Emitted Radiation: Understanding Radiative Damping & Frequency Multiples

[foobar]

In this page https://en.wikipedia.org/wiki/Matrix_mechanics I don't understand this statement :

"When a classical particle is weakly coupled to a https://en.wikipedia.org/w/index.php?title=Radiation_field&action=edit&redlink=1, so that the radiative damping can be neglected, it will emit radiation in a pattern which repeats itself every orbital period.The frequencies which make up the outgoing wave are then integer multiples of the orbital frequency,..."

What specifically is happening here, how is the radiation produced ?

 

[Orodruin]

The radiation is produced via the coupling to the radiation field. Clearly the damping is not insignificant for the radiation, the idea is that it should be negligible for the particle’s motion. Think the Earth-Moon system. Very little energy is lost due to gravitational waves.