  We conduct a multiparametric study of driven magnetic reconnection relevant
to recent experiments on colliding magnetized laser produced plasmas using
particle-in-cell simulations. Varying the background plasma density, plasma
resistivity, and plasma bubble geometry, the 2D simulations demonstrate a rich
variety of reconnection behavior and show the coupling between magnetic
reconnection and the global hydrodynamical evolution of the system. We consider
both the collision between two radially expanding bubbles where reconnection is
seeded by the pre-existing X-point, and the collision between two flows in a
quasi-1D geometry with initially anti-parallel fields where reconnection must
be initiated by the tearing instability. In both geometries, at a baseline case
of low-collisionality and low background density, the current sheet is strongly
compressed to below scale of the ion-skin-depth scale, and rapid,
multi-plasmoid reconnection results. Increasing the plasma resistivity, we
observe a collisional slow-down of reconnection and stabilization of plasmoid
instability for Lundquist numbers less than approximately $S \sim 10^3$.
Secondly, increasing the background plasma density modifies the compressibility
of the plasma and can also slow-down or even prevent reconnection, even in
completely collisionless regimes, by preventing the current sheet from thinning
down to the scale of the ion-skin depth. These results have implications for
understanding recent and future experiments, and signatures for these processes
for proton-radiography diagnostics of these experiments are discussed.
