We describe the design, manufacture, and performance of bare-fiber integral field units (IFUs) for the SDSS-IV survey MaNGA (Mapping Nearby Galaxies at APO) on the the Sloan 2.5 m telescope at Apache Point Observatory (APO). MaNGA is a luminosity-selected integral-field spectroscopic survey of 10,000 local galaxies covering 360-1030 nm at R ~ 2200. The IFUs have hexagonal dense packing of fibers with packing regularity of 3 um (RMS), and throughput of 96+/-0.5% from 350 nm to 1 um in the lab. Their sizes range from 19 to 127 fibers (3-7 hexagonal layers) using Polymicro FBP 120:132:150 um core:clad:buffer fibers to reach a fill fraction of 56%. High throughput (and low focal-ratio degradation) is achieved by maintaining the fiber cladding and buffer intact, ensuring excellent surface polish, and applying a multi-layer AR coating of the input and output surfaces. In operations on-sky, the IFUs show only an additional 2.3% FRD-related variability in throughput despite repeated mechanical stressing during plate plugging (however other losses are present). The IFUs achieve on-sky throughput 5% above the single-fiber feeds used in SDSS-III/BOSS, attributable to equivalent performance compared to single fibers and additional gains from the AR coating. The manufacturing process is geared toward mass-production of high-multiplex systems. The low-stress process involves a precision ferrule with hexagonal inner shape designed to lead inserted fibers to settle in a dense hexagonal pattern. The ferrule inner diameter is tapered at progressively shallower angles toward its tip and the final 2 mm are straight and only a few um larger than necessary to hold the desired number of fibers. This process scales to accommodate other fiber sizes and to IFUs with substantially larger fiber count. (Abridged)
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