Calculations of synchrotron radiation emission in the transverse coherent limit.

We present approximations for the synchrotron radiation emission for low emittance light sources, which provide a connection between user needs and the electron beam parameters. The results and calculations are a consequence of the phase coherence in the emission from the electrons. We derive the remarkable result that if the electron beam is energetic enough, the emitted flux is independent of the photon energy, electron beam energy, or bending radius in the transverse coherent limit. Similarly the brightness is identical for all machines at a given current.