On the brightness of diluted photon source in synchrotron light facilities

The undulator radiation spectral brightness in storage ring is studied taking into account the effects of the electron beam oscillating trajectory and the beam transverse size variation along the undulator. The modified optimal beta function at the source point to reach maximum brightness is obtained that is in direct relation with the emitted photons wavelength. It is shown that the maximum spectral brightness in long wavelength range is achieved with low beta lattice, while in short wavelength range with larger beta.