Net emission of ArH2He thermal plasmas at atmospheric pressure

Transcription

1 Net emission of ArHHe therma pasmas at atmospheric pressure Y Cressaut, M E Rouffet, A Geizes, E Meiot To cite this version: Y Cressaut, M E Rouffet, A Geizes, E Meiot. Net emission of ArHHe therma pasmas at atmospheric pressure. Journa of Physics D: Appied Physics, IOP Pubishing, 010, 43 (33), pp < /00-377/43/33/33504>. <ha > HAL Id: ha Submitted on 5 Feb 011 HAL is a muti-discipinary open access archive for the deposit and dissemination of scientific research documents, whether they are pubished or not. The documents may come from teaching and research institutions in France or abroad, or from pubic or private research centers. L archive ouverte puridiscipinaire HAL, est destinée au dépôt et à a diffusion de documents scientifiques de niveau recherche, pubiés ou non, émanant des étabissements d enseignement et de recherche français ou étrangers, des aboratoires pubics ou privés.

2 Net emission of Ar-H -He therma pasmas at atmospheric pressure Y Cressaut 1,, M E Rouffet 1,, A Geizes 1, and E Meiot 3 1 Université de Tououse, UPS, INPT, LAPLACE (Laboratoire Pasma et Conversion d'energie), 118 route de Narbonne, F-3106 Tououse Cedex 9, France CNRS, LAPLACE, F-3106 Tououse, France 3 CEA-DAM, Le Ripaut, F-3760 Monts, France. E-mai: cressaut@apace.univ-tse.fr Abstract The Net Emission Coefficient (NEC) has been cacuated for Ar-H -He therma pasmas and for a temperature range from 5000K to 30000K. The pasma is supposed to be in Loca Thermodynamic Equiibrium (LTE) at atmospheric pressure. This study takes into account the radiation resuting from the atomic continuum, the moecuar continuum, and the atomic ines. A particuar attention has been paid to the treatment of heium ines broadenings. The resuts of net emission coefficients are presented for pure gases and Ar-H -He mixtures. Radiation is weak in pure heium at ow temperatures because of the high ionization energy of this species. On the opposite, at very high temperature, the infuence of hydrogen tends to decrease because ionic ines do not exist for this ast species. Finay, a sma proportion of heium in Ar-H mixtures does not change the net emission coefficient because of the weak intensity of the heium ines. 1. Introduction In pasma spraying, the arc and the jet are often estabished in an argon-hydrogen mixture, thus creating a rather high pasma enthapy brought by hydrogen combined to a arge momentum due to the argon mass. Nevertheess, in industria conditions, different microstructures of the materia deposition are required and depend on the veocity, size and meting conditions of the spashing partices [1]. Changing these parameters is not easy but can be obtained by using various types of gases or gas mixtures. Ternary mixtures, particuary those containing argon, hydrogen and heium, are known to be good candidates such as pasma gases. In this case, the operating conditions and the pasma characteristics can be either measured with the hep of various diagnostics or cacuated by physica modeing. In the ast case, a pasma properties (equiibrium composition, thermodynamic properties, transport coefficients and radiative transfer data) must be cacuated in advance. Some references can be found for the transport properties of Ar-H -He mixtures in [-5], at equiibrium or with departure from equiibrium. In the same case, the iterature proposes the radiative properties for pure gases or Ar-H binary mixtures [5-9] but no data are avaiabe for Ar-He and Ar-H -He mixtures. 1

3 Consequenty, the bases of cacuation and some resuts reative to the net emission of radiation for the binary and ternary mixtures are presented in this paper. The cacuation of the radiation is based upon the previous knowedge of the equiibrium composition and on the cacuation of a emission and absorption phenomena incuding atomic continuum (radiative attachment, Bremsstrahung, radiative recombination), moecuar continuum (photodissociation and photo-ionization) and ine radiation (ine profie and broadenings). The main difficuties concerned the bibiographica study of the basic data and the study of the ine broadening mechanisms. The ine contribution is treated using the notion of escape factor which is cacuated for each ine as a function of temperature. In the case of hydrogen and heium, inear Stark effect must be taken into account contrariy to the genera case where quadratic Stark effect is dominant. Indeed, for hydrogen-ike species (H, He + ), the interactions are characterized by a r - inear dipoar potentia. The ine profie is then broadened by inear Stark effects due to the presence of the ions. For atoms having more than one eectron, the eectric fied eads to shift the energy eves proportionay to the square of the force corresponding to this eectric fied. Consequenty, the interactions can be characterized by two potentias: a r -3 quadrupoar potentia or a r -4 quadratic potentia. The iterature proposes many numerica or experimenta vaues for the broadenings of argon or hydrogen ines [10-16] whereas data for heium ines are often given by measured or cacuated Stark Broadenings of seected ines [17-19]. Therefore, this work studies with a particuar attention the broadening ines of heium atoms and their absorption. The net emission coefficient (NEC) is then cacuated in a cassica way for therma pasmas, i.e. considering an isotherma pasma sphere of radius R p. The resuts are presented for atmospheric therma pasmas in a temperature range between 5000K and K, and various gas proportions in the mixture. In this paper, the first part briefy presents the cacuation of the pasma composition, whie the second part is devoted to a presentation of the net emission coefficient method and to various radiative processes responsibe for the radiation of a therma pasma. A study of heium ines is done and their broadenings are compared to experimenta resuts issued from iterature and used to vaidate our cacuations. Finay, the ast part presents some resuts of the net emission coefficient obtained at atmospheric pressure for pure gases (Ar, H and He), binary gases with moar proportions (Ar-H and Ar-He) and a typica ternary mixture 53%Ar-1%H -35%He.. Pasma composition The first step consists in cacuating the equiibrium composition of the pasma versus the temperature and the pressure. At atmospheric pressure, the foowing gaseous species are ony taken into account: eectrons, Ar, He, H, H, Ar +, He +, H +, H +, Ar ++, He ++, Ar +++, H -, He -, H -. The numerica method used to cacuate the equiibrium composition of the pasma is based upon the mass action aw and on the basic chemica concept defined by Godin and Trepanier [0]. This aw

4 enabes the generation of as many equations as there are independent chemica processes existing in a pasma. For a given reaction, this aw is written as: N i= 1 n ν i i = N i ν ( QTot, Vo ) i= 1 i (1) With N the tota number of chemica species considered in this reaction, ν i the corresponding stoechiometric coefficients, n i and function of the species i respectivey. Q, the number density and the tota voumetric partition i Tot Vo Q, is given by : i Tot Vo Q i Tot 3/ ref πm ik BT i Ei = Q T, Vo ( T ) int ( ) exp () h k BT where Q i ( T) int is the interna partition function of the species i and E i ref its reference energy cacuated from the formation enthapy defined in Janaf tabes [1]. The knowedge of the partition function is essentia to enabe the estabishment of the composition cacuation. This step requires a great amount of data which can be determined either from iterature or thanks to appropriate formuas depending on the nature of the species: atomic or moecuar species [3, 4]. Interna partition functions of atoms and their positive ions are taken from Drawin and Feenbok []; interna partition functions were assumed to be equa to the degeneracy of the ground state for negative atomic ions; they were cacuated with the Morse potentia minimization method [3, 4] for diatomic species. The spectroscopic data (Dunham coefficients, vibrationa frequencies and degeneracies, rotationa constants, moments of inertia and symmetry numbers) essentia to the cacuation of the interna partition functions of moecues were taken from Chase et a [1] and Huber and Herzberg [5]. Finay, the charged species generate a Couombian fied which creates an interaction potentia modifying the state of the pasma. This effect is crucia at high temperature when the popuation number densities of charged partices are important. Aso, at ow temperatures and for pressures higher than the atmospheric pressure, the interactions between neutra partices impy a correction of the perfect gas aw. Therefore, the Debye-Hücke and the Virie corrections [8] have been considered. Figure 1 shows the pasma composition obtained for the 53%Ar-1%H -35%He (in moar proportions) mixture at atmospheric pressure whereas Figure compares the eectron number density obtained in the case of pure pasmas (Ar, H, He) and binary mixtures (50%Ar-50%H, 50%Ar- 50%He in moar proportions). 3

5 % Ar - 1% H - 35% He P = 0.1 MPa Popuation number density (m -3 ) Ar He H Ar + H + Ar ++ H He + e He H Ar Ar Figure 1. Pasma composition at atmospheric pressure for 53%Ar-1%H -35%He mixture P = 0.1 MPa Eectron number density (m -3 ) 1x Pure argon Pure hydrogen Pure heium 50% Ar-50% He 50% Ar-50% H Figure. Eectron number density for pure gases, 50%Ar-50%He and 50%Ar-50%H mixtures. at atmospheric pressure (moar proportions). The ionization energies of argon and hydrogen being rather cose, a sight difference in the eectron number density for these two pure pasmas or mixtures can be noticed in this temperature range. On one hand, for temperatures above 5 kk, the absence of muti-charged partices for pure hydrogen pasma generates a faster decrease of the eectron number density contrariy to the case of pure argon or pure heium pasma whose eectrica neutraity is sti ensured by the presence of the positive ions 4

6 Ar + and Ar ++, or He + and He ++. Between 5kK and 30kK, the eectron number density decreases of some 5 % for pure argon or heium pasmas whie it decreases of approximatey 17 % in the case of a pure hydrogen pasma. On the other hand, for temperatures ower than 5kK, the eectron number density for pure heium pasmas is argey ower than the eectron number densities for pure argon or pure hydrogen. This resut is due to the high ionization energy of the neutra heium He (4,580eV) in opposite to the ionization energies of argon Ar (15,7596eV) and hydrogen H (13,598eV). 3. The method of the Net Emission Coefficient cacuation The divergence of the radiative fux is an important term in the energy baance. The atter represents the radiative osses and can be determined by the resoution of the radiative transfer equation. For a direction defined by the norma unit vector n, we have: r F rad r r r r = Lλ (, dω) S n dω dλ (3) dl ( s) ' λ λ λ ds λ o ' with = L ( T) K ( s) K ( s) L ( T ) (4) λ where F r rad is the radiative fux (W/m ), L? (T) is the spectra radiation intensity (W.m -.sr -1.m -1 ), S r is the vector orthogona to the surface S, dω is the soid ange, s is the distance aong the considered direction. In equation (4), ' K λ represents the spectra absorption coefficient at waveength λ and corrected by induced emission. L o λ (T ) is the spectra radiation intensity of the back body. A rigorous cacuation woud consist in resoving this equation for a waveengths of the spectrum and for a directions. For a practica probem, the cacuation time woud be extremey ong. Some methods have therefore been deveoped in order to simpify the spectra or geometrica dependencies of the radiation whie keeping a good accuracy. For a detaied description of the different existing methods, the reader wi find references into the genera works of Siege [9] and Modest [30]. One of the frequenty appied methods in the numerica modes destined to therma pasmas is the NEC [31, 3] which takes into account emission and absorption of radiation in isotherma conditions To cacuate this coefficient, three assumptions have to be considered: - the pasma is homogeneous. - the pasma is isotherma. The radia profie of temperature in the arc pasmas is often characterized by weak gradients in the hottest regions and by an abrupt decrease on the edges of the discharge. Thus, in a first approximation, the temperature of the discharge can be considered as a constant and its variation can be approximated by a rectanguar profie [31, 5

7 3]. This assumption is satisfactory for the centra regions of the arc where the temperatures are the highest, the gradients the weakest and the emission the most important. - the pasma is assimiated to a sphere of radius R p. Libermann and Lowke [33] have shown that an isotherma cyindrica pasma coud be assimiated to an isotherma sphere which woud have the same temperature (with a discrepancy of 10%) as the emitting point in its centre. The radiation is then cacuated at this centre and considers the emission and absorption of the points incuded in this sphere. For a given pressure, the expression of the NEC is the foowing: ε ' ( K ( T R ) dλ o ' N ( T, Rp ) = Lλ ( T ) Kλ ( T ) exp λ ) 0 P (5) In spite of the strong approximation of isotherma pasma, this net emission coefficient gives acceptabe vaues for the radiative baance in the hottest regions of therma pasmas [34]. Indeed the oca emission depends on the oca temperature, whereas the main sef-absorption occurs in the very near surroundings of the emission point as it wi be pointed in the resuts. The main difficuty of this method consists not ony of the cacuation of the spectra absorption ' coefficient K λ ( T) which strongy varies according to the waveength and temperature, but aso of the cacuation of the radiation ines incuding their absorption. Therefore, various physica phenomena must be considered: the radiation of the atomic continuum (radiative recombination, Bremsstrahung and radiative attachment), the radiation of the H moecuar continuum (photo-dissociation, photoionization and photo-attachment) and the radiation of the atomic ines (by taking into account the absorption phenomena). 4. Continuum radiation Two types of transitions constitute the atomic continuum: the free-free (Bremsstrahung) and the bound-free (radiative attachment and radiative recombination) transitions. - The radiative attachment: the radiation due to the attachment is cacuated according to the expression given by Geizes et a [34]. To obtain the absorption coefficient for hydrogen H -, the photodetachment cross section given by McDanie [35] was used. The radiative attachment of heium He - is negected in the tota spectra absorption coefficient. - The radiative recombination: this mechanism is important in the continuum emission for therma pasmas. The radiation is cacuated according to the method of the Scaed Thomas-Fermi potentia [36] that supposes a Maxwe veocity distribution. This method takes into consideration a Couombian potentia for great distances. For short distances, a more compex potentia is used in 6

8 comparison to the potentia used in the quantum defect method deveoped by Seaton [37]. Therefore, the foowing expression for the radiative recombination is obtained: 1 3 rec + + z ( z 1) λ 0 ξ λ ε 8 π e c NeN + Z + Z z ( T) = c 3k m 4 Z b e πεo λ Qint ( T) T ( J. m. K 1/. sr 1 ) hc 1 exp g kbt λ ( T) (6) where + Z Q int is the interna partition function of the Z + ion, Z is its charge number, + N, are the + z e N Z popuation number densities of eectrons and ions Z + respectivey, + z g 0 is the statistica weight of the ground state eve of Z + and + ( z 1) ξ λ represents the Biberman-Schüter factor of the + ( z 1 ) Z atom. This factor, introduced by Biberman and Norman [38,39], is a correction for the difference between the photoionization cross section of the energy eves and the corresponding hydrogen-ike cross section. For argon (Ar + Ar, Ar ++ Ar + ) and heium (He + He), Hofsaess [40] gives vaues of + ( z 1) ξ λ for temperatures ranging from 6000K to 30000K and waveengths from 30nm to 1000nm. Figure 3 shows this coefficient for heium recombination. For other temperatures and waveengths, these data are extrapoated. Unfortunatey, the Hofsaess data do not cover the range of energy higher than the ionization energy of He (E>4.580eV i.e λ<50nm). In the case of pure heium pasmas, we aso compared the spectra absorption coefficients obtained with this extrapoated Biberman-Schüter factor and the resuts deduced from the hydrogen-ike atoms approximation deveoped by Okuda [41]. For a temperature equa to 10kK, this comparison is shown in figure 4 and highights a good agreement for waveengths between 100nm and 1000nm ( Hz < ν < Hz) whereas the resuts obtained with the Biberman-Schüter factor H e ξ λ diverge for waveengths inferior to 100nm. Consequenty, the radiative recombination for heium (He + He) is cacuated using the Biberman- Schüter factor for λ > 100nm and according to the formua given by Okuda for waveengths λ < 100nm. The radiative recombination for hydrogen (H + H) and ionized heium (He ++ He + ) is aso cacuated according to the hydrogen-ike atoms method for a temperatures and a waveengths. For this ast method, the energy eves and principa quantum numbers of the considered species are issued from the tabes of Moore [4], corrected by the recent data of the NIST [43] and competed if necessary by those of Kurucz and Peytremann [44]. 7

9 10 1 e Biberman-Schüter factor ξ Η λ K 000 K K K K 6000 K waveength (nm) Figure 3. Biberman-Schüter factor for heium[40]. 1x10 3 1x10 1 1x10-1 with ξ He factor λ hydrogen-ike method our cacuation 10kK K' He rec (m-1 ) 1x10-3 1x10-5 1x10-7 0kK 1x kK P = 0.1 MPa Frequency (10 15 Hz) Figure.4. Recombination radiation for pure heium pasma - The Bremsstrahung radiation: the expressions used to cacuate the corresponding radiation are given by Cabannes and Chapee [45]. The eastic cross-section for eectron-argon coisions are given by Tanaka and Lowke [46] versus the kinetic energy of the eectron whereas Neynaber et a [47] give the cross-section for eectron-hydrogen coisions. Finay, the eastic cross section characterizing the eectron-heium coisions is reconstituted in figure 5 from data of Fursa and Bray [48], Goden and Bande [49], and Kennery and Bonham [50]. 8

10 7 6 Eastic cross section (A ) Used vaues Fursa and Bray [44] Goden and Bande [45] Kennery and Bonham [46] Energy (ev) Figure 5. Eastic cross section for eectron-heium coisions. - The moecuar continuum: the presence of hydrogen H is aso considered. In therma pasmas, the moecuar continuum spectrum corresponds to absorption to which two mechanisms contribute, namey photo-ionization and photodissociation. The moecuar continuum of moecuar hydrogen is obtained by the mutipication of the moecuar H density and the photoabsorption cross-section issued from the works of Cook and Metzger [51] and Broey et a [5]. We assume that the corresponding cross-section does not depend on temperature. ' Exampes of the continuum absorption coefficient K ν ( T ) are shown as functions of frequency and temperature for pure pasmas (fig.6 and fig.7) and for the ternary mixture 53%Ar-1%H -35%He (fig.8). 9

11 Spectra absorption coefficient (m -1 ) x10-1x10-3 1x kK 30kK Ar Ar He H H He P = 0.1MPa Ar H frequency (10 15 Hz) H He Ar Figure 6. Spectra absorption coefficient for pure gases. 1x10 4 Spectra absorption coefficient (m -1 ) 1x10 1x10 0 1x10-1x10-4 1x10-6 1x10-8 1x x10-1 P = 0.1 MPa 5kK 5kK T = 5kK T = 15kK T = 0kK T = 5kK frequency (10 15 Hz) Figure 7. Spectra absorption coefficient for pure heium pasma. 10

12 Spectra absorption coefficient (m -1 ) x10-4 P = 0.1 MPa 15 kk 30 kk 5kK 5kK 30 kk T = 5 kk T = 15 kk T = 0 kk T = 5 kk T = 30 kk frequency (10 15 Hz) Figure 8. Spectra absorption coefficient for 53%Ar-1%H -35%He mixture. 5. Emission of the spectra ines ines (8708 ines for argon species, 30 ines for hydrogen and 1650 ines for heium species) have been considered, whose characteristics (energy eves, quantum numbers, transition probabiities, osciator strengths ) are issued from the tabes of Moore [4], corrected by the recent data of the NIST [43] and competed if necessary by those of Kurucz and Peytremann [44]. Radiation transfer requires the knowedge of ine profies which are cacuated by taking into account the Dopper broadening, pressure effects (resonance and Van der Waas broadenings) and the Stark broadening. Griem and Traving [53-56] give a review of different cassica and semicassica methods to cacuate the shape of spectra ines. To simpify the cacuation of the emission ine, the ine overapping is assumed to have a very ow infuence on the radiative transfer. Each ine is then treated individuay by the use of an escape factor which depends on the ine intensity and on its profie [57, 58]. The phenomenon of absorption is then taken into account through this factor Λ ines, ranging between 0 and 1 and which represents the ratio between the radiative fux escaping isotherma pasma of thickness R p with the consideration of the absorption and the radiative fux without absorption. Its introduction consideraby diminishes the computing time but sometimes tends to over-estimate the net radiation if the ines are not separated enough from to one other. The vaues are however acceptabe assuming the precision of the method [3]. Indeed, the use of an escape factor is fuy justified in this study since the error obtained between this cacuation and the exact cacuation remains inferior to 1% whatever the temperature or the thickness of the pasma. Futhermore, the oca emission depends on the oca temperature, whereas the main sefabsorption 11

13 occurs in the very near surroundings of the emission point as it wi be pointed in the resuts. So sefabsorption occurs in the region where the temperature is not far from that of the emitting point (ow temperature gradients near the axis or the centre of the pasma) and thus the assumption of isotherma pasma is rather vaid. The ine radiation is written as: ε ine λ ( T, R p e ) = 4πε o π L mec o λ ( T) f n ( T) Λ hc 1 exp λkbt u ine (7) where m e is the mass of the eectron, λ is the waveength corresponding to the transition between the upper energy eve E u and the ower energy eve E, f u is the osciator strength of this transition, n is the average number density of the ower energy eve and function of the temperature and R p. Λ ine is the escape factor of the ine, Dopper broadening: for therma pasmas in a steady state, the emitting atoms are moving and contribute to the broadening of the ines by therma motion. For an emitted ine centred in λ o, the Dopper Effect is due to the reative veocity of these emitting atoms compared to an observer. The ine shape is a Gaussian profie and its fu width at haf maximum (FWHM) is given by (SI units) [59]: 8k B T n δλ Dopper = λ0 (8) mc where m is the mass (kg) of the emitting atom. Pressure Effects: this type of broadening is due to the perturbation of the energy eves of an emitting atom or ion by the presence of the other surrounding partices. These interactions cause the broadening and the shift of the ines. The interpretation of the pressure effects depends not ony on the distance between the two atoms but aso on the nature of the disturbers. The ine shape is assimiated to a Lorentzian profie [56] and two theories are aso used to cacuate the FWHM: the impact approximation and the quasi-static approximation [10, 11, 54]. - Van der Waas broadening: This interaction is usuay described by the C 6 /r 6 Lennard-Jones potentia [8] where r represents the distance between the emitting atom and the disturber (identica neutra atom or different neutra atom if the higher energy eve of the emitting atom is not couped to its ground state energy eve) and C 6 the Van der Waas constant. The first order of the interaction gives the Hartree-Fock mean fied whereas the impact approximation is obtained in second order where coisions are described in Born approximation. The FWHM (SI units) is obtained according to the detaied investigations of Wakup et a [60]: 1

14 δλ VanDerWaas 3 λ 5 5 * 0 = 8.16 C6 v n (9) πc Where v = 8k B T πµ is the mean veocity of the radiating species and n * is the popuation number density of the perturbing partice. The constant C 6 (m 6 s -1 ) is cacuated with the expressions given by Hirschfeder [8] and the poarizabiity [61] of each partice (α Ar =1.643Å -3, α H = Å -3, α He =0.05Å -3 ). In Ar-H -He mixtures, this broadening ine is negigibe in comparison with the Dopper and the Stark broadenings when the partice is an atom of hydrogen H or heium HeII. A review of Van der Waas broadening is given in the impact approximation method by Traving [56]. - The resonance broadening: this phenomenon is treated within the impact approximation method and a C 3 /r 3 interaction potentia. For an atom, this phenomenon is mainy important if the higher energy eve is couped with its ground state. The FWHM (SI units) can be expressed in the fourth order approximation [53, 56]: 1 g e f n nm λo δλ Re sonance= 5.48 π o n0 g m 4 0 m e c λ (10) πε π where n 0 is the popuation number density of the atom in its ground state eve. - Stark broadening: Stark broadening is the consequence of a disturbance from the atom or emitting ion by the eectric fied due to the surrounding charged partices (ions and eectrons). For Ar- H -He mixtures, the Stark broadening was not treated in an identica way for argon, hydrogen and heium partices. For the argon atoms, the interaction potentia exists in two forms: quadripoar in r -3 [6-64] and quadratic in r -4 [54], where r represents the distance between the atom or the emitting ion and the disturber. The veocity of the eectrons being more important than the veocity of the ions, the effect of the atter is often weaker than the infuence of the former. Griem [54] added a correction term to take into account the infuence of the ions in the Stark broadening ines. In the frame of the impact approximation method (for neutra atoms) and the quasi-static theory (for ions), the FWHM are written as (SI units) [54, 56, 65]: Ar 3 3 λ0 δλ Stark = C / v 1/ 4 e ne [ A ( R) ] (11) πc ' ' [ A ( 1 1. R )] Ar, Ar 00.8 / 5 4 / 5 1/ λ0 δλ Stark = C4 Z ion T ne (1) πc 13

15 where v = 8k T πm is the eectron mean veocity, Z ion is the charge number of the radiating ion, e B e and C 4 (m 4 s -1 ) is a constant characteristic of the transition [56, 66]. The term in brackets is the Griem s correction [54] cacuated with the quasi-static approach where r, r, A and A are respectivey the Debye shieding parameters and the ion broadening parameters given by Griem [54] and Konjevic [65]. For hydrogen atoms, the quantum weight for a given energy eve and the mutua permutation of the states having the same principa quantum number but not the same orbita quantum number cause a shift of the energy eves. Hydrogen ines profie is we described by Keppe and Griem [54, 67]. The Stark broadening is mainy due to the ions, its form is inear and the resuting shape is more compex than a Lorentzian profie when the dynamics of the ions is considered. Severa approaches were deveoped to characterize the shape of the spectra ines: the microfied method that incudes the dynamics of the ions and the rotation of the ionic fied in the tota profie [68-70]; the generaized impact theory and the unified cassica path theory which are considered as better methods to cacuate the hydrogen shapes [1-16, 71]; the quantum statistica approach based on the many-partice Green functions method used by Günter [7] and deveoped for charged perturbers and appied to pasmas as hydrogen [7,74] or heium [74,75]. The normaized profie used in cacuation is deduced from works of Vida, Copper and Smith [1, 14-16] who considered the unified theory and the impact approximation at the centre of the ine and the quasi-static approximation on the edges. Finay, for heium atoms, Griem et a [76] indicated that the ine broadening was aso a inear Stark broadening. They specified that the shape of the spectra ines did not depend too much on the veocity distribution of the ions and the eectrons and did not depend on the temperature when the Stark broadening dominates the other broadenings. Some references and comparisons of cacuated vaues and measurements of Stark broadening for neutra-heium ines are avaiabe in works of Dimitrijevic and Saha-Brechot [17] and Bassao et a [77]. Whereas the HeII ines are supposed to be opticay thin (Λ ines = 1), the FWHM for the HeI ines is given by Griem (in SI units): δ He Stark ( T) = α γ g 6 ( α 1) u α 3 u n ( T ) where n e is the eectron number density (m -3 ), and u are the index of the ower and upper energy eves for a given transition, α j is the principa quantum number of the energy eve, γ is a constant equa to ¼ for α = 1 and α u = e (13), and equa to unity for the other transitions. Indexes u and correspond respectivey to the upper and ower eves of the ine transition. 6. Resuts on spectra ine broadenings 14

16 6.1. Spectra ine broadenings of neutra heium. For pure heium pasma, figure 9 and figure 10 present the Stark broadenings obtained for 9 ines of neutra heium These ines correspond to transitions eading to the two first energy eves. Whereas Figure 9 presents the Stark broadenings at atmospheric pressure in function of temperature, Figure 10 is drawn for various pressures according to the eectron number density. The characteristics of the 9 ines are reported in tabe 1. Tabe 1. Characteristics of the HeI seected ines. (nm) α -1 α A u u (s ) E (cm -1 ) E u (cm -1 ) (1s ) (1s7p) (1s ) (1s6p) (1s ) (1s5p) (1s ) (1s4p) (1s ) (1s3p) (1s ) (1sp) (1ss) (1s5p) (1ss) (1s4p) (1ss) (1s3p) Tabe 1 and figure 9 show that the resonance ines ( α = 1) are more intense and ess broadened than the others so that they are the most absorbed within the pasma. For the three ines characterized by α =, Figure 10 shows a good agreement between our resuts and some experimenta vaues issued from the iterature [77]. 1x10 1 Stark broadening (nm) 1x P = 0.1 MPa nm 5.1nm nm nm nm nm 50,999nm 51.09nm, nm

17 Figure 9. Tota Stark broadenings versus temperature for the 9 HeI ines Bassao [73] Tota Stark broadening (nm) x nm nm nm nm 5.1nm nm nm nm 51.09nm Eectron number density (m -3 ) Figure 10. Tota Stark broadenings versus eectron number density for 9 ines of He I. Figures 11 and 1 compare the evoution of broadenings of two HeI ines: a resonance ine centred at 53,703nm (with α = 1) and a sighty absorbed ine centred at 388,865nm (with α = ) δ Linear Stark P = 0.1 MPa 10 1 δ Van Der Waas δ Dopper FWHM (nm) x10-5 δ Resonance Bassao [73] 53,703nm 388,865nm Figure 11. Contributions of the various broadenings to the FWHM of the ines nm and nm for pure heium pasma. 16

18 Line broadenings contribution (% of tota FWHM) δ Dopper δ VanDerWaas δ Stark nm nm Figure 1. Contribution of the ine broadenings (53.703nm and nm) in tota FWHM for pure heium pasma. First, Figure 11 shows a good agreement between the vaues given by Bassoo [77] for the nm ine and our cacuation reative to the FWHM Stark broadening. It aso highights the fact that this inear broadening does not represent the principa broadening of HeI ines at ow temperature. Finay, the FHWM are higher for the 388,865 nm ine. Figure 1 shows the importance of the Dopper broadening for temperature inferior to 10kK since it represents more than 99% of the FWHM. The same behaviour is observed for the 7 other HeI ines reported in tabe. Even if the FWHM of the Stark effect is smaer than the FWHM of the Dopper effect, the escape factor of a ine strongy depends on the behaviour of the edges of this ine. Consequenty, the Lorentzian profie (Stark and pressure) can be predominant in comparison to Gaussian profie (Dopper). Tabe. Broadening of HeI seected ines at 10kK and 0kK. T = 10kK T = 0kK (nm) δλ He Dopper (nm) He δλ VanDerWaas (nm) He δλ Stark (nm) He δλ Dopper (nm) He δλ VanDerWaas (nm) He δλ Stark (nm)

19 For higher temperatures, Stark broadening becomes increasingy important so as to represent neary 70% of the FWHM when temperatures are above 0kK. The remaining 30% are mainy due to Dopper broadening for resonance ines, or Dopper and Van der Waas broadenings for ines with α =. In opposition to ArI and H ines, Van der Waas broadening of HeI ines can pay a significant roe since heium atoms are ony ionized at very high temperature. Consequenty, the neutra heium ines must be treated with a Voigt profie for temperatures above 10000K. 6.. The escape factor For pure argon pasma, Figure 13 shows the escape factors obtained for some neutra argon ines according to the thickness of the pasma (1mm and 5cm). Figure 14 presents the same resuts for the 10 HeI seected ines. 1,0 1,0 Escape factor 0,8 0,6 0,4 0, P = 0.1Mpa R p = 1mm , Escape factor 0,8 0,6 0, P = 0.1Mpa R p = 5cm , , Figure 13. Escape factor for severa neutra argon ines versus the pasma thickness. 18

20 Escape factor 1,0 0,8 0,6 0,4 0, P = 0.1Mpa R p = 1mm Escape factor 1,0 0,8 0,6 0,4 0, P = 0.1Mpa R p = 5cm , , Figure 14. Escape factor for severa HeI ines versus the pasma thickness. s These resuts highight how Λ ine for a specific ine depends on the temperature and the considered ine. The ine absorption becomes important for the first miimetre of pasma and the resonance ines are the most affected. An exampe is shown in Figure 13 for severa neutra argon ines. For heium pasma and temperatures ower than 15kK, the most absorbed ines are characterized by α = 1 as shown in figure 14. For a given temperature, we aso observe that Λ ine is weaker (and is thus strongy absorbed) when the upper energy eve of the ine is cose to the ground state energy eve ( α = 1). Figure 15 presents the radiation of the HeI ines for pure heium pasma and for three pasma thicknesses (0mm, 1mm and 1cm). The tota radiation of the ines having α = 1 (the ower energy eve is the ground state), α = (the ower energy eve is the first excited eve), and α > (the ower energy eve is higher than the first excited eve) are distinguished. 19

21 10 10 Pure heium Lines radiation (W.m -3.sr -1 ) P = 0.1MPa α > α = α = 1 ; R p =0mm α = 1 ; R p =1mm α = 1 ; R p =1cm Figure 15. Radiation of the HeI ines in the case of pure heium pasma. It can be observed that resonance ines of HeI are strongy absorbed. The ines verifying α = are very sighty absorbed. Their tota radiation becomes important for high pasma thicknesses due to the strong absorption of the first ines ( α = 1). Indeed, the ines having the ower energy eve corresponding to their ground state are characterized not ony by a strong emission for thin pasma but aso by a strong absorption for high pasma thicknesses. Even if the pasma thickness is often inferior to a few centimetres (thus a sight absorption), the absorption phenomena for these ines are aso taken into consideration. Finay, the ines with α > are not absorbed. As a consequence of that, we assume that these ines are opticay thin ines with an escape factor Λ ine equa to unity. It can aso be observed that their tota radiation is ower than the tota radiation of the other ines. This effect can be expained by the important energy gap between the ground state and the first excited eve of HeI ( ε=159856cm -1 ). It is thus very difficut to popuate the excited eves of HeI which impies a very weak popuation number for these eves. According to reation 7, the contribution of theses ines ( α > ) wi be assumed negigibe in front of the transitions eading on the ground state or the first excited state. 7. Resuts on Net Emission Coefficients 7.1. Net Emission Coefficient of pure pasmas Figure 16 shows the net emission coefficient of pure heium pasmas versus temperature and pasma thickness. The case R p = 0mm is a fictitious case corresponding to an opticay thin pasma. The 0

22 differences between the curve R p = 0mm and the others show a typica trend: the strong absorption of the radiation in the first miimetres around the emitting point. This phenomenon is due to the resonance ines that are strongy absorbed when R p 0mm [7]. Our resuts are coherent with those of Moscicki [9] for opticay thin pasmas. However, we denote important discrepancies for R p =1mm at ow temperature. Nevertheess, our cacuations present a good agreement when the atomic ines contribution is ony considered in the tota radiation. The differences are thus mainy due to the continuum radiation which presents a weak absorption for this radius vaue unike the atomic ines which are strongy absorbed. We propose two reasons to expain these discrepancies corresponding to assumptions used by Moscicki: the first one is a waveength range imited from 30nm to 500nm (inferior to our waveength range); and the second one concerns the eectron-heium Bremsstrahung. Indeed, the author does not give reference about the eectronheium cross-section. Therefore, we then suppose that he has not taken into account this phenomenon. By using these assumptions in cacuations, coser vaues are obtained: they are represented by the curve with trianges in Figure Pure heium P = 0.1MPa ε n (W.m -3.sr -1 ) R p = 0 mm R p = 1 mm R p = 10 mm [8] R p = 1 mm (a) Figure 16. Net emission coefficient of pure heium pasma for different pasma sizes. (a) is the net emission coefficient obtained with the same assumptions of [9]. Figure 17 compares the continuum and ines contributions to the tota radiation for an opticay thin heium pasma (R p =0mm) and for a thickness equa to 1mm. Whie the radiation of the atomic ines is dominant when the pasma is opticay thin, these ines are strongy absorbed when the thickness of the 1

23 pasma increases. This tendency is visibe in the majority of pure gases or mixtures except for nobe gases and hydrogen P = 0.1 MPa 10 8 ε n (W.m -3.sr -1 ) R p = 0 mm Tota Continuum Lines R p = 1 mm Tota Continuum Lines Figure 17. Continuum and ines contributions to the radiation of pure heium pasma. Figure 18 compares the net emission coefficient of the three pure pasmas for R p =1mm P = 0.1 MPa R p = 1 mm ε n (W.m -3.sr -1 ) pure Ar pure H pure He H -Riad [74] Ar-Erraki [75] Figure 18. Net emission coefficient of pure gases for R p =1mm. For pure argon and hydrogen pasmas, a good agreement is observed with the works of Riad [78] and Erraki [79]. Our net emission coefficient for hydrogen pasma is sighty higher for ow temperatures due to the moecuar continuum of hydrogen H that Riad had not considered in his work. Aso note that hydrogen pasmas have a particuar behaviour at high temperature because ionic ines do not exist [5].

24 For pure heium pasma, the NEC is the weakest for temperatures inferior to 0kK. Compared to pure argon pasma, the NEC is 300 times weaker at 10000K, 5 times (weaker) at 15000K and 1,35 times at 0000K. For higher temperatures, the NEC is simiar to the previous ones. This behaviour can be expained by a very high ionization potentia of heium. 7.. The Net Emission Coefficient of binary mixtures : Ar-H and Ar-He The NEC of severa Ar-H mixtures for a pasma thickness of R p =1mm is drawn in Figure P = 0.1 MPa R p =1mm Ar 10 8 H ε n (W. m -3. sr -1 ) H Ar Pure Ar 75% Ar-5% H 50% Ar-50% H 5% Ar-75% H Pure H Figure 19. Net emission coefficient of Ar-H mixtures at atmospheric pressure. In industria pasma processes such as pasma spraying or gas-tungsten arc weding, heium is widey used with argon. Argon is used for its high mass density whereas heium increases the enthapy of the pasma. The presence of heium aso increases the therma conductivity of the mixture compared to the pure gases and imits the penetration of the surrounding gas. Consequenty, the mixture exhibits a higher viscosity due to its high ionization energy. However, heium can create a departure from equiibrium because of the high excitation potentia of its first excited eves and of its ight mass which faciitates the diffusion phenomena. In Figure 0, heium ony pays a roe at very high temperatures (centre of pasma) and for important proportions (>70% app). This phenomenon can be expained by a higher ionization potentia for heium than argon. Murphy [80] had observed this phenomenon whie studying experimentay demixing of heium in an argon-heium mixture in a free burning arc. A pink coour appeared, characteristic of heium concentration in the arc centre whie the vioet coour, characteristic of argon, was concentrated toward the arc fringes. Murphy showed that the pink region was discernabe for a heium proportion higher than 75% (in voume) which is in agreement with our concusions. 3

25 10 1 Ar P = 0.1 MPa R p =1mm 10 8 ε n (W. m -3. sr -1 ) Ar He Pure Ar 75% Ar-5% He 50% Ar-50% He 5% Ar-75% He Pure He Figure 0. Net emission coefficient of Ar-He mixtures at atmospheric pressure The Net Emission Coefficient of 53%Ar-1%H -35%He mixture The combination of the three gases (argon, hydrogen and heium) gives pasmas whose therma conductivity is more important than that of pure or binary mixtures for temperatures inferior to 10kK. Those mixtures present a cear interest for transferred arcs or in pasma spraying: best heat transfer and highest ength of pasma jet [81]. Figure 1 presents the net emission coefficient of the 53%Ar- 1%H -35%He mixture at atmospheric pressure, for pasma thicknesses R p =0mm and R p =1mm. It can be observed that: - When the pasma is opticay thin, the radiation ine is more important than continuum. This radiation is mainy due to the resonance ines of hydrogen and argon. The radiation of the hydrogen ines represents more than 70% of the net emission coefficient for temperatures ower than 10kK whereas the radiation of the argon ines represents more than 80% of the tota radiation for temperatures higher than 0kK. The heium radiation is not reay important for this mixture since its contribution does not exceed 3% of the tota radiation (maximum at 1kK). The contribution of heium pays an important roe in Ar-H -He mixtures either for a heium proportion higher than 70% in voume, or for sma thicknesses of the pasma and high temperatures (strongy ionized pasmas). - The increase in the pasma thickness generates an increase in the absorption phenomena and the decrease in the ines contribution in the tota radiation. The continuum then becomes fundamenta for temperatures inferior to 15kK (around 95% of the tota radiation at 5kK and 45% for temperatures between 15kK and 30kK). For these temperatures range (5kK<T<15kK), the argon and hydrogen ines are so strongy absorbed that they do not pay the main contribution to the tota radiation. Finay, for high temperatures (T>0kK), the net emission coefficient is mainy due to the argon ines radiation. 4

26 ε n (W.m -3.sr -1 ) %Ar-1%H -35%He P = 0.1 MPa R p = 0mm Tota Lines Continuum R p = 1mm Tota Lines Continuum Fig.1: Net emission coefficient of Ar-H -He mixtures at atmospheric pressure. 8. Concusions Different moar compositions have been studied to deduce generaities on the infuence of the heium species in ternary mixtures Ar-H -He. The resuts showed that an increase in the heium proportion (up to 70% in moar proportion) in the mixture with fixed 5% of hydrogen ed to a decrease in the net emission coefficient for a temperatures and a pasmas thicknesses. It has been showed that this was mainy due to a smaer radiation of the argon ines whose popuation number densities of the atoms were weakest. The infuence of the hydrogen proportion in the mixture has aso been evauated. For a fixed proportion of argon (53%), an increase in hydrogen proportion (up to 40%) strongy enhanced the tota radiation for temperatures inferior to 15kK. this phenomenon can be expained not ony by the radiation of the H moecuar continuum which was more important but aso by the radiation of hydrogen ines which was higher. Consequenty, we highighted the fact that the radiation of heium ony payed an essentia roe in the tota radiation of the Ar-H -He mixtures when the pasma was opticay thin and when the moar proportion of heium was very important in the mixture. For industria appications such as pasma spraying where proportions of heium are up to 10% and pasma thickness cose to the centimetre, we finay concude that the presence of heium in Ar-H -He mixtures does not reay modify the radiative properties of these mixtures. Appendix : specific references for basic data - Partition functions: Reference energies : Janaf tabes [1] Interna partition function of atomic species: Drawin and Feenbok [] Interna partition function of diatomic species: Janaf tabes [1], Herzberg [4] 5

27 - Continuum radiation : Energy eves, quantum numbers: Moore [4], NIST [43], Kurucz and Peytremann [44] Biberman factor for argon recombination: Hofsaess [40] Biberman factor for heium recombination: Hofsaess [40] Cross section for the radiative attachment of hydrogen: McDanie [35] Cross section for the Bremsstrahung radiation e-argon : Tanaka and Lowke [46] Cross section for the Bremsstrahung radiation e-hydrogen : Neynaber et a [47] Cross section for the Bremsstrahung radiation e-heium: Fursa and Bray [48], Goden and Bande [49], Kennery and Bonham [50] Cross section for the moecuar continuum of H : Cook and Metzger [51], Broey et a [5] - Lines radiation Energy eves, quantum numbers, osciator strength, atomic transition probabiity: Moore [4], NIST [43], Kurucz and Peytremann [44] Dopper broadening : Laux [59] Van der Waas broadening: Traving [59], Wakup et a [60] Resonance broadening: Ai and Griem [53], Traving [56] Stark broadening of argon ines: Griem [54], Traving [56], Konjevic and Konjevic [65] Stark broadening of hydrogen ines: Keppe and Griem [54, 67], Vida, Copper and Smith [1, 14-16] Stark broadening of heium ines: Griem et a [76], Dimitrijevic and Saha-Brechot [17], Bassao et a [77] Poarisabiity constant : Handbook of Chemistry and Physics [61] Rerefences [1] Fauchais P 004 Journa of Physics D: Appied Physics 31 R86 R108 [] Pateyron B, Echinger M F, Deuc G and Fauchais P 199 Pasma Chemistry and Pasma Processing [3] Aubreton J, Echinger M F, Fauchais P, Rat V and Andre P 004 Journa of Physics D: Appied Physics [4] Aubreton J, Echinger M F, Rat V and Fauchais P 004 Journa of Physics D: Appied Physics [5] Cressaut Y and Geizes A 001 Progress in Pasmas Processing of Materias 433 (New York, Ed. Bege House, Pierre Fauchais) [6] Sooukhin R I 1987 Handbook of radiative heat transfer in High-Temperature gases (New York, Hemisphere Pubishing Corporation) 6

28 [7] Geizes A, Gonzaez J J, Liani B and Rayna G 1993 Journa of Physics D: Appied Physics [8] Essotani A, Proux P, Bouos M I and Geizes A 1994 Pasma Chemistry and Pasma Processing [9] Moscicki T, Hoffman J and Szymanski Z 008 Optica Appicata [10] Griem H R, Kob A C and Shen K Y 1959 Physica Review [11] Griem H R and Shen K Y 1961 Physica Review, [1] Smith E W, Vida C R and Cooper J 1969 Journa of Research of the Nationa Bureau Standards 73A 405 [13] Vida C R 1964 Zeitschrift für Naturforschung 19A 947 [14] Vida C R, Cooper J and Smith E W 1970 Journa of Quantitative Spectroscopy and Radiative Transfer [15] Vida C R, Cooper J and Smith E W 1971 Journa of Quantitative Spectroscopy and Radiative Transfer [16] Vida C R, Cooper J, and Smith E W 1973 Astrophysica Journa Suppement Series [17] Dimitrijevic M S and Saha-Bréchot S 1985 Physica Review A [18] Benjamin R A, Skiman E D and Smits D P 00 The Astrophysica Journa [19] Scott C D 1970 Line broadening of the heium tripet diffuse series of heium in arc-jet pasma (Houston, Texas, Nationa Aeronautics and Space Administration, Technica Memorandum, NASA TM X-58050, N ) [0] Godin D and Trépanier J Y th Internationa Symposium on Pasma Chemistry 1 39 [1] Chase M W Jr, Davies C A, Downey J R Jr, Frurip D J, McDonad R A and Syverud A N 1985 JANAF Thermochemica Tabes 3 rd Edition, Journa of Physica and Chemica Reference Data 14 suppement n 1 American Chemica Society [] Drawin H W and Feenbok P 1965 Data for pasma in oca thermodynamic equiibrium (Gauthier-Viars, Paris) [3] Bacri J and Raffane S 1987 Pasma Chemistry and Pasma Processing [4] Herzberg G, 1950 Moecuar Spectra and Moecuar Structure I : Spectra of diatomic moecues. (New York, Van Nostrand Reinhod, 658p.) [5] Dreishak K S, Aeschiman D P and Buent Cambe A 1965 Phys. Fuids [6] Bacri J, Lagreca M and Medani A 198 Physica C [7] Huber K P and Herzberg G 1978 Moecuar Spectra and moecuar structure: IV. Constants of Diatomic Moecues, (New York: Van Nostrand-Reinhod) [8] Hirschfeder J O, Curtiss C F and Byron Bird R 1964 Moecuar theory of gases and iquids (New York, John Wiey and Sons) [9] Siege R and Howe J R 199 Therma radiation and heat transfer (New York and London, Tayor & Francis, 3 th Edition) 7