Thermodynamically Consistent Vibrational-Electron Heating: Generalized Model for Multi-Quantum Transitions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908879777955840 |
|---|---|
| author | Parent, Bernard Fuentes, Felipe Martin Rodriguez |
| author_facet | Parent, Bernard Fuentes, Felipe Martin Rodriguez |
| contents | Accurate prediction of electron temperature ($T_{\rm e}$) is critical for non-equilibrium plasma applications ranging from hypersonic flight to plasma-assisted combustion. We recently proposed a thermodynamically consistent model for vibrational-electron heating [Phys. Fluids 37, 096141 (2025)] that enforces the convergence of $T_{\rm e}$ to the vibrational temperature ($T_{\rm v}$) at equilibrium. However, the original derivation was restricted to single-quantum transitions, limiting its validity to low-temperature regimes ($T_{\rm e} \lesssim 1.5$ eV). In this Letter, we generalize the model to include multi-quantum overtone transitions, extending its applicability to high-energy regimes. We demonstrate that previous models neglecting hot-band transitions incur a systematic heating error of $\exp(-θ_{\rm v}/T_{\rm v})$, where $θ_{\rm v}$ is the characteristic vibrational temperature. This error exceeds 40% when $T_{\rm v}$ is greater than $θ_{\rm v}$, effectively preventing thermal relaxation. To correct this, we derive a formulation where the total heating rate is a summation of channel-specific cooling rates $Q_{\rm e-v}^{(m)}$, each associated with a quantum jump $m$, scaled by a thermodynamic factor $\exp(mθ_{\rm v}/T_{\rm e}-mθ_{\rm v}/T_{\rm v})$. This generalized model preserves thermodynamic consistency by ensuring zero net energy transfer at equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamically Consistent Vibrational-Electron Heating: Generalized Model for Multi-Quantum Transitions Parent, Bernard Fuentes, Felipe Martin Rodriguez Plasma Physics Accurate prediction of electron temperature ($T_{\rm e}$) is critical for non-equilibrium plasma applications ranging from hypersonic flight to plasma-assisted combustion. We recently proposed a thermodynamically consistent model for vibrational-electron heating [Phys. Fluids 37, 096141 (2025)] that enforces the convergence of $T_{\rm e}$ to the vibrational temperature ($T_{\rm v}$) at equilibrium. However, the original derivation was restricted to single-quantum transitions, limiting its validity to low-temperature regimes ($T_{\rm e} \lesssim 1.5$ eV). In this Letter, we generalize the model to include multi-quantum overtone transitions, extending its applicability to high-energy regimes. We demonstrate that previous models neglecting hot-band transitions incur a systematic heating error of $\exp(-θ_{\rm v}/T_{\rm v})$, where $θ_{\rm v}$ is the characteristic vibrational temperature. This error exceeds 40% when $T_{\rm v}$ is greater than $θ_{\rm v}$, effectively preventing thermal relaxation. To correct this, we derive a formulation where the total heating rate is a summation of channel-specific cooling rates $Q_{\rm e-v}^{(m)}$, each associated with a quantum jump $m$, scaled by a thermodynamic factor $\exp(mθ_{\rm v}/T_{\rm e}-mθ_{\rm v}/T_{\rm v})$. This generalized model preserves thermodynamic consistency by ensuring zero net energy transfer at equilibrium. |
| title | Thermodynamically Consistent Vibrational-Electron Heating: Generalized Model for Multi-Quantum Transitions |
| topic | Plasma Physics |
| url | https://arxiv.org/abs/2512.23072 |