Stability of the Tonks–Langmuir discharge pre-sheath

The article formulates the stability problem of the plasma sheath in the Tonks–Langmuir discharge. Using the kinetic description of the ion gas, i.e., the stability of the potential shape in the quasi-neutral pre-sheath regarding the high and low frequency, the perturbations are investigated. The electrons are assumed to be Maxwell–Boltzmann distributed. Regarding high-frequency perturbations, the pre-sheath is shown to be stable. The stability problem regarding low-frequency perturbations can be reduced to an analysis of the "diffusion like" equation, which results in the instability of the potential distribution in the pre-sheath. By means of the Particle in Cell simulations, also the nonlinear stage of low frequency oscillations is investigated. Comparing the figure obtained with the figure for linear stage, one can find obvious similarity in the spatial-temporal behavior of the potential.