 Solution

Near the critical photon energy, the characteristic vertical divergence of synchrotron radiation is ${\sigma }_{\theta }\simeq 1/\gamma =1.70\times 10^{-4}\mathrm{rad}$ in the approximation requested. Ignoring electron source size and divergence, the rms vertical width $10\mathrm{m}$ downstream isThe full aperture width is $10\mathrm{mm}$, so its half-width is $5\mathrm{mm}=2.94{\sigma }_y$. It therefore passes almost all the central $8\mathrm{keV}$ photon beam. A Gaussian angular approximation would giveThe exact synchrotron angular distribution is not Gaussian, so this number is an illustrative containment estimate, not an exact throughput calculation. A finite aperture cannot transmit every photon in a distribution with tails. The assumed infinite horizontal aperture removes horizontal fan clipping.