So, every electron in the electron bunch radiates independently.

In the same sense, the photons that an electron radiates as it curves don't change its charge either.

A classical electron orbiting a nucleus experiences acceleration and should radiate.

As a result, the electrons radiate a continuous stream of radiation as they travel through the undulator.

(Completely free electrons cannot radiate, because this would violate the simultaneous conservation of energy and momentum.)

This process of being accelerated into and out of the wall causes the electrons to radiate light all over the spectrum, including high harmonics.

But the classical theory predicted that the electrons would radiate electromagnetic waves.

As a result, an electron could always radiate energy and fall into a negative energy state.

The electron will radiate due to the acceleration for everyone.

For the case of electrons, the electrons will radiate which causes a damping effect.