The Herschel Multi-tiered Extragalactic Survey ( HerMES ) has identified large numbers of dusty star-forming galaxies ( DSFGs ) over a wide range in redshift .
A detailed understanding of these DSFGs is hampered by the limited spatial resolution of Herschel .
We present 870 \mu m 0 \farcs 45 resolution imaging from the Atacama Large Millimeter/submillimeter Array ( ALMA ) of 29 HerMES DSFGs with far-infrared ( FIR ) flux densities in between the brightest of sources found by Herschel and fainter DSFGs found in ground-based sub-millimeter ( sub-mm ) surveys .
We identify 62 sources down to the 5 \sigma point-source sensitivity limit in our ALMA sample ( \sigma \approx 0.2 mJy ) , of which 6 are strongly lensed ( showing multiple images ) and 36 experience significant amplification ( \mu > 1.1 ) .
To characterize the properties of the ALMA sources , we introduce and make use of uvmcmcfit , a publicly available Markov chain Monte Carlo analysis tool for interferometric observations of lensed galaxies .
Our lens models tentatively favor intrinsic number counts for DSFGs with a steep fall off above 8 mJy at 880 \mu m. Nearly 70 % of the Herschel sources comprise multiple ALMA counterparts , consistent with previous research indicating that the multiplicity rate is high in bright sub-mm sources .
Our ALMA sources are located significantly closer to each other than expected based on results from theoretical models as well as fainter DSFGs identified in the LABOCA ECDFS Submillimeter Survey .
The high multiplicity rate and low projected separations argue in favor of interactions and mergers driving the prodigious emission from the brightest DSFGs as well as the sharp downturn above S _ { 880 } = 8 mJy .