We investigate the gravitational lensing properties of lines of sight containing multiple cluster-scale halos , motivated by their ability to lens very high-redshift ( z \sim 10 ) sources into detectability .
We control for the total mass along the line of sight , isolating the effects of distributing the mass among multiple halos and of varying the physical properties of the halos .
Our results show that multiple-halo lines of sight can increase the magnified source-plane region compared to the single cluster lenses typically targeted for lensing studies , and thus are generally better fields for detecting very high-redshift sources .
The configurations that result in optimal lensing cross sections benefit from interactions between the lens potentials of the halos when they overlap somewhat on the sky , creating regions of high magnification in the source plane not present when the halos are considered individually .
The effect of these interactions on the lensing cross section can even be comparable to changing the total mass of the lens from 10 ^ { 15 } M _ { \odot } to 3 \times 10 ^ { 15 } M _ { \odot } .
The gain in lensing cross section increases as the mass is split into more halos , provided that the lens potentials are projected close enough to interact with each other .
A nonzero projected halo angular separation , equal halo mass ratio , and high projected halo concentration are the best mass configurations , whereas projected halo ellipticity , halo triaxiality , and the relative orientations of the halos are less important .
Such high mass , multiple-halo lines of sight exist in the SDSS .