Is the Abraham-Lorents force formula in wikipedia correct?

[snoopies622]

So if I ask, "I have a particle of rest mass m₀ and charge q and I want to accelerate it at rate a, what force must I apply to it?", classical electromagnetism cannot answer this question?

Perhaps I should ask a more modest question: what are the experimental values? Even if the data can't be explained using classical physics, I would like to know what the relationship looks like. Has an electromagnetic reaction force ever been measured for a charged particle undergoing constant acceleration?

 

[Bob_for_short]

When the electron is non relativistic, its radiative losses are calculated with Lorentz-Abraham formula considered as a small perturbation. In that case the "friction" term is a known function of time (third derivative of non perturbed trajectory) and no mathematical problem arise. This approach is sufficiently accurate since the electron radiated many photons (classical radiation). In QED it corresponds to the inclusive picture (sum over different final photon states) which coincides with the classical results. This is what is done in linear accelerators.

I know that in case of ultra relativistic electron in a magnetic field the electron radiates very energetic photons that spread the electron orbit in an arbitrary way (radiation happens not continuously but by chance). So the beam radial width is determined with quantum rather than classical radiation mechanism.

Bob.

 

[snoopies622]

I'm afraid I don't know what you mean by, "considered as a small perturbation". For constant acceleration, the Abraham-Lorentz formula gives no reaction force at all. Are you saying that the force is so small that it can be ignored? I should note that I am not asking specifically about the case of an elementary particle like an electron, just any object with charge q accelerating at rate a.

 

[Bob_for_short]

I'm afraid I don't know what you mean by, "considered as a small perturbation". For constant acceleration, the Abraham-Lorentz formula gives no reaction force at all. Are you saying that the force is so small that it can be ignored? I should note that I am not asking specifically about the case of an elementary particle like an electron, just any object with charge q accelerating at rate a.

Yes, for non relativistic case is it really small, so zero is as good as non zero but very small correction. For a more massive body (with a smaller ratio charge/mass) the radiative losses are even smaller. That is why the Newtonian mechanics (without radiative "friction") works fine for macroscopic bodies.

Bob.

 

[snoopies622]

Thanks, Bob. I didn't realize we were talking about such small quantities. I just did a quick calculation using the Larmor formula to find how much power would be emitted by one Coulomb of charge accelerating at one meter per second squared. Very small indeed!