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Results for “Theoretical Kinetics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Theoretical kinetics predictions for NH 2 + HO 2

Recent modeling studies of NH 3 oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies between existing literature mechanisms. In this study high level theoretical kinetics predictions have been obtained for the reaction of NH 2 with HO 2 , which has previously been highlighted as an important reaction with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations including large basis sets and high-level corrections to yield high accuracy (~0.2 kcal/mol) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature and pressure dependent kinetics. For the radical-radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constant as well as the branching to the NH 3 + O 2 , H 2 NO + OH, and HNO + H 2 O channels. Rate constants are also reported for the H 2 NO + OH reaction as they arise naturally from the analysis. The rate constant and branching fraction determined in this work for the NH 2 + HO 2 reaction deviate significantly from values used in most previous modeling studies. The fact that the main product channel is chain terminating, rather than propagating, has strong implications for modeling NH 3 ignition and oxidation, in particular at intermediate temperatures and elevated pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Theoretical Kinetics Predictions for Reactions on the NH 2 O Potential Energy Surface

Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NH 2 O potential energy surface, including the NH 2 + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH 3 oxidation with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations, including large basis sets and high-level corrections to yield high-accuracy (~0.2 kcal/mol 2σ uncertainty) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature- and pressure-dependent kinetics. For radical–radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constants as well as the branching ratios. We find that the NO + H 2 channel contributes 10% of the total NH 2 + O flux at combustion temperatures, although this channel is not included in modern NH 3 oxidation mechanisms. Modeling is used to illustrate the ramifications of these rate predictions on the kinetics of NH 3 oxidation and NO x formation. Finally, the present results for NH 2 + O are important for predicting the chain branching and formation of NO in the oxidation of NH 3 and thermal DeNO x .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Theoretical kinetic computations in complex reacting systems

Nasa Lewis' studies of complex reacting systems at high temperature are discussed. The changes which occur are the result of many different chemical reactions occurring at the same time. Both an experimental and a theoretical approach are needed to fully understand what happens in these systems. The latter approach is discussed. The differential equations which describe the chemical and thermodynamic changes are given. Their solution by numerical techniques using a detailed chemical mechanism is described. Several different comparisons of computed results with experimental measurements are also given. These include the computation of (1) species concentration profiles in batch and flow reactions, (2) rocket performance in nozzle expansions, and (3) pressure versus time profiles in hydrocarbon ignition processes. The examples illustrate the use of detailed kinetic computations to elucidate a chemical mechanism and to compute practical quantities such as rocket performance, ignition delay times, and ignition lengths in flow processes.

Bittker, David A.↗
DOE OSTI2025

A theoretical kinetic study of ĊH 3 + ṄH 2 : From electronic structure to NH 3 /CH 4 combustion modelling implications

Carbon–nitrogen interaction reactions play an important role in governing the reactivity of ammonia blended fuels. However, there remains uncertainties regarding their detailed reaction pathways and rate constants, hampering the development of high-fidelity chemical kinetic models. In this study, the kinetics of ĊH 3 + ṄH 2 , a key C–N interaction reaction in ammonia/methane blend combustion have been investigated. The potential energy surface has been explored using the high-level ANL0F method, yielding highly accurate stationary point energies that agree with ATcT values within 0.1 kcal mol –1 . Variable reaction coordinate transition state theory is used to treat the barrierless association and decomposition reaction channels, based on directly sampled radical-radical interaction energies at the CASPT2-F12(2e,2o)/cc-pVTZ-F12 level of theory. The minimum transitional mode numbers of states obtained are then coupled with the RRKM/master equation to calculate temperature- and pressure-dependent rate constants. Our a priori calculations capture available experimental measurements from the literature very well. The calculated rate constants have been incorporated into an NH 3 /CH 4 chemical kinetic model currently under development at the University of Galway. The effect of the updated kinetic data for ĊH 3 + ṄH 2 on model predicted NH 3 /CH 4 fuel reactivity is elucidated.

ab initio↗
DOE OSTI2026

Theoretical and kinetic modeling study of hydrazine oxidation

The present work constitutes the first theoretical and kinetic modeling study of hydrazine oxidation, which may be important for burnout in ammonia-fueled combustion. The kinetics of the oxidation of N 2 H 4 , N 2 H 3 and tHNNH by molecular oxygen were investigated via a quantum chemistry/canonical transition state theory approach. Geometries and anharmonic frequencies were obtained with density functional theory, and energies from coupled cluster calculations (CCSD(T)) extrapolated to the infinite basis set limit, with corrections for core-valence electron correlation, scalar relativistic effects, and higher level correlation up to lambda coupled cluster, CCSDT(Q) Λ . The key reactions occurred on the N 2 H 4 O 2 potential energy surface, where the results indicated a fast reaction of N 2 H 3 with HO 2 via singlet adducts to yield tHNNH + H 2 O 2 and HNN(H)O + H 2 O, while reaction on the triplet surface proceeds via a bound complex followed by a tight, submerged barrier to yield N 2 H 4 + O 2 . The results were incorporated in a detailed reaction mechanism, which was used to interpret the shock tube results from Michel and Wagner (1965) on the effect of O 2 on hydrazine conversion at 1100–1400 K. The kinetic model captured qualitatively the observed behavior, but underestimated the reaction rate under oxidizing conditions. The hydrazine pyrolysis chemistry dominated conversion at reducing conditions and/or high temperature. At oxidizing conditions and intermediate temperatures (≲ 1400 K), reactions of N 2 -amines with HO 2 and O 2 were important for the oxidation rate.

Ab initio calculations↗
DOE OSTI2025

Theoretically Informed Kinetics (ThInK): Establishing a modern C 0 -C 3 mechanism for combustion modeling

In contrast to the adage “Models are to be used, not believed”, combustion kinetics models have been intended to be predictive in nature. Theoretical chemical kinetics is now understood to provide a firm foundation for the reaction parameters, thereby facilitating predictive simulations of chemical reactivity, even in regimes that are poorly characterized by chemical kinetic and/or combustion experiments. In this study, we describe a theory-informed kinetics model (ThInK) for small molecule combustion chemistry (H 2 and C 1 – C 3 species) that is based on the prodigious use of theoretical predictions for reaction rate coefficients, thermochemistry, and transport parameters. The distinct features of this kinetics model, which was developed over the course of several decades, are illustrated through simulations of flame propagation and auto-ignition.

Energy transfer↗
DOE OSTI2021

Automated theoretical chemical kinetics: Predicting the kinetics for the initial stages of pyrolysis

Large scale implementation of high level computational theoretical chemical kinetics offers the prospect for dramatically improving the fidelity of combustion chemical modeling. To facilitate such efforts, we have developed a suite of codes, collectively referred to as AutoMech, that allow for the automatic prediction of the kinetics for large sets of reactions via ab initio transition-state-theory based master-equation calculations. The primary input is simply the mechanism, a dictionary relating chemically identifiable species descriptors (e.g., SMILES or InChIs) to species labels in the mechanism, and a specification of the electronic structure and transition state theory models to be implemented. Here we illustrate the current utility of AutoMech through a study of the initial stages of pyrolysis for 3 sets of fuels: sequences of alkanes, alcohols, and aldehydes. For simplicity, the analysis focuses on abstractions from the fuel by H, CH 3 , and OH, and the decomposition of the resulting radicals. Altogether, there are a total of 166 input channels in these sets (more than 363 forward reactions when expanded to the full set of elementary reactions). The code successfully produces high quality rate estimates (with apparent uncertainties less than a factor of two in limited comparisons with experiment) for > 95% of these. For the radical decomposition reactions, the analysis includes predictions for the pressure dependence of the kinetics. This wide-ranging exploration illustrates (i) the effect of different levels of prediction on the expected accuracy, (ii) the branching between abstractions at different sites for different abstractors, (iii) the dependence of the rates on the chemical structure, and (iv) the variation in radical stabilities across chemical families. These results, as well as the demonstrated feasibility of the methodology, should find further utility in the development of accurate rate expressions for arbitrary fuels. (c) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Elliott, Sarah N.↗
DOE OSTI2025

Theoretical and kinetic modeling study of H 2 S pyrolysis

Hydrogen sulfide pyrolysis was investigated theoretically and through chemical kinetic modeling. Reactions on the SHH potential energy surface, primarily S + H 2 (+Ar) ⇌ H 2 S (+ Ar) (R1) and S + H 2 ⇌ SH + H (R6b) were characterized by ab initio calculations. Results for k 1 were in good agreement with experiment, but deviated strongly below 2000 K from values previously used in modeling. Collider efficiencies for H 2 S, S 2 , and N 2 compared to Ar were calculated for R1. Hydrogen sulfide decomposition experiments reported in literature were re-examined in terms of an updated detailed chemical kinetic model. Concentration profiles for the atomic S at high temperature in shock tubes supported the present value of k 1 and served to constrain the rate constants for reaction of S with SH and H 2 S. To explain results from batch and flow reactors, conducted at high H 2 S concentrations in the 900–1400 K range, a very fast rate constant was required for HSS + H ⇌ SH + SH. Under dilute conditions, the gas-phase chemistry was too slow to compete and the decomposition of H 2 S was controlled by loss on the reactor surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1988

Current driven instabilities of an electromagnetically accelerated plasma

Quantitative measurements of the plasma instability that strongly affects the efficiency and lifetime of electromagnetic plasma accelerators were obtained. Experimental results are presented for the dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries of accelerators. The measured critical wave parameters are found to agree well with theoretical predictions. A kinetic theoretical model was used to study current driven instabilities which are intrinsic to the high-current-carrying magnetized plasma of a magnetoplasmadynamic accelerator. Under certain conditions, marginally stable waves travelling almost perpendicular to the magnetic field are found which travel at a velocity equal to that of the electron current.

Kelly, A. J.↗
DOE OSTI2024

An experimental, theoretical, and kinetic modeling study of post-flame oxidation of ammonia

The post -flame oxidation rate of ammonia was investigated in a novel atmospheric pressure flow reactor at temperatures of 1280 ± 16 K and as a function of residence time and mixture composition (1-10% O 2 , dry and moist). The experimental results, as well as selected data from literature, were analyzed using an updated detailed chemical kinetic model. The medium temperature, very lean conditions enhance the importance of reactions of the nitroxyl (HNO) intermediate. High-level theory was used to calculate the rate constant for HNO + NH 2 , indicating that this step is significantly faster than values used in literature. Furthermore, a trajectory based approach was used to determine collision efficiencies for selected bath gases for HNO + M. The experimental results show that the NH 3 oxidation rate increases with temperature and O 2 concentration, while the presence of water vapor slightly inhibits reaction. Formation of NO and N 2 O was strongly promoted at higher levels of O 2 . Modeling results agreed well with the measurements, except at the lowest level of O 2 . The predicted oxidation rate of NH 3 was shown to result from a delicate balance between chain branching and terminating steps involving NH 2 , H 2 NO, and HNO. Recent theoretical work on reactions of these species by Klippenstein and coworkers and Stagni et al. was instrumental in improving modeling predictions. After initiation, NO reached a pseudo -steady-state level, where the pathways to NO were largely balanced by the NH 2 + NO reaction. Nitric oxide was partly oxidized to NO 2 , with the NH 2 + NO 2 reaction responsible for most of the N 2 O formation. Novelty and significance statement: This study provides the first detailed kinetic analysis of the lean postflame oxidation of ammonia, based on time -resolved flow reactor data in a novel reactor. In addition to the post -flame oxidation rate of ammonia, data for formation of NO and N 2 O were compared with modeling predictions. The medium temperature, very lean conditions enhance the importance of reactions of the HNO and H 2 NO intermediates. Inclusion in the model of results from recent high-level theoretical work, including present calculations for HNO + NH 2 and HNO + M, was crucial for capturing the observed behavior. It is argued that the post -initiation steady-state NH 3 oxidation rates constitute important data for model validation, along with ignition delays and laminar flame speeds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

An experimental, theoretical and kinetic modeling study of the N 2 O-H 2 system: Implications for N 2 O + H

The reaction of N 2 O with His the key step in consumption of nitrous oxide in thermal processes. The major product channel is N 2 + OH, while NH + NO constitute minor products. In addition, a pathway involving HNNO, initiated by N 2 O + H (+M)$\rightleftarrows$HNNO (+M) (R3, R4), has been inferred from experiment and theory by Burke and coworkers. At longer reaction times, the reaction may reach partial equilibration, and in addition to k 3 and k 4 the importance of this channel depends on the thermodynamic properties of HNNO and its consumption reactions, mainly HNNO + H. In the present work, we re-examined the thermochemistry of HNNO and calculated rate constants and branching fractions for the HNNO + H reaction. Experiments on the N 2 O-H 2 system were conducted in a high-pressure flow reactor at 100 atm as a function of temperature (600-925 K) and stoichiometry and explained in terms of an updated chemical kinetic model. The results support the importance of the HNNO pathway, which results in inhibition of N 2 O consumption and formation of NH 3 . In addition, selected literature results on the N 2 O-H 2 system are re-examined and the implications for the other product channels of N 2 O + H, in particular NH + NO, are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Insertion products in the reaction of carbonyl oxide Criegee intermediates with acids: Chloro(hydroperoxy)methane formation from reaction of CH 2 OO with HCl and DCl

The reactions of carbonyl oxides (“Criegee intermediates”) with organic and inorganic acids have been postulated to proceed predominantly by an insertion mechanism, and the hydroperoxy-substituted ester products from reactions with organic acids have been spectroscopically observed. Here this work characterizes the products from one of the simplest reactions of carbonyl oxides with inorganic acids, that of formaldehyde oxide, CH 2 OO, with hydrogen chloride, which occurs via a 1,2-insertion in the H–Cl bond. Reactions of both HCl and DCl isotopologues yield product signal at the mass of the insertion product chloro(hydroperoxy)methane and a dissociative ionisation peak at the mass of the protonated (or deuteronated) Criegee intermediate. The isotopic composition of the insertion product has been measured for reaction mixtures where both HCl isotopologues are present, and the H/D ratio of the product is consistently higher (by a factor of 1.6 ± 0.3) than that of the reactants. This isotope selectivity in the products has smaller uncertainty than the ratio of measured rate coefficients and suggests a normal (k H > k D ) kinetic isotope effect in the reaction. Theoretical kinetics calculations predict a small normal kinetic isotope effect for the overall reaction (k H / k D = 1.35 at 20 Torr N 2 and k H / k D = 1.2 for 1 atm N 2 ) but predict a substantial inverse kinetic isotope effect (k D > k H ) for the stabilisation fraction, in disagreement with the experimental observation.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Modeling–Experiment–Theory Analysis of Reactions Initiated from Cl + Methyl Formate

Methyl formate (MF; CH 3 OCHO) is the smallest representative of esters, which are common components of biodiesel. The present study characterizes the thermal dissociation kinetics of the radicals formed by H atom abstraction from MF—CH 3 OCO and CH 2 OCHO—through a combination of modeling, experiment, and theory. For the experimental effort, excimer laser photolysis of Cl 2 was used as a source of Cl atoms to initiate reactions with MF in the gas phase. Time-resolved species profiles of MF, Cl 2 , HCl, CO 2 , CH 3 , CH 3 Cl, CH 2 O, and CH 2 ClOCHO were measured and quantified using photoionization mass spectrometry at temperatures of 400–750 K and 10 Torr. The experimental data were simulated using a kinetic model, which was informed by ab initio-based theoretical kinetics calculations and included chlorine chemistry and secondary reactions of radical decomposition products. Here, we calculated the rate coefficients for the H-abstraction reactions Cl + MF → HCl + CH 3 OCO (R1a) and Cl + MF → HCl + CH 2 OCHO (R1b): k 1a,theory = 6.71 × 10 –15 ·T 1.14 ·exp(—606/T) cm 3 /molecule·s; k 1b,theory = 4.67 × 10 –18 ·T 2.21 ·exp(—245/T) cm 3 /molecule·s over T = 200–2000 K. Electronic structure calculations indicate that the barriers to CH 3 OCO and CH 2 OCHO dissociation are 13.7 and 31.6 kcal/mol and lead to CH 3 + CO 2 (R3) and CH 2 O + HCO (R5), respectively. The master equation-based theoretical rate coefficients are k 3,theory (P = ∞) = 2.94 × 10 9 ·T 1.21 ·exp(—6209/T) s –1 and k 5,theory (P = ∞) = 8.45 × 10 8 ·T 1.39 ·exp(—15132/T) s –1 over T = 300–1500 K. The calculated branching fractions into R1a and R1b and the rate coefficient for R5 were validated by modeling of the experimental species time profiles and found to be in excellent agreement with theory. Additionally, we found that the bimolecular reactions CH 2 OCHO + Cl, CH 2 OCHO + Cl 2 , and CH 3 + Cl 2 were critical to accurately model the experimental data and constrain the kinetics of MF-radicals. Inclusion of the kinetic parameters determined in this study showed a significant impact on combustion simulations of larger methyl esters, which are considered as biodiesel surrogates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Bimolecular Peroxy Radical (RO 2 ) Reactions and Their Relevance in Radical Initiated Oxidation of Hydrocarbons

The kinetics of peroxy radical (RO 2 ) reactions have been of long-standing interest in atmospheric and combustion chemistry. Nevertheless, the lack of kinetic studies at higher temperatures for their reactions with other radicals such as OH has precluded the inclusion of this class of reactions in detailed kinetics models developed for combustion applications. In this work, guided by the limited room temperature experimental studies on selected alkyl-peroxy radicals and literature theoretical kinetics on the prototypical CH 3 O 2 + OH system, we have performed parametric studies on the effect of uncertainties in the rate coefficients and branching ratios to potential product channels for RO 2 + OH reactions at higher temperatures. Literature kinetics models were used to simulate autoignition delays, laminar flame speeds, and speciation profiles in flow and stirred reactors for a variety of common combustion-relevant fuels. Inclusion of RO 2 + OH reactions was found to retard autoignition in fuel-lean (φ = 0.5) mixtures of ethane and dimethyl ether in air. The observed effects were noticeably more pronounced in ozone-enriched combustion of ethane and dimethyl ether. The simulations also examined the influence of ozone doping levels, pressures, and equivalence ratios for both ethane and dimethyl ether oxidation. Sensitivity and flux analyses revealed that the RO 2 + OH reaction is a significant sink of RO 2 radicals at the early stage of autoignition, affecting fuel oxidation through RO 2 ↔ QOOH, RO 2 ↔ alkene + HO 2 , or RO 2 + HO 2 ↔ ROOH + O 2 . Additionally, the kinetic stability of the trioxide formed from RO 2 + OH reactions was investigated using master equation analyses. Last, we discuss other bimolecular reactions that are missing in literature kinetics models but are relevant to hydrocarbon oxidation initiated by external radical sources (plasma-enhanced, ozone-enriched combustion, etc.). In conclusion, the present simulations provide a strong motivation for better characterizing the bimolecular kinetics of peroxy radicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Position-specific isotope effects during alkaline hydrolysis of 2,4-dinitroanisole resolved by compound-specific isotope analysis, 13 C NMR, and density-functional theory

Compound-specific isotope analysis (CSIA), position-specific isotope analysis (PSIA), and computational modeling (e.g., quantum mechanical models; reactive-transport models) are increasingly being used to monitor and predict biotic and abiotic transformations of organic contaminants in the field. However, identifying the isotope effect(s) associated with a specific transformation remains challenging in many cases. We describe and interpret the position-specific isotope effects of C and N associated with a SN 2 Ar reaction mechanism by a combination of CSIA and PSIA using quantitative 13 C nuclear magnetic resonance spectrometry, and density-functional theory, using 2,4-dinitroanisole (DNAN) as a model compound. The position-specific 13 C enrichment factor of O–C 1 bond at the methoxy group attachment site (ε C1 ) was found to be approximately -41‰, a diagnostic value for transformation of DNAN to its reaction products 2,4-dinitrophenol and methanol. Theoretical kinetic isotope effects calculated for DNAN isotopologues agreed well with the position-specific isotope effects measured by CSIA and PSIA. This combination of measurements and theoretical predictions demonstrates a useful tool for evaluating degradation efficiencies and/or mechanisms of organic contaminants and may promote new and improved applications of isotope analysis in laboratory and field investigations.

13C NMR↗
DOE OSTI2025

Progress in modeling hydrogen assisted ammonia oxidation with new experiments and a further reconciliation of the NH 3 + OH rate constant

Hydrogen-assisted oxidation of ammonia in a premixed, laminar flow tubular reactor under reducing conditions was investigated experimentally and through chemical kinetic modeling. Due to its impact on the competition for OH among ammonia and hydrogen, the rate constant for NH 3 + OH (R1) was determined through state-of-the-art theoretical kinetics calculations, employing composite energies that include the effects of higher order electronic excitations on the electronic energies along the variational reaction path and treating the limitations in the kinetics posed by the passage through a hydrogen-bonded complex. The resulting rate constant was in close agreement with the recent experimental value from Zaczek et al. (2025), settling a long-term dispute about the high-temperature value of k 1 and confirming within 20% the value previously used in modeling. The chemical kinetic model, with no other changes, captured well measured concentrations of NH 3 , H 2 , NO, and N 2 O from flow reactor oxidation of NH 3 /H 2 at slightly reducing conditions over a range of temperature (900-1350 K) and NH 3 /H 2 ratios (0.5-2.0). Comparison of the present results with reported data from a non-premixed setup indicates that for laminar flow tubular reactors, the reactor configuration may have implications for the observed H 2 consumption due to the possibility of preferential oxidation during mixing.

Ab initio theory↗
NASA NTRS1988

Current driven instabilities of an electromagnetically accelerated plasma

A plasma instability that strongly influences the efficiency and lifetime of electromagnetic plasma accelerators was quantitatively measured. Experimental measurements of dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries are reported. The measured critical wave parameters are in excellent agreement with theoretical instability boundary predictions. The instability is current driven and affects a wide spectrum of longitudinal (electrostatic) oscillations. Current driven instabilities, which are intrinsic to the high-current-carrying magnetized plasma of the magnetoplasmadynmic (MPD) accelerator, were investigated with a kinetic theoretical model based on first principles. Analytical limits of the appropriate dispersion relation yield unstable ion acoustic waves for T(i)/T(e) much less than 1 and electron acoustic waves for T(i)/T(e) much greater than 1. The resulting set of nonlinear equations for the case of T(i)/T(e) = 1, of most interest to the MPD thruster Plasma Wave Experiment, was numerically solved to yield a multiparameter set of stability boundaries. Under certain conditions, marginally stable waves traveling almost perpendicular to the magnetic field would travel at a velocity equal to that of the electron current. Such waves were termed current waves. Unstable current waves near the upper stability boundary were observed experimentally and are in accordance with theoretical predictions. This provides unambiguous proof of the existence of such instabilites in electromagnetic plasma accelerators.

Chouetri, E. Y.↗