# 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?

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.

• Wow. So there are photons that are not multiple of some Planck constant? – Winston Mar 23 at 10:50
• Also thank you for this valuable answer. – Winston Mar 23 at 10:51
• Do you really get recoil if nothing is measuring the individual photons or the electron? I'd imagine that in bremsstrahlung we actually initially get an entangled state of the electron + a state of indefinite photon number (the radiation), and you only get definite recoil events if you either position a photon detector or measure the electron position to high accuracy (but how you'd do that without disturbing its circular motion I'm not sure). – ACuriousMind Mar 23 at 10:54
• Actuallly there are so many fascinating things in your answer. Infinite number of photons. How can this integrate to a finite energy? – Winston Mar 23 at 10:54
• @Exocytosis Just as an illustration, imagine there's 1 photon of $1~\rm eV$, 1 of $.5~\rm eV$, 1 of $.25~\rm eV$ and so on. There are an infinite number, but the energy converges to $2~\rm eV$. – Chris Mar 23 at 19:59