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.

在我们的相关论文 [Zhao SX (2021) Chin. 物理。B 30055201]，通过流体模拟给出了负离子的delta分布，并通过分解的阴离子传输方程进行了初步解释。在目前的工作中，首先建立了正电等离子体传输方程和弹簧振子动力学方程之间的内在联系。受此相似性启发，根据阴离子方程所体现的数学设计了具有分散力而不是恢复力的改进的“弹簧振荡器”方程，该方程给出了准δ解，这对原子物理学和天文学学科也具有潜在意义. 为了解决“扩散混淆”，在复合损耗源项起漂移通量作用的基础上，探索了确定连续性方程中的δ剖面的物理学，适用于低温等离子体的流体模型，但不适用于普通的流体动力学。此外，这项工作中揭示的数学和物理学预测重组或附着（对于电子）频率的比率与物种扩散系数的关系是确定 delta 分布的一个非常重要的参数，因为它作为物体的加速度，根据重组的振荡器方程。利用该理论，解释了著名的负电容耦合等离子体漂移和双极扩散加热机制中电子密度的类似δ分布。