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Before I explain the BK79 model I'll begin by just briefly describing
synchrotron radiation. Wherever there is a magnetic field (of sufficient
strength) and free relativistic electrons (such as found in astrophysical plasmas) synchrotron emission will occur. The acceleration of the electrons as they circle the magnetic field lines causes them to emit photons.

A collection of electrons with energies distributed according to a power
law will produce the radiation spectrum shown on the lower left, when
there is no re-absorption i.e. a completely optically thin source. Where
self-absorption occurs the synchrotron emission spectrum appears as in
the lower right, with the lower frequency photons are preferentially