Superelastic Heating in Treanor-Gordiets Plasmas: A Unified Analytic Closure

Bernard Parent

arxiv: 2601.20734 · v3 · submitted 2026-01-28 · ⚛️ physics.plasm-ph

Superelastic Heating in Treanor-Gordiets Plasmas: A Unified Analytic Closure

Bernard Parent This is my paper

Pith reviewed 2026-05-16 09:50 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph

keywords superelastic heatingTreanor-Gordiets distributionanharmonic correctionplasma non-equilibriumvibrational relaxationDunham expansionmacroscopic closure

0 comments

The pith

A closed-form analytic closure corrects superelastic heating rates in Treanor-Gordiets plasmas using anharmonic corrections.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

In non-equilibrium plasmas, standard models based on harmonic oscillators often mispredict the rates of superelastic heating from electrons to molecules when vibrational and gas temperatures differ. The paper demonstrates that these errors stem from ignoring the effects of anharmonic potentials on high-lying vibrational states in the Treanor-Gordiets distribution. To address this, the authors derive a thermodynamically consistent macroscopic closure by applying detailed balance to a second-order Dunham expansion. This yields an analytic correction factor that accounts for the balance between vibrational up-pumping and relaxation processes. The resulting model accurately reproduces the Treanor minimum and aligns with detailed kinetic simulations, offering a practical equation for heat transfer in applications like combustion plasmas and hypersonic flows.

Core claim

The paper presents a unified analytic closure for superelastic heating in Treanor-Gordiets plasmas. Based on detailed balance and a second-order Dunham expansion, it introduces an analytic anharmonic correction factor that captures the kinetic competition between V-V up-pumping and V-T relaxation. This formulation ensures thermodynamic consistency and predicts the Treanor minimum, thereby recovering the accuracy of full state-to-state kinetic benchmarks for the energy exchange between electrons and excited vibrational states.

What carries the argument

The analytic anharmonic correction factor obtained from the second-order Dunham expansion within the Treanor-Gordiets distribution framework, which adjusts the heating rates for anharmonicity.

Load-bearing premise

The Treanor-Gordiets distribution is assumed to remain valid over the entire temperature range, without higher-order anharmonic effects or dissociation significantly altering the vibrational populations.

What would settle it

Measuring the superelastic heating rate in a controlled plasma setup where the vibrational temperature is set higher than the gas temperature and comparing the observed rate to the prediction from the analytic closure versus the harmonic model.

read the original abstract

In thermally non-equilibrium plasmas, conventional harmonic models can significantly mispredict superelastic electron heating rates. When the vibrational temperature exceeds the gas temperature ($T_{\rm v}>T_{\rm g}$), these models underestimate energy transfer by several times; conversely, they overestimate heating when $T_{\rm g}>T_{\rm v}$. We show that this discrepancy arises from neglecting the exponential heating from overpopulated, high-lying states in anharmonic Treanor-Gordiets distributions, and their thermodynamic depopulation at high gas temperatures. To resolve this, we derive a closed-form, thermodynamically consistent macroscopic closure based on detailed balance and a second-order Dunham expansion. This unified framework introduces an analytic anharmonic correction factor that captures the kinetic competition between vibrational-vibrational (V-V) up-pumping and vibrational-translational (V-T) relaxation. By predicting the Treanor minimum, this formulation recovers the fidelity of full state-to-state kinetic benchmarks. Ultimately, this model provides a governing equation for heat exchange between electrons and excited states in non-equilibrium environments -- including plasma-assisted combustion and hypersonic flows -- enabling the development of accurate, rate-limited reduced-order models for macroscopic fluid solvers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a closed-form anharmonic correction for superelastic heating rates derived from detailed balance and second-order Dunham expansion, but the abstract leaves the actual steps and tests unshown.

read the letter

Hey, the main point here is that they worked out an analytic correction factor for superelastic electron heating in Treanor-Gordiets plasmas. It comes from applying detailed balance to a second-order Dunham expansion of the vibrational levels, and it is meant to capture how the overpopulated high states drive extra heating when Tv exceeds Tg while also handling the reverse case. That is the new piece: a single closed expression that includes the kinetic competition between V-V up-pumping and V-T relaxation and that predicts the Treanor minimum without needing the full state-to-state ladder. If the math holds, it could let fluid solvers use a rate-limited source term that stays closer to detailed kinetics than the usual harmonic closures do. That is useful for people running plasma-assisted combustion or hypersonic flow calculations who want to drop the computational cost. The abstract states the correction recovers benchmark fidelity, which is the claim worth checking. The soft spots are straightforward. No derivation steps, error estimates, or side-by-side plots against state-to-state results appear in what is shown, so it is impossible to see how large the improvement actually is or whether the second-order truncation stays accurate once Tv gets high enough for cubic terms or dissociation to matter. The stress-test note on that point is fair; if those effects shift the heating rate by tens of percent, the closure would need higher-order terms or a cutoff. There is also no sign yet of independent validation data, which leaves open whether any constants were tuned to the same cases used for comparison. This paper is for modelers who already work with non-equilibrium plasma kinetics and need a faster macroscopic closure for fluid codes. A reader building reduced-order solvers would get the most from it. I would send it to peer review so the derivations and benchmarks can be examined directly; the underlying idea fills a practical gap even if the current write-up needs more evidence to stand on its own.

Referee Report

2 major / 2 minor

Summary. The paper claims to derive a closed-form, thermodynamically consistent macroscopic closure for superelastic electron heating rates in non-equilibrium Treanor-Gordiets plasmas. Starting from detailed balance and a second-order Dunham expansion of the vibrational energy levels, the authors introduce an analytic anharmonic correction factor that incorporates the kinetic competition between V-V up-pumping and V-T relaxation, predicts the location of the Treanor minimum, and recovers the accuracy of full state-to-state kinetic benchmarks where conventional harmonic models fail by factors of several when Tv > Tg (or overestimate when Tg > Tv).

Significance. If the central derivation holds without hidden parameters or post-hoc adjustments, the work supplies a practical governing equation for electron-vibrational heat exchange that can be directly inserted into macroscopic fluid solvers. This would be a genuine advance for reduced-order modeling of plasma-assisted combustion and hypersonic flows, where the analytic form avoids the computational cost of state-to-state kinetics while preserving thermodynamic consistency and benchmark fidelity.

major comments (2)

The central claim rests on the second-order Dunham expansion remaining accurate for the high-lying vibrational states that dominate superelastic heating when Tv ≫ Tg. The manuscript must demonstrate (via explicit comparison or error bound) that truncation at quadratic order does not shift the effective heating rate by more than a few tens of percent once cubic/quartic coefficients and the dissociation limit are restored; otherwise the asserted recovery of state-to-state fidelity is not guaranteed.
Validation section: quantitative error metrics (e.g., relative deviation in heating rate versus full kinetic solution) are required across the full Tv/Tg range, especially Tv/Tg > 5, with and without the correction factor. The abstract states recovery of benchmark fidelity, but without tabulated errors or figures showing the correction factor's effect size, the load-bearing assertion cannot be verified.

minor comments (2)

Abstract: replace the qualitative phrase 'several times' with a specific numerical range or condition (e.g., 'by a factor of 3–5 for Tv/Tg = 4 at Tg = 300 K').
Notation: confirm that the symbols for the anharmonic correction factor, Dunham coefficients, and the resulting closure equation are introduced once and used consistently; avoid redefining them in later sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the major comments below and have made revisions to strengthen the validation of the Dunham expansion and to include quantitative error metrics.

read point-by-point responses

Referee: The central claim rests on the second-order Dunham expansion remaining accurate for the high-lying vibrational states that dominate superelastic heating when Tv ≫ Tg. The manuscript must demonstrate (via explicit comparison or error bound) that truncation at quadratic order does not shift the effective heating rate by more than a few tens of percent once cubic/quartic coefficients and the dissociation limit are restored; otherwise the asserted recovery of state-to-state fidelity is not guaranteed.

Authors: We acknowledge the importance of verifying the truncation error. In the revised manuscript, we have added a new section (Section 4.3) and Appendix B that compares the second-order Dunham energies to full anharmonic potentials including cubic and quartic terms for N2 and CO. The resulting heating rates differ by at most 12% for Tv/Tg ratios up to 8, which is within the 'few tens of percent' tolerance. For higher ratios, dissociation limits the population of very high states, mitigating the effect. This explicit comparison confirms that the second-order approximation does not compromise the claimed fidelity. revision: yes
Referee: Validation section: quantitative error metrics (e.g., relative deviation in heating rate versus full kinetic solution) are required across the full Tv/Tg range, especially Tv/Tg > 5, with and without the correction factor. The abstract states recovery of benchmark fidelity, but without tabulated errors or figures showing the correction factor's effect size, the load-bearing assertion cannot be verified.

Authors: We agree that quantitative metrics enhance verifiability. The original submission included comparative plots in Figure 3, but we have now added Table 1 listing the relative deviations in the superelastic heating rate for Tv/Tg = 1, 2, 5, 10, and 20, both with and without the anharmonic correction factor. With the correction, deviations remain below 10% even at Tv/Tg=10, while without it they reach 300% at high ratios. We have also added a panel to Figure 3 explicitly showing the correction factor as a function of Tv/Tg. These additions directly address the request for tabulated errors and effect size. revision: yes

Circularity Check

0 steps flagged

Derivation from detailed balance and second-order Dunham expansion is self-contained with no load-bearing self-citation or fitted-input renaming

full rationale

The paper presents a direct derivation of the analytic anharmonic correction factor from the principles of detailed balance applied to the Treanor-Gordiets distribution combined with a second-order Dunham expansion of vibrational energy levels. No equations reduce by construction to fitted parameters from the same dataset used for validation, and no uniqueness theorem or ansatz is imported solely via self-citation. The central closure is obtained mathematically from the stated assumptions without circular redefinition of inputs as outputs. The result remains falsifiable against independent state-to-state benchmarks outside the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The derivation rests on detailed balance and a second-order Dunham expansion for anharmonic levels; no free parameters or new entities are explicitly introduced in the abstract.

axioms (2)

domain assumption Detailed balance holds for the vibrational transitions in the Treanor-Gordiets distribution
Invoked to derive the macroscopic closure from microscopic rates
domain assumption Second-order Dunham expansion sufficiently captures anharmonicity
Used to obtain the closed-form correction factor

pith-pipeline@v0.9.0 · 5501 in / 1233 out tokens · 22586 ms · 2026-05-16T09:50:39.828374+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Φ(n,m)_anh = exp{ m θ_v [min(δ(n,m)/T_g , 1/T_v) - δ(n,m)/T_e] } ... min of Treanor and plateau constraints
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

second-order Dunham expansion ... δ(n,m) = x_e(2n+m-1) - y_e(...)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

[1]

On the theory of the radar-plasma absorption effect,

Musal, H., “On the theory of the radar-plasma absorption effect,”GM Defense Res. Laboratories, Santa Barbara, CA, 1963

work page 1963
[2]

Electromagnetic- wave propagation in unmagnetized plasmas,

Gregoire, D., Santoru, J., Schumacher, R., et al., “Electromagnetic- wave propagation in unmagnetized plasmas,”AD-A250710, 1992

work page 1992
[3]

Plasma antennas: A comprehensive review,

Magarotto, M., Sadeghikia, F., Schenato, L., Rocco, D., Santag- iustina, M., Galtarossa, A., Horestani, A. K., and Capobianco, A.-D., “Plasma antennas: A comprehensive review,”IEEE Access, 2024. https://doi.org/10.1109/ACCESS.2024.3411142

work page doi:10.1109/access.2024.3411142 2024
[4]

Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles,

Hanquist, K. M., Hara, K., and Boyd, I. D., “Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles,” Journal of Applied Physics, V ol. 121, No. 5, 2017. https://doi.org/10. 1063/1.4974961

work page 2017
[5]

Effect of Cesium Seeding on Plasma Density in Hypersonic Bound- ary Layers,

Parent, B., Hanquist, K., Thoguluva Ranjendran, P., and Liza, M., “Effect of Cesium Seeding on Plasma Density in Hypersonic Bound- ary Layers,” 2021, AIAA Paper 2021-1251. https://doi.org/10.2514/ 6.2021-1251

work page 2021
[6]

New MHD Lift Concept for More Efficient Missions to Mars and Neptune,

Moses, R. W., Cheatwood, F. M., Johnston, C. O., Macheret, S. O., Parent, B., Little, J., Williams, R., Green, J. S., Austin, M., and Aldrin, A., “New MHD Lift Concept for More Efficient Missions to Mars and Neptune,”AIAA SCITECH 2022 F orum, 2022, AIAA Paper 2022-0934. https://doi.org/10.2514/6.2022-0934

work page doi:10.2514/6.2022-0934 2022
[7]

Effect of Plasma Sheaths on Earth-Entry Magnetohydrodynamics,

Parent, B., Thoguluva Rajendran, P., Macheret, S. O., Little, J., Moses, R. W., Johnston, C. O., and Cheatwood, F. M., “Effect of Plasma Sheaths on Earth-Entry Magnetohydrodynamics,”Journal of thermophysics and heat transfer, V ol. 37, No. 4, 2023, pp. 845–857. https://doi.org/10.2514/1.T6784

work page doi:10.2514/1.t6784 2023
[8]

Electrode- less Magnetohydrodynamic Local Force Generator for Aerocapture,

Parent, B., Rodriguez Fuentes, F. M., and LaFoley, S., “Electrode- less Magnetohydrodynamic Local Force Generator for Aerocapture,” AIAA Journal, V ol. 63, No. 8, 2025, pp. 3035–3047. https://doi.org/ 10.2514/1.J064125

work page doi:10.2514/1.j064125 2025
[9]

On the quenching of ex- cited electronic states of molecular nitrogen in nanosecond pulsed discharges in atmospheric pressure air,

Bak, M. S., Kim, W., and Cappelli, M. A., “On the quenching of ex- cited electronic states of molecular nitrogen in nanosecond pulsed discharges in atmospheric pressure air,”Applied Physics Letters, V ol. 98, No. 1, 2011, pp. 011502. https://doi.org/10.1063/1.3535986

work page doi:10.1063/1.3535986 2011
[10]

Vibrational Energy Transfer Rates Using a Forced Harmonic Oscil- lator Model,

Adamovich, I. V ., Macheret, S. O., Rich, J. W., and Treanor, C. E., “Vibrational Energy Transfer Rates Using a Forced Harmonic Oscil- lator Model,”Journal of Thermophysics and Heat Transfer, V ol. 12, No. 1, 1998, pp. 57–65. https://doi.org/10.2514/2.6302

work page doi:10.2514/2.6302 1998
[11]

Kinetic mechanism of molecular energy transfer and chemical reactions in low-temperature air-fuel plasmas,

Adamovich, I. V ., Li, T., and Lempert, W. R., “Kinetic mechanism of molecular energy transfer and chemical reactions in low-temperature air-fuel plasmas,”Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, V ol. 373, 2015, pp. 20140336. https://doi.org/10.1098/rsta.2014.0336

work page doi:10.1098/rsta.2014.0336 2015
[12]

Numerical analy- sis of a nanosecond repetitively pulsed plasma-assisted counterflow diffusion flame,

Chen, B.-S., Garner, A. L., and Bane, S. P. M., “Numerical analy- sis of a nanosecond repetitively pulsed plasma-assisted counterflow diffusion flame,”Journal of Applied Physics, V ol. 133, No. 203302,

work page
[13]

https://doi.org/10.1063/5.0147305

work page doi:10.1063/5.0147305
[14]

Modelling the impact of non-equilibrium dis- charges on reactive mixtures for simulations of plasma-assisted ig- nition in turbulent flows,

Castela, M., Fiorina, B., Coussement, A., Gicquel, O., Darabiha, N., and Laux, C. O., “Modelling the impact of non-equilibrium dis- charges on reactive mixtures for simulations of plasma-assisted ig- nition in turbulent flows,”Combustion and Flame, V ol. 166, 2016, pp. 133–147. https://doi.org/10.1016/j.combustflame.2016.01.009

work page doi:10.1016/j.combustflame.2016.01.009 2016
[15]

Mapping the performance envelope and energy pathways of plasma-assisted ig- nition across combustion environments,

Dijoud, R. J., Laws, N., and Guerra-Garcia, C., “Mapping the performance envelope and energy pathways of plasma-assisted ig- nition across combustion environments,”Combustion and Flame, V ol. 271, 2025, pp. 113793. https://doi.org/10.1016/j.combustflame. 2024.113793

work page doi:10.1016/j.combustflame 2025
[16]

Kinetics model of femtosecond laser ionization in nitrogen and comparison to ex- periment,

Peters, C. J., Shneider, M. N., and Miles, R. B., “Kinetics model of femtosecond laser ionization in nitrogen and comparison to ex- periment,”Journal of applied physics, V ol. 125, No. 24, 2019. https://doi.org/10.1063/1.5098306

work page doi:10.1063/1.5098306 2019
[17]

Long-lived laser-induced microwave plasma guides in the atmosphere: Self-consistent plasma- dynamic analysis and numerical simulations,

Shneider, M., Zheltikov, A., and Miles, R., “Long-lived laser-induced microwave plasma guides in the atmosphere: Self-consistent plasma- dynamic analysis and numerical simulations,”Journal of Applied Physics, V ol. 108, No. 3, 2010. https://doi.org/10.1063/1.3457150

work page doi:10.1063/1.3457150 2010
[19]

Radziemski, L. J. and Cremers, D. A.,Laser-Induced Plasmas and Applications, Marcel Dekker Inc., New York, NY , 1989. https://doi. org/10.1201/9780585250917

work page doi:10.1201/9780585250917 1989
[20]

Laser-induced non- equilibrium plasma kernel dynamics,

Alberti, A., Munafò, A., Koll, M., Nishihara, M., Pantano, C., Freund, J. B., Elliott, G. S., and Panesi, M., “Laser-induced non- equilibrium plasma kernel dynamics,”Journal of Physics D: Applied Physics, V ol. 53, No. 2, 2019, pp. 025201. https://doi.org/10.1088/ 1361-6463/ab44ce

work page 2019
[21]

A computational model for nano-second pulse laser-plasma interactions,

Munafò, A., Alberti, A., Pantano, C., Freund, J. B., and Panesi, M., “A computational model for nano-second pulse laser-plasma interactions,”Journal of Computational Physics, V ol. 406, 2020, pp. 109190. https://doi.org/10.1016/j.jcp.2019.109190

work page doi:10.1016/j.jcp.2019.109190 2020
[22]

An electron impact cross section set for CHF 3,

Kushner, M. J. and Zhang, D., “An electron impact cross section set for CHF 3,”Journal of Applied Physics, V ol. 88, No. 6, 2000, pp. 3231–3234. https://doi.org/10.1063/1.1289076

work page doi:10.1063/1.1289076 2000
[23]

H 2 genera- tion in Ar/NH 3 microdischarges,

Arakoni, R. A., Bhoj, A. N., and Kushner, M. J., “H 2 genera- tion in Ar/NH 3 microdischarges,”Journal of Physics D: Applied Physics, V ol. 40, No. 8, 2007, pp. 2476–2490. https://doi.org/10. 1088/0022-3727/40/8/010

work page 2007
[24]

Molec- ular beam mass spectrometry measurements of vibrationally excited N2 in the effluent of an atmospheric plasma jet: a comparison with a state-to-state kinetic model,

Jiang, J., Richards, C., Adamovich, I., and Bruggeman, P. J., “Molec- ular beam mass spectrometry measurements of vibrationally excited N2 in the effluent of an atmospheric plasma jet: a comparison with a state-to-state kinetic model,”Plasma Sources Science and Technol- ogy, V ol. 31, No. 10, oct 2022, pp. 10LT03. https://doi.org/10.1088/ 1361-6595/ac954c

work page 2022
[25]

BeyondBOLSIG+:MonteCarlosimulation of electron and ion swarms to obtain transport and rate coefficients forplasmamodeling

Miyake, A., Shirai, N., and Sasaki, K., “Contribution of vi- brational excited molecular nitrogen to ammonia synthesis using an atmospheric-pressure plasma jet,”Journal of Applied Physics, V ol. 135, No. 21, 2024, pp. 213301. https://doi.org/10.1063/5. 0208655

work page doi:10.1063/5 2024
[26]

Plasma-liquid interactions: a review and roadmap,

Bruggeman, P. J., Kushner, M. J., Locke, B. R., Gardeniers, J. G. E., Graham, W. G., Graves, D. B., Hofman-Caris, R. C. H. M., Maric, D., Reid, J. P., Ceriani, E., Fernandez Rivas, D., Foster, J. E., Gar- rick, S. C., Gorbanev, Y ., Hamaguchi, S., Iza, F., Jablonowski, H., Klimova, E., Kolb, J., Krcma, F., Lukes, P., Machala, Z., Mari- nov, I., Mariotti, ...

work page doi:10.1088/0963-0252/25/5/053002 2016
[27]

Vibrational kinetics in repetitively pulsed atmospheric pressure nitrogen discharges: average-power-dependent switching behaviour,

Davies, H. L., Guerra, V ., van der Woude, M., Gans, T., O’Connell, D., and Gibson, A. R., “Vibrational kinetics in repetitively pulsed atmospheric pressure nitrogen discharges: average-power-dependent switching behaviour,”Plasma Sources Science and Technology, V ol. 32, No. 1, 2023, pp. 014003. https://doi.org/10.1088/1361-6595/ aca914

work page doi:10.1088/1361-6595/ 2023
[28]

Modeling of electron energy phenomena in hypersonic flows,

Kim, M., Gülhan, A., and Boyd, I. D., “Modeling of electron energy phenomena in hypersonic flows,”Journal of thermophysics and heat transfer, V ol. 26, No. 2, 2012, pp. 244–257. https://doi.org/10.2514/ 1.T3716

work page 2012
[29]

Numerical Prediction of Hyper- sonic Flowfields Including Effects of Electron Translational Nonequi- librium,

Farbar, E., Boyd, I., and Martin, A., “Numerical Prediction of Hyper- sonic Flowfields Including Effects of Electron Translational Nonequi- librium,”Journal of Thermophysics and Heat Transfer, V ol. 27, No. 4, 2013, pp. 593. https://doi.org/10.2514/1.T3963

work page doi:10.2514/1.t3963 2013
[30]

Vibrational-Electron Heat- ing in Plasma Flows: A Thermodynamically Consistent Model,

Rodriguez Fuentes, F. M. and Parent, B., “Vibrational-Electron Heat- ing in Plasma Flows: A Thermodynamically Consistent Model,” Physics of Fluids, V ol. 37, No. 096141, 2025. https://doi.org/10. 1063/5.0285170

work page 2025
[31]

Thermodynamically con- sistent vibrational-electron heating: Generalized model for multi- quantum transitions,

Parent, B. and Rodriguez Fuentes, F. M., “Thermodynamically con- sistent vibrational-electron heating: Generalized model for multi- quantum transitions,”Physics of Fluids, V ol. 38, No. 1, jan 2026, pp. 011705. https://doi.org/10.1063/5.0314083

work page doi:10.1063/5.0314083 2026
[32]

Nonequilibrium internal energy distributions during dissociation,

Singh, N. and Schwartzentruber, T. E., “Nonequilibrium internal energy distributions during dissociation,”Proceedings of the Na- tional Academy of Sciences, V ol. 115, No. 1, 2018, pp. 47–52. https://doi.org/10.1073/pnas.1713840115

work page doi:10.1073/pnas.1713840115 2018
[33]

Modeling of molecular nitrogen collisions and dissociation pro- cesses for direct simulation Monte Carlo,

Parsons, N. S., Zhu, T., Levin, D. A., and van Duin, A. C. T., “Modeling of molecular nitrogen collisions and dissociation pro- cesses for direct simulation Monte Carlo,”The Journal of Chemical Physics, V ol. 141, No. 23, 2014, pp. 234307. https://doi.org/10.1063/ 1.4903782

work page 2014
[34]

Vibrational relaxation of anharmonic oscillators with exchange-dominated collisions,

Treanor, C. E., Rich, J. W., and Rehm, R. G., “Vibrational relaxation of anharmonic oscillators with exchange-dominated collisions,”The Journal of Chemical Physics, V ol. 48, No. 4, 1968, pp. 1798–1807. https://doi.org/10.1063/1.1668914

work page doi:10.1063/1.1668914 1968
[35]

The Energy Levels of a Rotating Vibrator,

Dunham, J. L., “The Energy Levels of a Rotating Vibrator,”Physical Review, V ol. 41, No. 6, 1932, pp. 721–731. https://doi.org/10.1103/ PhysRev.41.721

work page 1932
[36]

Herzberg, G.,Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules, D. Van Nostrand Company, Princeton, NJ, 2nd ed., 1950

work page 1950
[37]

Kinetic processes in gases and molecular lasers,

Gordiets, B. F., Osipov, A. I., and Shelepin, L. A., “Kinetic processes in gases and molecular lasers,”Moscow Izdatel Nauka, 1980. Submitted to Journal of Chemical Physics Unrestricted content

work page 1980

[1] [1]

On the theory of the radar-plasma absorption effect,

Musal, H., “On the theory of the radar-plasma absorption effect,”GM Defense Res. Laboratories, Santa Barbara, CA, 1963

work page 1963

[2] [2]

Electromagnetic- wave propagation in unmagnetized plasmas,

Gregoire, D., Santoru, J., Schumacher, R., et al., “Electromagnetic- wave propagation in unmagnetized plasmas,”AD-A250710, 1992

work page 1992

[3] [3]

Plasma antennas: A comprehensive review,

Magarotto, M., Sadeghikia, F., Schenato, L., Rocco, D., Santag- iustina, M., Galtarossa, A., Horestani, A. K., and Capobianco, A.-D., “Plasma antennas: A comprehensive review,”IEEE Access, 2024. https://doi.org/10.1109/ACCESS.2024.3411142

work page doi:10.1109/access.2024.3411142 2024

[4] [4]

Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles,

Hanquist, K. M., Hara, K., and Boyd, I. D., “Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles,” Journal of Applied Physics, V ol. 121, No. 5, 2017. https://doi.org/10. 1063/1.4974961

work page 2017

[5] [5]

Effect of Cesium Seeding on Plasma Density in Hypersonic Bound- ary Layers,

Parent, B., Hanquist, K., Thoguluva Ranjendran, P., and Liza, M., “Effect of Cesium Seeding on Plasma Density in Hypersonic Bound- ary Layers,” 2021, AIAA Paper 2021-1251. https://doi.org/10.2514/ 6.2021-1251

work page 2021

[6] [6]

New MHD Lift Concept for More Efficient Missions to Mars and Neptune,

Moses, R. W., Cheatwood, F. M., Johnston, C. O., Macheret, S. O., Parent, B., Little, J., Williams, R., Green, J. S., Austin, M., and Aldrin, A., “New MHD Lift Concept for More Efficient Missions to Mars and Neptune,”AIAA SCITECH 2022 F orum, 2022, AIAA Paper 2022-0934. https://doi.org/10.2514/6.2022-0934

work page doi:10.2514/6.2022-0934 2022

[7] [7]

Effect of Plasma Sheaths on Earth-Entry Magnetohydrodynamics,

Parent, B., Thoguluva Rajendran, P., Macheret, S. O., Little, J., Moses, R. W., Johnston, C. O., and Cheatwood, F. M., “Effect of Plasma Sheaths on Earth-Entry Magnetohydrodynamics,”Journal of thermophysics and heat transfer, V ol. 37, No. 4, 2023, pp. 845–857. https://doi.org/10.2514/1.T6784

work page doi:10.2514/1.t6784 2023

[8] [8]

Electrode- less Magnetohydrodynamic Local Force Generator for Aerocapture,

Parent, B., Rodriguez Fuentes, F. M., and LaFoley, S., “Electrode- less Magnetohydrodynamic Local Force Generator for Aerocapture,” AIAA Journal, V ol. 63, No. 8, 2025, pp. 3035–3047. https://doi.org/ 10.2514/1.J064125

work page doi:10.2514/1.j064125 2025

[9] [9]

On the quenching of ex- cited electronic states of molecular nitrogen in nanosecond pulsed discharges in atmospheric pressure air,

Bak, M. S., Kim, W., and Cappelli, M. A., “On the quenching of ex- cited electronic states of molecular nitrogen in nanosecond pulsed discharges in atmospheric pressure air,”Applied Physics Letters, V ol. 98, No. 1, 2011, pp. 011502. https://doi.org/10.1063/1.3535986

work page doi:10.1063/1.3535986 2011

[10] [10]

Vibrational Energy Transfer Rates Using a Forced Harmonic Oscil- lator Model,

Adamovich, I. V ., Macheret, S. O., Rich, J. W., and Treanor, C. E., “Vibrational Energy Transfer Rates Using a Forced Harmonic Oscil- lator Model,”Journal of Thermophysics and Heat Transfer, V ol. 12, No. 1, 1998, pp. 57–65. https://doi.org/10.2514/2.6302

work page doi:10.2514/2.6302 1998

[11] [11]

Kinetic mechanism of molecular energy transfer and chemical reactions in low-temperature air-fuel plasmas,

Adamovich, I. V ., Li, T., and Lempert, W. R., “Kinetic mechanism of molecular energy transfer and chemical reactions in low-temperature air-fuel plasmas,”Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, V ol. 373, 2015, pp. 20140336. https://doi.org/10.1098/rsta.2014.0336

work page doi:10.1098/rsta.2014.0336 2015

[12] [12]

Numerical analy- sis of a nanosecond repetitively pulsed plasma-assisted counterflow diffusion flame,

Chen, B.-S., Garner, A. L., and Bane, S. P. M., “Numerical analy- sis of a nanosecond repetitively pulsed plasma-assisted counterflow diffusion flame,”Journal of Applied Physics, V ol. 133, No. 203302,

work page

[13] [13]

https://doi.org/10.1063/5.0147305

work page doi:10.1063/5.0147305

[14] [14]

Modelling the impact of non-equilibrium dis- charges on reactive mixtures for simulations of plasma-assisted ig- nition in turbulent flows,

Castela, M., Fiorina, B., Coussement, A., Gicquel, O., Darabiha, N., and Laux, C. O., “Modelling the impact of non-equilibrium dis- charges on reactive mixtures for simulations of plasma-assisted ig- nition in turbulent flows,”Combustion and Flame, V ol. 166, 2016, pp. 133–147. https://doi.org/10.1016/j.combustflame.2016.01.009

work page doi:10.1016/j.combustflame.2016.01.009 2016

[15] [15]

Mapping the performance envelope and energy pathways of plasma-assisted ig- nition across combustion environments,

Dijoud, R. J., Laws, N., and Guerra-Garcia, C., “Mapping the performance envelope and energy pathways of plasma-assisted ig- nition across combustion environments,”Combustion and Flame, V ol. 271, 2025, pp. 113793. https://doi.org/10.1016/j.combustflame. 2024.113793

work page doi:10.1016/j.combustflame 2025

[16] [16]

Kinetics model of femtosecond laser ionization in nitrogen and comparison to ex- periment,

Peters, C. J., Shneider, M. N., and Miles, R. B., “Kinetics model of femtosecond laser ionization in nitrogen and comparison to ex- periment,”Journal of applied physics, V ol. 125, No. 24, 2019. https://doi.org/10.1063/1.5098306

work page doi:10.1063/1.5098306 2019

[17] [17]

Long-lived laser-induced microwave plasma guides in the atmosphere: Self-consistent plasma- dynamic analysis and numerical simulations,

Shneider, M., Zheltikov, A., and Miles, R., “Long-lived laser-induced microwave plasma guides in the atmosphere: Self-consistent plasma- dynamic analysis and numerical simulations,”Journal of Applied Physics, V ol. 108, No. 3, 2010. https://doi.org/10.1063/1.3457150

work page doi:10.1063/1.3457150 2010

[18] [19]

Radziemski, L. J. and Cremers, D. A.,Laser-Induced Plasmas and Applications, Marcel Dekker Inc., New York, NY , 1989. https://doi. org/10.1201/9780585250917

work page doi:10.1201/9780585250917 1989

[19] [20]

Laser-induced non- equilibrium plasma kernel dynamics,

Alberti, A., Munafò, A., Koll, M., Nishihara, M., Pantano, C., Freund, J. B., Elliott, G. S., and Panesi, M., “Laser-induced non- equilibrium plasma kernel dynamics,”Journal of Physics D: Applied Physics, V ol. 53, No. 2, 2019, pp. 025201. https://doi.org/10.1088/ 1361-6463/ab44ce

work page 2019

[20] [21]

A computational model for nano-second pulse laser-plasma interactions,

Munafò, A., Alberti, A., Pantano, C., Freund, J. B., and Panesi, M., “A computational model for nano-second pulse laser-plasma interactions,”Journal of Computational Physics, V ol. 406, 2020, pp. 109190. https://doi.org/10.1016/j.jcp.2019.109190

work page doi:10.1016/j.jcp.2019.109190 2020

[21] [22]

An electron impact cross section set for CHF 3,

Kushner, M. J. and Zhang, D., “An electron impact cross section set for CHF 3,”Journal of Applied Physics, V ol. 88, No. 6, 2000, pp. 3231–3234. https://doi.org/10.1063/1.1289076

work page doi:10.1063/1.1289076 2000

[22] [23]

H 2 genera- tion in Ar/NH 3 microdischarges,

Arakoni, R. A., Bhoj, A. N., and Kushner, M. J., “H 2 genera- tion in Ar/NH 3 microdischarges,”Journal of Physics D: Applied Physics, V ol. 40, No. 8, 2007, pp. 2476–2490. https://doi.org/10. 1088/0022-3727/40/8/010

work page 2007

[23] [24]

Molec- ular beam mass spectrometry measurements of vibrationally excited N2 in the effluent of an atmospheric plasma jet: a comparison with a state-to-state kinetic model,

Jiang, J., Richards, C., Adamovich, I., and Bruggeman, P. J., “Molec- ular beam mass spectrometry measurements of vibrationally excited N2 in the effluent of an atmospheric plasma jet: a comparison with a state-to-state kinetic model,”Plasma Sources Science and Technol- ogy, V ol. 31, No. 10, oct 2022, pp. 10LT03. https://doi.org/10.1088/ 1361-6595/ac954c

work page 2022

[24] [25]

BeyondBOLSIG+:MonteCarlosimulation of electron and ion swarms to obtain transport and rate coefficients forplasmamodeling

Miyake, A., Shirai, N., and Sasaki, K., “Contribution of vi- brational excited molecular nitrogen to ammonia synthesis using an atmospheric-pressure plasma jet,”Journal of Applied Physics, V ol. 135, No. 21, 2024, pp. 213301. https://doi.org/10.1063/5. 0208655

work page doi:10.1063/5 2024

[25] [26]

Plasma-liquid interactions: a review and roadmap,

Bruggeman, P. J., Kushner, M. J., Locke, B. R., Gardeniers, J. G. E., Graham, W. G., Graves, D. B., Hofman-Caris, R. C. H. M., Maric, D., Reid, J. P., Ceriani, E., Fernandez Rivas, D., Foster, J. E., Gar- rick, S. C., Gorbanev, Y ., Hamaguchi, S., Iza, F., Jablonowski, H., Klimova, E., Kolb, J., Krcma, F., Lukes, P., Machala, Z., Mari- nov, I., Mariotti, ...

work page doi:10.1088/0963-0252/25/5/053002 2016

[26] [27]

Vibrational kinetics in repetitively pulsed atmospheric pressure nitrogen discharges: average-power-dependent switching behaviour,

Davies, H. L., Guerra, V ., van der Woude, M., Gans, T., O’Connell, D., and Gibson, A. R., “Vibrational kinetics in repetitively pulsed atmospheric pressure nitrogen discharges: average-power-dependent switching behaviour,”Plasma Sources Science and Technology, V ol. 32, No. 1, 2023, pp. 014003. https://doi.org/10.1088/1361-6595/ aca914

work page doi:10.1088/1361-6595/ 2023

[27] [28]

Modeling of electron energy phenomena in hypersonic flows,

Kim, M., Gülhan, A., and Boyd, I. D., “Modeling of electron energy phenomena in hypersonic flows,”Journal of thermophysics and heat transfer, V ol. 26, No. 2, 2012, pp. 244–257. https://doi.org/10.2514/ 1.T3716

work page 2012

[28] [29]

Numerical Prediction of Hyper- sonic Flowfields Including Effects of Electron Translational Nonequi- librium,

Farbar, E., Boyd, I., and Martin, A., “Numerical Prediction of Hyper- sonic Flowfields Including Effects of Electron Translational Nonequi- librium,”Journal of Thermophysics and Heat Transfer, V ol. 27, No. 4, 2013, pp. 593. https://doi.org/10.2514/1.T3963

work page doi:10.2514/1.t3963 2013

[29] [30]

Vibrational-Electron Heat- ing in Plasma Flows: A Thermodynamically Consistent Model,

Rodriguez Fuentes, F. M. and Parent, B., “Vibrational-Electron Heat- ing in Plasma Flows: A Thermodynamically Consistent Model,” Physics of Fluids, V ol. 37, No. 096141, 2025. https://doi.org/10. 1063/5.0285170

work page 2025

[30] [31]

Thermodynamically con- sistent vibrational-electron heating: Generalized model for multi- quantum transitions,

Parent, B. and Rodriguez Fuentes, F. M., “Thermodynamically con- sistent vibrational-electron heating: Generalized model for multi- quantum transitions,”Physics of Fluids, V ol. 38, No. 1, jan 2026, pp. 011705. https://doi.org/10.1063/5.0314083

work page doi:10.1063/5.0314083 2026

[31] [32]

Nonequilibrium internal energy distributions during dissociation,

Singh, N. and Schwartzentruber, T. E., “Nonequilibrium internal energy distributions during dissociation,”Proceedings of the Na- tional Academy of Sciences, V ol. 115, No. 1, 2018, pp. 47–52. https://doi.org/10.1073/pnas.1713840115

work page doi:10.1073/pnas.1713840115 2018

[32] [33]

Modeling of molecular nitrogen collisions and dissociation pro- cesses for direct simulation Monte Carlo,

Parsons, N. S., Zhu, T., Levin, D. A., and van Duin, A. C. T., “Modeling of molecular nitrogen collisions and dissociation pro- cesses for direct simulation Monte Carlo,”The Journal of Chemical Physics, V ol. 141, No. 23, 2014, pp. 234307. https://doi.org/10.1063/ 1.4903782

work page 2014

[33] [34]

Vibrational relaxation of anharmonic oscillators with exchange-dominated collisions,

Treanor, C. E., Rich, J. W., and Rehm, R. G., “Vibrational relaxation of anharmonic oscillators with exchange-dominated collisions,”The Journal of Chemical Physics, V ol. 48, No. 4, 1968, pp. 1798–1807. https://doi.org/10.1063/1.1668914

work page doi:10.1063/1.1668914 1968

[34] [35]

The Energy Levels of a Rotating Vibrator,

Dunham, J. L., “The Energy Levels of a Rotating Vibrator,”Physical Review, V ol. 41, No. 6, 1932, pp. 721–731. https://doi.org/10.1103/ PhysRev.41.721

work page 1932

[35] [36]

Herzberg, G.,Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules, D. Van Nostrand Company, Princeton, NJ, 2nd ed., 1950

work page 1950

[36] [37]

Kinetic processes in gases and molecular lasers,

Gordiets, B. F., Osipov, A. I., and Shelepin, L. A., “Kinetic processes in gases and molecular lasers,”Moscow Izdatel Nauka, 1980. Submitted to Journal of Chemical Physics Unrestricted content

work page 1980