  The self-interaction of short electron bunches with their own radiation field
can have a significant impact on the longitudinal beam dynamics in a storage
ring. While higher bunch currents increase the power of the emitted CSR which
can be provided to dedicated experiments, it simultaneously amplifies the
strength of the self-interaction. Eventually, this leads to the formation of
dynamically changing micro-structures within the bunch and thus fluctuating CSR
emission, a phenomenon that is generally known as micro-bunching or micro-wave
instability. The underlying longitudinal dynamics can be simulated by solving
the VFP equation, where the CSR self-interaction can be added as a perturbation
to the Hamiltonian. In this contribution, we focus on the perturbation of the
synchrotron motion that is caused by introducing this additional wake field.
Therefore, we adopt the perspective of a single particle and eventually comment
on its implications for collective motion. We explicitly show how the shape of
the parallel plates CSR wake potential breaks homogeneity in the longitudinal
phase space and propose a quadrupole-like mode as potential seeding mechanism
of the micro-bunching instability. Moreover, we consider synchrotron motion
above the instability threshold and thereby motivate an approach to control of
the occurring micro-bunching dynamics. Using dynamically adjusted RF amplitude
modulations we can directly address the continuous CSR-induced perturbation at
the timescale of its occurrence, which allows for substantial control over the
longitudinal charge distribution. While the approach is not limited to this
particular application, we demonstrate how this can significantly mitigate the
micro-bunching dynamics directly above the instability threshold. The gained
insights are supported and verified using the VFP solver Inovesa and put into
context with measurements at KARA.
