Numerical investigations on strong pattern selecting Eckhaus instabilities in neon glow discharges

Abstract

Starting from the hydrodynamic description of the positive column in a neon glow discharge, a numerical approach is used in order to study the nonlinear properties of ionization waves. Within the instability region of the homogeneous equilibrium state, a secondary instability of the Eckhaus type is found. Compared to the classical results, the plasma system shows some peculiarities, e.g., an asymmetric stability band and strong selection of periodic patterns. The dependency of the shape and the width of this band on the discharge parameters is investigated. The spatiotemporal dynamics connected with the transitions from the stability band to the instability region have been studied showing different behavior on the upper and lower border of the stability region. Normally a subcritical Eckhaus instability has been revealed. Moreover, at selected sets of plasma parameters the phenomenon of spatiotemporal intermittency is found.

Improved Understanding of the Nonlinear Properties of Ionization Instabilities in Plasmas

“…The first one is to solve the equations by means of a numerical simulation. Of course, this method is restricted to calculations at selective points of the space of plasma parameters only [27]. The second method uses approximations of the full set of balance equations that are valid in the weakly nonlinear region.…”

Numerical Analysis and Simulation Analysis for Space‐Time Data

“…The coefficients can be calculated at different plasma parameters [9]. In equation (3) the index r means a real part, and i stands for the imaginary part of the complex coefficients.…”

Hysteresis of ionization waves

“…ref. [20]) provides the asymmetric stability band observed in neon, which is the prerequisite for the understanding of the hysteresis phenomenon.…”