Delta distribution of electronegative plasma predicted by reformed “spring oscillator” dynamic equation with dispersing force

Abstract

In our relevant paper [Zhao S X (2021) Chin. Phys. B 30 055201], a delta distribution of negative ions is given by fluid simulation and preliminarily explained by decomposed anions transport equation. In the present work, first, the intrinsic connection between the electropositive plasma transport equation and spring oscillator dynamic equation is established. Inspired by this similarity, reformed “spring oscillator” equation with dispersing instead of restoring force that gives quasi-delta solution is devised according to the math embodied in the anion equation, which is of potential significance to the disciplines of atomic physics and astronomy as well. For solving the “diffusion confusion”, the physics that determines the delta profile within the continuity equation is explored on the basis that recombination loss source term plays the role of drift flux, which is applicable for fluid model of low temperature plasma, but not the ordinary fluid dynamics. Besides, the math and physics revealed in this work predict that the ratio of recombination or attachment (for electrons) frequency versus the species diffusion coefficient is a very important parameter in determining the delta distribution, as it acts as the acceleration of object, according to the reformed oscillator equation. With this theory, the analogous delta profile of electrons density in the famous drift and ambi-polar diffusion heating mechanism of electronegative capacitively coupled plasma is interpreted.