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At least 667 records · Page 37

Carbidic Mo is the sole kinetically-relevant active site for catalytic methane dehydroaromatization on Mo/H-ZSM-5

Systematic variation of Mo/Al = {0.10, 0.25, 0.35} in Mo/H-ZSM-5 catalysts effects ~20× change of Mo-to-H + ratio during methane dehydroaromatization (DHA) reactions at steady state and on deactivating catalysts. Mo and Brønsted-acid site count, respectively enumerated by ethane hydrogenolysis probe reaction and dimethyl ether chemical titration, evolve disparately during DHA catalysis, indicating the two sites reduce in number by distinct mechanisms. Here, the deactivation of Mo/H-ZSM-5 catalytic activity is uniquely attributed to the loss of active, or accessible, Mo sites, evinced by (i) the non-selective nature of deactivation (i.e. that deactivation occurs without modification of residual active sites), (ii) invariance in product distribution from Mo/H + = 0.10–2.1, and (iii) linear correspondence between Mo-catalyzed ethane hydrogenolysis rate and active site count during DHA on deactivating samples. DHA forward rate – the intrinsic kinetic descriptor of catalyst activity – normalizes by Mo content at steady state and on deactivating catalysts with Mo/Al = 0.10–0.35 for Mo-based contact times in the range τ Mo = 0.79–44 mol Mo s mol –1 C , unequivocally establishing Mo aggregates as the sole kinetically-relevant active site on Mo/H-ZSM-5. Brønsted-acid site content over a ~40× range in τ H+ = 1.4–54 mol H+ s mol –1 C has no discernable correlation with or effect on DHA rate, methane conversion, or product distribution – demonstrating H + does not catalyze any rate- or selectivity-determining steps in the benzene formation pathway and suggesting that the benefits of zeolitic acid sites are only to disperse Mo during catalyst synthesis and, conceivably, to catalyze equilibrated reaction steps.

02 PETROLEUM↗

H 2 O-assisted O 2 reduction by H 2 on Pt and PtAu bimetallic nanoparticles: Influences of composition and reactant coverages on kinetic regimes, rates, and selectivities

Hydrogen peroxide (H 2 O 2 ) can replace hazardous oxidants in industrial processes but is currently too expensive for many such applications. While direct synthesis of H 2 O 2 (H 2 + O 2 → H 2 O 2 ) may reduce costs in comparison to incumbent technology, current catalysts lack the requisite stability and selectivity. Here, we examine the direct synthesis of H 2 O 2 on bimetallic Pt 1 Au x (0 ≤ x ≤ 230) and Pt catalysts at steady-state in pure water and relate kinetic parameters for H 2 O 2 and H 2 O formation to possible active site structures informed by complementary characterization methods. X-ray photoelectron spectra show significant Pt surface enrichment compared to the bulk composition. Analysis of infrared spectra of mixed monolayers of 12 CO* and 13 CO* indicate that Pt and Au form substitutional surface alloys. The Pt 1 Au x nanoparticles with the greatest mole fractions of Au predominantly expose Pt monomers (i.e., isolated Pt atoms), yet Pt atoms exposed upon all these nanoparticles possess electronic structures distinct from bulk Pt. Despite these differences, rate measurements are consistent with product formation through proton-electron transfer pathways for all Pt 1 Au x catalysts. In situ XAS indicate that Pt remains metallic during H 2 O 2 synthesis. Under the most oxidizing conditions, selectivities toward H 2 O 2 increase strongly with the Au to Pt ratio from 2% for monometallic Pt to 85% for Pt 1 Au 170 . However, selectivities are similar among all catalysts within reducing conditions. Comparisons of apparent activation enthalpies for the formation of H 2 O 2 and H 2 O across these catalysts and the range of conditions suggest that Pt monomers within Au provide the greatest selectivities for H 2 O 2 formation, because these active sites present high barriers for O-O bond rupture. Further, selectivities decrease with increasing ratios of H 2 to O 2 pressures, because Pt atoms aggregate and form oligomers that readily dissociate dioxygen intermediates. The combined use of spectroscopy, kinetics, and concepts employed in reaching these conclusions take inspiration from the legacy of Prof. Michel Boudart, and specifically his elegant methods for interrogating bimetallic catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Cartesian-diffusion Langevin method for hybrid kinetic-fluid Coulomb scattering in particle-in-cell plasma simulations

A novel, drag-diffusion Langevin method of hybrid, kinetic-fluid Coulomb scattering in plasmas is presented. Unlike previous methods, the frictional drag is always applied in the simulation frame of reference. The velocity-space diffusion is performed in the stationary-fluid frame of reference when anisotropic, and in the laboratory frame when isotropic. While the general method is mass-ratio independent, we focus on interactions of kinetic-ions and fluid-electrons to show first-order modifications to the electron velocity distribution function that are an important correction for the accurate calculation of electric resistivity. Inclusion of sub-cycling and a limit to the maximum collision frequency is shown to allow for arbitrarily large timesteps without numerical failure. Here the Langevin method is compared with a grid-based binary method and found to require a much less restrictive timestep in cases of ion–electron slowing and temperature equilibration; this finding differs from previous work and is dependent on the mass ratio.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The role of amorphous ZIF in ZIF-8 crystallization kinetics and morphology

Understanding the composition and structure of amorphous precursor phases is fundamental for elucidating two-step crystallization mechanisms and designing shape- and size-controlled nanomaterials. However, that understanding is largely lacking for metal–organic framework compounds despite their growing significance as functional materials. Here, in this study, we report the crystallization of zeolite imidazolate frameworks-8 (ZIF-8, Zn(C 4 H 5 N 2 ) 2 ) via an amorphous ZIF (am-ZIF) solid precursor phase with a rough stoichiometric composition of Zn(C 4 H 5 N 2 ) 1.78 (C 4 H 6 N 2 ) 0.17 (CH 3 COO) 0.22 . The formation of am-ZIF is attributed to the incomplete deprotonation of 2-Methylimidazole (HmIm) and the involvement of the hydrogen bond between CH 3 COO– and –HN, which can further transform into the dense Dia(Zn) structure with a diamondoid crystal topology in pure water. Taking am-ZIF as a precursor, the tunable dissolution and recrystallization kinetics of am-ZIF into ZIF-8, due to the addition of EtOH and CTAB, allows the selective fabrication of dodecahedral, cubic, and hollow ZIF-8. Overall, an in-depth understanding of the differences in composition and structure of am-ZIF from ZIF-8 and the resulting crystallization kinetics suggests a novel approach to designing metal–organic frameworks with controlled crystal morphology.

36 MATERIALS SCIENCE↗

Challenges in Kinetic modeling of ammonia pyrolysis

Ammonia pyrolysis reactions have implications for its ignition and oxidation in engines and gas turbines. In the present work, the chemistry of ammonia pyrolysis is investigated by kinetic modeling and theory. Rate constants for key reactions are carefully evaluated based on available experimental and theoretical results. The high pressure limit k1,∞ for NH 2 + H (+M) ⇄ NH 3 (+M) (R1) is calculated to be essentially the collision frequency, indicating that dissociation of ammonia in combustion processes will be at or close to the low pressure limit even at engine and gas turbine conditions. The chemical kinetic model is validated against reported shock tube measurements of NH 3 , NH 2 , and NH in ammonia pyrolysis. Predictions are in good agreement with observations for dilute conditions (≤ 0.5% NH 3 ), but the model appears to underpredict the NH 3 consumption rate at longer times in less dilute mixtures. At short reaction times, thermal dissociation of NH3, together with the NH 3 + H reaction, controls conversion. At longer times, secondary reactions involving NH 2 and NH become important due to their impact on the radical pool. Predictions become sensitive to formation and consumption of diazene (tHNNH and cHNNH). Several of the key steps in the ammonia pyrolysis mechanism are radical-radical reactions that are difficult to measure accurately and challenging to calculate theoretically, and a more comprehensive experimental characterization is desirable to support further model development.

10 SYNTHETIC FUELS↗

The effect of water vapor on surface oxygen exchange kinetics of thin film (La,Sr)(Co,Fe)O 3-δ

Oxygen reduction and transport in electrochemical applications are strongly affected by the reactant gas composition, including impurities such as water. Understanding the relationship between oxygen reactivity and humidity is key for attaining stability and high efficiency of solid oxide fuel cells, which are especially attractive for transportation applications as low emission power generation devices. Both short- and long-term effects of moisture have previously been associated with use of ambient air. To better understand these effects, we study oxygen exchange kinetics at the cathode surface and the cathode/electrolyte interface using La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ (LSCF) epitaxial thin films as a model-surface system. In situ synchrotron X-ray techniques evaluate the oxygen reduction reaction (ORR) kinetics in response to environmental variables. The results suggest a clear enhancement of the ORR rate upon short term exposure of the perovskite-structured films to water. Finally, on the basis of these measurements, along with in situ X-ray characterization of Sr segregation and computational first-principles studies, we suggest a model for this increased ORR activity that may lead to further improvements by stabilizing active cathode surface configurations.

25 ENERGY STORAGE↗

An automated multiplexed turbidometric and data collection system for measuring growth kinetics of anaerobes dependent on gaseous substrates

Standard methods of monitoring the growth kinetics of anaerobic microorganisms are generally impractical when there is a protracted or indeterminate period of active growth, and when high numbers of samples or replications are required. As part of our studies of the adaptive evolution of a simple anaerobic syntrophic mutualism, requiring the characterization of many isolates and alternative syntrophic pairings, here we developed a multiplexed growth monitoring system using a combination of commercially available electronics and custom designed circuitry and materials. This system automatically monitors up to 64 sealed, and as needed pressurized, culture tubes and reports the growth data in real-time through integration with a customized relational database. The utility of this system was demonstrated by resolving minor differences in growth kinetics associated with the adaptive evolution of a simple microbial community comprised of a sulfate reducing bacterium, Desulfovibrio vulgaris, grown in syntrophic association with Methanococcus maripaludis, a hydrogenotrophic methanogen.

59 BASIC BIOLOGICAL SCIENCES↗

Experimental study on kinetic oxidation of graphite IG-110 by steam

Graphite is proposed for use in High-temperature Gas-cooled Reactors (HTGRs) as the fuel matrix, neutron moderator/reflector, and core structural material. One important property of nuclear grade graphite is their resistance to oxidation in high-temperature environment. Extensive investigation has been performed in the literature for graphite oxidation by air. However, available experimental data are still limited for graphite oxidation by steam under conditions comparable to a postulated steam ingress accident in HTGRs. In this study, the oxidation rate of graphite IG-110 by steam was measured at temperatures from 850 to 1100 °C with the steam partial pressure varying from 0.5 to 20.0 kPa and the hydrogen partial pressure varying from 0 to 2.0 kPa. Further analysis confirms the oxidation process in this present study is dominated by the chemical kinetics, which lends credit to the data for being used to develop numerical models. It was observed that the increase of the kinetic oxidation rate with the steam partial pressure tends to become less apparent if the steam partial pressure keeps increasing. In addition, it was found that the partitioning of hydrogen inhibits the graphite-steam reaction process even with the steam partial pressure up to 20.0 kPa. However, this inhibiting effect starts to become saturated when the hydrogen partial pressure exceeds 1.0 kPa. The oxidation rates were fitted to the conventional Langmuir-Hinshelwood (LH) and Boltzmann-enhanced Langmuir-Hinshelwood (BLH) models by a multivariable optimization algorithm. The BLH model exhibits a better accuracy than the LH model within the specified experimental conditions. The predicted oxidation rate using the BLH model shows a mean relative difference of about 24% with the maximum difference of about 55% when compared with our experimental data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Kinetics of photogenerated carbon dangling bonds in organic photovoltaic thin Films: An EPR study

Here, we report an investigation of the early kinetics of photogenerated carbon dangling bond (CDB) formation and annealing in organic photovoltaic bulk heterojunction (BHJ) thin film blends under oxygen- and moisture-free conditions, using X-band electron paramagnetic resonance (EPR) spectroscopy. The study focuses on donor:acceptor BHJ blends of PCE12:PCBM and PCE12:ITIC films, where PCE12 is PBDB-T. The time evolution of CDBs in such drop-cast BHJ films irradiated at 300 nm is monitored. The early kinetics of CDB formation, critical for understanding OPV degradation mechanisms, is studied. Theoretical analysis of the defect growth mechanism suggests a monomolecular defect creation model where the defect count follows a power-law t β with irradiation time t, where β ∼ 0.55–0.58, in excellent agreement with the theoretically expected value of β = 1/2. This model is compatible with CDB formation by the holes in donor sites adjacent to acceptors, likely assisted by energy released from quenching of nearby excitons by the holes, elucidating the physical mechanism underlying CDB formation. This is significant for designing improved materials, which mitigate defect creation, and consequently advancing the development of stable OPV systems.

42 ENGINEERING↗

Thermodynamic and Kinetic Roles of H2 in Structure Evolution of Urchin-like Co: A density functional theory study

Small gas molecules working as good capping agents play important roles in controlling the morphologies and surface structures of the metal nanocrystals. In present work, the thermodynamic and kinetic roles of H2 molecule played on the morphology of Co nanocrystal were systematically studied based on density functional theory (DFT). The Gibbs surface free energies (?) of Co(100), Co(110) and Co(111) under different hydrogen surface coverages were investigated by ab initio thermodynamics, based on which i) the phase diagrams of stable H coverage on each plane were obtained; ii) the morphology evolutions of the Co nanocrystals with various surface hydrogen coverages were further predicted by Wulff construction. It was revealed that addition of H2 could change the facet stability generating diverse morphological Co nucleus. The kinetic role of H2 was further explored by DFT during adatom Co surface diffusions under different H coverages (?H), which suggested that except for Co(100) at ?H of 0.56 ML, the surface H would hinder Co surface diffusions. The projected density of state (PDOS) gave a deeper insight that the electronic structures of the Co adatom could be alerted by addition of the surface H, which thereby affected its surface diffusion ability. X. Wang, N. Liu, Q. Zhang, X. Liang, and B. Chen were financially supported by the National Natural Science Foundation of China (No. 21476012, 21571012, and 91534201). D. Mei was supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. Computing time was granted by the facility user proposal grand challenge of computational catalysis of the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL). EMSL is a national scientific user facility located at Pacific Northwest National Laboratory (PNNL) and sponsored by DOE’s Office of Biological and Environmental Research.

Nanocrystal Co, Surface free energy, Surface diffu↗

Kinetics and extinction of non-premixed cool and warm flames of dimethyl ether at elevated pressure

Here, the growing demand of clean and efficient propulsion and energy systems has sparked an interest in understanding low-temperature combustion at high pressure. Cool flame transition and extinction limits as well as oxygen concentration dependence at elevated pressures provide insights of the low-temperature and high-pressure fuel reactivity. A new experimental high-pressure counterflow burner platform was designed and developed to achieve the studies of high-pressure cool flames. Dimethyl ether (DME) was chosen to study its non-premixed cool flame in high-pressure counterflow burner at pressure up to 5 atm, perhaps for the first time. This paper investigates the effects of pressure on cool flame structure, extinction and transition limits, and oxygen concentration dependence as well as ozone assisted warm flames of DME in experiments and numerical simulations. The results show that the reignition transition from cool flame to hot flame occurs either with the decrease of the strain rate at a given fuel concentration and pressure or with the increase of fuel mole fraction or pressure at a given strain rate. Furthermore, it is shown that the higher pressure shifts the cool flame to higher strain rates and results in higher cool flame extinction strain rates. However, the existing kinetic model of DME fails in predicting the cool flame extinction limit at elevated pressures. Besides, the cool flame extinction limits are proportional to nth power of the oxygen concentration, [O 2 ] n , and the increase of pressure leads to stronger extinction limit dependence (larger n) on oxygen concentration. The present experiment and detailed kinetic analysis show clearly that increasing pressure promotes the low-temperature chemistry including the oxygen addition reactions. In addition, stable warm flame was first experimentally observed by using DME at elevated pressure with ozone sensitization.

33 ADVANCED PROPULSION SYSTEMS↗

Kinetics of low temperature plasma assisted NH 3 /H 2 oxidation in a nanosecond-pulsed discharge

Ammonia (NH 3 ) has been widely recognized as one of the carbon-neutral fuels. However, ammonia combustion suffers low reactivity and high N 2 O/NO x emissions. Here, to overcome these issues, this work reports plasma assisted NH 3 /H 2 oxidation and unveils the kinetics of fuel oxidation and N 2 O/NO x formation by combining time-resolved laser diagnostics with plasma modeling. Firstly, we found that the NH 3 consumption is promoted with a H 2 blending ratio of 0.3, due to enhancements of H and OH formation by plasma assisted H 2 dissociation. Secondly, at a high reduced electric field, when the H 2 blending ratio increases, the NH 3 oxidation is promoted due to both the HO 2 formation and strong NO kinetic enhancement via NO-HO 2 and NO 2 -H pathways. In the meantime, it is shown that the NO mole fraction also increases with H 2 blending ratio, because the NO formation is enhanced via N( 2 D)-O 2 pathways, and the DeNO x chemistry is weakened with less NH 2 production. By contrast, at a lower reduced electric field, when the H 2 blending ratio increases, the decreased N( 2 D) formation does not produce enough NO to replenish the NO formation drop caused by lower NH 3 concentration. Thirdly, the reduced electric field non-monotonically affects fuel consumption and N 2 O/NO x formation by manipulating electron energy deposition pathways. The NH 3 consumption is maximized with an optimal reduced electric field where N 2 * excitation and O 2 dissociation are most efficient. When the reduced electric field deviates from its optimum, the NH 3 consumption decreases due to the discharge energy deposition to either vibrational excitation or dissociation of N 2 . The N 2 O/NO x emissions governed by the NH 3 oxidation follow the above NH 3 consumption trend.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Pressure-dependent kinetics of cyclopentene consumption

Recent experiments have uncovered deficiencies in the ability of current kinetic models for cyclopentane combustion to predict species profiles as a function of O2 concentration. One likely source of these discrepancies flows from the limited availability of relevant kinetic data for key functionalized intermediates, requiring the use of distant analogies to estimate their rates. This work fills this gap for cyclopentene, the most prominent C5 intermediate in low-temperature cyclopentane combustion. Ab initio transition-state-theory based master equation methods are used to calculate pressure-dependent rate constants across four potential energy surfaces (C5H8 + OH, C5H8 + HO2, C5H7, and C5H7 + O2). Potential energy surfaces are characterized at the CCSD(T)-F12/cc-pVDZ-F12//revDSD-PBEP86-D3BJ/def2-TZVPP level of theory. Pressure-dependent rate constants and branching fractions are determined via 1D master equation calculations. The results are used to analyze the competition for radicals between cyclopentene and cyclopentane in the intermediate temperature region, and to identify the dominant pathways flowing from these initiation channels. On the OH initiation surface, we find good agreement with recently published experimental rate constants at high temperature, and we elucidate the complex temperature dependence below 800 K, where 𝜋𝜋 addition becomes prominent. On the HO2 initiation surface, we find an interesting alternative route to bicyclic ether formation via well-skipping over the HO2 adduct well. On the cyclopentenyl radical surface, the major product is cyclopentadiene plus H. On the cyclopentenyl + O2 surface, we find that resonance stabilization largely prevents the allylic radical from undergoing oxidation, whereas the alkylic radical has a somewhat elevated propensity for oxidation pathways relative to cyclopentyl.

ab initio calculations↗

A simple model for short-range ordering kinetics in multi-principal element alloys

Short-range ordering (SRO) in multi-principal element alloys influences material properties such as strength and corrosion. While some degree of SRO is expected at equilibrium, predicting the kinetics of its formation is challenging. We present a simplified isothermal concentration-wave (CW) model to estimate an effective relaxation time of SRO formation. Estimates from the CW model agree to within a factor of five with relaxation times obtained from kinetic Monte Carlo (kMC) simulations when above the highest ordering instability temperature. Further, the advantage of the CW model is that it only requires mobility and thermodynamic parameters, which are readily obtained from alloy mobility databases and Metropolis Monte Carlo simulations, respectively. The simple parameterization of the CW model and its analytical nature makes it an attractive tool for the design of processing conditions to promote or suppress SRO in multicomponent alloys.

36 MATERIALS SCIENCE↗

Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock

The Richtmyer–Meshkov instability (Richtmyer, Commun. Pure Appl. Maths , vol. 13, issue 2, 1960, pp. 297–319; Meshkov, Fluid Dyn. , vol. 4, issue 5, 1972, pp. 101–104) of a twice-shocked gas interface is studied using both high spatial resolution single-shot (SS) and lower spatial resolution, time-resolved, high-speed (HS) simultaneous planar laser-induced fluorescence and particle image velocimetry in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. This IC is accelerated by a shock of nominal strength Mach number $M = 1.75$ , and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An ensemble of experiments is analysed after reshock while the interface mixing width grows linearly with time. The kinetic and scalar energy spectra and the terms of their evolution equation are calculated and compared between SS and HS experiments. The inertial range scaling of the scalar power spectrum is found to follow Gibson's relation (Gibson, Phys. Fluids , vol. 11, issue 11, 1968, pp. 2316–2327) as a function of Schmidt number when the effective turbulent Schmidt number is used in place of the material Schmidt number that controls equilibrium scaling. Further, the spatially integrated scalar flux follows similar behaviour observed for the kinetic energy in large eddy simulation studies by Zeng et al. ( Phys. Fluids , vol. 30, issue 6, 2018, 064106) while the spatially varying scalar flux exhibits back scatter along the centre of the mixing layer and forward energy transfer in the spike and bubble regions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Drift kinetic theory of alpha transport by tokamak perturbations

We report that upcoming tokamak experiments fuelled with deuterium and tritium are expected to have large alpha particle populations. Such experiments motivate new attention to the theory of alpha particle confinement and transport. A key topic is the interaction of alpha particles with perturbations to the tokamak fields, including those from ripple and magnetohydrodynamic modes like Alfvén eigenmodes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power and damage to device walls. Alpha interaction with these perturbations is often studied with single-particle theory. In contrast, we derive a drift kinetic theory to calculate the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided these can be studied drift kinetically). Novel features of the theory include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits and finite orbit effects. Heat fluxes are considered for the example cases of ripple and the toroidal Alfvén eigenmode (TAE). The ripple heat flux is small. The TAE heat flux is significant and scales with the square of the perturbation amplitude, allowing the derivation of constraints on mode amplitude for avoidance of significant alpha depletion. A simple saturation condition suggests that TAEs in one upcoming experiment will not cause significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, which could be accompanied by the onset of stochasticity, could cause significant transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations

Plasma supports collective modes and particle–wave interactions that lead to complex behaviour in, for example, inertial fusion energy applications. While plasma can sometimes be modelled as a charged fluid, a kinetic description is often crucial for studying nonlinear effects in the higher-dimensional momentum–position phase space that describes the full complexity of the plasma dynamics. We create a differentiable solver for the three-dimensional partial-differential equation describing the plasma kinetics and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion-relevant configuration and find that the optimization process exploits a novel physical effect.

plasma nonlinear phenomena↗

Electron kinetics in a high- Z plasmoid

The problem of the electron dynamics on a closed magnetic field line passing through a high-Z plasmoid is considered. The electron kinetic equation is integrated over bounce motion and pitch angle, reducing the independent variables to a single adiabatic invariant plus time. Integration of the full Landau self-collision operator is carried out exactly, resulting in a nonlinear integro-differential operator in the new invariant. Conservation laws and the H theorem of the integrated self-collision operator are proven. Numerical solutions of the integrated kinetic equation are obtained with a self-consistent quasineutral electric potential, given the initial condition of a cold plasmoid immersed in a hot ambient plasma. The fact that cold electrons are deeply trapped in a potential with a parabolic peak leads to exactly 3/4 the usual rate of collisional heating by the ambient plasma, independent of any other parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗