Synchrotron radiation
Synchrotron radiation is produced when moving particles accelerate, e.g. when electrons move freely in a magnetic field. This is similar to a radio antenna, but with the difference that, in theory, the relativistic speed will change the observed frequency due to the Doppler effect by the Lorentz factor . Relativistic length contraction then bumps the frequency observed by another factor of , thus multiplying the gigahertz frequency of the resonant cavity that accelerates the electrons into the X-ray range. The radiated power is given by the relativistic Larmor formula, while the force on the emitting electron is given by the Abraham–Lorentz–Dirac force.