Using a one-way coupled model of neutral gas flow and plasma dynamics we report a mechanism to explain the ring-shaped emission pattern that has been observed experimentally in plasma bullets at atmospheric pressure. We solve a fluid model with the local field approximation in one-dimensional cylindrical coordinates, corresponding to a cross-section of a plasma bullet. Pulselike uniform electric field is assumed to be applied perpendicular to the simulation domain. Time and spatially resolved spectroscopic measurements support the simulation results

Graves, David B.

Jarrige, Julien

Laroussi, Mounir

Sakiyama, Yukinori

English

Old Dominion University

Old Dominion UniversityODU Digital CommonsElectrical & Computer Engineering FacultyPublications Electrical & Computer Engineering1-2010Finite Element Analysis of Ring-Shaped EmissionProfile in Plasma BulletYukinori SakiyamaDavid B. GravesJulien JarrigeOld Dominion UniversityMounir LaroussiOld Dominion University, mlarouss@odu.eduFollow this and additional works at: https://digitalcommons.odu.edu/ece_fac_pubsPart of the Electrical and Computer Engineering Commons, Engineering Physics Commons, andthe Plasma and Beam Physics CommonsThis Article is brought to you for free and open access by the Electrical & Computer Engineering at ODU Digital Commons. It has been accepted forinclusion in Electrical & Computer Engineering Faculty Publications by an authorized administrator of ODU Digital Commons. For more information,please contact digitalcommons@odu.edu.Repository CitationSakiyama, Yukinori; Graves, David B.; Jarrige, Julien; and Laroussi, Mounir, "Finite Element Analysis of Ring-Shaped Emission Profilein Plasma Bullet" (2010). Electrical & Computer Engineering Faculty Publications. 14.https://digitalcommons.odu.edu/ece_fac_pubs/14Original Publication CitationSakiyama, Y., Graves, D.B., Jarrige, J., & Laroussi, M. (2010). Finite element analysis of ring-shaped emission profile in plasma bullet.Applied Physics Letters, 96(041501), 1-3. doi: 10.1063/1.3298639Finite element analysis of ring-shaped emission profile in plasma bulletYukinori Sakiyama, David B. Graves, Julien Jarrige, and Mounir Laroussi  Citation: Applied Physics Letters 96, 041501 (2010); doi: 10.1063/1.3298639 View online: http://dx.doi.org/10.1063/1.3298639 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/96/4?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Propagation of plasma bullet in U-shape tubes AIP Advances 5, 027110 (2015); 10.1063/1.4908005  Transient photoluminescence from silicon wafers: Finite element analysis J. Appl. Phys. 114, 163105 (2013); 10.1063/1.4826896  Plasma wave simulation based on a versatile finite element method solvera) Phys. Plasmas 17, 056119 (2010); 10.1063/1.3396371  Full wave simulation of lower hybrid waves in Maxwellian plasma based on the finite element method Phys. Plasmas 16, 090701 (2009); 10.1063/1.3216548  Prediction of plasma‐facing ICRH antenna behavior via a Finite‐Element solution of coupled IntegralEquations AIP Conf. Proc. 787, 230 (2005); 10.1063/1.2098231    This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:128.82.253.83 On: Wed, 13 Jan 2016 14:58:29Finite element analysis of ring-shaped emission profile in plasma bulletYukinori Sakiyama,1,a David B. Graves,1 Julien Jarrige,2 and Mounir Laroussi21Department of Chemical Engineering, University of California, Berkeley, California 94720, USA2Laser and Plasma Engineering Institute, Old Dominion University, Norfolk, Virginia 23529, USAReceived 23 September 2009; accepted 5 January 2010; published online 26 January 2010Using a one-way coupled model of neutral gas flow and plasma dynamics we report a mechanismto explain the ring-shaped emission pattern that has been observed experimentally in plasma bulletsat atmospheric pressure. We solve a fluid model with the local field approximation inone-dimensional cylindrical coordinates, corresponding to a cross-section of a plasma bullet.Pulselike uniform electric field is assumed to be applied perpendicular to the simulation domain.Time and spatially resolved spectroscopic measurements support the simulation results. © 2010American Institute of Physics. doi:10.1063/1.3298639Several research groups demonstrated that atmosphericpressure plasma jets are not continuous jets but discrete fast-moving plasma packets or bullets.1–4 The discharge mecha-nisms are however not fully understood. Lu and Laroussi2proposed a photoionization model. Sands et al.3 reported thatplasma jets exhibit properties similar to positive streamers.More interestingly, cross-sectional images of jets showring-shaped emission pattern, corresponding to a hollowstructure.1,5 In this study, we focus on modeling of the ring-shaped emission patterns.We employed a one-way coupled model between neutralgas flow and plasma dynamics. The models are solved usingCOMSOL6 with MATLAB.7 The steady state neutral gas flowmodel describes convection of helium gas flow and air back-diffusion into helium flow in two-dimensional cylindrical co-ordinates. The “air” in the current model is assumed to bepure nitrogen to avoid complicated oxygen plasma chemis-try. The governing equations for the neutral gas flow consistof total mass continuity equation, momentum continuityequation i.e., compressible Navier–Stokes equation, andmass continuity equation for nitrogen. The temperature ofthe background gas is fixed at 300 K. More detailed discus-sion and formulation of neutral gas flow equations are givenin Ref. 8. Figure 1 shows simulation results of two-dimensional distribution of mole fraction of nitrogen. A tubeplasma reactor is located near the left bottom corner of thesimulation domain. A fully developed laminar flow i.e., Poi-seuille flow enters the domain at z=−20 mm with flow rateof 7 l /min. Our model clearly shows that helium-rich regionstretches over 50 mm near the axis of symmetry. Nitrogenconcentration rapidly increases in radial direction due to dif-fusion, thus creating a narrow helium channel. In the follow-ing sections, we discuss the plasma structure at two differentcross-sections: an upstream point z=20 mm and a down-stream point z=40 mm. Background gas composition iskept constant as shown in the inset graph in Fig. 1.Our time-dependent plasma model is based on a fluidmodel with the local field approximation in one dimensionalcylindrical coordinates. The simulation region corresponds toa cross section of a plasma bullet i.e., r direction in Fig. 1.The plasma model is almost identical to our previous report,9which includes six different species and 13 elementary reac-tions. The governing equations consist of Poisson’s equationin radial direction and species continuity equations with thedrift-diffusion approximation for electrons, heavy positiveions, and metastables. The major difference is that the cur-rent model includes nitrogen metastable N2 C3 and threeadditional reactions as follows: N2+e→N2C3+e, N2+e→N2++e, and N2 C3→N2+h k=2.45107 s−1 Ref.10. In addition, we reconstructed look-up tables for elec-tron impact reactions and electron transport coefficients sothat the coefficients are expressed as functions of both thelocal electric field and the mole fraction of nitrogen. Anotherimportant difference is that pulselike uniform electric fieldEz is given perpendicular to the simulation domain i.e., zdirection in Fig. 1. The pulse consists of a 200 ns flat pla-teau and 100 ns rise/decay time. The pulse duration wasestimated from the duration of conduction current carried bya bullet in Ref. 2. We note that the pulselike electric fielddoes not represent the applied voltage pulse in our experi-ment described later. The repetition frequency is 8 kHz. Themagnitude of the electric field 3105 V /m is uniform in rdirection and chosen so that a periodic steady state solutioncan be obtained. Thus, the current plasma model is not self-consistent though we solve Poisson’s equation in r direction.The equation system reaches a periodic steady state in tencycles, starting from uniform and low particle density1012 m−3.Figure 2 show instantaneous distributions of electrondensities and ionization rate at z=20 mm at the end of therise of the pulselike electric field t=100 ns and at thebeginning of the decay of the pulselike electric fieldt=300 ns. In the early stage t=100 ns, the discharge issubstantially sustained by electron impact ionization of he-lium. The density of electrons and ions shows relativelybroad peaks near the center r=0 though the applied electricfield Ez is uniform. Interestingly, Penning ionization betweenhelium metastables and background nitrogen shows thepeak around r=0.4 mm. In addition, the peak of nitrogenmetastable density is observed at off-centered positionaElectronic mail: ysaki@berkeley.edu.APPLIED PHYSICS LETTERS 96, 041501 20100003-6951/2010/964/041501/3/$30.00 © 2010 American Institute of Physics96, 041501-1 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:128.82.253.83 On: Wed, 13 Jan 2016 14:58:29r=0.5 mm although we do not show the plot here. Theseare explained by the sharp gradient of nitrogen density asshown in Fig. 1. Nitrogen density near the center is signifi-cantly low, whereas nitrogen density far away from the cen-ter is so high that electron energy is quenched. Consequently,nonuniform distribution of electron impact excitation/ionization rate is formed in the simulation domain. Penningionization plays only minor role in sustaining the plasma atthe early stage of the discharge t=100 ns. Through nonlin-ear electron multiplication process, however, the off-centeredPenning ionization peak eventually generates off-centeredpeak of electron density in the late stage of the discharget=300 ns.We performed spectroscopic measurements to investi-gate the structure of the plasma bullets and to compare withthe simulation results. A schematic diagram of the experi-mental setup is shown in Fig. 3. The plasma jet was gener-ated by a dielectric barrier discharge reactor in a cylindricalconfiguration. The reactor was made of an acrylic tube withan internal diameter of 3 mm and a thickness of 1.5 mm. Theelectrodes consist of two copper foils wrapped around thetube. The reactor was driven by a unipolar positive highvoltage pulse forming system. The pulse amplitude was 7 kV,the pulse width 2 s, and the repetition frequency 8 kHz.The rise time and fall time were around 40 ns. The dischargereactor was fed with pure helium and the flow rate was fixedat 7 l /min using mass flow controllers. These conditions areclose to the simulation conditions described above. Theplasma jet propagating in ambient air was characterized byoptical emission spectroscopy. We used a monochromatorSpectra Pro 500i, Acton Research with a grating of 3600grooves/mm and a photomultiplier tube PD-471, Roper Sci-entific. The relative density of N2 C3u and N2+ B2u+were obtained using the intensity of, respectively, 0–0 bandof N2 second positive system SPS at 337.1 nm, and 0–0band of N2+ first negative system FNS at 391.2 nm. Thespatial distribution of N2 C was determined by measuringthe intensity of SPS at different radial positions. The radialprofile was then calculated using Abel inversion method.Figure 4 shows spatially resolved emission profilesfrom N2 SPS, upstream z=20 mm and downstreamz=40 mm. Light emission from nitrogen clearly shows anoff-centered peak at the upstream point. On the other hand,the emission profile shifts to the center and the ring-shapealmost collapses at the downstream point. Our plasma modelreproduces the experimental observation. Both experimentsand simulation indicate that the diameter of the plasma bullet100.20.40.60.80 10 20 30 50[mm]40zr-10-201020010-410-2100molefraction2.01.51.00.50.0r [mm]20 mm40 mmmolefractionFIG. 1. Color online Two-dimensional distribution of mole fraction of nitrogen. The inset graph shows mole fraction of nitrogen in radial direction at z=20 and 40 mm.1015101610171018101910201021density[m-3]2.01.51.00.50.0r [mm]102310241025102610271028ionizationrate[m-3s-1 ]electron densityelectron impactPenning( a )1015101610171018101910201021density[m-3]2.01.51.00.50.0r [mm]102310241025102610271028ionizationrate[m-3s-1 ]stepwiseelectron densityPenningelectron impact( b )FIG. 2. Color online Instantaneous distribution of electron density leftaxis and various ionization rates right axis at z=20 mm a at 100 ns andb 300 ns. FIG. 3. Color online A schematic diagram for spectroscopic measurement.041501-2 Sakiyama et al. Appl. Phys. Lett. 96, 041501 2010 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:128.82.253.83 On: Wed, 13 Jan 2016 14:58:29decreases as it propagates away from the tube exit. This isconsistent with previous experimental observations by Luand Laroussi2 and Begum et al.11 Again, the off-centeredpeaks are due to diffusion of air nitrogen into the heliumflow as we discussed above.Figures 5a and 5b show a comparison of time-resolved emission intensity from helium, nitrogen, and nitro-gen ion at the upstream point z=20 mm between experi-ment and modeling. In Fig. 5b, we plot electron impactionization rate of helium as an indicator of emission fromhelium. The sum of Penning ionization and charge transferreaction are used as an indicator of emission from nitrogenion.12 Our experimental observation shows that at a fixedpoint emission from helium is observed first, followed byemission from nitrogen and nitrogen ion. The simulation re-sults qualitatively agree with the measurement. Our modelindicates the delay between emission from helium and fromnitrogen/nitrogen ion is due to difference in electron impactreaction rate. We think discrepancy in the decay time ofemission from nitrogen ion is due to the simplified chemistrymodel, especially lack of oxygen. Also the current one-dimensional model is unable to reproduce the small “bump”between 100 and 200 ns observed by our experiments. Thiscould come from two-dimensional effects of the bullet and/ornonuniformity of the electric field. We however emphasizethat the non-self-consistent plasma model we report here iscapable of capturing many essential features of the plasmabullet, which have been experimentally validated.In summary, our one-way coupled model of neutral gasflow and plasma dynamics shows that air diffusion againsthelium convection creates the unique ring-shape emissionprofile in atmospheric pressure plasma bullets. Our spectr-scopic measurements support the simulation results. It isworth noting that the discharge mechanisms are analogous tothe plasma needle discharge although the discharge condi-tions are different.131M. Teschke, J. Kedzierski, E. G. Finantu-Dinu, D. Korzec, and J. Enge-mann, IEEE Trans. Plasma Sci. 33, 310 2005.2X. P. Lu and M. Laroussi, J. Appl. Phys. 100, 063302 2006.3B. L. Sands, B. N. Ganguly, and K. Tachibana, Appl. Phys. Lett. 92,151503 2008.4J. Shi, F. Zhong, J. Zhang, D. W. Liu, and M. G. Kong, Phys. Plasmas 15,013504 2008.5N. Mericam-Bourdet, M. Laroussi, A. Begum, and E. Karakas, J. Phys. D42, 055207 2009.6COMSOL 3.5a COMSOL, Burlington, MA, 2008.7MATLAB 7.4 Mathworks, Natick, MA, 2007.8R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport PhenomenaWiley, New York, 2002.9Y. Sakiyama and D. B. Graves, J. Phys. D 39, 3644 2006.10M. Capitelli, C. M. Ferreira, B. F. Gordiets, and A. I. Osipov, PlasmaKinetics in Atmospheric Gases Springer, Berlin, 2000.11A. Begum, E. Karakas, and M. Laroussi, 61st Annual Gaseous ElectronicsConference, p. 47, Dallas, TX, October 2008.12Y. Sakiyama, D. B. Graves, and E. Stoffels, J. Phys. D 41, 095204 2008.13Y. Sakiyama and D. B. Graves, Plasma Sources Sci. Technol. 18, 0250222009.1.00.80.60.40.20.0normalizedintensity4003002001000-100time [ns]HeN2 (C)N2+(B)( a )1.00.80.60.40.20.0normalizedintensity4003002001000-100time [ns]HeN2(C)N2+(B)( b )FIG. 5. Color online Time-resolved emission profile at r ,z= 0,20 ofhelium, nitrogen, and nitrogen ion by a experiment and b simulation. Theorigin of time is the moment when emission from helium shows the peakvalue.1.00.80.60.40.20.0normalizedintensity-2 -1 0 1 2r [mm]modelexperiment, 20 mm , 40 mmFIG. 4. Color online Time-averaged relative emission profiles from N2SPS. The right half shows simulation results and the left half experimentalresults. The solid lines and circles are results at z=20 mm and the trianglesand dashed lines are at 40 mm.041501-3 Sakiyama et al. Appl. Phys. Lett. 96, 041501 2010 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. 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Finite Element Analysis of Ring-Shaped Emission Profile in Plasma Bullet

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