One of the challenges for next generation FELs is improve the stability of the xray pulses by improving the shot-to-shot stability of the energy, charge, peak current, and timing jitter of the electron beam. A high repetition rate FEL with a CW linac presents an opportunity to use a variety of broadband feedbacks to stabilize the beam parameters. To understand the performance of such a feedback system, we are developing a dynamic model of the machine with a focus on the longitudinal beam properties. The model is being developed as an extension of the LITrack code and includes the dynamics of the beam-cavity interaction, RF feedback, beam-based feedback, and multibunch effects. In this paper, we present a detailed description of this model