- #1
Robin-Whittle
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I would appreciate some help regarding the movement of an electron in a plane-wave linearly polarized electromagnetic field. Its simple enough question, but I am not sure what approach to take.
Let's say the electron is at rest in our frame of reference and the plane wave is continuous 300GHz, so it has a wavelength of 1mm. The electron is alone in space - there's no other particles for at least a few mm around. The field strength is not so high as to accelerate the electron to relativistic velocities.
The electrostatic field will move the electron a little side-to-side, coupling some of its energy to the electron, but the electron gives some or all of it back to the field, with a phase lag, just as a weight on a spring follows a sinusoidal motion, with a phase lag. Or does the electron's movement scatter some or all of this energy into different directions than that of the plane wave which excites it?
How much does the electron move? Where does the momentum come from to move it, since there is only the oscillating field in the vicinity? There's no other particle with momentum to push against.
If there were a thousand electrons all quite close to each other, say within 0.1mm of each other, I doubt that they would move as far as if there was just one, so the movement of even one electron will be affecting the field in its vicinity, weakening or at least somewhat phase-shifting it.
In high-power laser research, the electron's movement may be referred to with terms such as "quiver velocity", "quiver energy", "excursion amplitude" and "excursion length". But there, the electron has just been ejected from an atom, so there are other particles within a wavelength of the electron, so the papers I am turning up with these search terms are not very helpful.
Quantum electrodynamics, I think, would say that the electromagnetic wave doesn't interact with lone electrons, because that is not what photons do. But I am interested in classical theory which is applicable to this situation.
There's plenty of material on Thompson scattering, but that seems to be concerned with the behaviour of the radiation which is scattered, rather than the movement of the electron or whether it is within a few wavelengths of other charged particles.
- Robin
Let's say the electron is at rest in our frame of reference and the plane wave is continuous 300GHz, so it has a wavelength of 1mm. The electron is alone in space - there's no other particles for at least a few mm around. The field strength is not so high as to accelerate the electron to relativistic velocities.
The electrostatic field will move the electron a little side-to-side, coupling some of its energy to the electron, but the electron gives some or all of it back to the field, with a phase lag, just as a weight on a spring follows a sinusoidal motion, with a phase lag. Or does the electron's movement scatter some or all of this energy into different directions than that of the plane wave which excites it?
How much does the electron move? Where does the momentum come from to move it, since there is only the oscillating field in the vicinity? There's no other particle with momentum to push against.
If there were a thousand electrons all quite close to each other, say within 0.1mm of each other, I doubt that they would move as far as if there was just one, so the movement of even one electron will be affecting the field in its vicinity, weakening or at least somewhat phase-shifting it.
In high-power laser research, the electron's movement may be referred to with terms such as "quiver velocity", "quiver energy", "excursion amplitude" and "excursion length". But there, the electron has just been ejected from an atom, so there are other particles within a wavelength of the electron, so the papers I am turning up with these search terms are not very helpful.
Quantum electrodynamics, I think, would say that the electromagnetic wave doesn't interact with lone electrons, because that is not what photons do. But I am interested in classical theory which is applicable to this situation.
There's plenty of material on Thompson scattering, but that seems to be concerned with the behaviour of the radiation which is scattered, rather than the movement of the electron or whether it is within a few wavelengths of other charged particles.
- Robin
