JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 11 1 JUNE 2000

Populations of excited atomic states along argon surface-wave plasmacolumns at low and intermediate pressures

C. Lao, A. Gamero, and A. SolaDepartamento de Fisica, Universidad de Co´rdoba, E-14071 Co´rdoba, Spain

Ts. PetrovaFaculty of Physics, Sofia University, BG-1164 Sofia, Bulgaria

E. BenovaDepartment of Physics, Institute for Foreign Students, BG-1111 Sofia, Bulgaria

G. M. PetrovInstitute of Solid State Physics, Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria

I. Zhelyazkova)

Faculty of Physics, Sofia University, BG-1164 Sofia, Bulgaria

~Received 12 August 1999; accepted for publication 21 February 2000!

The axial distributions of the electrons and 3p54s and 3p54p excited atoms in argon plasmacolumns sustained by traveling electromagnetic waves have been studied both experimentally andtheoretically in the gas pressure range of 0.2–2.8 Torr. Various diagnostic methods~surface-waveinterferometry, emission and absorption spectroscopy! have been used in data gathering. Thetheoretical model includes a self-consistent solution to the electron Boltzmann equation, electronenergy balance equation, a set of balance equations for excited atoms and charged particles, the gasthermal balance equation, the wave dispersion relation, and the wave energy balance equation. Theagreement between experimental data and theoretical results is very good. ©2000 AmericanInstitute of Physics.@S0021-8979~00!00411-4#

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I. INTRODUCTION

In the past 2 decades, surface-wave produced plasattracted increasing interest in both technological appltions and fundamental research. This type of discharge ofan efficient way of creating plasma over a wide rangevariation in the characteristics both of the discharge andthe wave. An additional advantage of these dischargetheir comprehensive modeling which has led to significprogress in the understanding of the high-frequency~hf!plasmas in general.

Among the articles devoted to studying the physicsargon plasma columns sustained by traveling electromnetic waves there are only a few considering the excstates of the argon atom and most of them study the radistributions. The first measurements of the radial numdensity profile of metastable atoms in argon plasma pduced by hf surface waves were done by Moisan aRicard.1 They show that in surface-wave discharges a lavariety of excited atom number density profiles can betained that are of interest in applications~for example, gaslasers and lighting!. Recent experiments2 on the radial distri-bution of radiative states performed in argon in the pressdomain from 50 mTorr to 1 Torr in the 200–900 MHz frequency range investigated by optical emission spectrosc~using a tomography technique to obtain spatial resoluti!show the influence of both the wave frequency and the

a!Author to whom correspondence should be addressed; electronicizh@phys.uni-sofia.bg

7650021-8979/2000/87(11)/7652/8/$17.00

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pressure on the radial profiles of emission intensity fromradiative state at a constant cross section averaged elenumber density. More specifically, at a gas pressure ofmTorr the increasing frequency generates wider profiNote that such profiles were modeled theoretically inearly 1980s.3 The radial distribution of long-lived states wastudied in a surface-wave discharge at 600 MHz by usdifferent techniques,4 namely the spatial integration technique ~the so-called end-on measurements! and line absorp-tion measurements—the latter yielding absolute number dsities of excited atoms instead of relative concentrationsobtained from line emission recordings. One observesthe radial distributions of the3P2 metastable and1P1 reso-nant states for the surface-wave plasma are flatter as cpared with those in the positive column of a dc dischargethe maximum values attained radially do not differ markedWe conclude our review on the radial distributions of excitargon atoms by noting that a larger yield of metastable atocould, under certain circumstances, increase the reactionin plasma chemistry while the flatter radial distributionresonant state atoms in a surface-wave plasma could leamore efficient~UV! radiation compared to that from a postive column plasma.

The plasma sustained by a traveling electromagnwave is not only radially but also axially inhomogeneousthe plasma density decreases going away from the wlauncher. The electron number density axial distributionlow gas pressures has been widely studied both experimtally and theoretically.5 At such pressures the main proceof electron creation is the direct ionization from the grouil:

2 © 2000 American Institute of Physics

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7653J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lao et al.

state. With the pressure increasing, the contribution of swize ionization and, respectively, the role of excited atomincreases. As it has been pointed out by Sa´ et al.6 for nor-malized pressures of about 500 mTorr cm the discharge cacteristics for argon may be considerably modified byexcited atoms. The role of the excited atoms on the chateristics of a surface-wave sustained argon plasma columthe pressure range from 100 to 600 mTorr in a glass twith a radius of 1.4 cm at a wave frequency of 130 MHz hbeen investigated by Bo¨hle and Kortshagen.7 In this article,dependences of the population of the 4s argon levels on theplasma density have been reported. It is shown that for psures higher than 300 mTorr the stepwize ionization isdominant process. The authors offer a theoretical mowhich, in fact, being based on a collisional–radiative mofor an argon positive column proposed by Ferreiraet al.,8

yields a very good agreement with the experimental msurements.

A theoretical study of discharge characteristics ofnonequilibrium argon plasmas performed by Cotrino aGordillo-Vazquez9 from a three-level atomic model assuming a Maxwellian electron energy distribution functio~EEDF! yields the population number densities of the fiargon excited state (3p54s levels considered as a block! as afunction of the electron number density in a wide gas prsure range~from 0.28 to 10 Torr!. The first self-consistenmodel giving the axial distributions of the population of ecited 3p54s argon states has been recently proposedBenovaet al.10 This model uses a configuration of the argatom excited states identical to that of Bo¨hle andKortshagen7 ~or to the original scheme of Ferreiraet al.8!,assuming a Maxwellian EEDF. An improved model11 em-ployed in the present work includes a self-consistent soluto the electron Boltzmann equation, the electron energyance equation, a set of particle balance equations for etrons, excited atoms, atomic and molecular ions, gas tperature balance equation, as well as Maxwell’s equatiwith appropriate boundary conditions. It is the theoretibackground of our article and is exposed in Sec. II. SecIII offers a description of the experimental setup and plasdiagnostic methods. A presentation of both theoretical resand experimental data accompanied with a discussion isported in Sec. IV. The conclusion~Sec. V! summarizes thearticle content.

II. THEORETICAL PART

The model is based on the simultaneous numerical sing of a complete set of kinetic and electrodynamequations:11 the electron Boltzmann equation, the electrenergy balance equation, a set of particle balance equafor electrons, excited argon atoms, atomic and molecions, the gas temperature balance equation, the local wdispersion relation, and the wave energy balance equati

The EEDF, obtained by solving the electron Boltzmaequation, is assumed to be time independent becausewave frequencyv is larger than the energy relaxation frquency and the condition for stationarity12 is fulfilled. Theheating of the electrons by the hf wave electric field is tak

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into account in the Boltzmann equation through the effectelectric field frequently used in the literature

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whereE0 is the radially averaged wave electric field for sutaining the discharge,v is the wave angular frequency,nc isthe electron–neutral collision frequency for momentutransfer, andu is the electron energy.

We consider that argon level configuration in which tAr(3p54s) four levels~two metastable and two resonant! aretreated separately and the Ar(3p54p) as one lumped blockof levels ~Fig. 1!. It is applicable at gas pressures up to feTorr at degrees of ionization less than 1022. Those involvedin the model ionization processes for electron creationthe direct ionization, stepwize ionization, Penning, and asciative ionization13–16

Ar~m!1e→Ar11e1e, m51S0 , 3P2 , 3P0 , 3P1 , 1P1, 4p

Ar~m!1Ar~m!↗Ar11Ar1e, m53P2 , 3P0

↘Ar211e, m53P2

.

The loss of electrons is due to diffusion and dissociatrecombination

Ar211e→Ar~4p!1Ar.

The contributions of the other kind of recombination prcesses are negligibly small and are not taken into accoThe diffusion frequency isndiff[(m/R)2Da , whereR is theplasma column radius,Da is the ambipolar diffusion coeffi-cient, andm52.405 assuming a Bessel radial number densprofile of the charged particles.

The balances of heavy particles~excited atoms and ions!are governed by the following processes: diffusion towall, excitation from the ground state14,17

Ar~1S0!1e→Ar~m!1e, m53P2 , 3P0 , 3P1 , 1P1, 4p,

electron impact excitation and deexcitation between excstates13,18–22

Ar~m!1e↔Ar~q!1e, m,q53P2 , 3P0 , 3P1 , 1P1, 4p,

FIG. 1. Energy levels’ diagram of the argon atom.

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7654 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lao et al.

molecular ion formation23

Ar112Ar→Ar211Ar,

and radiative transitions with accounting for the trappingradiation in all allowed radiative processes undconsideration.11 The references associated with a particuprocess give cross sections or rate coefficients. The full sebalance equations can be seen in Ref. 10.

The heavy particle kinetics is coupled with the electrkinetics in a self-consistent way in order to satisfy all balanequations, allowing us to determine the populations ofexcited states and atomic and molecular ions’ number deties at a given electron number densityne .

The electrodynamic part of the model describespropagation of an electromagnetic wave of a constant anlar frequencyv in the ionized medium by Maxwell’s equations with appropriate boundary conditions. The hf plaspermittivity ep is derived from the simplest model of a coweakly collisional electron plasma with an effectivelectron–neutral collision frequency for momentum transneff ,v

ep512vp

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wherevp5A4pe2neff /m is the electron plasma angular frequency andneff is the effective electron number density24

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The effective electron–neutral collision frequency for mmentum transfer

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has been introduced since for argon it is energy dependUnder these assumptions, one gets the basic equations oelectrodynamic part of the model—the local wave dispersrelation and the wave energy balance equation.11 The disper-sion equation

D~v,R,ep ,ed ,g,h,k!50, ~1!

with the geometric factorsg5Rd /R andh5Rm /R ~whereRand Rd are the internal and external radii of the dielecttube, respectively, andRm is the metal screen radius! yields arelation between the electron number density (ne or neff! andthe wave numberk at a given axial positionz— the so calledphase diagram. The wave energy balance equation reads

dS

dz52Q, ~2!

where S is the wave energy flux being a sum of the axcomponents of Poynting’s vector averaged over the wperiod 2p/v and integrated over the plane normal to tplasma column, from the axis to the metal screen radiusthe given axial positionz:

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Herep, d, andv denote plasma, dielectric, and vacuum, rspectively, and

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is the axial component of the Poynting’s vector. The wapower per unit column length absorbed by the electrons

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where the angular brackets mean averaging over the wperiod and

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is the radially averaged squared wave electric field.The self-consistent link between kinetic and electrod

namic parts of the model is accomplished by the electenergy balance equation: the absorbed powerQ should equalthe power expended in elastic and inelastic collisions—tbalance equation consequently takes the form

Q5pR2neu, ~5!

whereu(ne) is the mean power required for sustainingelectron–ion pair in the discharge. It is calculated in thenetic part@for details see Eq.~2! in Ref. 11#.

Solving the wave energy balance equation~2! togetherwith the electron energy balance equation~5! and the localwave dispersion relation, Eq.~1!, we derive the axial distri-butions of the plasma density, the wave number, andwave field components. This enables us to derive the adistributions of all plasma characteristics that have beentained as functions ofne in the kinetic part.

III. EXPERIMENTAL PART

A. Experimental setup

Surface-wave plasma columns have been producedPyrex cylindrical tube (R50.45 cm, Rd50.6 cm, ed54.8)by coupling the 2.45 GHz hf energy via a surfatron-tylauncher25 to produce the azimuthal (m50) mode. The tubewas surrounded by a metal screen of radiusRm52.0 cm.Argon gas is used in the discharge at five work pressunamely 0.2, 0.5, 1.1, 1.8, and 2.8 Torr~low and intermediatedomain!, and the absorbed power in the discharge is fixed100 W, the lengths of the columns ranging from 40 to 58depending on the gas pressure. Compared from their ecolumns produced by different powers are equivalent in sa way that the total power dissipated in producing the dcharges is not a relevant parameter but the axial positiozalong the columns measured from their common ends,only difference among them being their total lengths whgrow with hf power at the launcher side.26 Figure 2 shows ablock diagram of the discharge production and the diagnosetup which also includes optical elements for spectroscomeasurements~lens, optical fiber, analog to digital convertemonochromator, etc.!. A PC controls the whole sequencemeasurements.

7655J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lao et al.

FIG. 2. Block diagram of the experi-mental setup.

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B. Diagnostic methods

Various diagnostic methods have been employed inwork that will be described briefly. For determination of thaxial ~in z direction! electron number density profiles, a weknown technique previously reported27,28 has been used. Bymixing a signal picked up by an antenna along the propation z direction from the progressing surface wave producthe discharge and a sample~attenuated! signal coming fromthe hf power supplied by the generator, a signal proportioto cos(kz2f0) is achieved, wherek52p/l is the wave num-ber andl is the wavelength of the azimuthal surface-wamode. The phase diagram obtained by solving the local wdispersion relation, Eq.~1!, is used to obtain a radially averaged plasma density at eachz position of the column oncelhas been experimentally measured.

Spectroscopic diagnostics for determining the absopopulations of some excited levels in the argon atomic etation space, notably 4s and 4p levels, are used. The lighspontaneously emitted by the plasma is collected ontooptical fiber connected to the monochromator entranceby focusing with a lens a 1:1 image at eachz position alongthe column. In this manner, the ‘‘apparent’’ populatiomeasured correspond to the brightest~central! part of thecolumn. Different intensity lines corresponding to opticelectron transitions involving the studied atomic levelsmeasured.

For determining the population of some 4p excited lev-els, an intensity-calibrated ribbon lamp is used in ordermeasure the absolute line intensities corresponding todeexcitation of such levels, and then to find out their polations. The spectroscopic parameters of the transitions uare listed in Table I. For the 4s levels, a self-absorptiontechnique modified with respect to previously reported o

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is applied.29,30 To obtain the metastable and resonant ablute population, quotients between the relative intensitiestwo emission lines produced by deexcitation to two 4s levels~resonant or metastable! from two other higher excited level(4p) are done. The method is suitable provided that thecillator strength of the one of aforementioned lines is mularger than the other, i.e., one of these lines is very sabsorbed against the other line in the plasma. The lines uin this determination come two by two from the same initlevel and fall two by two to the same final level~see Fig. 3for a typical case!.31 Repeating the method for another paof levels and pair of lines, all 4s populations are achieved bthis self-absorption spectroscopy technique. The resultsbe displayed along the plasma column positions as axialfiles of excited level populations:n4s andn4p , respectively.

IV. RESULTS AND DISCUSSION

In order to test the validity range of the theoretical moda large number of experimental data are compared with cputed curves. For the electron number density axial profiFigs. 4~a!–4~e! show a comparison between the experimen

TABLE I. Relevant spectroscopic data of lines used for determining theplevel populations.

l~nm!

Transition4p→4s

Upper level energy~eV!

Upper levelstatistical weight

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714.70 4p8@3/2#1→4s@3/2#2 13.28 3(p4→3P2)

763.50 4p@3/2#2→4s@3/2#2 13.17 5(p6→3P2)

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7656 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lao et al.

results~symbols! and the calculated ones assuming the wtemperatureTw to be 300 K~solid lines! at five gas pressureas follows: ~a! 0.2 Torr, ~b! 0.5 Torr, ~c! 1.1 Torr, ~d! 1.8Torr, and~e! 2.8 Torr. ~For convenience, the origin of thezposition is placed at the columns’ end.! The agreement isindeed, very acceptable~into a factor of 1.5 or less, practically negligible in some cases!, bearing in mind that the experimental errors in determining the plasma densityreach 20%. Slight differences are found in the slope~gradi-ent! of those axial profiles. One of the possible explanatiois the influence of the gas temperature. Dashed lines in F4~a! and 4~e! are calculated with a wall temperature of 40K. It can be seen that the agreement with the experimedata for 2.8 Torr is very good. An increase of the gas teperature~and respectively ofTw! with the pressure increashas to be expected, and therefore, has to be taken intocount. Unfortunately, there are no experimental data formagnitude ofTw at different pressures.

The axial profiles of the 4s excited state population~two metastable and two resonant levels! are plotted in Figs.5~a!–5~e! and the symbols refer to levels3P2 ~full boxes!,3P0 ~full circles!, 3P1 ~full triangles!, and1P1 ~full invertedtriangles! at the same argon gas pressures as in Figs. 4~a!–4~e!. The agreement between calculated and experimeresults is also acceptable in the same accuracy obtainethe electron number density profiles~a factor of 1.5 higherthen the experimental data!. Note that the 4s levels’ popula-tion can decrease or increase along the column dependinthe gas-discharge conditions, which can be seen from F7~a! and 7~b! in Ref. 11. At our conditions, an increasethese levels’ populations from the launcher to the coluend is observed both theoretically and experimentally. Tpopulations of 4s levels, calculated when the EEDF is asumed to be Maxwellian, always decrease alongcolumns,10 such a behavior is not in accordance with texperimental data. This simply illustrates how importantstrict calculation of the EEDF from the Boltzmann equatiis.

Both experimental and theoretical results show thatmost populated of the 4s levels is the metastable3P2 and theleast populated is the other metastable3P0 . On the otherhand, the populations of the two resonant levels3P1 and1P1

are nearly the same. The fact that the resonant level1P1 ismore populated than the metastable3P0 is due to an inten-sive deexcitation by both electron impact and radiative tra

FIG. 3. Transitions used for determining the3P0 and3P2 ~metastables! 4slevel populations~an illustrative example!.

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fers from 4p to 1P1 . It can be seen from Fig. 5~e! that theassumption ofTw5400 K ~dashed lines! significantly im-proves the agreement between experimental and theoreresults for the 4s levels’ populations at higher pressures.

Contrary to the axial course of the 4s state populations,a decrease of the 4p level populations is observed—bottheoretically and experimentally—from the launcher to tend of the columns as is shown in Fig. 6. Experimenpoints at each pressure correspond to thep6 ~full symbols!and thep4 ~open symbols! level population, respectivelyinto the 4p block of levels, while the calculated results~solidlines! apply for the whole 4p block. Insofar asp6 is the mostpopulated level and that these two partial populations repsent only half of the total 4p block population~see Baranovet al.22 for similar work conditions!, a factor of 2 differencebetween experimental and calculated values should besidered.

With the pressure increasing, the total populationsboth 4s and 4p levels decrease while the electron numbdensity tends to increase. But at the same time, the menergy of electrons—which determines the rate coefficieof elementary processes—decreases@see Fig. 12~a! in Ref.11#. In the balances for the 4s and 4p populations, that lattereffect becomes more important than the electron densitycreasing. In addition, with pressure growing, the stepwionization that depopulates the 4s levels becomes more intense than the direct ionization. The impact of the electmean energy explains the opposite behavior of the elecnumber density and the excited state populations dependon the gas pressure.

The numerical model gives us the opportunity to stuthe population and depopulation mechanisms of the excstates, which is a useful tool for understanding the dynamof the population of the excited states under various dcharge conditions. For convenience, the excitation and decitation between both 4s and 4p block of levels are treatedas one effective process.~We note that these results are otained assuming the wall temperature to beTw5300 K.! Themain population mechanism for all 4s levels except1P1 isthe excitation from the ground state. The population of1P1 level is owing to transitions from other excited statebut the role of the ground state excitation increases withpressure growing and becomes nearly 50% at a pressu2.8 Torr.

The depopulation mechanism of each 4s level is differ-ent. At a gas pressure of 0.5 Torr the depopulation of the3P2

metastable level is as follows: 70% are due to mixing wother excited states, 25% are due to the stepwise ionizaand 5% come from the diffusion to the wall and from thPenning ionization. With the gas pressure increasing thetial contribution of the various processes changes and atTorr the mixing with other levels accounts for 84% of thdestruction rate, the stepwise ionization 15%, and the oprocesses provide only 1%. The depopulation of the otmetastable state,3P0 , is mainly owing to transitions to othelevels and to the stepwise ionization; both having appromately equal contribution regardless of the gas pressLess than about 2% of the depopulation is due to the dision and Penning ionization. The depopulation of the3P1

7657J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lao et al.

FIG. 4. Calculated axial profiles of the electron number densityne com-pared with the experimental data at various gas pressures:~a! 0.2 Torr, ~b!0.5 Torr, ~c! 1.1 Torr, ~d! 1.8 Torr, and~e! 2.8 Torr.

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resonant level is due to radiation, stepwise ionization,mixing with other excited states and their contributionapproximately equal and independent on the gas pressThe depopulation of the1P1 resonant state is a result oradiation and stepwise ionization. The role of radiatigrows from 10% to 50% with the gas pressure increase.

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V. CONCLUSION

In this article, the axial distributions of the electron number density and excited atomic state populations of arhave been studied both experimentally and theoreticallylow and intermediate gas pressures~0.2–2.8 Torr!. The

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7658 J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lao et al.

FIG. 5. Calculated axial profiles of the population of excited 4s states at thesame gas pressures as in Figs. 4~a!–4~e! compared with the correspondinexperimental data.

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agreement between experimental data and theoretical reis very good. It has been confirmed that with the pressincreasing the electron number density increases whilepopulations of all the 4s and 4p levels decrease. The latterowing to the decrease of the electron mean energy with psure growing. It is established that the 4p populations~andthe electron number density! decrease from the wavlauncher to the plasma column end, while the 4s levels’

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populations increase. The theoretical results for the acourse of the 4s levels’ populations confirm the experimentone if the rate coefficients of the processes are determusing the electron energy distribution function calculatfrom the Boltzmann equation. When the EEDF is assumebe Maxwellian the populations of the 4s levels decreasefrom the launcher to the end, in contradiction with the eperimental observations. The model enables us to eval

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7659J. Appl. Phys., Vol. 87, No. 11, 1 June 2000 Lao et al.

the contribution of the various population and depopulatmechanisms of the 4s levels—two metastable (3P2 and3P0)and two resonant (3P1 and1P1)—which results in their dis-tinctive number densities. The most populated is the3P2

metastable level, the least populated turns out to be the o3P0 metastable level, while the two3P1 and 1P1 resonantlevels have nearly the same populations lying between thof the metastable states. Such a distribution is far fromdistribution usually observed in dc discharges wherepopulations of corresponding metastable and resonant leare very close because of a strong mixing between them32

With increasing gas pressure one can expect somecrease in the gas temperature and, accordingly, in theperature of the tube wall. If it is taken into account in tcalculations, the agreement between experimental and tretical results both for the electron number density andnumber densities of excited atoms is significantly improvThis implies that the role of the gas temperature in the dcharge modeling of surface-wave plasmas, up to now unrated, might be really important.

ACKNOWLEDGMENTS

The authors are indebted to the Spanish–BulgaCommittee of Scientific and Technological Cooperationmaking possible this common article within the framewoof the VIIth Meeting’s Project No. 18. The Spanish pawishes to thank the Spanish Ministry of Education and C

FIG. 6. Calculated axial profiles~solid lines! of the population of thelumped 4p block of levels compared with the corresponding experimendata at various gas pressures: 0.2 Torr~circles!, 0.5 Torr ~down triangles!,1.1 Torr ~boxes!, 1.8 ~up triangles!, and 2.8~diamonds!.

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ture for the partial support of the experimental work undGrant No. PB96-0508 and the Bulgarian part, the NatioFund for Scientific Research, for the partial financial suppof the theoretical work under Grant No. F-821/98. The athors are also pleased to acknowledge Dr. Alexander Bgoev for helpful discussions.

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