Stratification of discharge in noble gases from the viewpoint of the discrete dynamics

Abstract

Based on the analysis of electron phase trajectories in sinusoidal electric fields, a new point of view on discharge stratification is proposed. It is shown that the positive column can be considered as a spatial resonator in which electric fields with a fundamental period length LS or higher mode length qpLS establish, where p and q are integers and p > q. The fundamental mode length LS is equivalent to the distance on which electrons gain energy equal to the lowest excitation threshold. This distance determines a length of the S-striation. Unlike kinetic theory, in the presented model resonance properties of the discharge column are not connected with elastic collision energy losses. A point map is used to obtain the resonance trajectories of electrons in the phase plane. Stable points for the positions of inelastic collisions in the resonance trajectories have been found at the positions of field maxima in the case of integer ratios pq. For non-integer ratios pq, multiple resonance trajectories arise according to a more complex stability criterion. From this point of view, S-, P-, and R-striations in noble gas discharges can be explained. Due to energy losses in elastic collisions, initial electron energy distribution functions converge to the resonance trajectories (the so-called “bunch effect”). The findings of the discrete model agree with results of kinetic theory and experiment. The new approach avoids difficulties of the kinetic theory in the case of exceptionally large relaxation lengths which can even exceed the positive column length.