Plasma Chemistry and Plasma Processing, Vol. 14, No. 3, 1994

Effect o f the Presence of Iron Vapors on the

Volumetric Emiss ion of Ar /Fe and A r / F e / H 2 P lasmas

A. Essoltani, ~ P. Proulx, ~ M. I. Boulos, ~ and A. Gleizes 2

Received August 20, 1993; revised December 15, 1993

The net volumetric emission coe~cient was calculated using the escape factor method for Ar/Fe and Ar/H2/Fe plasmas, at atmospheric pressure, over the tem- perature range from 3000 K to 30,000 K. The calculation involved 712 lines for Ar l, Ar H, and Ar lll, 3481 lines for Fe l, Fell, and Fe lll. and230 lines for H in the Ar/H2/Fe case. A semiempirical method was used for the determination of line profiles and line broadening. The results show a strong influence of the presence of even traces of iron vapors at low temperatures where the volumetric emission increases by several orders of magnitude. Special attention is given to self:absorp- tion of the argon resonance lines which prevents the radiation from escaping within a few millimeters from the emission source.

KEY WORDS: Volumetric emission; argon plasma; iron emission; atmospheric plasma.

1. I N T R O D U C T I O N

In applications of the thermal plasmas such as spray coating, powder treatment, near-net shape metal deposition, ultrafine powder production, to name a few, as well as in high-power arcs where electrode erosion can be important, plasmas are contaminated by the presence of metallic vapors. These vapors not only modify considerably the thermodynamic and trans- port properties of the plasmas C~) but also have a strong influence on the radiative losses from the plasma, C2) and subsequently on the plasma tempera- ture field. °) It is well known that a metallic vapor radiates in general much more than normal gases used for plasma generation such as At, N2, H2, and He. Cram ~4) and Essoltani et al. ~2) have studied the influence of metallic vapors on the radiative losses of an argon plasma. Their results show that

ZPlasma Technology Research Centre (CRTP), Department of Chemical Engineering, Univer- sity of Sherbrooke, Sherbrooke, Qu6bec, Canada, J1K-2Rl.

2Centre de Physique Atomique, Universit6 Paul Sabatier, Toulouse, France.

301 0272-4324/94/0900-0301507.00/0 (~ 1994 Plenum Publishing Corporation

302 Essoltani et al.

even small amounts of metal vapors can have a considerable influence on the volumetric emission coefficient of the plasma.

Since for thermal plasmas line emission is the major source of radiation, the diffusion method is not a practical solution. Cram ¢4) proposed the use of a statistical method for the evaluation of the transition probabilities (A,,,) needed for the calculation of line emission. He further applied this technique to the case of the iron atom. In order to account for self-absorption, Lowke ~5) proposed a simplified method based on the concept of the "net emission coefficient" in which the plasma is assumed to be locally homogeneous and isothermal. In spite of its relative simplicity and the important assumptions involved, the method has been showed to give results comparable to more rigorous radiative transfer methodsJ 6) As one can expect, the net emission coefficient method gives good results in the hot core of the plasma and is expected to be less accurate where the temperature gradients are more pronounced.

In the present work we have used the net emission coefficient method for the calculation of the volumetric emission coefficient for Ar /Fe and Ar / Fe/H2 plasmas. Instead of using the statistical method for the prediction of the A,,,, which is only accurate within a factor of 2 according to Cram, ca) we based our calculation on available spectroscopic data for these values. This involves the consideration of more than 3400 spectral lines for the iron emission spectrum and more than 700 spectral lines for argon. These lines were all calculated individually since they are assumed not to overlap accord- ing to the proposed method. ~5)

2. THEORETICAL BACKGROUND

2.1. Equilibrium Composition

The composition of an Ar /Fe plasma at atmospheric pressure was cal- culated over the temperature range 3000 to 30,000 K assuming local thermo- dynamic equilibrium (LTE). The atomic species, the electron, and the first three ions were considered. The equilibrium composition is determined through the solution of the Saha and mass action law equations, Dalton's law, under chemical and electric neutrality constraints. The corresponding partition functions are calculated based on the known energy levels and the lowering of ionization potential according to Griem. <7) The partition functions were compared to those calculated by Shozo ~s) and were found to be in close agreement. The resulting nonlinear system of equations is solved using Newton's method. The composition of the plasma for the Ar /H2/Fe cases was calculated in the same fashion.

Volumetric Emission in Argon Plasmas 303

2.2. Net Emission Coefficient

The net radiation emitted by the plasma was evaluated as the difference between the local volumetric emission and self-absorption within the elemen- tal control volume assumed to be at constant pressure and temperature. The amount of self-absorption depends generally on the emission spectrum from the plasma, which makes the formal calculation of the net emission a very heavy and complex procedure. Lowke c5) proposed a simplified approach by assuming a uniform cylindrical element of the plasma of radius R. The resulting expression for the net emission coefficient is

eu = B v K ' G I ( K ' R ) dv (1)

where By is the Planck function, K" is the monochromatic absorption coefficient, and G~ is a function accounting for the geometry of the system. Under LTE conditions, KirchhoWs law is valid. The function G~ can be approximated by an exponential expression, which gives rise to the following equation for the net emission coefficient

eu = BvK" exp[-(K;R)l dv (2)

The local emission includes both the line emission and the continuum emis- sion. Under the present conditions (Ar plasma in the presence of iron vapors) line radiation is by far the dominating emission mechanism. Furthermore, in thermal plasmas the energy radiated as continuum emission is mostly due to recombination, while Bremstrahlung has only a minor contribution over the temperature range investigated (9) (less than 1% for T< 30,000 K).

2.2.1. Continuum Radiation

When a z-charged ion recombines with an electron to give an excited atom or ion, ( z - 1 ) charged, there is emission according to the following mechanism :

A~.p+e- ---* A ~ t + h v (3)

where A ~ is the parent ion "p," with z positive charges, and A~.~ -~ is an atom or ion, with a parent "p" and z - 1 positive charges in excited state i. The energy of the photon emitted is given by

h v ( E ~ i ~ - AE) + Ee - E~- ' (4)

where .-- i Elim~ is the ionization energy of the atom or ion A~,~ ~ of parent "p," AE is the lowering of the ionization potential, Ee is the energy of the free electron, and E~-t is the energy of the atom or ion A ~ ~ .

304 Essoltani et aL

The rate of recombination given by the number of recombinations with electrons with velocities between v and v +d r per unit volume and time is given by

dn~ = ne " , n~ff(v)v • dv~r~(v) (5)

where n,, is the electron density, n~.p is the number density of parent "p" with z positive charges,f (v) is the distribution function of the electron velocities, and cr~,(v) is the cross-section for radiative recombination. The spectral emis- sion coefficient for the level i, p is written as

E~;; 1(v) - hv dn~ (6) 4zr dv

Using Milne's relation, and the expression my" dv=h dr, the emission coefficient can be written as

h a v 3 I e [ ; ' ( v ) = : f(v) g~- o.~,7~(v ) (7)

• nent,p 4rcrn3c2 ¥2 g'-t,p

where cr~.p~(V) is the photoionization cross-section, g~-~ and g~'p are the degeneracies of A~.~ t and Al, p.

If the distribution function is Maxwellian and the population of the levels follows Boltzmann's law, we have

ef.p ' (v)= t~ ( 1 )3/2 v3 nenf., ~ cr:p(v)exp[-E,,/kT,,] (8) c- \2~mkmk] T,3,/z g,,p '

n,a~: v3 gf-i o-f, pl(V) exp[(E~ - ~ - h v - E f - I - A E ) / k T ~ ] e~.;'(~) = c , ~ U:(T,,) (9)

where h 1

Cl = (10)

n-- is the total population of the z-charged ions, U:(T,,) is the partition function of the z-charged ion, and E~- t is the first ionization energy of the atom or ion (of charge z - 1). From the summation of all the levels of the atom or ions corresponding to the frequency v, the total emission coefficient is obtained as

?le nz V 3 e-'-I(v) = Ct~73/_, - - exp[(E~ -I - h v ) / k T e ]

T,, - U--(T~)

× ~g:~-t~r:g.-~(v) e x p [ - ( E ~ - ' + A E ) / k T e ] (11) i,p

Volumetric Emission in Argon Plasmas 305

The main difficulty in the evaluation of the total emission is the cross-sections for photoionization. It is usual to express the total emission as a function of eh- t (v) obtained when using the cross-sections of Kramers tt°) valid for hydrogenoid atoms or ions. The following formulation is obtained:

C~nan:Z z e:- '(v) = U._(T,,)T~/2 (1-exp[-hv/kT~])g~.~

[v3 exp[(E~-'-AE)/kTe]~,g~-' cr,f, '(v) exp[-E~-' /kTe].] (12)

x Teg~t- 'Z2(exp[hv/kTe] - 1 )

which can be rewritten as

e:-'(v)= C3nen: Z 2

U-'(T,.) T,)/2 ( 1 - exp [ -h v/k Te])g:l.i

× I.Cjv3 exp[(E~S' - AE)/kTe] Zg~-' cr~.pt( V) exp[-E~-' /k T,,] 1 - - - I ") C3T,,gh Z'(exp[hv/kTe]- 1)

(13)

e:- ' (v)= e~-'(v) . ~-'-'(v, T,,) (14)

where ~:-~ is the Biberman-Schluter factor which takes into account the atomic structure of the [ z - 1] charged ion (or atom).

~-'-'(v, Te)=[ C2v3 exp[(E~-AE)/kT']zg'pg~-' exp[-E:i-'/kT,,]cr:~,;'(v)] T,,g~,Z2(exp[h v/kT~] - 1 )

(15)

with

C2 - 3x/~h4c (16) 327r2k( e2 /4zr e, o) 3

and

C3 = 5.44 x 10-szJ - m 3 - sr -t . K j/2 (17)

In the case of argon, we used, for the Biberman-Schluter factors, the values calculated by Hofsaess~J~ with the scaled Thomas-Fermi potential method. For iron we assumed a hydrogenoid structure; the factor 4: - ~ was therefore calculated using the photoionization cross-sections of Kramers. ~°~

306 Essoltani et aL

2.2.2. Line Emission The emission coefficient for a transition between an upper level i and

a lower level j is given by

hv~j e,j (v) = ~ ,4 ~,P,j(v) (18)

where v U and A0 are the frequency and probability of spontaneous emission of the line, ni is the density of the emitting ion or atom, and P0 is a normalized function for the line profile. This profile could be, depending on the broaden- ing mechanism, a Lorentz, Gaussian, or Voigt profile.

In order to calculate the net emission from each line, we introduce here the escape factor A~j, which is defined as the ratio of the net power eu,, emitted by the plasma (taking into account self-absorption) to that of an optically thin plasma:

A ~ - 4tr su,j (19) hvoAijni

where n~ is the number of atoms or ions in the excited state i. This escape factor has been calculated following the method of Drawin and EmardC6):

AU= fo~p~j(v) exp(_rij P~(v) I e,AG-;= Vo)) dv (20)

where Vo is the natural frequency of the line and, r~j is the monochromatic optical thickness of the line, given by

l~e 2

•ij = --fipjRPq( v = v0) (21) m o c

wheref, j is the absorption oscillator strength of the line and nj is the density of the absorbing atoms.

Since the Drawin-Emard method is based on the assumption of a homo- geneous and isothermal plasma, the above approach will apply only for small values of the elemental control volume. This is not a serious limitation since, as shown in the next section, most of the self-absorption takes place within a 1 mm radius of the control volume over which the assumption of homogeneity would be valid for most plasma sources. The assumption breaks down, however, in the fringes of the arc or dc plasma jet where steep temperature gradients of the order of l0 s K / m m are present. Because of the relatively low temperatures in these fringe zones, radiative energy losses have a negligible effect on the calculated temperature fields, which are dominated by conduction and convective transfer mechanisms.

Volumetric Emission in Argon Plasmas 307

The calculation of the escape factor for an actual Voigt profile was proposed by DrawinJ 6~ The following form is assumed for the escape factor:

Ao .v _- AoC + f (a i j , ri/)A~. (22)

where A~ and A S are, respectively, the escape factors calculated using a Gaussian and a Lorentz profile. The following analytical expression for the function f is proposed by Drawin ~6> :

ao/3rij (23) f ( a ° " r ° )=z (U(O ' a°))°5 1 0.5 0.5 +/3(a~ r ~ + a : ~ )

where/3 = 100 and a 0 is the ratio of the Lorentz profile broadening to the Gaussian profile broadening.

1 ~o5[ a° I-' (24)

2.2.3. Line Profiles

The line profiles and line broadening phenomena appear directly in the expression for the calculation of the escape factor A~j according to Eq. (20). Line overlap was, however, not taken into account since it increased considerably the complexity of the computations from a numerical stand- point. Moreover, in a study of SF6 emission at atmospheric pressure, Gleizes et alJ 12) have shown that neglecting line overlap resulting in an overestima- tion of eu by less than 15% over the temperature range investigated, which is within the expected uncertainty of the present calculation.

Since here we do not take into account line overlap, there was also no need to calculate the line shift that may be present in thermal plasmas. We include therefore only line broadening mechanisms that were classified into two classes depending on the type of profile (Gaussian or Lorentzian). Other than the Doppler broadening which induces Gaussian profiles, all other broadening effects considered induce Lorentz profiles. Since we treat a large number of lines, we used the semiempirical methods of line broadening described by Traving. ~t3~

2.2.3.1. Gaussian Profiles. Doppler broadening can be expressed, if the atom velocity distribution is Maxwellian, as follows:

Pij(2Q - (log 2 ) 1 / - " exp - log 2 (25) (~ DT( I /2

308 Essoltani et aL

where the half-width of the Doppler broadening is given by Traving(~3):

250 = 22o( 2 log 2 kTI °s ~ c 5 j (26)

where rn is the atomic mass.

2.2.3.2. Lorentzian Profiles. In resonance broadening the interaction poten- tial has the form [C3/r3], where r is the distance between the atoms. The half-width of the resonance broadening is given by (~)

26 5.48 (~ff/2 noe:f~2~ (27) r = ~ - -- 4rCeo(2:ce)2me

where gz and gr are the degeneracies of the fundamental and resonant levels, no is the atom density in the fundamental state, and f~ is the oscillator strength of the resonant level.

In the case of Van der Waals broadening the interaction of an emitting atom with a neutral is dependent on a potential of the form [C6/r6]. Using the collision approximation, the half-width of the line is given by

25o = 8.16C26/5 V3dSno 2~ (28) 2rr c

V 7~ \ mam b ]

where no is the density of the neutrals and V,b is the average speed of the two particles. The Van der Waals constant (76 is calculated using the hydrogenoid hypothesis. (la)

In the case of Stark broadening, when the interaction involves electrons, the potential is of the type [Ca/r a] and the collision approximation leads to the following two equations for neutrals and ions, respectively:

for neutrals

25e = l l.37C~/3VL)/3ne 2~ (30) 2zrc

for ions

"US Z4/5ne ~0 25, = 200.284C4 ~ 2rrc (31)

where V,, is the mean speed of the electrons ( lie = v f~T/ t rme . The constant (?4 is calculated taking into account all the lines connected to the lower and

Volumetric Emission in Argon Plasmas 309

upper levels of the line. The influence of the ions on the width is taken into account with the quasi-static method of Griem. ~71 The total profile resulting from these three effects is a Lorentzian profile, and the total half-width is given by the sum of the individual widths.

2.2.3.3. Voigt Profiles. The profile of the line broadened by thermal and collision effects is the convolution of a Gaussian function with a Lorentzian function, resulting in the so-called Voigt profile. Its analytical form is given by

I ~ +~- exp(_y2) Pu(X) - j a dy (32)

2~D/r 3/2 (b - y)2 + a2

with

6L 2)0.5 a = - (log (33) ~D

b = ~ ' - 2° (log 2) (34) 6D

3. RESULTS AND DISCUSSION

The calculation of the net volumetric emission of the plasmas is made according to the following procedure:

The composition of the plasma is calculated as described in Section 2. I. The line emission is calculated for all the species considered: 417, 268, and 27 lines for ArI, ArII, and ArIII, respectively, and 3288, 131, and 62 lines for FeI, FeII, and FeIII. For H the total number of lines considered was 230. The following calculation procedure is followed:

- -The escape factor is calculated according to Eq. (20). - -The total line emission is calculated according to Eq. (18). - -The net line emission is calculated by multiplying the total line emis-

sion by the escape factor. - -The continuum emission is calculated according to Eqs. (2) and (13). - -The net volumetric emission of the plasma is the sum of the net

continuum emission and the net line emission for the lines considered.

3.1. Composit ion of the Mixture Ar/Fe

The composition of the plasma at atmospheric pressure was calculated assuming LTE. The species taken into account are Fe, Fe ÷, Fe ÷÷, Fe ÷+÷,

310 Essoltani et al.

log n [m "3]

28 Ar

24 ~ ne C^

~ . . . , , . . _ . . . . . . . . . ~,

- e + s " 1 " ; • . . ' ' : . . . . . . . . . 2O

16

12

," . , ' s A t + / 8 / _ ' " ++

, ' , / , / . . . . . . . . . . 0

2 6 10 14 18 22 26 30

T x 1000 [K]

Fig. I. Composition of an argon plasma at atmospheric pressure in the presence of 0.0l molar fraction of iron vapor.

Ar, Ar +, Ar ++, Ar +++, and e-. The temperature range considered is from 3000 to 30,000 K.

Figure 1 gives the densities of the species present in an atmospheric Ar / Fe plasma containing 0.01 mole fraction of iron vapors. At low temperatures 3000 K < T< 7000 K, the gas is essentially composed of neutral atoms of iron and argon, with few ionic species. With the increase of the plasma temperature beyond 7000 K, the number density of neutral argon decreases monotonically while the iron atom concentration decreases sharply. Because of the low ionization potential of iron (7.9 eV), the electrons produced at these temperatures are essentially due to iron. As can be observed, in the low- temperature region, the number density curve for the electrons is identical to that for Fe +. The contribution of the ionization of argon at low temperatures is small due to its high ionization potential (15.75 eV). At higher tempera- tures ( T > 12,000 K), argon becomes the principal source for electrons as the ionization of iron is almost complete. The concentration of electrons n, slowly increases due to its dependence on multiple ionization phenomena which are important at much higher temperatures.

3.2. Volumetric Emission Coefficient

In this section calculated data for the volumetric emission coefficients of the plasma in the presence of different concentrations of iron vapors is

Volumetric Emission in Argon Plasmas 311

presented over the temperature range 300 to 30,000 K. These are discussed in relation to the contribution of the different emission and self-absorption mechanisms to the net energy emission coefficient. Results are also presented in the presence of hydrogen in the plasma to access its influence on the basic mechanisms involved and the net emission data under such conditions. All the results are reported for an atmospheric pressure discharge.

3.2.1. Contribution of the Different Em&sion Mechan&ms to the Total Radiative Power of the Plasma

Figure 2 shows the net radiative emission coefficient for an argon plasma in the presence of 0.01 mole fraction iron vapor. The calculation was carried out in this case for a small cylindrical control volume of radius R = 1 mm. At low temperatures ( T < 7000 K) the iron contribution to total radiation is orders of magnitude stronger than that of argon. This is due to the low ionization potential of iron and its low energy of the first excited levels (0.051 eV) compared to that of argon ( l l . 5eV) . At high temperatures ( r > 20,000) iron contribution to the net emission from the plasma becomes small compared to that of argon.

This figure also shows the relative importance of line emission compared to continuum emission. At low temperatures, due to the important fraction

log EN[W/m 3j 14

13 Total radiation Une radiation

11

I0 ~ . . . f - - - ~ - ' ' " , , . _ . . . . . . .

8

7

6

5

4 3 -

1 / ! I o _ , _ _ / I , . ./ , , , , , . . . . ~ ~ 0

2 6 10 14 18 22 26 30

T x looo [~q

Fig. 2. Net radiative emission coefficient for an argon plasma at atmospheric pressure in the presence of 0.01 molar fraction of iron vapor.

312 Essoltani e t al.

log £N[W/m 3j

]4

13 12 11

8 • ,

7

6

5 l

4

2

1

0 ! I

... = . ~ . = . - - - - " - - . . . . . - ~

pure Fe

/ , , , . . \ \ . / \ \ - .,o e r ~ ,01 Fe

pure Ar

2 6 10 14 18 22 26 30

T x 1000 [K]

Fig. 3. Effect of the iron vapor concentration on the net emission coefficient for an Ar/Fe plasma.

of iron ionized, the continuum emission of iron is higher than the contribu- tion of argon.

Figure 3 presents the results in terms of the net emission coefficient for varying iron vapor concentrations. The curve for pure argon is included for comparison. We observe that most of the radiated energy is due to iron. A mole fraction of 0.01 iron vapor is enough to have a dominating effect on the mixture up to 15,000 K. At higher temperatures, argon emission increases considerably and dominates the total volumetric emission from the plasma above 20,000 K.

3.2.2. Self-absorption

Special attention was given to the question of self-absorption which can have a strong influence on the net emission coefficient from the plasma. The effect is demonstrated in Fig. 4 which shows the results of calculation of the net emission coefficient for an Ar /Fe plasma (0.01 molar fraction Fe) as a function of temperature, for different radii of the cylindrical control volume elements. The curve given for R = 0 corresponds to the case of an optically thin plasma when self absorption is not taken into account.

As expected, the results show a decrease of the net emission coefficient with an increase in the radius of the control volume. The effect is, however

Volumetric Emission in Argon Plasmas 313

l o g eN[W/m 3J 14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

X Fe = .01

I i i ! I * * * | * | * 1 i *

2 6 10 14 18 22 26 30

T x 1000 [K]

Fig. 4. Effect of the radius of the control volume on the net emission coefficient for an Ar /Fe plasma.

particularly important in the first millimeter surrounding the emission source when a substantial fraction of the emitted radiation is absorbed. For larger control volumes (R > 1 mm), only a smaller level of self-absorption is noted, which supports the view that the plasma could still be considered as being optically thin (as a first approximation) as long as self-absorption over the first millimeter of the radiation path is taken into account in the evaluation of net volumetric emission coefficient data.

3.2.3. Effect of the Presence of Hydrogen

Figure 5 shows the influence of the presence of hydrogen on the radia- tion of the mixture Ar /Fe /H2. It is clear that even with a 30% mole fraction of hydrogen in the plasma the total radiation is still dominated by the presence of metal vapors. The presence of hydrogen has only a minor influ- ence, suppressing slightly the total emission at temperatures above 18,000 K. This is mostly due to the fact that at these temperatures the hydrogen atoms are completely ionized. The effect is, however, considerably smaller than that caused by the presence of even the smallest traces of metallic vapors.

314 Essoltani et aL

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

X H 2 =0'01 " ~

=0.30

2 6 10 14 18 22 26 30 T x 1000 [K] Fig. 5. Effect of the hydrogen concentration on the net emission coefficient for an Ar /H2 /Fe

plasma.

4. CONCLUSION

In the present paper we present the results of calculation of the net radiative emission coefficient for an argon plasma contaminated with iron vapors, using the escape factor method in which the lines are treated indi- vidually and is therefore useful for the study of spectra. In the implementa- tion of the method we used a semiempirical approach for the calculation of line profiles and broadening calculation. The results show a strong influence of the presence of iron vapors on the net emission of the argon plasma at atmospheric pressure. The effect is particularly important at temperatures below 18,000 K. At higher temperatures, argon emission dominates the total volumetric radiation from the plasma. The results imply that in the modeling of plasma discharges in the presence of metal vapors the increased volumetric emission coefficient will decrease significantly the predicted plasma temperatures.

Self-absorption also plays an important role at low temperatures. As was shown, a significant fraction of the emitted radiation is locally absorbed within the first millimeter from the emission source. The importance of the metal vapor radiation is noted both for Ar/Fe and the Ar/Fe/H2 mixtures. The results show that the presence of a 30% mole fraction of hydrogen has a negligible influence on the net volumetric emission of the plasma.

Volumetric Emission in Argon Plasmas 315

ACKNOWLEDGMENTS

Financial support of the National Sciences and Engineering Research Council of Canada and of the Minist6re de l'Education du Qu6bec is grate- fully acknowledged. This study was conducted as part of a France-Qu6bec scientific exchange program.

REFERENCES

1. H. Abdelhakim, J.-P. Dinguirard, and S. Vacqui6, J. Phys. 13, 1427 (1980). 2. A. Essoltani, P. Proulx, M. I. Boulos, and A. Gleizes, J. of Analytical Atomic Spectrometry,

5, 543 (1990). 3. P. Proulx, J. T. Mostaghimi, and M. I. Boulos, Int. J. Heat Mass Transfer34, 2571 (1991). 4. L. Cram, J. Phys. D. 18, 401 (1985). 5. J. Lowke, J. Quant. Spectrosc. Radiat. Transfer 14, I I (1974). 6. H. W. Drawin and F. Emard, Beitr. Plasmaphys. 13, 143 (1973). 7. H. R. Griem, Plasma Spectroscopy, McGraw-Hill, New York (1962). 8. T. Shozo and T. Kuroda, Spectrochim. Acta 42b, l l05 (1987). 9. P. Ranson, Doctoral Thesis, Universit6 d'Orl6ans, 1978.

10. H. A. Kramers, Philos. Mag. 46, 836 (1923). I I. D. Hofsaess, J. Quant. Spectrosc. Radiat. Transfer 19, 339 (1978). 12. A. Gleizes, B. Rahmani, J. J. Gonzales, B. Liani, J. Phys. D. 24, 1300 (1991). 13. G. Traving, Plasma Diagnostics, W. Lochte-Holtgrevcn, ed., Elsevier, Amsterdam (1968). 14. R. L. Kenieth, Astrophysical Formulae, Springer-Verlag, Berlin (1978).