Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S19 / 2 / b / Solution

State a radiation-width convention. For rms Gaussian-equivalent single-electron undulator radiation take ${\sigma }_r=\sqrt{\lambda L}/(4\pi )$ and ${\sigma }_r^{\prime }=\sqrt{\lambda /L}$, so the diffraction emittance is $\lambda /(4\pi )$. These give 11.3 micrometres and 70.7 microradians. Convolve independent electron and radiation widths in quadrature. The total photon source is thenSome approximate undulator width conventions differ by order-one factors; these must be kept consistent in the following brightness comparison.