IMPACT PARAMETER PROFILE OF SYNCHROTRON RADIATION

The horizontal impact parameter profile of synchrotron radiation, for fixed vertical angle of the photon, is calculated. This profile is observed through an astigmatic optical system, horizontally focused on the electron trajectory and vertically focused at infinity. It is the product of the usual angular distribution of synchrotron radiation, which depends on the vertical angle $\psi$, and the profile function of a caustic staying at distance $\bcl = (\gamma^{-2} + \psi^2) \RB/2 $ from the orbit circle, $\RB$ being the bending radius and $\gamma$ the Lorentz factor. The {\it classical impact parameter} $\bcl$ is connected to the Schott term of radiation damping theory. The caustic profile function is an Airy function squared. Its fast oscillations allow a precise determination of the horizontal beam width.