Paul Dragolin
Reading, Chapter 6: Synchrotron Radiation.
Electric charges radiate when accelerated by magnetic fields in open spiral trajectories. For non-relativistic particles the radiation is classified as "cyclotron radiation" whereas for highly relativistic particles the frequency spectrum is different and the radiation is called "synchrotron radiation." Using the relativistic Newton's law and conservation of energy equations the total emitted power of synchrotron radiation is proportional to the velocity squared and the relativity factor gamma and the energy density of the magnetic field. The spectrum of the radiation is affected by the relativistic motion because of the relativistic beaming and hence an observer will see short pulses of light as the electron is momentarily headed their way. As can be shown by the energy-time uncertainty principle, this short time interval will result in a broad frequency distribution. The polarization of this radiation will have elliptical components and linear ones. The elliptical components should cancel out with a significant number of observed emitters in a given region. The linear components that are left are rather significant (~75%).
Reading, Chapter 7: Compton Scattering
Compton scattering is the inelastic scattering of light and electrons in which the photon typically gives some of its energy to the electron. The change in wavelength is on the order of the Compton wavelength (lc = h/(m*c)). In scenarios where in the rest frame of the electron the incoming photon energy h*v ~ me*c^2 then it is probable that the net energy transfer will be from the electron to the photon. This effect is called "inverse" Compton scattering.