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Synchrotron radiation is a type of electromagnetic radiation that is emitted by a charged particle undergoing acceleration while it is traveling at near the speed of light. It was first observed in a synchrotron (a type of particle accelerator). Nature can generate synchrotron radiation in space within magnetic fields. Characteristics:
Analogous radiation from slower-moving charged particles is termed cyclotron radiation.
Since synchrotron radiation is (at least somewhat) directional, thus sometimes not aimed at us, often it con only be inferred by its effects, e.g., clouds that scatter it or are warmed and produce black body radiation. The synchrotron luminosity of directly-observed synchrotron radiation can be worked out by the spectrum, indicated by its particular power law "shape", but when indirectly observed, more modeling is required to work it out.
Proton synchrotron radiation is that specifically generated by protons to distinguish it from the more frequent electron-generated radiation. It is found in proton accelerators and in astrophysical phenomena that accelerate protons to relativistic speeds. It is less common because a proton's much larger mass makes achieving the relativistic speeds less common.
A contributor to the spectrum of observed synchrotron radiation is synchrotron self-absorption and synchrotron self-scattering. The latter refers to absorption and subsequent emission, and a synchrotron-specific radiative transfer, with photons generated, then absorbed/re-emitted before leaving the medium. Within the synchrotron spectrum, the lower-frequency (longer-wavelength) photons are more likely to be absorbed, thus the net effect on the spectrum viewed externally is a reduction at the low-frequency end.