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I'm reading this chapter of Essential Radio Astronomy.

It says that we can divide bremsstrahlung into electric or magnetic breaking radiation, depending on which field is the source of the acceleration of electrons. Synchrotron radiation is another name for magnetic breaking radiation, and it is usually non-thermal, because the relativistic electrons creating the emissions tend to have a power-law distribution.

My question would be: why does synchrotron radiation only occur in the case of relativistic electrons? Why cannot any non-relativistic electron that is moving in the presence of a magnetic field emit synchtron radiation?

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They can, but it would be called cyclotron emission. The difference is that cyclotron emission occurs at a discrete frequency for a given B-field, whereas the relativistic electrons emit at a broad spread of frequencies that form a continuum under realistic conditions.

Hence this is a terminology thing as well as a physics thing. Cyclotron radiation becomes synchrotron radiation as the electrons become relativistic.

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  • $\begingroup$ And cyclotron radiation is beamed with a certain opening angle, which is a purely relativistic effect. $\endgroup$ Jul 9, 2022 at 19:01
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    $\begingroup$ @AtmosphericPrisonEscape Synchrotron radiation can be beamed (if the B-field is spatially uniform). Cyclotron radiation is not. $\endgroup$
    – ProfRob
    Jul 9, 2022 at 19:19
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    $\begingroup$ This is really interesting decades ago I worked at a cyclotron lab, these days at a synchrotron lab. I never thought about cyclotron radiation at the former and make great use of the forward-emitted synchrotron radiation (and the narrow and coherent beams from wigglers and undulators and now I can't stop wondering what happens between the two limits. It seems that the mechanisms are pretty different, so both happen to some extent even in both limits, it's just a question of amplitudes. Now I'll go off and think about it... $\endgroup$
    – uhoh
    Jul 9, 2022 at 21:01
  • $\begingroup$ Thank you @ProfRob for the answer! $\endgroup$
    – Loika
    Jul 10, 2022 at 10:32
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    $\begingroup$ @uhoh It's called gyro-synchrotron radiation. $\endgroup$
    – ProfRob
    Jul 10, 2022 at 10:47

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