The electromagnetic radiation given off by accelerating charged particles. This is what happens in an ordinary antenna, but the term usually refers to the radiation emitted when a charged particle beam is bent in a particle-accelerator.

This radiation is not only produced in synchrotrons, but in any circular accelerator and is significant only for electrons. In a free electron laser synchrotron radiation is created by wiggler magnets which bends the electron beam in tight turns.

The radiation produced has a very broad spectrum and the peak frequency depends on the electron energy and the turning radius. The peak frequency is typically around UV and soft X-rays.

Synchrotron radiation is commonly observed from astronomical phenomena involving large amounts of energy, particularly in quasars and active galaxies, and in supernovae. In these objects, electrons are ejected from the central power source like a supermassive black hole or (in supernovae) are accelerated by shocks in a process called Fermi acceleration. These electrons can be accelerated to extremely high energies, reaching speeds very near the speed of light (often much more than .999 c). When these electrons encounter a magnetic field, they move in circular orbits around the field lines, due to the Lorentz force. Any charged particle gives off radiation when it accelerates, and circular motion is essentially a constant acceleration with a changing direction, so the electrons radiate like crazy.

The amount of energy extragalactic radio sources put out is enormous, often amounting to millions of times the energy output of the Sun, just in radio waves. Supernovae are also very luminous synchrotron sources, and because they accelerate electrons to very high energies the synchrotron emission can extend into optical and X-Ray wavelengths as well.

Synchrotron radiation has some useful properties that make it a useful diagnostic tool in astronomy. For one, synchrotron radiation is highly linearly polarized, and this can tell us about the energy spectrum of the electrons, and also about the ambient magnetic fields in the source. One good example of this is the Crab Nebula. Here, the electron energies are so high that some of the optical light is actually synchrotron emission. When you observe the Crab Nebula through a polarizing filter, you can see the features change as you rotate the polarization axis.

The spectrum of synchrotron radiation can also tell us about the electrons that made it. If the electron energy distribution follows the form

N(E)dE = const × E-p dE

(N(E)dE is the number of electrons at a given energy, and p is the slope of the electron distribution) then the synchrotron spectrum will go as

P(nu) = const × nu-(p-1)/2

where P is the total emitted power, and nu is the frequency.

One more note about synchrotron radiation: the observed shape of the spectrum can also tell you about the "age" of the parent electrons. As the electrons radiate they lose energy, and the electrons at high energies (radiating at high frequencies) lose energy faster. Thus, the spectral slope -(p-1)/2 will steepen at higher frequencies as these electrons are depleted, and the frequency of this "knee" can tell you something about the electrons. At very low frequencies, the synchrotron radiation generated by the electrons will end up being Compton scattered in a process called synchrotron self-absorption or synchrotron self-Compton (often abbreviated SSC). Thus if you were to make a plot of a synchrotron spectrum, it would look something like a tilted letter n.

Sources: Radiative Processes in Astrophysics by Rybicki and Lightman, and more lectures on radio galaxies than I care to remember....

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