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Title: Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges

Abstract

In this paper, the effect of nonlinear processes (such as three-body collisions and stepwise ionizations) on the similarity law in high-pressure argon discharges has been studied by the use of the Kinetic Global Model framework. In the discharge model, the ground state argon atoms (Ar), electrons (e), atom ions (Ar+), molecular ions (Ar2+), and fourteen argon excited levels Ar*(4s and 4p) are considered. The steady-state electron and ion densities are obtained with nonlinear processes included and excluded in the designed models, respectively. It is found that in similar gas gaps, keeping the product of gas pressure and linear dimension unchanged, with the nonlinear processes included, the normalized density relations deviate from the similarity relations gradually as the scale-up factor decreases. Without the nonlinear processes, the parameter relations are in good agreement with the similarity law predictions. Furthermore, the pressure and the dimension effects are also investigated separately with and without the nonlinear processes. It is shown that the gas pressure effect on the results is less obvious than the dimension effect. Without the nonlinear processes, the pressure and the dimension effects could be estimated from one to the other based on the similarity relations.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [1];  [3]
+ Show Author Affiliations
  1. Michigan State Univ., East Lansing, MI (United States). Dept. of Computational Mathematics, Science and Engineering; Michigan State Univ., East Lansing, MI (United States). Dept. of Electrical and Computer Engineering
  2. Michigan State Univ., East Lansing, MI (United States). Dept. of Electrical and Computer Engineering
  3. Michigan State Univ., East Lansing, MI (United States). Dept. of Computational Mathematics, Science and Engineering; Michigan State Univ., East Lansing, MI (United States). Dept. of Electrical and Computer Engineering; Michigan State Univ., East Lansing, MI (United States). Dept. of Mathematics
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1540130
Alternate Identifier(s):
OSTI ID: 1420639
Grant/Contract Number:  
SC0001939
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 11; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics

Citation Formats

Fu, Yangyang, Parsey, Guy M., Verboncoeur, John P., and Christlieb, Andrew J. Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges. United States: N. p., 2017. Web. doi:10.1063/1.5005112.
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Fu, Yangyang, Parsey, Guy M., Verboncoeur, John P., & Christlieb, Andrew J. Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges. United States. https://doi.org/10.1063/1.5005112
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Fu, Yangyang, Parsey, Guy M., Verboncoeur, John P., and Christlieb, Andrew J. Tue . "Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges". United States. https://doi.org/10.1063/1.5005112. https://www.osti.gov/servlets/purl/1540130.
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@article{osti_1540130,
title = {Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges},
author = {Fu, Yangyang and Parsey, Guy M. and Verboncoeur, John P. and Christlieb, Andrew J.},
abstractNote = {In this paper, the effect of nonlinear processes (such as three-body collisions and stepwise ionizations) on the similarity law in high-pressure argon discharges has been studied by the use of the Kinetic Global Model framework. In the discharge model, the ground state argon atoms (Ar), electrons (e), atom ions (Ar+), molecular ions (Ar2+), and fourteen argon excited levels Ar*(4s and 4p) are considered. The steady-state electron and ion densities are obtained with nonlinear processes included and excluded in the designed models, respectively. It is found that in similar gas gaps, keeping the product of gas pressure and linear dimension unchanged, with the nonlinear processes included, the normalized density relations deviate from the similarity relations gradually as the scale-up factor decreases. Without the nonlinear processes, the parameter relations are in good agreement with the similarity law predictions. Furthermore, the pressure and the dimension effects are also investigated separately with and without the nonlinear processes. It is shown that the gas pressure effect on the results is less obvious than the dimension effect. Without the nonlinear processes, the pressure and the dimension effects could be estimated from one to the other based on the similarity relations.},
doi = {10.1063/1.5005112},
journal = {Physics of Plasmas},
number = 11,
volume = 24,
place = {United States},
year = {Tue Nov 21 00:00:00 EST 2017},
month = {Tue Nov 21 00:00:00 EST 2017}
}
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margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Fu, Yangyang; Krek, Janez; Parsey, Guy M.</span> </li> <li> Physics of Plasmas, Vol. 25, Issue 3</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1063/1.5020097" class="text-muted" target="_blank" rel="noopener noreferrer">10.1063/1.5020097<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1088/1361-6463/ab394b" target="_blank" rel="noopener noreferrer" class="name">Study of scaling law for particle-in-cell/Monte Carlo simulation of low-temperature magnetized plasma for electric propulsion<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2019-08-28">August 2019</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Li, Jian; Wu, Jianjun; Zhang, Yu</span> </li> <li> Journal of Physics D: Applied Physics, Vol. 52, Issue 45</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1088/1361-6463/ab394b" class="text-muted" target="_blank" rel="noopener noreferrer">10.1088/1361-6463/ab394b<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1088/1361-6595/ab3c82" target="_blank" rel="noopener noreferrer" class="name">Transition of low-temperature plasma similarity laws from low to high ionization degree regimes<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2019-09-01">September 2019</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Fu, Yangyang; Krek, Janez; Wen, Deqi</span> </li> <li> Plasma Sources Science and Technology, Vol. 28, Issue 9</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1088/1361-6595/ab3c82" class="text-muted" target="_blank" rel="noopener noreferrer">10.1088/1361-6595/ab3c82<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1088/2516-1067/ab6c84" target="_blank" rel="noopener noreferrer" class="name">Electrical breakdown from macro to micro/nano scales: a tutorial and a review of the state of the art<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2020-02-07">February 2020</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Fu, Yangyang; Zhang, Peng; Verboncoeur, John P.</span> </li> <li> Plasma Research Express, Vol. 2, Issue 1</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1088/2516-1067/ab6c84" class="text-muted" target="_blank" rel="noopener noreferrer">10.1088/2516-1067/ab6c84<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="sr-only">Previous Page</span><span class="fa fa-angle-left"></span></a> <ul class="pagination d-inline-block" style="padding-left:.2em;"></ul> <a class="pure-button next page" href="#" rel="next"><span class="sr-only">Next Page</span><span class="fa fa-angle-right"></span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All Cited By</a></li> <li class="small" style="margin-left:.75em; 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float:none;">[ × clear filter / sort ]</a> </div> <input type="submit" id="sort_submit_citations" name="submit" aria-label="submit" style="display: none;"/> </form> </div> </div> </div> </section> <section id="biblio-related" class="tab-content tab-content-sec " data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <section id="biblio-similar" class="tab-content tab-content-sec active" data-tab="related"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;">Similar Records in DOE PAGES and OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="1" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1979311-similarity-properties-capacitive-radio-frequency-plasmas-nonlinear-collision-processes" itemprop="url">Similarity properties in capacitive radio frequency plasmas with nonlinear collision processes</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Yang, Dong</span> ; <span class="author">Fu, Yangyang</span> ; <span class="author">Zheng, Bocong</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Plasma Sources Science and Technology</span> </span> </div> <div class="abstract">Abstract Similarity laws (SL) are essential for correlating the characteristics of plasmas at different dimensional scales, which have been validated for radio frequency (rf) discharges at low pressure but under limited conditions. In this work, we evaluate the effects of nonlinear collisions (e.g. stepwise ionization) on the similarity properties in capacitive rf discharges in argon across a wide range of pressure regimes via fully kinetic particle-in-cell simulations. The SL scalings of fundamental discharge parameters, e.g. the electron power absorption and electron energy probability function, are examined with and without nonlinear collisions, respectively. Without the nonlinear collisions, the similarity scalings are<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> found to be rigorously valid. When the nonlinear collisions are considered, the similarity properties in rf discharges still exist approximately, which indicates that the violations caused by the nonlinear collisions are still minor in the studied cases. The reasons for the effectiveness of SL scalings with nonlinear collision processes are also discussed. The results from this study confirmed the validity of similarity transformations with more complex reaction kinetics, which may promote the applicability of the SL scalings for the design and fabrications of plasma devices.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1088/1361-6595/ac2f0a" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1979311" data-product-type="Journal Article" data-product-subtype="AC" >https://doi.org/10.1088/1361-6595/ac2f0a</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/21136929-theoretical-study-plasma-parameters-dependence-gas-temperature-atmospheric-pressure-argon-microwave-discharge" itemprop="url">Theoretical Study of Plasma Parameters Dependence on Gas Temperature in an Atmospheric Pressure Argon Microwave Discharge</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Pencheva, M</span> ; <span class="author">Benova, E</span> ; <span class="author">Zhelyazkov, I</span> <span class="text-muted pubdata"> - AIP Conference Proceedings</span> </span> </div> <div class="abstract">The gas temperature is an important parameter in many applications of atmospheric pressure microwave discharges (MW). That is why it is necessary to study the influence of that temperature on the plasma characteristics. Our investigation is based on a self-consistent model including the wave electrodynamics and gas-discharge kinetics. We adopt a blocks' energy structure of the argon excited atom. More specifically, we consider 7 different blocks of states, namely 4s, 4p, 3d, 5s, 5p, 4d, and 6s. Each block k is characterized by its effective energy uk (derived as an average energy of all levels in the block), as well<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> as its effective g-factor and population. The argon dimmer, atomic and molecular ions are also taken into account in the model. We solve the Boltzmann equation in order to get the electron energy distribution function and the necessary rate constants of the elementary processes. The collisional-radiative part of the model is based on 87 processes. As a result we obtain the electron and ions' number densities, mean electron energy, mean power for sustaining an electron--ion pair in the discharge bulk, as well as the population of the excited blocks of states of the argon atom as functions of the gas temperature.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1063/1.2909133" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="21136929" data-product-type="Journal Article" data-product-subtype="" >https://doi.org/10.1063/1.2909133</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1236697-one-dimensional-time-dependent-fluid-model-very-high-density-low-pressure-inductively-coupled-plasma" itemprop="url">One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Chaplin, Vernon H.</span> ; <span class="author">Bellan, Paul M.</span> <span class="text-muted pubdata"> - Journal of Applied Physics</span> </span> </div> <div class="abstract">A time-dependent two-fluid model has been developed to understand axial variations in the plasma parameters in a very high density (peak n<sub>e~</sub> > 5x10<sup>19</sup> m<sup>–3</sup>) argon inductively coupled discharge in a long 1.1 cm radius tube. The model equations are written in 1D, with radial losses to the tube walls accounted for by the inclusion of effective particle and energy sink terms. The ambipolar diffusion equation and electron energy equation are solved to find the electron density n<sub>e</sub>(z,t) and temperature T<sub>e</sub>(z,t), and the populations of the neutral argon 4s metastable, 4s resonant, and 4p excited state manifolds are calculated in<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> order to determine the stepwise ionization rate and calculate radiative energy losses. The model has been validated through comparisons with Langmuir probe ion saturation current measurements; close agreement between the simulated and measured axial plasma density profiles and the initial density rise rate at each location was obtained at p<sub>Ar</sub> = 30-60 mTorr. Lastly, we present detailed results from calculations at 60 mTorr, including the time-dependent electron temperature, excited state populations, and energy budget within and downstream of the radiofrequency (RF) antenna.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 4<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1063/1.4938490" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1236697" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1063/1.4938490</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1236697" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1236697" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/22472271-numerical-investigation-effect-driving-voltage-pulse-shapes-characteristics-low-pressure-argon-dielectric-barrier-discharge" itemprop="url">Numerical investigation of the effect of driving voltage pulse shapes on the characteristics of low-pressure argon dielectric barrier discharge</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Eslami, E., E-mail: eeslami@iust.ac.ir</span> ; <span class="author">Barjasteh, A.</span> ; <span class="author">Morshedian, N.</span> <span class="text-muted pubdata"> - Plasma Physics Reports</span> </span> </div> <div class="abstract">In this work, we numerically compare the effect of a sinusoidal, triangular, and rectangular pulsed voltage profile on the calculated particle production, electric current, and gas voltage in a dielectric barrier discharge. The total argon gas pressure of 400 Pa, the distance between dielectrics of 5 mm, the dielectric thickness of 0.7 mm, and the temperature of T = 300 K were considered as input parameters. The different driving voltage pulse shapes (triangular, rectangular, and sinusoidal) are considered as applied voltage with a frequency of 7 kHz and an amplitude of 700 V peak to peak. It is shown that<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> applying a rectangular voltage, as compared with a sinusoidal or triangle voltage, increases the current peak, while the peak width is decreased. Higher current density is related to high production of charged particles, which leads to the generation of some highly active species, such as Ar* (4s level), and Ar** (4p level) in the gap.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1134/S1063780X15060021" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="22472271" data-product-type="Journal Article" data-product-subtype="AC" >https://doi.org/10.1134/S1063780X15060021</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="5" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/22599971-investigation-reaction-mechanisms-generation-loss-oxygen-related-species-atmospheric-pressure-pulsed-dielectric-barrier-discharge-argon-oxygen-mixture" itemprop="url">Investigation on the reaction mechanisms of generation and loss of oxygen-related species in atmospheric-pressure pulsed dielectric barrier discharge in argon/oxygen mixture</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Pan, Jie</span> ; <span class="author">Tan, Zhenyu</span> ; <span class="author">Pan, Guangsheng</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physics of Plasmas</span> </span> </div> <div class="abstract">This work presents a numerical investigation, using a 1-D fluid model, on the generation and loss of oxygen-related species and the spatial-temporal evolutions of the species densities in the atmospheric-pressure pulsed dielectric barrier discharge in the argon/oxygen mixture. The reaction pathways as well as their contributions to the generation and loss of oxygen-related species are given. The considered oxygen-related species include O, O({sup 1}D), O{sub 2}({sup 1}Δ{sub g}), O{sub 3}, O{sup +}, O{sub 2}{sup +}, O{sup −}, O{sub 2}{sup −}, and O{sub 3}{sup −}. The following significant results are obtained. O, O({sup 1}D), O{sub 2}({sup 1}Δ{sub g}), and O{sup −}<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> are produced mainly via the electron impact with O{sub 2}. Ar{sup +} plays an essential role in the generation of O{sup +} and O{sub 2}{sup +}. Almost all of O{sub 3} derives from the reaction O{sub 2} + O{sub 2} + O → O{sub 3} + O{sub 2}. The O{sub 3}-related reactions produce an essential proportion of O{sub 2}{sup −} and O{sub 3}{sup −}. The substantial loss of O{sup −}, O{sub 2}{sup −}, and O{sub 3}{sup −} is induced by their reactions with O{sub 2}{sup +}. Loss of O{sup +}, O, and O({sup 1}D) is mainly due to their reactions with O{sub 2}, loss of O{sub 2}({sup 1}Δ{sub g}) due to O{sub 2}({sup 1}Δ{sub g}) impacts with O{sub 3} as well as the de-excitation reactions between O{sub 2}({sup 1}Δ{sub g}) and e, O{sub 2}, and O, and loss of O{sub 3} due to the reactions between O{sub 3} and other neutral species. In addition, the densities of O{sup +} and O({sup 1}D) present two obvious peaks at the pulse duration, but the densities of O{sub 2}{sup +}, O, O{sub 2}({sup 1}Δ{sub g}), and O{sub 3} are almost unchanged. The densities of negative oxygen ions increase at the pulse duration and then decline. O{sup −} density is obviously large nearby the dielectric surfaces and the densities of O{sub 2}{sup −} and O{sub 3}{sup −} present generally uniform distributions.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1063/1.4960119" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="22599971" data-product-type="Journal Article" data-product-subtype="AC" >https://doi.org/10.1063/1.4960119</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9;"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator"/> <br/> <div class="col text-center mt-3"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item"> <a href="https://www.osti.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="col text-center small" style="margin-top: 0.5em;margin-bottom:2.0rem;"> <div class="row justify-content-center" style="color:white"> <div class="pure-menu pure-menu-horizontal" style='white-space:normal'> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="https://www.osti.gov/disclaim" class="pure-menu-link" target="_blank" ref="noopener noreferrer"><span class="fa fa-institution"></span> Website Policies <span class="d-none d-sm-inline d-print-none" style="color:#737373;">/ Important Links</span></a></li> <li class="pure-menu-item" style='float:none;'><a href="/pages/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span>Contact Us</a></li> <li class="d-block d-md-none mb-1"></li> <li class="pure-menu-item" style='float:none;'><a target="_blank" title="Vulnerability Disclosure Program" class="pure-menu-link" href="https://doe.responsibledisclosure.com/hc/en-us" rel="noopener noreferrer">Vulnerability Disclosure Program</a></li> <li class="d-block d-lg-none mb-1"></li> <li class="pure-menu-item" style="float:none;"><a href="https://www.facebook.com/ostigov" target="_blank" class="pure-menu-link social ext fa fa-facebook" rel="noopener noreferrer"><span class="sr-only" style="background-color: #fff; color: #333;">Facebook</span></a></li> <li class="pure-menu-item" style="float:none;"><a href="https://twitter.com/OSTIgov" target="_blank" class="pure-menu-link social ext fa fa-twitter" rel="noopener noreferrer"><span class="sr-only" style="background-color: #fff; color: #333;">Twitter</span></a></li> <li class="pure-menu-item" style="float:none;"><a href="https://www.youtube.com/user/ostigov" target="_blank" class="pure-menu-link social ext fa fa-youtube-play" rel="noopener noreferrer"><span class="sr-only" style="background-color: #fff; color: #333;">Youtube</span></a></li> </ul> </div> </div> </div> </div> </div> </footer> <link href="/pages/css/pages.fonts.240327.0205.css" rel="stylesheet"> <script src="/pages/js/pages.240327.0205.js"></script><noscript></noscript> <script defer src="/pages/js/pages.biblio.240327.0205.js"></script><noscript></noscript> <script defer src="/pages/js/lity.js"></script><noscript></noscript> <script async type="text/javascript" src="/pages/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- DOE PAGES v.240327.0205 --> </html>