Synchrotron radiation along the radial direction

We investigate the radiation of a high-energy electron in circular orbit, along the direction defined by a straight line that goes through the center of the orbit. In this case, the angular spread of the radiation decreases while the radiation intensity increases as we approach the electron's orbit. In particular, for detection almost touching the orbit all the electron's radiation tends to be concentrated into a line. We find the explicit dependence on the distance, the angle, and the electron's energy, for the total intensity of radiation as well as for the different spectral components of the radiation. Our formulas are valid even very close to the electron's orbit