If the radiation emitted by an accelerated electron was sent back to the electron, would the electron decelerate? Basically I am asking if photons can be used to change the speed of an electron. Electrons emits electromagnetic radiation when they are accelerated (cyclotron radiation, etc). Can this be reversed? I suspect I might be merely asking if a receiving antenna exists -- which obviously does -- but I am not sure this is the same.
 A: Electrons and photons are elementary particles  and their interaction is described  as electron photon scattering by quantum electrodynamis (QED) . As with all interactions input energy-momentum has to be conserved, and there is a probability both for a higher momentum for the electron (acceleration) or higher energy/momentum of the photon. ( quantum mechanical calculations lead to probability distributions)


Electrons emits electromagnetic radiation when they are accelerated (cyclotron radiation, etc).


This is the classical , i.e using Maxwell's equations  framework for accelerated charged particles.  Classically it is not photons that come out, but electromagnetic radiation. The classical calculation  is also correct for an accelerated electron because the classical and QED calculations are consistent with each other. But when one is at the particle frame one uses the energy-momentum four vectors of the particles.
At the QED calculation level   it is a part of the electron photon interaction ( virtual photons given by  the accelerating electric field) that gives the probability for real photon emission.

Can this be reversed

At the QED level it is reversed, when electrons are accelerated with an electric field, except the photon is a virtual photon provided by the field.

If the radiation emitted by an accelerated electron was sent back to the electron, would the electron decelerate?

So , because the electron emits single photons it is not radiation that can be sent back but a photon that will interact and give a probability for deceleration.
Now in a collective electron beam radiating classical electromagnetic waves, an experiment of sending back that radiation to the beam one would have to calculate the disruption to the beam energy by the individual electron photon scatterings.
