Projective and non-projective systems of first order nonlinear differential equations

It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait. In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas] The xi may generally be considered to be concentrations of species in a chemical reaction, in which case the k\u27s are rate constants. In some cases the xi may be considered to be position and momentum variables in a mechanical system. We will divide the equations into two classes: those in which the evolution can be carried out by the action of one of Lie\u27s transformation groups of the plane, and those for which this is not possible. Members of the first class can be integrated by quadrature either directly or by use of an integrating factor; those in the second class cannot. Of those in the first class the most interesting evolve by transformations of the projective group, and these, as well as the equations that cannot be integrated by quadrature, we study in some detail. We seek a qualitative analysis of systems which have no linear terms in their evolution equations when the origin from which the xi are measured is a critical point. The standard, linear, phase plane analysis is of course not adequate for our purposes

Electron capture by Ne2+ ions from atomic hydrogen

Using a merged-beam technique, the absolute, total electron-capture cross section has been measured for collisions of Ne2+ ions with hydrogen (deuterium) atoms at collision energies between 139 and 1490 eV/u. These data are compared to three other published measurements, two of which differ from one another by a factor greater than two. Early quantal rate coefficient calculations for Ne2+ ions with hydrogen at eV/u energies predict a cross section many orders of magnitude below the previously measured cross section at 40 eV/u. A possible explanation is given for the discrepancy between theory and experiment

Electron capture by Ne3+ ions from atomic hydrogen

Using the Oak Ridge National Laboratory ion-atom merged-beam apparatus, absolute total electron-capture cross sections have been measured for collisions of Ne3+ ions with hydrogen (deuterium) atoms at energies between 0.07 and 826 eV∕u. Comparison to previous measurements shows large discrepancies between 50 and 400 eV∕u. Previously published molecular-orbital close-coupling (MOCC) calculations were performed over limited energy ranges, but show good agreement with the present measurements. Here MOCC calculations are presented for energies between 0.01 and 1000 eV∕u for collisions with both H and D. For energies below ∼1 eV∕u, an enhancement in the magnitude of both the experimental and theoretical cross sections is observed which is attributed to the ion-induced dipole attraction between the reactants. Below ∼4 eV∕u, the present calculations show a significant target isotope effect

Simulation of a Hall Effect Thruster with Krypton Propellant

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143098/1/6.2017-4633.pd

Electron capture by Ne4+ ions from atomic hydrogen

Using the Oak Ridge National Laboratory ion-atom merged-beams apparatus, the absolute total electron-capture cross section has been measured for collisions of Ne4+ with hydrogen and deuterium at relative energies in the center-of-mass frame between 0.10 and 1006 eV/u. Comparison with previous measurements shows large discrepancies between 80 and 600 eV/u. For energies below ∼1 eV∕u, a sharply increasing cross section is attributed to the ion-induced dipole attraction between the reactants. Multichannel Landau-Zener calculations are performed between 0.01 and 5000 eV/u and compare well to the measured total cross sections. Below ∼5 eV∕u, the present total cross section calculations show a significant target isotope effect. At 0.01 eV/u, the H:D total cross section ratio is predicted to be ∼1.4 where capture is dominated by transitions into the Ne3+ (2s22p23d) configuration

Ethanol reforming in non-equilibrium plasma of glow discharge

The results of a detailed kinetic study of the main plasma chemical processes in non-equilibrium ethanol/argon plasma are presented. It is shown that at the beginning of the discharge the molecular hydrogen is mainly generated in the reaction of ethanol H-abstraction. Later hydrogen is formed from active H, CH2OH and CH3CHOH and formaldehyde. Comparison with experimental data has shown that the used kinetic mechanism predicts well the concentrations of main species at the reactor outlet.Comment: 16 pages, 8 figure

Quantum-Mechanical Calculations of Cross Sections for Electron Collisions With Atoms and Molecules

An overview of quantum‐mechanical methods to generate cross‐section data for electron collisions with atoms and molecules is presented. Particular emphasis is placed on the time‐independent close‐coupling approach, since it is particularly suitable for low‐energy collisions and also allows for systematic improvements as well as uncertainty estimates. The basic ideas are illustrated with examples for electron collisions with argon atoms and methane. For many atomic systems, such as e‐Ar collisions, highly reliable cross sections can now be computed with quantified uncertainties. On the other hand, while electron collision calculations with molecules do provide key input data for plasma models, the methods, and computer codes presently used require further development to make these inputs robust

QDB: A new database of plasma chemistries and reactions

One of the most challenging and recurring problems when modeling plasmas is the lack of data on the key atomic and molecular reactions that drive plasma processes. Even when there are data for some reactions, complete and validated datasets of chemistries are rarely available. This hinders research on plasma processes and curbs development of industrial applications. The QDB project aims to address this problem by providing a platform for provision, exchange, and validation of chemistry datasets. A new data model developed for QDB is presented. QDB collates published data on both electron scattering and heavy-particle reactions. These data are formed into reaction sets, which are then validated against experimental data where possible. This process produces both complete chemistry sets and identifies key reactions that are currently unreported in the literature. Gaps in the datasets can be filled using established theoretical methods. Initial validated chemistry sets for SF 6 /CF 4 /O 2 and SF 6 /CF 4 /N 2 /H 2 are presented as examples