Search NASA⌕ Search

SEARCH · Search NASA

Results for “density”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Incoherent Scattering of Electromagnetic Waves by Langmuir Fluctuations Trapped in a Plasma Density Well

Incoherent scattering of a probing wave by Langmuir fluctuations trapped and enhanced near a local minimum of the electron density (plasma density well) in plasma with a parabolic density profile is considered. Steady-state amplitudes of fluctuations are calculated for arbitrary velocity distribution functions of plasma particles with allowance for electron collisions. It is shown that quasi-periodic oscillations with two characteristic scales can be present in the spectrum of the plasma line. The smaller scale is due to the wellknown effect of discretization of the spectrum of Langmuir fluctuations in a plasma density well. The larger scale is associated with the generation of scattered waves in two spatial regions and subsequent interference of these waves at the exit from the density well. Oscillations with this scale are more stable under unsteady plasma conditions and can be more often observed in experiments. The results of this work can be used to experimentally determine the plasma parameters, such as the electron collision frequency and the size and lifetime of the plasma density well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10 6 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Transition of Blast Furnace Slag from Silicate Based to Aluminate Based: Density and Surface Tension

The effects of the Al{sub 2}O{sub 3} concentration and Al{sub 2}O{sub 3}/SiO{sub 2} ratio on the density and surface tension of molten aluminosilicate CaO-SiO{sub 2}-Al{sub 2}O{sub 3}-9 mass pct MgO-1 mass pct TiO{sub 2} slag were investigated at temperatures from 1723 K to 1823 K (1450 °C to 1550 °C) using the Archimedean method and the maximum bubble pressure (MBP) technique, respectively. The mechanism of the changes in density and surface tension with composition was analyzed from the viewpoint of the degree of polymerization in the structure and the types of oxygen species in the melts. At a fixed CaO/SiO{sub 2} ratio of 1.20, the density decreased with increasing Al{sub 2}O{sub 3} content up to 25 mass pct, subsequently increasing. Increasing the Al{sub 2}O{sub 3}/SiO{sub 2} ratio from 0.47 to 0.92 caused an increase in the density at a fixed CaO content, and the density decreased slightly when the Al{sub 2}O{sub 3}/SiO{sub 2} ratio was greater than 0.92. Based on the structural information, the density decreased when the Al{sub 2}O{sub 3} content enhanced the network structure and increased when the (Q{sub 2} + Q{sub 3})/(Q{sub 0} + Q{sub 1}) ratio and structural complexity decreased. The surface tension increased with increasing Al{sub 2}O{sub 3} content and Al{sub 2}O{sub 3}/SiO{sub 2} ratio. On the one hand, the surface-active component of SiO{sub 2} decreased; on the other hand, the concentration of [AlO{sub 4}]{sup 5−} tetrahedra and metal cations that act as charge compensators increased at the melt surface. A model based on the anionic and cationic radii and the Butler equation was employed to predict the surface tension, and an iso-surface tension diagram was obtained at 1773 K (1500 °C).

36 MATERIALS SCIENCE↗
DOE OSTI2020

Quantifying dislocation density in Al-Cu coatings produced by cold spray deposition

This work quantifies the plastic deformation in terms of dislocation density for a series of cold sprayed Al-Cu coatings with copper contents from 2 mass% to 5 mass%. The success of the deposition and consolidation of the feedstock powders during the cold spray process rely on the occurrence of significant plastic deformation. Inert gas atomized Al-Cu alloy powders were sprayed onto substrates made of an Al-Cu-Mg-Mn alloy (AA2024) to produce dense coatings using a low pressure cold spray system with helium as the carrier gas. X-ray diffraction patterns were obtained from the Al-Cu feedstock powder material and the cold sprayed coatings using a monochromatic X-ray source, and the dislocation density was determined via an X-ray whole profile analysis. Increasing the Cu alloy content (from 2 mass% to 5 mass%) systematically increased the dislocation density in the Al-Cu coatings from (4.3 ± 0.5) × 10 14 m -2 to (7.5 ± 0.8) × 10 14 m -2 . The dislocation densities in the feedstock powders ranging from (0.4 ± 0.1) × 10 14 m -2 to (1.8 ± 0.2) × 10 14 m -2 were all lower than the dislocation densities in the corresponding coatings. The increasing deformation level in the Al-Cu coatings with Cu additions were confirmed by the classic and modified Williamson-Hall analyses of X-ray diffraction data, and peak breadth measurements from neutron diffraction data. Finally, a high density of dislocations was also observed in these coatings via electron backscatter diffraction and transmission electron microscopy.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

The development of next-generation molten salt reactors relies on accurate knowledge of the thermophysical properties of the candidate coolant and fueled molten salts. These thermophysical properties include density, viscosity, thermal conductivity, and heat capacity. Because of difficulties in measuring thermophysical properties of molten salts, there are many gaps in the current state of thermophysical property knowledge of these salts, particularly those that contain actinides or beryllium. Therefore, leveraging modeling techniques to estimate unknown molten salt thermophysical properties and guide future experimental measurements has high value for the nuclear industry. Here, the densities of molten fluoride pseudo-ternary salt systems, which are of interest to the nuclear industry, were estimated using Redlich-Kister expansion and Muggianu interpolation techniques. The pseudo-ternary systems considered for estimation in this study were NaF-LiF-ZrF 4 , LiF-BeF 2 -ZrF 4 , LiF-BeF 2 -ThF 4 , NaF-LiF-BeF 2 , NaF-KF-BeF 2 , NaF-ZrF 4 -UF 4 , and NaF-BeF 2 -UF 4 . This Redlich-Kister estimation approach accounts for nonideal mixing behavior based on pseudo-binary subsystem interaction parameters determined from experimentally measured pseudo-binary system density data sets. The Redlich-Kister estimation was compared with the method of additive molar volumes, which assumes ideal mixing. Additionally, the Redlich-Kister approach was used to determine previously unknown binary and ternary interaction parameters based on experimentally measured density data sets for select pseudo-ternary salt systems. The results of this study show improvement in density estimation using the Redlich-Kister approach for all systems considered compared with estimation by additive molar volumes. Furthermore, this analysis allowed for the estimation of nonideal density behavior in experimentally unstudied ZrF 4 -UF 4 and BeF 2 -UF 4 , as well as the quantification of ternary interaction in NaF-LiF-ZrF 4 , NaF-BeF 2 -UF 4 , and NaF-ZrF 4 -UF 4 .

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

Elucidating the temperature and density dependence of silver chloride hydration numbers in high-temperature water vapor: A first-principles molecular simulation study

Hydration numbers of metal complexes in low-density aqueous solutions are required for developing geochemical models for ore-forming metals and for designing supercritical desalination processes. In this study, we investigate the temperature and density dependence of the hydration numbers of silver chloride at 623 K, 673 K, and 713 K and densities of 10–100 kg/m 3 . Experimental estimates of the hydration number in the literature for AgCl at these conditions are inconclusive and possibly contradictory as to the temperature and density dependence. First-principles molecular simulation presents an attractive alternative to experimental measurements. Specifically, recent work shows that machine-learning-accelerated nested Monte Carlo simulations provide reliable estimates for the hydration numbers of CuCl at 623 K from 10 to 100 kg/m 3 . Using the same technique, we find a monotonic temperature dependence, with the hydration number decreasing slightly with increasing temperature. In addition, the simulation-predicted hydration numbers steadily increase with increasing density. These temperature and density trends are in agreement with certain experimental data sets. Therefore, this work demonstrates how first-principles Monte Carlo simulations assist in resolving discrepancies between experimental data sets. Our simulation results also correctly predict that the hydration number, and thus also the solubility, of AgCl is lower than that of CuCl under the same conditions. Furthermore, the bond length and angle formed between the water complex and AgCl differ from those for CuCl, consistent with the lower solubility of AgCl.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A sparse matrix–vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

Here we present an efficient sparse matrix–vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev–Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix–matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev–Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix–vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

42 ENGINEERING↗
DOE OSTI2018

Rapid high density cryogenic pressure vessel filling to 345 bar with a liquid hydrogen pump

Cryogenic pressurized hydrogen (H 2 ) vessels promise maximum storage density with potential to enabling practical H 2 vehicles with maximum driving autonomy and minimum cost of ownership. This paper adds a more complete evaluation of the benefits of cryogenic vessel technology by establishing a methodology for evaluating fill density for any initial vessel thermodynamic state. This is accomplished by assessing 24 cryogenic pressure vessel fill experiments with a liquid hydrogen (LH 2 ) pump manufactured by Linde and installed at the Lawrence Livermore National Laboratory (Livermore, CA) campus. The LH 2 piston pump takes LH 2 from the station Dewar at near ambient pressure (3 bar) and very low temperature (24.6 K) and pressurizes it to the vessel pressure in two stages of compression, up to 875 bar, although the rating of the cryogenic vessel used for these experiments limits fill pressure to 345 bar. Experiments spanned initial vessel temperatures from ambient to 22 K, enabling pump testing over a broad range of conditions. Experimental results validate many of the virtues that make LH 2 pumping a promising technology for H 2 dispensing, both for filling cryogenic as well as ambient temperature vessels: high throughput (1.67 kg/min, 100 kg/h), unlimited capacity for back to back refueling, low electricity consumption at the station due to high density of LH 2 minimizing compression work, and highest fill density, up to 80 g/L (estimated) when dispensing cryogenic hydrogen at 700 + bar. Analysis of the experiments shows that fill density can be predicted with reasonable accuracy (±0.7 g/L) by assuming 10 kJ/kg K cryogenic vessel inlet entropy (pump delivery hose outlet entropy). Fill lines are finally generated on a H 2 phase diagram, producing charts that can be used for rapidly determining fill density for any vessel condition at the moment of fill initiation.

08 HYDROGEN↗
DOE OSTI2019

Line profile analysis of dislocation densities of the δ-phase 239 Pu-2.0 at%Ga alloy using neutron diffraction

Time-of-flight neutron diffraction measurements were conducted at ambient conditions to study microstructures of the δ-phase 239 Pu-2at% Ga alloy. Based on the line profile analysis of diffraction data we derived dislocation densities using a correction routine to account for the anisotropic strain broadening. Our results show here that the average dislocation density in the as-received sample, previously treated at cryogenic temperatures, is five times higher than the dislocation density measured after annealing the sample, indicating that the neutron instrumentation used in this work has sufficient resolution to detect the dislocation density changes in different sample processing. These results are also in reasonably good agreement with the dislocation densities previously reported based on TEM observations and x-ray diffraction data, suggesting that the simple correction routines applied in this work have a fairly good fidelity for deriving important microstructural information such as dislocation density for elastically highly anisotropic δ-phase 239 Pu-Ga alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Correlating the influence of porosity, tortuosity, and mass loading on the energy density of LiNi 0.6 Mn 0.2 Co 0.2 O 2 cathodes under extreme fast charging (XFC) conditions

Extreme fast charging capabilities along with high energy density of Li-ion batteries are the key factors to increase the adoption of electric vehicles while eliminating the problem of range anxiety. The U.S Department of Energy has a goal of <12 min charging time with energy density of > 200 Wh kg -1 . A combined improvement in the electrode architecture, electrolyte properties, and separator membrane is necessary to achieve this goal. Cells with thin electrodes are capable of extreme fast charging at the expense of low energy density and high cost. Electrode engineering can maximize energy density. In this work, the influence of porosity, mass loading and charging protocols on capacity and energy density and electrode kinetics are investigated under extreme fast charging conditions. Increasing the mass loading from 11.5 mg cm -2 to 25 mg cm -2 compromises the rate performance due to the mass transport limitation and underutilization of thick electrodes. Furthermore, reducing the electrode porosity from 50% to 35% improves the rate performance ascribed to shorter Li ion diffusion length. Symmetric cells are cycled to verify the performance of the half cells, suggesting that Li metal plating is the rate limiting step under high current density.

25 ENERGY STORAGE↗
DOE OSTI2019

Short communication: Assessment of the dislocation density using X-ray topography in Al single crystals annealed for long times near the melting temperature

Earlier work by the authors determined the dislocation density as a function of time in aluminum single crystals annealed near the melting temperature using etch-pits. It was found that the dislocation density is stable and unchanged even with annealing times up to one year for statically annealed Al single crystals with an initially low dislocation density. As several investigators have suggested that etch-pits are not reliable compared to transmission electron microscopy in assessing the dislocation density, the current study utilized x-ray topography at a synchrotron for dislocation density measurements. This work, then, is a short paper complementing the authors earlier work by using a new, reliable, but rarely utilized non-destructive technique to measure the dislocation density. The results confirm the trend of the earlier study using etch-pits by the authors.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Comparative H-mode density limit studies in JET and AUG

Identification of the mechanisms for the H-mode density limit in machines with fully metallic walls, and their scaling to future devices is essential to find for these machines the optimal operational boundaries with the highest attainable density and confinement. Systematic investigations of H-mode density limit plasmas in experiments with deuterium external gas fuelling have been performed on machines with fully metallic walls, JET and AUG and results have been compared with one another. Basically, the operation phases are identical for both tokamaks: the stable H-mode phase, degrading H-mode phase, breakdown of the H-mode with energy confinement deterioration usually accompanied by a dithering cycling phase, followed by the l-mode phase. The observed H-mode density limit on both machines is found close to the Greenwald limit (n/n GW = 0.8–1.1 in the observed magnetic configurations). The similar behavior of the radiation on both tokamaks demonstrates that the density limit (DL) is neither related to additional energy losses from the confined region by radiation, nor to an inward collapse of the hot discharge core induced by overcooling of the plasma periphery by radiation. It was observed on both machines that detachment, as well as the X-point MARFE itself, does not trigger a transition in the confinement regime and thus does not present a limit on the plasma density. It is the plasma confinement, most likely determined by edge parameters, which is ultimately responsible for the transition from H- to l-mode. The measured Greenwald fractions are found to be consistent with the predictions from different theoretical models, based on MHD instability theory in the near-SOL.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Intermolecular Interactions in Direct Air Capture Materials: Insights from Charge Density Analysis

Direct air capture (DAC) materials enable the removal of CO 2 from the atmosphere, but improving their efficiency requires a detailed understanding of the intermolecular interactions that govern CO 2 sorption and release. Here, we present an experimental electron density study of methylglyoxal-bis(iminoguanidine) (MGBIG), a promising DAC material, using high-resolution X-ray and neutron diffraction data combined with quantum crystallographic analysis. This approach bridges theoretical and experimental data by quantifying electron density distributions and revealing how hydrogen bonds stabilize CO 2 -derived carbonate phases and may influence the desorption behavior. We identify distinct hydrogen-bonding environments in two crystalline carbonate phases: P1, a transient kinetic product, and P3, a thermodynamically stable phase. Multipolar refinement and electrostatic potential and multipole moment calculations precisely map electron density distributions, revealing key hydrogen bonds involved in CO 2 capture. Topological analysis of electron density highlights a cooperative hydrogen-bonding network in the thermodynamically favored P3 phase, where enhanced electron density delocalization and water-mediated interactions contribute to a more stable lattice. Energetic analyses confirm that stronger hydrogen bonding networks enhance the stability of P3 with a binding energy of −607.0 kJ/mol and greater lattice stability (−847.3 kJ/mol) compared to P1 (−302.5 and −571.0 kJ/mol, respectively). Electrostatic potential maps further illustrate polarization patterns that may influence the stability of the binding of CO 2 and release conditions. These findings establish a direct experimental framework for linking electron density distributions to intermolecular interactions in DAC materials, providing a rational design strategy for optimizing sorbents with improved CO 2 capture efficiency and reduced energy demands.

Electron density↗
DOE OSTI2015

Investigation of the on-axis atom number density in the supersonic gas jet under high gas backing pressure by simulation

The supersonic gas jets from conical nozzles are simulated using 2D model. The on-axis atom number density in gas jet is investigated in detail by comparing the simulated densities with the idealized densities of straight streamline model in scaling laws. It is found that the density is generally lower than the idealized one and the deviation between them is mainly dependent on the opening angle of conical nozzle, the nozzle length and the gas backing pressure. The density deviation is then used to discuss the deviation of the equivalent diameter of a conical nozzle from the idealized d{sub eq} in scaling laws. The investigation on the lateral expansion of gas jet indicates the lateral expansion could be responsible for the behavior of the density deviation. These results could be useful for the estimation of cluster size and the understanding of experimental results in laser-cluster interaction experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Microtwins and their effect on accumulation of excess dislocation density in grains with different types of crystal lattice bending in deformed austenitic steel

The investigation of excess dislocation density accumulation in the deformed polycrystalline austenitic steel was carried out using transmission electron microscopy (TEM). The distributions of the excess dislocation density in the grains of the deformed austenitic steel with different bending types were obtained and plotted. It was established that in the austenitic polycrystalline steel at the deformation degrees ε = 14 and 25 % the distributions of the excess dislocation density are multimodal. In both cases the grain with compound bending is more stressed. The values of the average excess dislocation density in the grains with the compound and simple bending are less at ε = 25 % than that at ε = 14 %. This is explained by a significant relaxation of the internal stresses in steel with the increase of the deformation degree from 14 % to 25 %. The increase of the number of twinning systems and the material volume fraction covered by twinning leads to the internal stress relaxation and consequently to the increase of the excess dislocation density. The presence of microtwins in the deformed material has an influence on the distribution of the excess dislocation density. In the deformed polycrystalline austenitic steel the number of grains with compound bending is increased with the increase of the plastic deformation degree.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Anode current density distribution in a cusped field thruster

The cusped field thruster is a new electric propulsion device that is expected to have a non-uniform radial current density at the anode. To further study the anode current density distribution, a multi-annulus anode is designed to directly measure the anode current density for the first time. The anode current density decreases sharply at larger radii; the magnitude of collected current density at the center is far higher compared with the outer annuli. The anode current density non-uniformity does not demonstrate a significant change with varying working conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

In tokamak fusion plasmas, coherent fluctuations in the form of blobs or filaments are routinely observed in the scrape-off layer. Radio frequency (RF) electromagnetic waves, excited by antenna structures placed near the wall of a tokamak, have to propagate through the scrape-off layer before reaching the core of the plasma. While the effect of fluctuations on the properties of RF waves has not been quantified experimentally, it is of interest to carry out a theoretical study to determine if fluctuations can affect the propagation characteristics of RF waves. Usually, the difference between the plasma density inside the filament and the background plasma density is sizable, the ratio of the density difference to the background density being of order one. Generally, this precludes the use of geometrical optics in determining the effect of fluctuations, since the relevant ratio has to be much less than one, typically, of the order of 10% or less. In this study, a full-wave, analytical model is developed for the scattering of a RF plane wave by a cylindrical plasma filament. It is assumed that the plasma inside and outside the filament is cold and uniform and that the major axis of the filament is aligned along the toroidal magnetic field. The ratio of the density inside the filament to the density of the background plasma is not restricted. The theoretical framework applies to the scattering of any cold plasma wave. In order to satisfy the boundary conditions at the interface between the filament and the background plasma, the electromagnetic fields inside and outside the filament need to have the same k ∥ , the wave vector parallel to the ambient magnetic field, as the incident plane wave. Consequently, in contrast to the scattering of a RF wave by a spherical blob [Ram et al., Phys. Plasmas 20, 056110-1–056110-10 (2013)], the scattering by a field-aligned filament does not broaden the k ∥ spectrum. However, the filament induces side-scattering leading to surface waves and can also couple some power to the cold plasma wave different from the incident wave. The changes induced by a filament in the propagation of electron cyclotron waves and lower hybrid waves are illustrated by numerical results displaying the properties of the Poynting vector. The Poynting flux in the wake of the filament, and directed towards the core of the plasma, develops a spatial structure due to diffraction and shadowing. Finally and thus, the fluctuations affect the uniformity of power flow into the plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

A numerical study of the effect of various reactions, pressure and gas mixture ratio on the density distribution of etchant species (H, Br, Br{sup +}, and HBr{sup +}) in HBr/He plasma

In this study, a fluid model has been used to study the effect of gas mixing ratio and pressure on the density distribution of important etchant species, i.e., hydrogen (H), bromine (Br), Br{sup +}, and HBr{sup +} in HBr/He plasma. Our simulation results show that the densities of active etchant species H, Br, and HBr{sup +} increase with the increase in pressure as well as the HBr fraction in HBr/He mixture. On the contrary, the density of Br{sup +} decreases with the increase in He percentage in HBr/He mixture and with the increase in the pressure. Time averaged reaction rates (of the reactions involved in the production and consumption of these species) have been calculated to study the effect of these reactions on the density distribution of these species. The spatial distribution of these species is explained with the help of the time averaged reaction rates. Important reactions have been identified that contribute considerably to the production and consumption of these active species. The code has been optimized by identifying 26 reactions (out of 40 reactions which contribute in the production and consumption of these species) that have insignificant effect on the densities of H, Br, Br{sup +}, and HBr{sup +}. This shows that out of 40 reactions, only 14 reactions can be used to calculate the density and distribution of the important species in HBr/He plasma discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗