The Pierce diode as a model for the stability of thermionic gas discharges

In this work an attempt is made to understand theoretically the trigger mechanism of a Pierce-type hydrodynamic instability found experimentally in thermionic discharges at low pressure. Particle-in-cell simulations are used to obtain detailed information about plasma parameters such as phase space and potential distributions. In contrast to earlier studies, the simultaneous influence of the ion dynamics, collisions with neutrals, and the sheath capacitance is taken into account. This is done by adopting the Lagrangian description of a general Pierce diode model developed previously. The new results obtained are threefold. First, few ion - neutral collisions prevent the coupling between electron and ion dynamics on the electronic time-scale thus removing oscillatory growing Pierce - Buneman modes. Second, the classical Pierce-diode supplemented by an external capacitance to account for the damping effect of the sheath on the Pierce instability explains the existence of stable equilibria. It further reveals the nature of the bifurcation at the instability threshold, i.e. a Hopf bifurcation is the trigger mechanism of the non-linear relaxation oscillations observed in both simulation and experiment. Third, the transient behaviour prior to the instability onset is found to be qualitatively described within the hydrodynamic model.