Stationary nonlinear plasma oscillations with account for particle capture

Periodical plasma oscillations of a finite amplitude are investigated in hydrodynamic approximation with regard to capture and temperature spread of particles the stability conditions of the oscillations are cleared up. It is shown that the plasma waves of a finite amplitude are stable with respect to low longitudinal oscillations only in the presence of the particle heat spread; this spread must exceed a certain minimum. In particle capture the range of oscillation existence expands if the number of captured particles decreases with the growth of their potential energy. Otherwise the range of oscillation existence narrows