Quite surprisingly, most of the properties of (classical) synchrotron radiation were worked out by G.A. Schott in1907--1912 in his dissertation work.
Working in a 'pre-quantum' world, Schott wanted to explain the observed lines in the emission #spectra of atoms. He started with a ‘Rutherford-like' atomic model where point electrons move in closed orbits around a nucleus: what would the emission spectra of such accelerated particles be like?
Starting from these premises, Schott derived the emission spectrum of (what we know today as) synchrotron light!
As we understand today, the motion of bound electrons cannot be explained by classical #Electrodynamics. Schott's formulas didn't work in describing atomic spectra and his work was forgotten for a while, only to be rediscovered in the 1940s when the first synchrotron machines were being built.
Now, electrons moving on macroscopic curved trajectories are extremely well described by classical electrodynamics, and Schott's formulas work exceedingly well in predicting the properties of #synchrotron light.
3/N
