Emitted Radiation: Understanding Radiative Damping & Frequency Multiples

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Radiative damping occurs when a classical particle emits radiation while interacting with a radiation field, but in weak coupling scenarios, this damping can be considered negligible for the particle's motion. The emitted radiation follows a pattern that repeats every orbital period, with frequencies that are integer multiples of the orbital frequency. This phenomenon can be likened to the Earth-Moon system, where energy loss due to gravitational waves is minimal. The key point is that while radiation is produced through coupling to the radiation field, its effect on the particle's motion remains insignificant. Understanding this relationship is crucial for grasping the dynamics of radiative processes in classical mechanics.
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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 ?
 
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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.
 

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