Three mechanisms of plasma generation in low-pressure discharges are known. These are the capture of electrons in the region of the potential hump, the mutual compensation of the charges of the ion and electron flows, and the capture of ions into a potential well formed by an intense flow of primary electrons. The purpose of this work is to develop a kinetic model that allows one to calculate the plasma characteristics in the last of the above cases. The model uses the model collision integral in the t-approximation. The concentration of primary electrons is assumed to be uniform over the entire gap. To describe ions we use an approach related to the division into two groups - trapped and outgoing particles. For outgoing particles, under certain conditions, the probability of collisions can be neglected and we can assume that they go to the walls in the free flight mode. In this work, expressions are obtained for the distribution functions of trapped and outgoing ions. An expression is also obtained that relates the ionization frequency and the depth of the potential well.