In a synchrotron, do electrons make periodic recoils? Synchrotron radiation happens because circular motion of electrons produce a tangential acceleration-- or something along those lines.
Point is, photons are produced by these accelerated electrons.
As far as I know, emission of photons act as a brake and slows electrons down.
My question is this.
Given that photons are emitted in a quantized way, I.e. can only take certain energies, I would think that this is not a continuous process. Rather, these emissions would take place at a regular frequency (I assume this frequency is not the one of the emissions).
Is this true? Do electrons emit photons one by one, with a distinct recoil each time?
 A: This is a more complicated question than it appears on its face.
A free electron has a continuous energy spectrum. This means that the photons it emits are not constrained to quantized values like they would be for a bound system.
Photons are unusual in that they don't have any mass. Formally the number of photons emitted in bremsstrahlung radiation is infinite- an infinite number of very low energy photons that sum up to a finite energy. Since any method of detecting photons necessarily has an energy threshold, you can only ever detect a finite number of photons, but that exact number depends on how sensitive your detector is.
That said, for a given threshold, yes, the electron appears to emit the photons one at a time, with a distinct recoil for each one. It's just that you can never be sure how many photons below your detection threshold that you may have missed.
And as a practical matter in a real synchrotron, you have so many electrons that you can ignore the recoils and trajectories of individual particles and deal with averages instead.
