Nonequilibrium effects in supersonic induction plasma

Nonequilibrium effects in supersonic induction plasmaS. E. Selezneva and M. I. Boulos Citation: J. Appl. Phys. 91, 2622 (2002); doi: 10.1063/1.1432478 View online: http://dx.doi.org/10.1063/1.1432478 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v91/i5 Published by the American Institute of Physics. Related ArticlesZonal flow triggers the L-H transition in the Experimental Advanced Superconducting Tokamak Phys. Plasmas 19, 072311 (2012) Toroidal curvature induced screening of external fields by a resistive plasma response Phys. Plasmas 19, 072509 (2012) Asymmetric error field interaction with rotating conducting walls Phys. Plasmas 19, 072511 (2012) Magnetic bucket for rotating unmagnetized plasma Rev. Sci. Instrum. 83, 063502 (2012) Complex (dusty) plasmas—kinetic studies of strong coupling phenomena Phys. Plasmas 19, 055402 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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JOURNAL OF APPLIED PHYSICS VOLUME 91, NUMBER 5 1 MARCH 2002

Nonequilibrium effects in supersonic induction plasmaS. E. Selezneva and M. I. BoulosPlasma Technology Research Centre (CRTP), Department of Chemical Engineering, Universite´ deSherbrooke, Sherbrooke (Que´bec) J1K 2R1, Canada

~Received 5 March 2001; accepted for publication 12 November 2001!

Supersonic plasma jets find applications in plasma chemistry and plasma processing, metallurgy,experimental physics, and space technology. Usually the plasma in these jets deviates from chemicaland thermal equilibrium. To optimize the industrial process detailed study of nonequilibrium effectsin supersonic flow is required. In the article we apply numerical simulation to study thesupersonically accelerated argon plasma flow downstream of the induction plasma torch. Wecompare the jets exhausting from two different convergent-divergent nozzles by means of atwo-temperature model. The results show that the axial electron number density is rather convectiveflux controlled than recombination-ionization reaction controlled in both cases. However, therecombination resulting in electron gas heating is more essential in the jet flowing from the nozzlewith a higher outlet Mach number. The composition of the jet exhausting from the nozzle with alower outlet Mach number remains almost unchanged~‘‘frozen’’ ! until the end of the first expansionzone. These results confirm that the chamber pressure and the nozzle design changing leads to theinduction plasma jets with different chemical conditions. For low-pressure supersonic plasma, theseconditions vary from frozen to recombining. The conclusion is that depending on the industrialprocess, one can choose the proper torch nozzle geometry to have nonequilibrium plasma with therequired properties. ©2002 American Institute of Physics.@DOI: 10.1063/1.1432478#

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I. INTRODUCTION

In remote thermal plasma configuration,1 the plasma isformed by one of the traditional plasma torches. Passthrough the nozzle, the plasma flows into the depositchamber, where continuous pumping keeps the pressusubatmospheric values. Thus the plasma is accelerated ahigh velocity jet is formed. This technique separates spatithe reactive species formation region of the torch from thetransport region. Due to this separation the control and omization of the deposition process are easier in remplasma reactor comparing with the traditional thermplasma reactors. As an example of remote plasma apptions we can mention the expanding cascaded arc, whichbeen successfully used for the high rate deposition of hydgenated amorphous carbon and silicon,2 diamond, andpolimer-like films. In the present article we address anotexample of this technique, a radio-frequency induction towith supersonic nozzle. A standard subsonic inductivcoupled plasma~ICP! torch is a common tool for plasmprocessing and plasma chemistry. This torch can be qeasily modified to supersonic configuration.3 This configura-tion can give more possibilities for the material processapplications. If the chamber pressure is not low enoughcause sonic expansion, convergent nozzle adjustment ispable to speed-up the flow till the sonic velocity. If thnozzle contains not only convergent but also divergent p~de Laval nozzle!, plasma can reach supersonic velocity atoutlet. In this case a supersonic jet is formed in the expsion chamber. To sum up, the present article contributesthe study of supersonic argon jet flowing from thconvergent-divergent nozzle.

2620021-8979/2002/91(5)/2622/9/$19.00

Downloaded 23 Jul 2012 to 128.143.23.241. Redistribution subject to AIP l

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Interest to supersonic plasma jets appears in 1950thcause of the applications in aerospace industry and expmental physics.4 Since that time, various analytical, numercal, and experimental methods have been applied to ssupersonic plasma. One of the most important analyticalsults was the study of the adiabatic gas expansion from sorifice.5–7 Later it was shown that the results of this study avalid for the initial region of plasma expansion in neavacuum chamber.8,9 Also, a better understanding of the processes governed the plasma expansion was reached stuthe plasma nozzle10–12 and jet13–19 flows. As it was demon-strated,12 an important feature of supersonically expandiplasma is the absence of the local thermodynamic equrium ~LTE!.20,21 The deviations from both thermal anchemical equilibrium have been found. There are severalsons for these deviations in supersonic plasma. First, thepersonic characteristic flow time is very small comparedthe kinetic relaxation time between electrons and heavy pticles while there is a mechanism for preferential heatingcooling the electrons. Unlike the discharge region, whereelectrons are heated by Ohmic power dissipation, in plasexpansion the three-particle recombination with an electas the third body serves this heating mechanism. Secbecause the hydrodynamic and chemical characteristic tican be of the same scale,13 there are deviations from thionization equilibrium in supersonic plasma. The plasmchemistry can reach ‘‘frozen’’ conditions at some point of tnozzle expansion. The chemical nonequilibrium can perwithin the whole supersonic core of the jet as well assubsonic mixing region.

In the article we describe the numerical simulationsthe experiments22 conducted in the University of Sherbrook

2 © 2002 American Institute of Physics

icense or copyright; see http://jap.aip.org/about/rights_and_permissions

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2623J. Appl. Phys., Vol. 91, No. 5, 1 March 2002 S. E. Selezneva and M. I. Boulos

In these experiments the plasma is formed in the ICPcharge by means of a Tekna PL35 torch. The schematithe torch with the supersonic nozzle is shown in Fig. 1,nozzle dimensions are given in Table I. Passing throughconvergent-divergent nozzle the plasma flows into the woing chamber where the pressure valuePch51800 Pa is main-tained. We suppose that the supersonic nozzle design isadjusted to the chamber pressure value. It will be shownfor the considered nozzle configurations, the outlet stpressurePin is in fact higher thanPch, therefore the jetformed can be called underexpanded. Underexpandedare chosen as a subject of the experimental and mathemastudy because these jets are often encountered in prachowever, the complex barrel structure of their supersocore has not been studied yet in detail. For underexpanjets, the pressure ration5Pin /Pch has a significant impacboth on the hydrodynamic structure of the jet core and onphysical properties of the plasma. To illustrate the role ofparametern, we note that its values in our study are differefrom the typical conditions of rather well studied cascadarc expansion. The jets considered in this article areunderexpanded, i.e., the ration is smaller and closer to unityDue to this fact the supersonic core does not representbarrel ended with a normal shock~Mach disk!, after whichthere is a relaxing subsonic flow as in a remote cascadedInstead, the jet core has a number of barrels that are inclto the axis oblique expansion and compression stationwaves.

FIG. 1. Schematic of the induction plasma torch with a supersonic nozThe nozzle dimensions are given in Table I.

TABLE I. Nozzle dimensions.

M51.5 ~m! M53 ~m!

dc 0.012 85 0.004 57do 0.013 88 0.007 96L 0.018 38 0.0215


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In the present article, we apply a two-dimensional~2D!axisymmetric model to simulate remote ICP plasma floThe argon model takes into account kinetic and ionizatnonequilibrium. The computations are performed not ofor the nozzle flow or for the plasma jet flow, but instead fthe nozzle and jet flows as a single entity. Thus the effecthe nozzle design on the supersonic jet core propertiestudied. Although the physical assumptions of the momade are similar to that of the Ref. 23, its 2D characmakes the results more accurate. We would like to emphathe difference between the present model and the modeapproach that can be applied to the configuration with ationary normal shock a the end of the expansion zone. Inapproach one knows the shock position and can setboundary conditions at the shock.24 We use instead a shockcapturing technique, where the shock wave positions, areknown a priori, they should be predicted as a result of tcalculations. Because of the fact that there are several susonic barrels in the computational domain, we study not othe properties of the first barrel, but also the formation ofsecond barrel in nonequilibrium flow.

One should note that the chamber pressure considerethe present study is much higher comparing to the typchamber pressure 20–100 Pa of the cascaded arc expanOur choice of the higher pressure is justified by the fact tit can be maintained using a not very expensive pumpmechanism. The higher chamber pressure justifies theplantation of the continuum mechanics equations formathematical modeling. Besides, due to the higher presthe plasma does not expand much. The average radius ojet is much smaller than the chamber radius. This fact methat the role of the chamber geometry is less important tin an expanding cascaded arc and we do not model the wchamber flow.

The purpose of the article is to compare the plasmaflowing from the supersonic nozzles of two different cofigurations~Table I!. The nozzles were designed using isetropic flow assumption to accelerate argon flow up toM51.5 andM53 values of the outlet Mach number. We shothat unlike the cold gas flow, where a high Mach numberusually associated with a high velocity, in a supersoplasma flow, a high Mach number value can be explainalso by the low static temperature. If high Mach numbewere associated only with high velocities one could expmore frozen chemistry conditions in the plasma jet flowifrom the nozzle with a higher outlet Mach number comping with the plasma jet flowing from the nozzle with thlower outlet Mach number. In reality, however, the tempeture drops more in the nozzle with a higher outlet Manumber than in the nozzle with a lower outlet Mach numbThis temperature drop leads to the recombination and detions from frozen chemistry assumptions.

It is important to understand that the results of tpresent study are applicable to the configurations whereplasma is first formed in the region where the flow velocitylow and the pressure is close to atmospheric one. Becausthese conditions the state of the plasma formed is close toLTE. Downstream of the torch this thermal plasma is accerated and rarefied and the deviations from the LTE oc

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2624 J. Appl. Phys., Vol. 91, No. 5, 1 March 2002 S. E. Selezneva and M. I. Boulos

The described conditions are typical for the induction towith a supersonic nozzle. The same results cannotstraightforwardly applied to the typical configurations of spersonic direct current arc discharges, for examples. In thdischarges the plasma is usually formed inside the supersnozzle, where it is accelerated at the same time. Thismeans that depending on the nozzle design in thesesome deviations from the LTE can be observed even inplasma formation region.

II. NUMERICAL MODELING

A. Gas dynamic model

Although the main concern of the present article isstudy the deviation from equilibrium in supersonic plasmwe would like to summarize briefly the possible gas dynamstructures of the supersonic jet. According to the gas dynics, for a given gas, the nozzle geometry defines the MnumberM and the static pressurePin at its outlet assumingisentropic nozzle flow. For example, with a straight cylindcal nozzle maximal value of Mach numberM51 can beobtained at the inlet to the low-pressure chamber.convergent-divergent nozzle should be used to have awith a higher initial Mach number. Depending on the ratiothe static pressure ration, a variety of jet gas dynamic structures can be obtained from so-called underexpanded~if Pin

.Pch!, perfect~if Pin5Pch! to overexpanded~if Pin,Pch!.The core region of the under- and overexpanded jets is cacterized by the pattern of alternating expansion and cpression zones. It can be supersonic and containing onlylique Riemann waves ~in moderately over- andunderexpanded jets!, or it can have normal shock waves folowed by subsonic regions~so-called Mach diamonds instrongly over- or underexpanded jets!. For very low chamberpressures, the results of the continuum fluid dynamics theare not applicable anymore. The shock waves patchanges. The shock region thickens with the pressdecrease25 and finally disappears in the scattering regimSpecial methods developed in rarefield gas dynamics26,27

should be used to characterize the low-pressure flows.In the present study we assume that the pressure is

enough to describe plasma flow by continuum fluid dynamequations. We incorporated a two-temperature model intooriginally one-temperature computational fluid dynamic coFLUENT ~FLUENT is a registered trademark of FLUENT IncCeterra Resource Park, Lebanon, NH 03766! capable of re-solving both subsonic and supersonic problems.

The system of the governing Navier–Stokes equatiowritten to describe the mean flow properties, is cast in ingral, Cartesian form for an arbitrary control volume,V withdifferential surface areadA as follows:

]

]tEVWdV1 R @FÀG#•dA5E

VSdV,

where the vectorsW, F,andG are defined as


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and S vector can contain source terms such as body forand energy sources.

Herer, V, E, andP are the density, velocity, total energper unit mass, and static pressure of the fluid, respectivelu,y, v, andx,y,zare the velocity components and the coornates in the directions ofi , j ,k coordinate vectors.t is theviscous stress tensor, andq is the heat flux. Total energyE isrelated to the total enthalpyH, or to the static enthalpyh bythe following relations:

E5H2p

r,

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2.

The considered flow is mostly supersonic and the coupbetween momentum and energy equations of the NaviStokes system is very strong. That is why we chooscoupled technique28 simultaneously solving the equationwritten in matrix form. The Navier–Stokes equations bcome numerically very stiff at a low Mach number due to tdisparity between the fluid velocity and the speed of souThe numerical stiffness of the equations under these cotions results in poor convergence rates. This difficultyovercome in FLUENT’s coupled solver by employing a tecnique called time-derivative preconditioning.29 The jet is as-sumed to be turbulent; a realizablek-e model30 was used forturbulence simulation because this model predicts axismetric jet properties better than a usualk-e model.

B. Physical model

Besides the gas dynamic complexity, supersonic jetscharacterized by a number of interesting physical phenoena. In a low-pressure supersonic plasma jet there can babsence of thermal, Saha and Bolzmann equilibrium. Witthe shock region the translational temperature in the dirtion parallel to the jet axis is not equal to the translationtemperature in the direction normal to the jet axis, so teven one Maxwellian distribution function for the axial anradial velocity components does not exist. This phenomeis observed throughout the whole expansion in the scatteregime. It can be explained by the fact that the macroscokinetic energy parallel to the axis transforms first to the mcroscopic energy of random velocity parallel to the axis a


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then to the one normal to the axis. Nevertheless, due tocomparatively high chamber pressure~about 14 Torr! in theconsidered problem, we can simplify the study makingfollowing assumptions:

~1! the velocity distributions of electrons, atoms and heaparticles are assumed to be Maxwellian; the plasmaideal;

~2! the temperature of ions is taken to be equal to the teperature of atoms and is called a heavy particle tempture; this temperature can deviate from the electrons tperature;

~3! the mass fraction of double ions is negligible and onthe first ionization and three particle recombination retions are taken into consideration; and

~4! the quasielectroneutrality assumption is valid, that iselectron number density is assumed to be equal toion number density in every point; self-induced electfield is neglected.

We will use the subscriptsa, ion ande to denote atom, ionand electron values correspondingly. The electron mafraction Ce transport equation in axisymmetric cylindriccoordinatesx, r is written in the form

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whereU is the gas velocity axial component,V is the gasvelocity radial component,r is the gas density,m t is theturbulent viscosity, Sct50.9 is the turbulent Schmidt number, andDamb is the coefficient of ambipolar diffusion31

Damb53kTe/4rV ia ,

where k is the Boltzmann’s constant,V ia52.84310217T0.36 m2/s is the ion-atom collision integral, andT isthe heavy particle temperature.Se is the source term, whichincludes the changes of electron concentration due tothermal ionization and three particle recombination reactiAr1e2↔Ar11e21e2. The expression used for this teris the following:

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where them and C are the species mass and mass conctration respectively,K ion is the ionization rate, andK rec is therate of recombination.32 The electron temperature transpoequation is


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whereTe , ne , andle are the electron temperature, numbdensity, and thermal conductivity correspondingly. The righand side of the equation contains the termEeh representingthe net volumetric energy exchange between the electand the heavy particles, the ionization losses termEiSe, andthe net volumetric radiation losses termR0. The energy ex-change term is calculated as follows:

Eeh53me

maneveh~Te2T!,

whereT is the heavy particle temperature, the elastic cosion frequencyveh is a sum of the electron-atomvea andelectron-ionvei collision frequencies according to the formulas

veh5vea1vei ; vea5nasea~8kTe /pme!1/2;

vei5nesei~8kTe /pme!1/2.

The electron-atom cross-sectionsea is calculated accordingto Ref. 32, the electron–electron collision cross-sectionsee

is assumed to be the same as that of ion-electron33 sei . Theionization loss term containsEI is the argon ionization energy, and electron production termSe.

The volumetric radiation loss34 is represented as a sum:R0

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1.57—line radiation ~line 4p–4s is supposed to bedominant!, here ne5ne/1020, na5na/1024—dimensionlesselectron and neutral densities correspondingly,ne andna areexpressed in 1/m3. In this simple model no absorption iconsidered because only the radiation to the ground stastrongly absorbed. The radiation to the ground state is mematically taken into account in theSe source term. The stateequation can be written as follows:

p5k@naT1ne~Te1T!#,

wherep is the static pressure. Here, the quasineutralityne

5ni) is assumed. In the numerical procedure, each iteraconsists of the following steps: first the continuity, mometum, Ce transport energy, and turbulence equationssolved in a coupled way. Then the electron temperattransport equation is solved and the heavy particle tempture is updated using the calculated data of the mixture stenthalpyh and the composition. The argon material propties are taken from Ref. 35.


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The computational domain used for modeling an asymmetric jet flowing from the convergent-divergent nozzis shown in Fig. 2. The axial coordinatex is calculated fromthe nozzle inlet, the nozzle outlet values correspond tx50.0255 m forM53 nozzle and tox50.0244 m forM51.5 nozzle. The radius of the simulated chamber regioRch50.035 m, the length of the simulated chamber parLch50.08 m. Other dimensions are shown in Fig. 1 aTable I. Boundary conditions set in the present study arefollows. At the nozzle inlet the total mass flow rate 0.001kg/s is given. The constant heavy particle temperature 10K is assumed to be equal to the electron temperatureequilibrium value of the electron number density is assignat the inlet. The turbulence intensity is assumed to be 0.At the wall we use a constant condition for the heavy partitemperature~300 K!, a zero normal derivative condition fothe electron temperature, and nonslip velocity boundary cdition. At the chamber outlet the pressurePc51800 Pa isspecified. The computations start on a nonstructural grid ctaining 9856 cells of two types: quadrilateral and trianguAfter performing several hundreds iterations the grid

FIG. 2. Calculated contours of the Mach number~left part of the figures!and temperature~right part of the figures! for the jet flowing from theM53 ~top figure, for contour values useMm51! andM51.5 nozzles~bottomfigure, for contour values useMm50.650.


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adapted: about 1000 cells are added near the walls and injet region. The calculations proceed using the second oaccuracy scheme until the residuals of all the equationscome less than 1024.

III. RESULTS AND DISCUSSION

A. General structure of the jet

Figure 2 represents the calculated contours of the Mnumber and the heavy particle temperature in the jets flowfrom the nozzle withM53 ~top! andM51.5 ~bottom! jets.It can be noticed that because of the deviation from isenpic flow conditions and because of the effect of viscosity,transition from the subsonic flow to supersonic one occurlittle downstream of the nozzle critical section. Besides,Mach numbers at the nozzle outlets deviate from the pdicted ones by the isentropic assumption. Both jets arederexpanded, because the static pressure at the chambeis higher than the ambient static pressure, as can befrom Fig. 3. The model predicts well all the main featuresa moderately underexpanded supersonic jet. The flow althe jet axis within the computational area is wholly supsonic. By means of the alternating expansion and compsion zones, the pressure tends to equilibrate with the ambchamber pressure. One can see from Figs. 2–3 that theexpansion wave is the strongest one, the further fromnozzle the weaker the oblique waves are until the static psure becomes equal to the ambient chamber pressure.axial velocity rises about 100 times in the supersonic noz~Fig. 4!. It means that the supersonic jet performs a very ftransport of the reactive specie from the torch to the sstrate, providing small residence time.

FIG. 3. Predicted by the model axial profiles of static pressure~in Pas.! arecompared with the ionization nonequilibrium degreene /neq2eq, where theequilibrium values of the electron number densityne2eq, are calculated bythe Saha equation at the electron temperature. The coordinatex is calculatedfrom the nozzle inlet, the nozzle outlet values correspond tox50.0255 mfor M53 nozzle and tox50.0244 m forM51.5 nozzle.


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B. Nonequilibrium effects

Figures 5~a! 5~b! compare the heavy particle temperatuand electron temperature along the jet axis for two nozconfigurations. Both the heavy particles and the electtemperatures drop inside the nozzle. However, as can befrom the figures, the electron temperature does not dropmuch as the heavy particle temperature does. This is ecially true for the nozzle with the higher Mach number. Thigher the Mach number, the more the temperature dalong the nozzle axis, the more essential the recombinabecomes. In three-particle recombination, the electronsthird particles gain the energy. At the outlet of theM53nozzle the electrons are heated more by the recombinathan at the outlet of theM51.5 nozzle. The axial degree othermal nonequilibriumu5Te /T correlates well with the lo-cal Mach number~Fig. 6!. We can conclude that the deviation from the local thermal equilibrium is higher in the epansion regions. In these regions the pressure drops anvelocity rises. In the compression regions, where the presrises and the velocity drops, the electron temperaturecloser to the temperature of the heavy particles.

In the supersonic induction jet, the electron number dsity is rather convective flux controlled than ionizatiorecombination reaction controlled. That is why, its valuesseveral orders of magnitude higher than the equilibrium vues ne2eq calculated by the Saha equation at the electtemperature, and closer to the frozen valuesnfr . One can findthese deviations from ionization equilibrium in the both jeFigure 3 shows the axial profile ofne /ne2eq— the degree ofionization nonequilibrium and Fig. 7 showsne /ne2fr—thedeviation from the frozen chemistry assumption. The axdegree of ionization nonequilibrium is inversely related wthe static pressure~Fig. 3!. Figure 8 shows the degree othermal nonequilibrium in the jet with frozen chemistry. Uing Fig. 7 and making comparison of Figs. 6 and 8 we cconclude that in the jet flowing fromM51.5 nozzle, the

FIG. 4. Predicted by the model velocity axial profiles forM53 and M51.5 nozzle configurations. The coordinatex is calculated from the nozzleinlet, the nozzle outlet values correspond tox50.0255 m forM53 nozzleand tox50.0244 m forM51.5 nozzle.


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chemistry is close to frozen until the end of the first expasion zone, while in the jet formed byM53 nozzle the re-combination is more significant. These facts explain whydeviation from the thermal equilibrium is in general mopronounced in the jet exhausting from theM53 nozzle, thanfrom theM51.5 nozzle.

The thermal energy gained in the compression regionlost in the expansion zones from the kinetic energy transfeproportional to the mass of the particle.36 This fact explainswhy the gas compression and expansion influence moregas of the heavy particles, than the electron gas. The etrons also experience compression and expansion followthe ions due to the electrostatic forces establishing the etron neutrality. Similar to normal shock waves the obliqcompression waves have the structure that consists oflayer dominated by the electron thermal conduction, thinlayer controlled by heavy particle collisions and atom-ishock followed by a relaxation zone.37 The mentioned facts

FIG. 5. Comparison of the calculated electron and heavy particles temptures axial profiles~a! in the M53 configuration and~b! in M51.5 con-figuration.


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result in the more pronounced maximums and minimumsthe axial heavy particle temperature than the corresponelectron temperature, so that even regions with a higheavy particle temperature than electron temperature cancur. There is not enough time for full relaxation after eachthe first several oblique waves so that the next wave forma nonequilibrium gas. It makes the whole jet structure mcomplicated for the theoretical anlaysis.

Figures 9~a! and 10~a! show the heavy particle temperature and radial profiles for the two nozzle configurationThese profiles have the form of the curve with one axmaximum in the compression zones and with off axial mamum in the expansion zone, where the maximum cosponds to the barrel shock wave. The radial profiles ofelectron temperature@Figs. 9~b! and 10~b!# and the electron

FIG. 6. Comparison of the calculated axial profiles of Mach numberthermal nonequilibrium degreeTe /T for two nozzle configurations.

FIG. 7. Calculated axial profiles of the departure from the frozen chemiregimene /ne2fr , where the frozen valuene2fr of the electron number density is calculated by the present model when the ionization-recombinareaction is excluded from consideration.


fg

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number density~Fig. 11! also reflect the position of the compression, expansion zones, and oblique shock waves.can see that the deviation from the thermal equilibriumvery pronounced at the fringes of the jet where the gradie

d

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n

FIG. 8. Calculated thermal nonequilibrium degreeTe /T along the axis inthe flow with frozen chemistry when the ionization-recombination reactis excluded from consideration.

FIG. 9. Heavy particle temperature~a! and electron temperature~b! radialprofiles for the positions~1! x50.005 m, ~2! x50.025 m, and~3! x50.045 m from the nozzle outlet, forM53 nozzle configuration.


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of all macroscopic parameters are very big. Radial profilethe electron number density correspond well with the expmental data.22

IV. SUMMARY AND CONCLUSIONS

To understand the chemical kinetics mechanisms inplasma quenched by the nozzle expansion detailed studthe different deviations from the LTE in that flow is peformed. Argon plasma exhausting from two configurationsthe convergent-divergent nozzles are compared by meanthe numerical modeling. The considered jet core is chaterized by a rather long and strongly nonuniform supersoregion with alternating zones of oblique expansion and copression waves by means of which the static pressure tto equilibrate with the chamber pressure. Along the jet athe deviation from the thermal equilibrium is more essenin the jet flowing from the nozzle with the higher Macnumber. This fact is due to the increased role of the recobination resulting in the electron gas heating. Thereforeconclusion can be made that the nozzle design and cham

FIG. 10. Calculated heavy particle~a! electron temperature~b! radial pro-files for the positions~1! x50.005 m,~2! x50.025 m, and~3! x50.045 mfrom the nozzle outlet, forM51.5 nozzle configuration.


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pressure changing lead to the plasma jets with different prerties. The chemical conditions in these jets can be infollowing range:

~1! equilibrium ~when one uses the atmospheric presschamber and a straight cylindrical nozzle!;

~2! frozen ~when one uses low Mach number nozzle amoderately subatmospheric chamber pressure!; and

~3! recombining~when one uses high Mach number nozzand moderately subatmospheric chamber pressure oany nozzle when very low chamber pressure is used!.

In general, the results prove that the supersonic configuraof the induction plasma allows avoiding the ionization~andpossibly dissociation! processes downstream of the torcThis configuration can spatially separate the different futions of the plasma source such as the dissociation andization of the original material, transport of the producreactive particles towards the substrate, and surface procing. We can conclude, that in this configuration one can e

FIG. 11. Radial profiles of the electron number density for the positions~1!x50.005 m~2! x50.025 m, and~3! x50.045 m from the nozzle outlet,~a!for M515 nozzle configuration and~b! for M53 nozzle configuration.Predicted by the present model values of electron number density arepared with the measurements~see Ref. 22! performed forM53 nozzleconfiguration.


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ily control the properties of the plasma jet in the transpregion by choosing the appropriate nozzle design.

ACKNOWLEDGMENTS

Financial support by the National Sciences and Enneering Research Council of Canada and the MinistryEducation of the Province of Quebec is gratefully acknoedged.

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Nonequilibrium effects in supersonic induction plasma