Recently, novel experiments on magnetic reconnection have been conducted in laser-produced plasmas in a high-energy-density regime. Individual plasma bubbles self-generate toroidal, mega-gauss-scale magnetic fields through the Biermann battery effect. When multiple bubbles are created at small separation, they expand into one another, driving reconnection of this field. Reconnection in the experiments was reported to be much faster than allowed by both Sweet-Parker, and even Hall-MHD theories, when normalized to the nominal magnetic fields self-generated by single bubbles. Through particle-in-cell simulations (both with and without a binary collision operator), we model the bubble interaction at parameters and geometry relevant to the experiments. This paper discusses in detail the reconnection regime of the laser-driven experiments and reports the qualitative features of simulations. We find substantial flux-pileup effects, which boost the relevant magnetic field for reconnection in the current sheet. When this is accounted for, the normalized reconnection rates are much more in line with standard two-fluid theory of reconnection. At the largest system sizes, we additionally find that the current sheet is prone to breakup into plasmoids.
