Recent observations of ultrafine aerosol production in the atmosphere support the hypothesis of ions acting as nucleation agents. We use a numerical model of ion-induced aerosol formation based on experimental cluster ion thermodynamics to study the production of ultrafine aerosol in the troposphere and its response to variations in background ionization. An analytical model is used to explain the findings. Our results show a considerable ultrafine particle and surface area production due to ion-induced nucleation. Both particle and surface area production readily respond to variations in ionization, such as resulting from the modulation of the galactic cosmic ray intensity by the 11 year solar cycle. However, this response may be positive or negative, depending on ambient conditions. We explain the mechanism responsible for this behavior. The large particle production seen in our simulations suggests that ion-induced nucleation is an important atmospheric process, which may promote the solar cycle signal to the troposphere.