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Electron beams moving at variable speeds emit electromagnetic radiation. In a vacuum tube, an electron beam bent by a strong magnetic field in a circular motion emits light. The luminescence does not require the interaction of molecules or atoms in other media (such as rarefied gases) with electrons in the electron beam. Electrons glow by themselves. For example, the electron beam circling in the cathode ray tube and the electron beam in the synchrotron all do so. I don't have the means to do experiments. The question is, how much energetic the electron beams are needed in the vacuum and what is the minimum circling radius of the beam before visible light can be observed?

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  • $\begingroup$ Downvoted for incorrect statements. $\endgroup$ – Pieter Jul 20 at 7:51
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No. If you see the electron beam in a cathode ray tube it is the gas atoms that you see; the electrons do not glow. Kinetic energies are low.

In a synchrotron, the electrons are at relativistic speeds. The Bremsstrahlung at a bending magnet is then doppler-shifted when observed in the lab frame.

Classically, an electron radiates light with the same frequency as the orbital frequency. In the Bohr model, this agrees with the radiation caused by transition from the $n$ to the $n-1$ orbit for large $n$, in agreement with the correspondence principle. For large quantum numbers, these are called Rydberg atoms, large, but still tiny, radiating in the far infrared.

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  • $\begingroup$ In synchrotron, is there a minimum speed for the elections to start emitting em radiation? And what are the radiation frequencies? $\endgroup$ – Cang Ye Jul 20 at 7:58
  • $\begingroup$ @CangYe It does not depend on speed: in a straight section of the synchrotron there is no radiation. Only at bending magnets and in insertion devices (wigglers, undulators). $\endgroup$ – Pieter Jul 20 at 8:06
  • $\begingroup$ I agree. Running in straight line, no matter how fast, it will not radiate. I was asking when it moves in circule, what's the minimum speed $\endgroup$ – Cang Ye Jul 20 at 8:18
  • $\begingroup$ @CangYe It depends on the acceleration and on the relativistic gamma factor. Here is a calculator: henke.lbl.gov/optical_constants/bend2.html $\endgroup$ – Pieter Jul 20 at 8:45
  • $\begingroup$ In synchrotron, the circular moving radius is very very big, the acceleration is small. For electrons to emmit visible light, they must have a very big speed. But in the case of small radius moving, electrons don't need that big speed (energy) to radiate visible em radiation. Is this correct? $\endgroup$ – Cang Ye Jul 20 at 9:04
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The answer to your question is quite simple, because when the lorentz force equals the centripetal force due to curcular motion it is the condition when it starts emitting em radiations also you can say that when em energy becomes equal to hf then electron starts emitting radiations

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