Stable and unstable regimes of plasma diodes in the presence of electron collisions

A thermionic energy converter is modelled by the Pierce diode which inter-electrode region is filled uniformly with immovable ions. Stability features of such diode steady states in the presence of electron-gas background collision are studied. Time-independent solutions are analytically obtained by Lagrangian formalism. Using a perturbation approach we derived a relevant dispersion equation. Both aperiodic and oscillatory solutions of such an equation are studied. The regions corresponding to unstable aperiodic modes are specifed. On the other hand, all oscillatory modes are shown to be stable.