Laser ablation processes have applications from thin film deposition to isotope separation, through plasma plume generation, which suggests mass and charge separation of species as the plume evolves. However, they do not have a theoretical model that takes into account equilibrium configurations. The present work is dedicated to build a simplified non-neutral self-consistent two fluid model, based on a few parameters for the first and fast analysis of morphological and statistical features for typical experimental plasma plumes. The velocity field, density profiles, and normalized histograms for the velocity module associated with the species were determined. The electrostatic potential field was also depicted. The model was validated for laser-ablated plasma plumes and found to be in good agreement with the experimental molybdenum plasma jet generated by the interaction of the Nd:YAG nanosecond pulsed laser with the solid target expanding in air at atmospheric pressure.