In pulsed laser deposition, thin film growth is mediated by a laser-generated plasma, whose properties are critical for controlling the film microstructure. The advent of 2D materials has renewed the interest in how this ablation plasma can be used to manipulate the growth and processing of atomically thin systems. For such purpose, a quantitative understanding of the density, charge state, and kinetic energy of plasma constituents is needed at the location where they contribute to materials processes. Here, we study laser-induced plasmas over expansion distances of several centimeters from the ablation target, which is the relevant length scale for materials growth and modification. The study is enabled by a fast implementation of a laser ablation/plasma expansion model using an adaptive Cartesian mesh solver. Simulation outcomes for KrF excimer laser ablation of Cu are compared with Langmuir probe and optical emission spectroscopy measurements. Simulation predictions for the plasma-shielding threshold, the ionization state of species in the plasma, and the kinetic energy of ions, are in good correspondence with experimental data. For laser fluences of 1-4 J cm-2, the plume is dominated by Cu0, with small concentrations of Cu+ and electrons at the expansion front. Higher laser fluences (e.g. 7 J cm-2) lead to a Cu+ -rich plasma, with a fully ionized leading edge where Cu2+ is the dominant species. In both regimes, simulations indicate the presence of a low-density, high-temperature plasma expansion front with a high degree of ionization that may play a significant role in doping, annealing, and kinetically-driven phase transformations in 2D materials.