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Plasma generation in vibrationally nonequilibriummolecular gas flows

O.V. Achasov, N.A. Fomin, D.S. Ragozin, R.I. Soloukhin, S.A. Zhdanok

To cite this version:O.V. Achasov, N.A. Fomin, D.S. Ragozin, R.I. Soloukhin, S.A. Zhdanok. Plasma generation in vibra-tionally nonequilibrium molecular gas flows. Revue de Physique Appliquee, 1982, 17 (1), pp.15-20.�10.1051/rphysap:0198200170101500�. �jpa-00244963�

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Plasma generation in vibrationally nonequilibrium molecular gas flows

O. V. Achasov, N. A. Fomin, D. S. Ragozin, R. I. Soloukhin and S. A. Zhdanok

Heat and Mass Transfer Institute, Minsk 220728, USSR

(Reçu le 2 juin 1981, révisé le 15 septembre 1981, accepté le 12 octobre 1981)

Résumé. 2014 L’ionisation associative des molécules N2 et CO en refroidissement adiabatique après chauffage entube à choc est étudié expérimentalement et théoriquement. On montre que dans un large intervalle de conditions,la contribution des méchanismes d’ionisation associative dépasse considérablement (de plusieurs ordres de gran-deur) la contribution thermique.

Abstract. 2014 Experimental and theoretical studies are made of the associative molecular gas ionization phenomenain N2 and CO under the adiabatic expansion and cooling of a shock-heated gas. It is shown that for a wide rangeof conditions, the contribution of the associative ionization mechanism substantially exceeds (by several ordersof magnitude) the thermal one.

Revue Phys. Appl. 17 (1982) 15-20 JANVIER 1982, PAGE 15

ClassificationPhysics Abstracts47.40K - 52.90

1. Introduction. - Ionization processes in mole-cular gases are of great importance in the develop-ments of high-power gas lasers as well as in plasmachemistry, high-temperature gasdynamics and atmo-sphere physics. Ionization due to electron impactand photoionization are widely met in experimentswith high pressure glow discharges in molecular

gases and are at present well understood [1]. It hasbeen stated in [2] that an associative molecular gasionization may occur as a result of the vibrationally-excited molecule collisions according to a scheme :

if

where A(v) is the molecule in the v-th vibrationalstate with energy E(v) and E; is the ionization energy.(AA) + and A + are the complex and ordinary ions ofa molecule A. The recombination reaction step,inverse to (1), contributes to the electron balance inthe gas discharge plasma and is well known experi-mentally [3]. The investigation of the direct reaction (1)in the electric discharge involves considerable diffi-culties connected with a great variety of plasmachemical reactions which results in molecule ioniza-

tion, and a contribution of this particular reactionis difficult to separate among a great number of

possible ionization mechanisms in the experiments.The associative ionization can be more correctly

studied by measuring the molecular gas conductivityunder high vibrational excitation conditions in the

REVUE DE PHYSIQUE APPLIQUÉE. - T. 17, N° 1, JANVIER 1982

absence of any other sources of charged particles.These conditions can be easily implemented underthe fast adiabatic expansion of molecular gases in asupersonic nozzle flow. In this case, since the vibra-tional-translational (Y-T) relaxation time stronglydepends on gas temperature, the vibrational energysubstantially exceeds the translational and rotationalones. As the test gas is significantly cooled due tothe adiabatic expansion, the thermal ionization degreeunder these conditions is negligibly small, and thereaction (1) becomes the only possible electronsource. The first experiments on the associative

nitrogen ionization observations under the adiabaticnozzle expansion have been reported in [4]. Theresults obtained have confirmed the existence of theassociative ionization mechanism based on the vibra-tionally excited molecules interaction and shown itshigh efficiency. The present study is devoted to a

systematic investigation of the associative ionizationreactions in expanding flows of CO and N2. The dataobtained are compared with the corresponding avai-lable expérimental data obtained under the gasdischarge plasma conditions in N2 and CO.

2. Experimental. - The schematic of the pulsedgasdynamic installation used for studying quasi-steady vibrationally nonequilibrium gas flows waspresented in [5, 6]. The shock tube, 5 x 5 cm2 in

cross-section, was utilized to provide an adiabaticcompression of a test gas up to pressures of 3 to30 atm and temperatures in the range of 1 to 6 x 103 K..The quasi-steady flow time developing in the shock

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:0198200170101500

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tube end section, at the test gas (N 2, CO) pressuresof 0.03-0.1 atm. in the shock-tube expanding flow,was about 0.1 to 0.2 ms while that of a steady-flowwas 0.5 to 1 ms. The nozzle section was separatedfrom the main shock-tube channel by a thin hatchedcopper diaphragm and was pre-evacuated, whichensured a rapid quasi-steady development and sub-stantial increase in its working time [5]. The stagna-tion temperature and pressure of a shocked gasbefore expansion were determined with the use ofthe shock adiabatic relations at the given measuredshock velocity.The nozzle design and its parameters were similar

to those utilized in the gasdynamic laser experi-ments [6]. The nozzle throat height was 0.55 mm, theexpansion area ratio A/A * was equal to 52, and theoutput flow Mach number was equal to 6. The sharp-edge fast expansion Prandtl-Meyer nozzle, 5 cm inlength, was connected with the constant cross sec-tion shock tube channel. Such a nozzle design canprovide a fast decrease in the translational gas tem-perature in the nozzle throat area, at the uniform flowconditions, and hence it possesses the highest effi-

ciency for the vibrational energy freezing process.The constant area shock channel walls were made ofdielectric (textolite), in which the round 1 cm dia,copper, electrodes were installed (Fig. 1).

Fig. 1. - Schematic of the installation : 1, métal nozzle ;2, dielectric constant-cross section channel; 3, measuringelectrodes and typical oscilloscope records of measuringgas conductivity.

The plasma conductivity was measured by record-ing the semi-self-maintained current at the gap vol-tage of about 100 V. Note that the electrostatic effectshave caused parasitic signals on the oscilloscoperecords even with no electrode voltage applied. The

Fig. 2. - Current-voltage characteristics of measuringschemes; the stagnation temperature is 4 000 ± 150 K (1),2 250 ± 100 K (2), 2 800 ± 150 K (3) ; stagnation pressureis 10 ± 1 atm (1), 7 ± 1 atm (2), 9 ± 1 atm (3). The mea-suring electrodes are located at a distance of 8 (1, 2) and14 (3) cm from the nozzle throat. The gas in the plenumchamber is N2 (1, 2) and CO (3).

magnitude of these signals was measured and control-led on the identical measuring electrode pair andamounted to 10-2-10-1 of the main measured

signals. Figures 1 and 2 display typical oscilloscoperecords of current and current-voltage characteris-tics.

In the experiments, the gas flow velocity was about2 x 105 cm/s, whereas the electron drift velocity wasevaluated to be considerably higher, 2 x 106 cm/s.Since the ion drift velocity is substantially less, theelectron concentration in the expanded gas flow maybe evaluated as :

where S is the cross-section of an electrode and thevalue of the electron drift velocity vde(E/N ) for nitro-gen and carbon monoxide was determined in [7, 8].

It seems that ne calculated from eq. (2) may beunderestimated because of the ions space charge. Onthe other hand, the nonuniformity of the electricfield between electrodes leads to the overestimationof the electron density. Nevertheless, there seems to beno doubt that eq. (2) would give at least the correctorder of the value of ne-

Figures 2 through 6 show the values of ne measuredby the above method in adiabatically expanding N2and CO flows as well as the current-voltage charac-teristics. As is seen in figure 2, the current-voltagecharacteristics of gases are in agreement with Ohm’slaw, which points to the fact that eq. (2) is valid underthese experimental conditions. Figures 3a and 3bpresent the electron density as a function of the gas

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Fig. 3. - Logarithmic variation of electron concentration,ne, as a function of the inverse stagnation temperature fornitrogen (a) and carbon monoxide (b) at a stagnation pres-sure of 8.5 ± 1 atm (a) and 9.5 ± 1 atm (b) and at a gapvoltage of 100 V. The measuring electrodes are located ata distance of 14 (1) and 8 (2) cm from the nozzle throat.The dotted lines denote the electron density as a functionof the temperature of a thermally ionized gas in the plenumchamber calculated by the Saha formula.

stagnation témperature. When nitrogen served as atest gas (Fig. 3a1 the experimental dependencene(T0) is well approximated by the Arrhenius law,ne ~ exp( - E/T o), where the effective activation ener-gy is about 1 eV. The flow gas temperature is T N 0.1To, i.e. considering the ionization process at this

temperature evaluates the effective activation energyas Ea N 0.1 eV. The latter is in good agreement withthe results of [2] where the relation

was obtained for the rate constant of the associativeionization (1) based on a gas temperature, T, for

nitrogen. Figure 3a gives the comparison of the

experimentally measured ne with those calculated

by the Saha formula for a gas temperature correspond-ing to the stagnation one and the density equal tothe gas flow one. The coincidence of the expérimentaldata and the Saha equilibrium calculations at gastemperatures To > 4 x 103 K witnesses a negligiblysmall contribution of the electron losses in the whole

gasdynamic channel, which agrees with the data of[9, 10].The analysis of a temperature dependence ne(To)

for carbon monoxide (Fig. 3b) shows that, unlikenitrogen, the pronounced exponential law is not

observed in this case and at To > 2 000 K the elec-tron concentrations reach saturation ; at To > 4 000 Kthis law is governed by the exponential dependenceconsistent with the Saha equation. As is seen in

figure 3b, the electron concentrations at To > 4 000 Kare below the equilibrium ones, which points to

electron losses in the course of expansion.

3. Theory and discussion. - The vibrational energyof a molecule plays an important role in associativeionization processes. For instance, the reaction (1),with nitrogen used as a test gas, may proceed onlywhen the nitrogen molecules are populated up tothe 32nd vibrational energy level. Since the popula-tion of the appropriate states is negligibly small evenat a temperature of several thousands degrees, thereactions of the type (1) may be provided and studiedonly under substantially nonequilibrium conditions.Therefore, in the present work, the adiabatic nozzleflow expansion of a preheated shock-tube compressedgas is used to attain these conditions. The vibrationalrelaxation processes proceeded in the adiabatic nozzleflow expansions are detailed in a number of theoreticaland experimental works (cf. Review in [11]). One ofthe results has shown the role of the molecule vibra-tion anharmonicity in the course of relaxation andvibrational level energy re-distribution. The diffe-rence in the vibrational relaxation times measuredbehind a shock wave and in the adiabatically expand-ing gas flow has proved to be caused by a substantialpopulation of the upper vibrational energy levelsdue to specific V-V transfer processes under signifi-cant séparation of the vibrational and translationaltemperatures, Tv and T, in the nozzle expansion expe-

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riments. For the molecules modelled by the anharmo-nic oscillator this population is possible due to thedifférence in the energies of the vibrational quantaof the molécules participating in Y-V transfer proces-ses. If in direct processes the energy is released equalto the quantum energy difference then in inverse pro-cesses it must be compensated by the translationalone. With the condition Tv ~ T satisfied, the ratesof the appropriate processes differ by the factor

ex AE where l1E is the anharmonicity energy.

As a result, the nonequilibrium vibrational distribu-tion is formed that significantly differs from the Boltz-mann distribution.The theory developed in [12] may be adopted to

find the vibrational molecule distribution, f(v), underthe nozzle expansion conditions. According to thistheory, in the kinetics equations a set of the quantumvibrational numbers, v, is replaced by a continuousvariable. In this case, the system of the kinetics equa-tions for the evolution of f(v) is substituted for aone-differential equation which is similar to theFokker-Planck one. The analysis of this equationfor the pulse excitation of molécule vibrations withthe energy 60 has shown that for the upper vibrationallevels, f(v) is of the form given in [12] :

t

where r = v

dt and v is the effective frequency of0

the Y-V transfer. As the frozen gas flow under thenozzle expansion, when the vibrational energy is notthermalized, is similar to the pulse excitation of thelower vibrational states, the solution of (3) will be alsovalid for the gas expansion conditions. In this case, eowill stand for the frozen vibrational energy that canbe found from :

where e(x) and 03C4V - T(x) are the equilibrium vibratio-nal energy and V-T relaxation time, respectively,for the gas parameters in the test nozzle cross sectionx ; u is the flow velocity ; x* is the freezing cross sectioncoordinate. For the flow parameters typical of GDLs,the coordinate x* practically coincides with the nozzlethroat position. The value of T in eq. (3) for the effec-tive number of the V-V transfer processes under the

nqple expansion depends on the supersonic nozzlex

geometry and it is determined by i = ( v/u) dx.x

As follows from eq. (3), for the population of a vibra-tional state with the number v, the value of z shouldexceed r = (v + 1)2/12 03B50, and then considerableupper vibrational level populations may be created bychoosing proper nozzle parameters. Thus, for N2

flowing in the nozzle at Po = 10 atm, To = 2 500 Kand the expansion area ratio corresponding to a flowMach number of M = 6, f(32) ~ 10-4 may beattained in accordance with eq. (3). It should be notedthat the energy evolution effects of highly ionizedvibrational levels at constant stored vibrationalenergy were considered in [13] where the studies weremade of the inversion properties of molecular crystalsunder excitation conditions. Equation (3) allows deter-mination of the vibrational distribution functionin the absence of any excitation sources, which istypical of the adiabatic nozzle expansions.A knowledge of f(v) allows determination of the

electron concentration rates in the gas flow due to theassociative ionization mechanism (1) :

where N is the gas density ; K the constant of theprocess rate (1); vo is determined by E(v0)=Ei/2and v** is the vibrational quantum number, at whichthe rates of the V-V and V-T processes are equal.’The value of K was evaluated in [2] by analysing thedata in the case of a glow discharge in nitrogen. It was

found that K 3.5 ext(-1 160 T) x 10-15, cm3/s.Assuming (v** - v0) ~ 1 and allowing for this flowrate constant, it is easy to obtain from eq. (5) thatqvi ~ 1012 cm-3 s-1.The electron concentrations are determined by the

simultaneous action of source (5) and sink due to therecombination and attachment. With these processestaken into account, the equation for the gas ioniza-tion degree a may be given as :

where y and fl are the coefficients for the attachmentand volumetric recombination, respectively.The values of y and fl in eq. (6) are strongly affected

by the gas impurities and depend on the kind of theions appearing in reaction (1). So, under the adiabaticnitrogen expansion the constants fi for Ni and N’ions differ by the order of magnitude and the elec-tronegative impurities (02, CN, Fe(CO)5) availablein a gas may, by several orders, change the value of thecoefficient y. Therefore, équation (6) must be analysedwith ahowance for the specific experimental conditions.With the pure nitrogen flow from the nozzle, as thesimple estimâtes show, all mechanisms of electronlosses for a characteristic time of about 10-4 s maybe neglected. In this case, equation (6) easily gives :

The evaluation of the above gas flow parametersusing eq. (7) yields ce = 10-9, ne ~ 108 cm-3, which

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Fig. 4. - Semi-self-maintained current for the CO flowas a function of the distance from the nozzle throat at a gapvoltage of 100 V. The stagnation temperature is2 800 ± 150 K and the stagnation pressure is 10 ± 1 atm.

is many orders of magnitude higher than the equili-brium values of the flow parameters even in the ple-num chamber. Since at present there are no suitablemethods for measuring electron concentrations, withsuSicient accuracy, at a level of about 108 cm-3,the associative ionization effects can be experimentallychecked employing a simple estimation of ne from thedata on gas conductivity in the constant electric

field, Eo. The value of Eo is limited by a demand forthe absence of the impact ionization in the gas flow.This demand is fulfilled when the value of the parame-ter, Eo/N, for the electron energy is less than10-1S V cm2, which yields Eo 100 V/cm for theabove nitrogen flow parameters. Experiments weremade just adopting these parameters for Eo/N.

Finally, one must consider possible mechanismsof electron losses in the CO flow. The presence of

exponentially increasing ne(T0) on the curve sectionwitnesses that the main mechanism of electron lossesis connected with the attachment because otherwisethe volumetric recombination would give a weakdependence of ne on To. The analysis of the functionne(x) (Fig. 4) confirmes that the attachment processesare predominant in the CO flow. As the value of nefalls approximately as much as a factor two at a dis-tance of 17 to 24 cm downstream and assuming thatthe volumetric recombination is the main mechanismof electron losses, the condition fi > 2 x 10-5 cm3 s-1would be satished for fi, which substantially exceedsthe known values of fi for CO+ and C2O2 ions. In [14],it has been emphasized that even a small amount ofFe(COs) usually available in CO when stored inmetal vessels and having y - 10-9 CM3 s may favoura strong electron attachment. Assuming that in ourcase the electron losses are caused by this mechanismthe estimation of il > 10-4 may be obtained for

Fe(CO)5 concentration.Evaluation of the vibrational level populations

with v0 ~ 29 using eq. (3) in CO gives negativevalues of f(vo). This points that the rates of the V-Vprocesses are small, and the excitation wave governed

Fig. 5. - Measured current in the CO flow as a functionof the stagnation pressure at a temperature of2 600 + 150 K in the plenum chamber and at a gap vol-tage of 100 V. The measuring electrodes are located at adistance of 14 cm from the nozzle throat.

by eq. (3) cannot achieve the vibrational energy levelswith v - vo. However, the experimentally observedelectron concentrations occur due to a nonequili-brium ionization process.

This difference can be attributed to the approxi-mate nature of the analytical theory [12], to an inexactchoice of the V-V transfer constants or the otherionization sources existing in the flow and connectedwith the vibrationally excited CO molecules (e.g.when the foreign impurities are present in the flow).In some experimental runs a small amount of mole-cular hydrogen, that favours a strong CO moleculeV-T relaxation, was injected into the supersonic COflow with a low translational temperature (see Fig. 6).This practically cancelled the charged particles con-centration in the flow, which points out the predomi-nant role of the vibrational CO molecule excitationin ionization processes.The electron concentrations were also measured

using the same parameters in Ar, Xe, 02 flows to checkthe measuring schemes and to evaluate the thermalionization effects. No electric current was recordedin any of these gases within the framework of the

sensitivity of the method and cannot be indicative

Fig. 6. - Measured current in the CO flow as a functionof the pressure of hydrogen injected into the supersonicsection of the nozzle.

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of electron concentrations at a level of 10’ cm- 3 andabove. This fact emphasizes that the anomalous-

high conductivity of N2 and CO is indeed observedin the supersonic adiabatically expanding nozzleflows.

4. Conclusion. - The observed effects of highnonequilibrium electron concentration and plasmageneration in the thermally excited and vibrationallyfrozen molecular gas states can be widely utilized innumerous applications of molecular and laser physics,namely, for an active medium pre-ionization in anelectric discharge flowing laser, in the electric sub-excitation effects in the gasdynamic and chemicallasers, to serve as a diagnostic tool in evaluations ofthe GDL energy losses due to energy re-distributionin the upper vibrational levels, to develop electron

and molecular beams using gasdynamic methods,etc. Moreover, the use and allowance for this kind ofthe ionization mechanisms in a relaxing gas flow maybe predominant to describe thç phenomena in manyhypersonic gasdynamics and plasma chemistry pro-cesses when anomalously high electron concentrationsappear in the gas flow past vehicles moving at cosmicvelocities. The effect of electrons, ions and highlyvibrationally excited molecules on the mechanismsof chemical and plasma chemical reactions can be wellpronounced, too.

Acknowledginents. - The authors wish to acknow-ledge many helpful discussions with Drs. A. P. Napar-tovich and A. N. Starostin. Special appreciation is

expressed to V. N. Kamyushin and A. M. Orishichfor their valuable comments.

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