= Solution
Near the critical photon energy, the characteristic vertical divergence of <synchrotron radiation> is $\sigma_\theta\simeq1/\gamma=1.70\times10^{-4}\,\mathrm{rad}$ in the approximation requested. Ignoring electron source size and divergence, the rms vertical width $10\,\mathrm m$ downstream is
$$
\sigma_y\simeq L\sigma_\theta=1.70\,\mathrm{mm}.
$$
The 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 give
$$
\boxed{\mathcal T\simeq\operatorname{erf}\left(\frac{5\,\mathrm{mm}}{\sqrt2\,\sigma_y}\right)\simeq0.9967.}
$$
The 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.
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