Thermodynamically Consistent Vibrational-Electron Heating: Generalized Derivation for Excited State Populations

TL;DR

This paper generalizes a thermodynamically consistent vibrational-electron heating model to include vibrationally excited states, improving accuracy in predicting electron temperatures in non-equilibrium plasma flows.

Contribution

It extends the previous model by removing the ground-state dominance assumption, allowing for accurate electron temperature predictions when vibrationally excited states are significant.

Findings

The heating-to-cooling ratio remains valid with vibrationally excited states.

The model now applies to plasma flows with significant vibrational excitation.

The derivation enforces convergence of electron temperature to vibrational temperature.

Abstract

Accurate prediction of electron temperature ($T_{\rm e}$) in non-equilibrium plasma flows is critical for applications ranging from hypersonic flight to plasma-assisted combustion. We recently proposed a thermodynamically consistent model for vibrational-electron (V-e) heating [Phys. Fluids 37, 096141 (2025)] which enforces convergence of $T_{\rm e}$ to the vibrational temperature ($T_{\rm v}$) at equilibrium. While the original derivation assumed electron energy loss was dominated by collisions with ground-state molecules, this Letter presents a rigorous generalization of the model. We demonstrate that the heating-to-cooling ratio $\exp(\theta_{\rm v}/T_{\rm e}-\theta_{\rm v}/T_{\rm v})$ with $\theta_{\rm v}$ the characteristic vibrational temperature remains valid even when electron cooling interactions with vibrationally excited states are included. This derivation removes the previous constraint assuming ground-state dominance, thereby extending the model's validity to plasma flows where vibrationally excited populations contribute significantly to electron cooling.