The work is devoted to the development of the kinetic theory of phase focusing in a low-voltage beam discharge in rare gases at the Knudsen numbers for electron transport of order of 1, taking into account dispersion during the propagation of perturbations. It is shown that the dispersion leads to a significant increase in the phase focusing length. Taking into account the dependence of the electron beam intensity on the distance to the cathode, the simultaneous formation of several regions of negative charge (points of phase foci) corresponding to waves with the same frequency and different propagation increments and velocities is found. The phenomenon of locking electrons in a potential well between two simultaneously formed phase foci is discovered. The results of our calculations of the minimum phase focusing length describe well the known experimental data on the length of anomalous beam relaxation in a low-voltage beam discharge for He at the Knudsen numbers for electron transfer of the order of 1.