Gemini Frontier Fields: Wide-field Adaptive Optics $K_s$-band Imaging of the Galaxy Clusters MACS J0416.1-2403 and Abell 2744

We have observed two of the six Frontier Fields galaxy clusters, MACS J0416.1-2403 and Abell 2744, using the Gemini Multi-Conjugate Adaptive Optics System (GeMS) and the Gemini South Adaptive Optics Imager (GSAOI). With 0.08"-0.10" FWHM our data are nearly diffraction-limited over a 100"x100" wide area. GeMS/GSAOI complements the Hubble Space Telescope (HST) redwards of 1.6microns with twice the angular resolution. We reach a 5 sigma depth of Ks = 25.6 mag (AB) for compact sources. In this paper we describe the observations, the data processing and the initial public data release. We provide fully calibrated, co-added images matching the native GSAOI pixel scale as well as the larger plate scales of the HST release, adding to the legacy value of the Frontier Fields. Our work demonstrates that even for fields at high galactic latitude, where natural guide stars are rare, current multi-conjugated adaptive optics technology at 8m-telescopes has opened a new window on the distant Universe. Observations of a third Frontier Field, Abell 370, are planned.