The Alternative Low-Power Hybrid Ion Engine (alphie) is a new technology for space propulsion based on plasma. Its distinct characteristic is the counterflow of charges (ions and electrons) passing through its two-grid system. This means that electrons coming from an external cathode are accelerated toward the ionization chamber, in which a neutral gas (typically Ar) is injected. The strong magnetic field therein confines these electrons, which ionize and exchange energy with the propellant gas. Thus, the operation of alphie is strongly affected by the electrons coming from the external cathode and their collisions with the neutral atoms. This work studies the counterflow employing a particle-in-cell simulation of ions and electrons passing through a single hole as a function of the electron cathode currents (Ice) and potential drops between grids (VAC). Transparency of the grid system to ions and electrons and the ion current extracted by the grid system are studied under sweeps of these two parameters. The number of ionization events by each high-energy electron entering the ionization chamber is evaluated using a physical model based on the gas density and the cross section for ionization. These new ions are then extracted by the same electric field that accelerates the electrons inward. Thus, simulations are self-consistent, since the ionizing electron flow from the external cathode drives the ion outflow at the exit section of the two-grid system. The electrical transparency of the two-grid system to ions and electrons, related to the axial charge currents, is also studied under sweeps of aforementioned operation parameters. This new way to deal with ionizations can be useful to study other plasma thrusters in which electrons for ionization come from an external cathode without modeling the complex structure of the ionization chamber.