We consider the problem of how the momentum of ions created by electron impact ionization of neutrals moving at a speed &ngr;0 perpendicular to the magnetic field through a background plasma is coupled to this plasma. We find that the plasma accelerates and the relative velocity between neutrals and plasma decreases. If this decrease is rapid and large enough the critical ionization velocity (CIV) phenomenon may turn off. We derive equations for the evolution of plasma density, electron and ion thermal energy and plasma velocity. We find that the CIV process reaches an asymptotic quasi-steady state in which the ionization rate reaches a constant value which depends on the properties of the surrounding medium and the value of &ngr;0.