Stable and Unstable Regimes of Plasma Diodes in the Presence of Electron Collisions

A thermionic energy converter as the Pierce diode of which the interelectrode space is filled with a uniform background of immobile ions is considered. The features of stability of its time-independent solutions are investigated under electron collisions with background gas. The solutions are obtained analytically by the Lagrange method. A dispersion equation is derived using a perturbative approach. The aperiodic solutions of this equation, as well as the oscillatory ones, are obtained and their properties are studied too. The regions of unstable aperiodic modes are determined. It is shown that all the oscillatory modes are stable.