I'm currently trying to understand how microbunching develops in free electron lasers (FELs). As I understand it, electrons oscillate transversely as they pass through the undulator, emitting synchrotron radiation in the process. This radiation can then interact with the electron beam further downstream. Depending on their phase relative to the radiation field, electrons are either accelerated or decelerated.
What I'm struggling to grasp is why this energy exchange manifests primarily in the longitudinal degree of freedom. Intuitively, since the undulator induces transverse motion and the radiation field is also transverse, I would have expected the amplitude of the transverse oscillations to change, rather than the longitudinal velocity.
Could someone clarify why the interaction leads to longitudinal microbunching instead of modifying the transverse motion?
Thanks in advance!
