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.
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