APPEARANCE OF INFLECTION POINT MODES IN BEAM-PLASMA SYSTEMS

In a stable unbounded Vlasov-Poisson plasma, the phase velocity of a n eutrally stable mode with non-zero wavenumber must correspond to a poi nt on the equilibrium distribution which is simultaneously a critical point and an inflection point. The appearance of such inflection point modes in the spectrum of beam-plasma systems occurs when the linear s tability boundary develops a minimum at the wavenumber of the mode. In this event, the boundary of the parameter domain of linear instabilit y coincides with the boundary of the parameter domain of rigorous (non linear) stability.