Characterizing the Best Cosmic Telescopes with the Millennium   Simulations
  Certain configurations of massive structures projected along the line of sight maximize the number of detections of gravitationally lensed $z\sim10$ galaxies. We characterize such lines of sight with the \'etendue $\sigma_\mu$, the area in the source plane magnified over some threshold $\mu$. We use the Millennium I and Millennium XXL cosmological simulations to determine the frequency of high $\sigma_\mu$ beams on the sky, their properties, and efficient selection criteria. We define the best beams as having $\sigma_{\mu>3} >2000$ arcsec$^2$, for a $z\sim10$ source plane, and predict $477 \pm 21$ such beams on the sky. The total mass in the beam and $\sigma_{\mu>3}$ are strongly correlated. After controlling for total mass, we find a significant residual correlation between $\sigma_{\mu>3}$ and the number of cluster-scale halos ($>10^{14} M_\odot h^{-1}$) in the beam. Beams with $\sigma_{\mu>3} >2000$ arcsec$^2$, which should be best at lensing $z\sim10$ galaxies, are ten times more likely to contain multiple cluster-scale halos than a single cluster-scale halo. Beams containing an Abell 1689-like massive cluster halo often have additional structures along the line of sight, including at least one additional cluster-scale ($M_{200}>10^{14}M_\odot h^{-1}$) halo 28% of the time. Selecting beams with multiple, massive structures will lead to enhanced detection of the most distant and intrinsically faint galaxies. 
K. Decker French, Kenneth C. Wong, Ann I. Zabludoff, S. Mark Ammons,   Charles R. Keeton, Raul E. Angulo
astro-ph.CO