We studied the critical ionization velocity (CIV) process by first investigating a coupled system of equations describing the production of several ion species and electrons by impact ionization, their collisions with neutrals, and the heating of electrons. Analytic relations derived from this were tested with the help of a particle simulation including collisional processes between neutrals and plasma particles. It was found that resistive heating of electrons plays an important role when the density of the neutrals is high and that electron heating due to lower hybrid waves is significant when the neutral density is low. In both cases we verified the control of the plasma production rate by the ratio of the beam velocity to the critical velocity.