The collisional-radiative models from a dynamical system and a chemical reaction network perspective

The collisional-radiative (CR) model is governed by a system of nonlinear ODEs, whose solutions depend upon the plasma parameters such as electron density and temperature. The large number of species and complex reactions involved in the CR model can result in qualitatively different dynamical behaviors as the plasma conditions change. To understand the dynamical properties of a CR model, we perform an analysis for both the atomic and molecular CR models from a dynamical system and a chemical reaction network perspective, respectively. The molecular CR model shows a hysteresis bifurcation, such that under the variation of the electron temperature, its steady-state solution can jump from one stable branch to another at two bifurcation points. The two stable branches overlap at a specific range of electron temperature, showing the bistable behavior. In contrast, the atomic CR model doesn't exhibit bistable behavior, regardless of the rate constants. These different behaviors of atomic and molecular CR models can be understood from the chemical reaction network perspective, being inferred from the complexity of the species-reaction graphs. This bistability of molecular CR model opens new pathways to plasma detachment.