The kinetic theory of a low-voltage beam discharge instability in He is developed in the conditions, when the distance between electrodes is of the order of electron-atom collision length and the density of electrons in a primary beam is up to ten percent of the plasma density. The dispersion equation and its numerical and analytical solutions are obtained. The stability loss of this discharge is described in the framework of the problem with initial and boundary conditions. A significant dispersion is found in the propagation of harmonic disturbances in this system. On the basis of the developed theory, the areas of applicability of the hydrodynamic approach to the consideration of the system "cold electron beam - cold plasma"are elucidated. The theory significantly expands the range of parameters of the electron beam-plasma system, where a quantitative description of the spatial and temporal dynamics of wave propagation in such a system is possible. In the well-known special cases, such as a "weak electron beam - cold plasma,"the results obtained coincide with the data of other authors.