M Wendt
email: wendt@inp-greifswald.de

Net emission coefficients of argon iron plasmas with electron Stark widths scaled to experiments

Keywords: numbers: 52.25.Os, 52.77.Fv, 81.20.Vj

The net emission coefficient of plasmas containing argon and iron at atmospheric pressure is calculated and analysed for the case of cylindrical geometry. Its values are obtained by integrating the monochromatic net emission coefficient taking into account continuous and line radiation. The width of the spectral lines is determined by Doppler broadening, natural, resonance, van der Waals, electron and ion Stark broadening. As Stark broadening is the most important broadening mechanism in the considered pressure and temperature range, the electron Stark widths are calculated following the semi-empirical Stark broadening theory. Additionally, the electron Stark widths of Ar, Ar + , Fe and Fe + are multiplied by scaling factors in order to reproduce experimental electron Stark widths. The scaling factor is determined for each species separately. For small plasma radii the net emission coefficient determined here shows good agreement with literature values where spherical geometry is considered while they decrease faster with increasing plasma radius. This behaviour is caused by the increase of the irradiation of the symmetry axis when cylindrical instead of spherical geometry is considered. For radii and temperatures typical of the metal filled core of arcs occurring in gas metal arc welding processes, i.e. radii between 1 and 2 × 10 -3 m and temperatures between 5000 and 10000 K, the scaling of the Stark widths increases the net emission coefficient of iron plasmas by between 2 and 23 %. In this parameter range the net emission coefficient of iron plasmas for cylindrical geometry is between 30 and 37 % smaller than values calculated for spherical geometry.

Introduction

In atmospheric pressure arcs such as welding arcs [START_REF] Zielinska | Investigations of GMAW plasma by optical emission spectroscopy Plasma Sources[END_REF][START_REF] Rouffet | Spectroscopic investiagtion of the high-current phase of a pulsed GMAW process[END_REF] the energy transport by radiation has a significant influence on the energy balance and needs to be included in corresponding numerical models. The conditions in these arcs are such that the plasma is optically thick in a significant range of wavelengths so that a treatment of the radiation transport has to take into account reabsorption. An exact treatment of the radiation transport based on the radiation transport equation leads to high numerical costs, because application relevant species like iron show a multitude of spectral lines. In numerical models of atmospheric pressure arcs the exact radiation transport term is consequently often replaced by the net emission coefficient as introduced by Lowke [START_REF] Lowke | Predictions of arc temperature profiles using approximate emission coefficients for radiation losses[END_REF]. Thus net emission coefficients remain important input data for numerical modelling of welding arcs as done by e.g. Lowke et al [START_REF] Lowke | Metal vapours in MIG arcs cause (1) minima in central arc temperatures and (2) increased arc voltages[END_REF] and Schnick et al [START_REF] Schnick | Metal vapour causes a central minimum in arc temperature in gas-metal arc welding through increased radiative emission[END_REF]. The use of net emission coefficients in such models has the drawback that it does not take into account the inhomogeneity of the temperature and the spatial distribution of the elements in experimental arcs. More advanced approximations of the radiation transport equation are discussed by e.g. Modest [START_REF] Modest | Radiative heat transfer[END_REF].

Net emission coefficients of argon iron plasmas have been calculated by Cram [START_REF] Cram | Statistical evaluation of raditive power losses from thermal plasmas due to spectral lines[END_REF], Essoltani et al [START_REF] Essoltani | Radiation and self-absorption in arong-iron plasmas at atmospheric pressure[END_REF], Gleizes et al [START_REF] Gleizes | Calculation of net emission coefficient of thermal plasmas in mixtures of gas with metallic vapour[END_REF], and Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF]. Net emission coefficients for iron-helium plasmas have been calculated by Moscicki et al [START_REF] Moscicki | Net emission coefficients of low temperature thermal iron-helium plasma[END_REF].

Cram [START_REF] Cram | Statistical evaluation of raditive power losses from thermal plasmas due to spectral lines[END_REF] considers line radiation only. In this investigation the total number of lines is estimated from a subset of spectral lines by means of a statistical method [START_REF] Allen | Statistical spectroscopy[END_REF], so that the need for extensive line data tabulations is eliminated. The only considered broadening mechanism is Stark broadening, and absorption is accounted for by means of line escape factors [START_REF] Drawin | Optical escape factors for bound-bound and free-bound radiation from plasmas. I. Constant source function[END_REF][START_REF] Irons | Escape factors in plasma spectroscopy .1. Escape factors defined and evaluated[END_REF]. Essoltani et al [START_REF] Essoltani | Radiation and self-absorption in arong-iron plasmas at atmospheric pressure[END_REF] use line data tables from the National Institute of Standards and Technology (NIST), and include bound-free and free-free radiation. The line broadening takes account for natural, resonance, van der Waals, Stark and Doppler broadening while absorption is treated by line escape factors. Gleizes et al [START_REF] Gleizes | Calculation of net emission coefficient of thermal plasmas in mixtures of gas with metallic vapour[END_REF] also consider line and continuous radiation processes using improved line data tables from NIST and additional data from Kurucz and Peytremann [START_REF] Kurucz | A table of semi-empirical gf values Smithonian[END_REF]. Doppler broadening and pressure broadening are considered. Absorption of lines with high emissivity is treated using escape factors while lines with low emissivity and the continuum are considered as optically thin. Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF] take account for both line and continuum radiation. Their results are based on line data tables from NIST and the Kurucz database. Extrapolation procedures are employed to add missing atomic levels and lines so that these authors include still more spectral lines than Gleizes et al [START_REF] Gleizes | Calculation of net emission coefficient of thermal plasmas in mixtures of gas with metallic vapour[END_REF]. The net emission coefficients are calculated by integrating the monochromatic net emission coefficient. Moscicki et al [START_REF] Moscicki | Net emission coefficients of low temperature thermal iron-helium plasma[END_REF] also include line and continuum radiation. Their results are based on line data tables given by Bautista [START_REF] Bautista | Atomic data from the iron project -XX. Photoionization cross sections and oscillator strengths for Fe I Astron[END_REF] and Nahar [START_REF] Nahar | Atomic data from the iron project -VII. Radiative dipole transition probabilities for Fe II[END_REF]. These tables of theoretical transition probabilities provide approximately the same number of lines for neutral iron as used by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF] while the number of lines given for singly and doubly ionized iron ions is approximately a factor of two smaller.

Essoltani et al and Gleizes et al estimate the electron Stark widths via classical formulae [START_REF] Traving | Lochte-Holtgreven W Plasma diagnostics[END_REF]. The present work follows the more accurate method used by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF][START_REF] Menart | Line-by-line method of calculating emission ceofficients for thermal plasmas consisting of monatomic species[END_REF]. Menart et al calculate electron Stark widths using the semi-empirical theories of Griem [START_REF] Griem | Semiempirical formulas for the electron-impact widths and shifts of isolated ion lines in plasmas[END_REF], and Dimitrijević and Konjević [START_REF] Dimitrijević | Simple formulae for estimating Stark widths and shifts of neutral atom lines[END_REF][START_REF] Dimitrijević | Stark widths of doubly-and triply-ionized atom lines[END_REF]. These theories take into account quantum mechanical effects and inelastic collisions between the radiator and electrons. In order to use electron Stark widths that closely reproduce experimental electron Stark widths, a scaling factor is introduced for each species where experimental electron Stark widths are available. While this procedure is applied to argon and copper in [START_REF] Menart | Line-by-line method of calculating emission ceofficients for thermal plasmas consisting of monatomic species[END_REF] it is not mentioned in [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF] so that to our knowledge it is first applied to iron here.

The earlier investigations on argon iron plasmas [START_REF] Essoltani | Radiation and self-absorption in arong-iron plasmas at atmospheric pressure[END_REF][START_REF] Gleizes | Calculation of net emission coefficient of thermal plasmas in mixtures of gas with metallic vapour[END_REF][START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF][START_REF] Moscicki | Net emission coefficients of low temperature thermal iron-helium plasma[END_REF] consider an isothermal, homogenous plasma of spherical shape while this work assumes cylindrical geometry. This change of geometry leads to an increased irradiation at the symmetry axis so that the net emission coefficient is reduced. The net emission coefficients presented below are based on the monochromatic emission coefficient for argon iron plasmas assuming local thermodynamic equilibrium (LTE). The monochromatic emission coefficient includes line radiation, free-bound and free-free transitions. The spectral lines are broadened by natural, resonance, van der Waals, electron and ion Stark broadening and by Doppler broadening.

Theory

The net emission coefficient net is defined as the power lost by radiation per volume and solid angle, that is

net = λ ( λ -κ J λ ) dλ ( 1
)
where λ is the monochromatic emission coefficient per wavelength λ, κ the monochromatic absorption coefficient including induced emission and

J λ = 1 4π Ω L λ dΩ (2)
the solid angle averaged spectral radiance impinging onto the considered point in the plasma. On the axis of a homogeneous, cylindrical plasma column of radius R it holds

net (R, T ) = λ λ (T ) G 1 (κ R)dλ (3)
where G 1 is a function taking account for the considered geometry. For cylindrical geometry it holds [START_REF] Church | Studies of highly radiative plasmas using the wall-stabilzed pulsed arc discharge[END_REF] G

1 (x) = π/2 0 exp - x sin φ sin φ dφ . (4)
It can be shown that G 1 is identical to Ki 2 , the second integral of the modified Bessel function K 0 [START_REF] Abramowitz | Handbook of mathematical functions[END_REF]. It has the limits 1 -πx/2 and π/(2x) exp(-x) for small and for large x, respectively. While Lowke [START_REF] Lowke | Predictions of arc temperature profiles using approximate emission coefficients for radiation losses[END_REF] evaluated G 1 (x) by a numerical treatment of (4), Lee [START_REF] Lee | On the theory of radiation-dominated wall-stabilised arcs[END_REF] used series expansions based on modified Bessel functions. For spherical geometry it holds G 1 (x) = exp(-x).

In local thermodynamic equilibrium the monochromatic emission and absorption coefficients obey Kirchhoff's law

λ = κ L Pl λ (5)
where

L Pl λ = 2hc 2 λ 5 exp hc λkT -1 (6)
is the black body spectral radiance with h, c, k, and T being the Planck constant, the velocity of light, the Boltzmann constant and the temperature, respectively. In (3) Kirchhoff's law is used to express the absorption coefficient by the emissions coefficient. The total monochromatic emission coefficient λ is the sum of the species emission coefficients λ,r where r denotes the atomic and ionic species of the plasma. As the emission coefficients λ,r are proportional to the species densities N r , the plasma composition needs to be known. The plasma composition is calculated assuming LTE taking weakly non-ideal corrections due to the Coulomb interaction into account [START_REF] Ebeling | Ergebnisse der Plasmaphysik und der Gaselelectronik Band[END_REF]. The composition includes the species Ar, Ar + , Ar 2+ , Fe, Fe + , Fe 2+ , and electrons. The definition of the iron mole fraction x Fe , the equation of state and the Saha equation for stepwise ionization thus read

x Fe = N Fe + N Fe + + N Fe 2+ N Fe + N Fe + + N Fe 2+ + N Ar + N Ar + + N Ar 2+ (7)
P = kT r N r + kT N e + P Co (8
)

N e N z+1 N z = 2 Z z+1 Z z Λ 3 z Λ 3 e Λ 3 z+1 e -(Iz+µ Co e +µ Co z+1 -µ Co z )/(kT ) (9)
where P , N e , P Co , µ Co e and µ Co r are the total pressure, the electron density, the Coulombpressure, the non-ideal chemical potentials of the electrons, and the non-ideal chemical potentials of atoms or ions, respectively. Indices z and z + 1 denote an atomic or ionic species with charge number z and its ion of the next ionization step, respectively. In (9)

Z r (T ) = r g i,r e -E i,r /kT + e -Ir/kT E i,r -I r kT -1 (10)
is the Planck-Larkin partition function of species r with ionization energy I r , internal state energies 0 ≤ E i,r < I r , and statistical weights g i,r , and Λ k = h (2πm k kT ) -1/2 with k = r or e is the thermal DeBroglie wavelength of species k with mass m k . The Planck-Larkin partition function arises from the quantum statistical theory presented in [START_REF] Ebeling | Ergebnisse der Plasmaphysik und der Gaselelectronik Band[END_REF]. Using the Debye-Hückel screened potential with minimum contact distance Λ e /8 leads to the non-ideal terms

P Co = - 128kT πΛ 3 e q(q + 2) 2(q + 1) -log (1 + q) (11)
µ Co k = - (ez k ) 2 8π 0 r D 1 1 + q ( 12
)
where e is the elementary charge, 0 is the permittivity of free space, k = r or e,

r D = 0 kT e 2 (N e + r z 2 r N r ) 1/2 (13)
is the Debye length and q = Λ e /(8r D ). The non-ideal chemical potentials µ Co k lead to an apparent reduction of the ionization energies. For the plasmas considered here the above non-ideal corrections remain small. For pure argon and pure iron plasmas they lead to a maximum increase of the electron density by 8 and 13 %, respectively.

Emission coefficients

For each atom or ion r the monochromatic species emission coefficient is given by

λ,r = bb λ,r + fb λ,r + ff λ,r (14)
where the right hand side terms represent bound-bound, free-bound and free-free transitions corresponding to line radiation, radiation from the recombination continuum and bremsstrahlung, respectively. For each of these processes a corresponding induced emission process and an absorption process exists. The treatment of each emission process is described below. The subscript λ denotes that a spectral quantity is given per wavelength unit. The emission coefficient for line radiation of atomic or ionic species r is given by bb

λ,r = ul hc 4πλ ul A ul N u P λ (λ) ( 1 5 )
where λ ul , A ul , N u , and P λ (λ) are the wavelength of the transition from upper state u to lower state l, the transition probability, the upper state density and the line profile function, respectively. The index ul on P λ (λ) has been dropped. The width and shape of the profile function depends on temperature and the plasma composition and has to be calculated for each line separately. The line profile function used here is described in section 2.2. The emission due to the recombination of ions and electrons forming species r is given by the emission coefficient [START_REF] Richter | Plasma Diagnostics[END_REF] fb

λ,r = N r Z r 2hc 2 λ 5 e -hc/(λkT ) i σ i,r (λ)g i,r e -E i,r /(kT ) . (16)
Here, σ i,r is the photoionization cross section of internal state i. For excited states the semiclassical photoionization cross section [START_REF] Richter | Plasma Diagnostics[END_REF] σ i,r (λ) = 64π 3

√ 3 a 2 0 α f (z r + 1) 4 E H hc 3 λ 3 n * i,r 5 (17)
is used. Here, a 0 , α f , E H and n * i,r = [E H /(I r -E i,r )] 1/2 are the Bohr radius, the fine structure constant, the Rydberg energy and the effective main quantum number of state i. For wavelengths above hc/(I r -E i,r ) the photoionization cross section is zero.

For the ground states of argon, iron and their ions photoionization cross sections are used which are more accurate than those given by [START_REF] Nahar | Atomic data from the iron project -VII. Radiative dipole transition probabilities for Fe II[END_REF]. Following [START_REF] Aubrecht | Radiation properties of argon thermal plasma in various spectral regions[END_REF] theoretical Table 1. Parameters of the photoionization cross sections for atomic and ionic ground states as taken from [START_REF] Verner | Atomic data for astrophysics II. New analytic fits for photoionization cross sections of atoms and ions[END_REF] for argon and from [START_REF] Verner | Subshell photoionization cross sections and ionization energies of atoms and ions from He to Zn Atomic Data and[END_REF] for the energy region for iron species, a) 1.709+1 denotes 1.709 × 10 photoionization cross sections from the Opacity Project (OP) [START_REF] Seaton | Atomic data for opacity calculations: I[END_REF] are employed for the ground states of argon and its ions. Verner et al [START_REF] Verner | Atomic data for astrophysics II. New analytic fits for photoionization cross sections of atoms and ions[END_REF] smoothed these cross sections and presented them in the form

σ(E) = σ 0 y (P -11-2 )/2 (x -1) 2 + y 2 w 1 + y y a -P (18)
using the abbreviations x = E/E 0 -y 0 and y = (x 2 + y 2 1 ) 1/2 . Here, σ 0 , E 0 , y 0 , y 1 , y a , y w and P are fit parameters (Table 1), is the orbital quantum number of the photo electron and E = hc/λ is the photon energy. For neutral argon the photoionization cross section given in [START_REF] Verner | Atomic data for astrophysics II. New analytic fits for photoionization cross sections of atoms and ions[END_REF] is in good agreement with the recommended experimental values given by Marr and West [START_REF] Marr | Absolute photoionization cross-section tables for helium, neon, argon, and krypton in the VUV spectral regions[END_REF].

For iron and its ions the photoionization cross sections given in [START_REF] Bautista | Photoionization of neutral iron[END_REF][START_REF] Nahar | Atomic data for opacity calculations: XX. Photoionization cross sections and oscillator strengths for Fe II[END_REF] and [START_REF] Cunto | TOPbase at the CDS[END_REF] are used. Following the approach of Verner et al [START_REF] Verner | Atomic data for astrophysics II. New analytic fits for photoionization cross sections of atoms and ions[END_REF] the autoionization resonances contained in these cross sections are smoothed using a Gauss profile with a half width at half maximum of 5 nm. For high photon energies where cross sections are not given in the OP data, cross sections from Verner et al [START_REF] Verner | Subshell photoionization cross sections and ionization energies of atoms and ions from He to Zn Atomic Data and[END_REF] are employed. These cross sections are best fits to theoretical cross sections calculated using the Hartree-Dirac-Slater method which provides photoionization cross sections with correct non-relativistic high energy asymptotes. They are also given in the form [START_REF] Traving | Lochte-Holtgreven W Plasma diagnostics[END_REF]. While the OP photoionization cross sections for iron take account for ionization from both the 4s and the 3d subshell, the high energy photoionization cross sections of Verner et al [START_REF] Verner | Subshell photoionization cross sections and ionization energies of atoms and ions from He to Zn Atomic Data and[END_REF] treat each subshell separately. The cross sections of the 3d subshell ( = 2) are chosen here because they are approximately one order of magnitude higher than those of the 4s subshell.

The emission due to free-free transitions of electrons in the electric field of ions of species r is treated by the emission coefficient [START_REF] Richter | Plasma Diagnostics[END_REF] ff

λ,r = 16π 3 √ 3 e 2 4π 0 3 z 2 r (λm e c) 2 m e 2πkT e -hc/(λkT ) N e N r . (19)
The free-free radiation emitted in collisions of electrons with neutral species r is described by [START_REF] Brum | Contiuum radiation in a high pressure argon-mercury lamp Plasma Sources[END_REF][START_REF] Kasýanov | On theory of bremsstrahlung of slow electrons on atoms[END_REF] ff

λ,r = hc 4πλ 2 N e N r ∞ E=hc/λ Q(λ, E) 4 πm e kT E kT e -E/(kT ) dE (20)
with

Q(λ, E) = 1 - hc 2λE 1 - hc λE 1/2 8α f 3π E m e c 2 Q mom (E) . (21)
In these expressions E is the kinetic energy of the electron, and Q mom the momentum transfer cross section of the considered atom. In this work the momentum transfer cross sections given in [START_REF] Suzuki | Momentum transfer cross section of argon deduced from electron drift velocity data[END_REF] is used for Ar. For Fe the polarization cross section

Q(E) = 4πA[αe 2 /(4π 0 E)] 1/2
with A = 0.6037 [START_REF] Kihara | Transport properties for gases assuming inverse power intermolecular potentials[END_REF] and the polarization volume α = 8.4 × 10 -30 m 3 [START_REF] Lide | CRC Handbook of Chemistry and Physics[END_REF] is employed to approximate its momentum transfer cross section for elastic collisions with electrons.

Line profile function

In typical welding plasmas spectral lines are subject to natural, resonance, van der Waals, and Stark broadening. For typical temperatures van der Waals and Stark broadening can be treated in the impact approximation so that these broadening mechanisms lead to a Lorentz line profile with a half widths at half maximum (HWHM)

∆λ = ∆λ nat + ∆λ res + ∆λ vdW + ∆λ S (22)
where ∆λ nat , ∆λ res , ∆λ vdW , and ∆λ S are the half widths of natural, resonance, van der Waals and Stark broadening, respectively. Additionally, the spectral lines are broadened by the Doppler effect showing a Gauss line profile with width

∆λ Dpl = λ ul 2 ln 2 kT m r c 2 1/2 . ( 23
)
The total line profile is thus a Voigt profile. In this work it is treated by means of the numerical approximation given by Whiting [START_REF] Whiting | An empirical approximation to the Voigt profile[END_REF].

The natural width ∆λ nat of a line is given by the life times of its upper and lower states. Considering only spontaneous emission the natural line width is given by [START_REF] Traving | Lochte-Holtgreven W Plasma diagnostics[END_REF]

∆λ nat = λ 2 ul 4πc u <u A uu + l <l A ll . (24)
Here, u < u designates states u that are connected to the upper state u by a dipole transition and have an energy E u smaller than E u . Analogously, l < l designates states l with E l < E l .

Resonance broadening occurs in collisions where radiator and perturber species are identical and if a dipole transition exists between upper or lower level of the considered line and the state of the perturber. The line width due to one such so called resonant transition is [START_REF] Traving | Lochte-Holtgreven W Plasma diagnostics[END_REF]

∆λ res = λ 2 ul 2πc 5.48 64π 2 g uR g lR A ulR λ 3 R N p ( 25
)
where g uR , g lR , A ulR , λ R , and N p are the statistical weights, the transition probability and the wavelength of the resonant transition and the perturber state density, respectively. Considering the collisions of the radiator with different perturber states as statistically independent, an extension of ( 25) to all possible perturber states reads

∆λ res = λ 2 ul 2πc 5.48 64π 2 N r Z r × u >u g u g u g u A u u λ 3 u u e -E u /kT + u <u g u g u g u A uu λ 3 uu e -E u /kT + l >l g l g l g l A l l λ 3 l l e -E l /kT + l <l g l g l g l A ll λ 3 ll e -E l /kT . ( 26
)
While this sum is often dominated by the resonant state with the lowest energy, this state does not have to be the ground state of the radiator, e.g. for many lines of neutral iron the lowest resonant state is an excited state within the ground term a 5 D.

The lines of neutral radiators are subject to van der Waals broadening due to collisions with neutrals. The corresponding line width is [42]

∆λ vdW = λ 2 ul 2πc 4.24 |C 6,u -C 6,l | 2/5 zp=0 α 2/5 p 8kT πµ p 3/10 N p (27)
where α p is the polarization volume of perturber p, µ p = m p m r /(m p +m r ) is the reduced mass of the radiator perturber system and the interaction constant C 6,i is given by [42]

C 6,i = ha 0 2πm e (n * i,r ) 2 2 [5(n * i,r ) 2 + 1 -3 i,r ( i,r + 1)] ( 28
)
where i,r is the orbital quantum number of the radiating electron in state i.

Lines of neutral and charged species are subject to Stark broadening by electrons and by ions leading to line widths ∆λ Se and ∆λ Si , respectively. For typical parameters of atmospheric plasmas the impact approximation can be used for electron Stark broadening while the quasi-static approximation has to be applied to the Stark broadening by ions. Griem showed that in this case the total line profile for Stark broadening can in good approximation be described by a Lorentz profile with the effective width

∆λ S = ∆λ Se [1 + 1.75A(1 -ξR)] (29)
where ξ = 0.75 for neutral radiators and ξ = 1.25 for charged radiators [START_REF] Griem | Spectral line broadening by plasmas[END_REF]. Here [START_REF] Griem | Stark broadening on neutral helium lines in a plasma[END_REF],

A = F 2 0 2hc λ 2 ul ∆λ Se |α u -α l | 3/4 (30)
is the ion broadening parameter of the line,

F 0 = 1 2 4 15 2/3 e 0 j =e z j N 2/3 j (31)
is the normal field strength,

α i = 2 3π h 2 0 m e e 2 i R 2 ii ∆E ii (32)
is the polarizability of state i, ∆E ii = |E i -E i | is the energy separation of states i and i and R ii is the coordinate operator matrix element between these states, as described further below. The parameter

R = r p r D =   4π 3 z j >0 N j   -1/3 1 r D ( 33
)
is the ratio of the mean ion-ion distance r p and the Debye length r D . The approximation (29) can be applied for 0.05 ≤ A ≤ 0.5 and R ≤ 0.8. For A < 0.05 the total Stark broadening width has to be calculated by

∆λ S = ∆λ Se + ∆λ Si ( 34
)
where

∆λ Si = λ 2 ul 2πc ha 0 2πm e n * 2 u,r -n * 2 l,r z r + 1 2 zp>0 z p N p (35)
is the width of quadrupole ion broadening. For A > 0.5 a transition to linear Stark broadening occurs [START_REF] Griem | Spectral line broadening by plasmas[END_REF]. In the approach used here the ion Stark broadening widths are set to the maximum of ∆λ Si and 1.75A(1 -ξR)∆λ Se . For R > 0.8 or A > 0.5 the total Stark width ( 29) is evaluated at the corresponding boundary value.

The electron Stark broadening has to be treated differently for neutral atoms, singly and multiply charged ions. Dimitrijević and Konjević [START_REF] Dimitrijević | Simple formulae for estimating Stark widths and shifts of neutral atom lines[END_REF] give the following formulae for the electron Stark broadening of lines of neutral atoms

∆λ Se = s r N e λ 2 ul 2πc ha 0 m e 8 27
E H kT × u R 2 uu f w (η uu R uu ) + l R 2 ll f w (η ll R ll ) (36)
with the definition η ab = ∆E ab /(3kT ) and the effective Gaunt factor

f w (x) = e -1.33x ln 1 + 2.27 x + 0.487x 0.153 + x 5/3 + x 7.93 + x 3 . (37)
In ( 36) the scaling factor s r for species r is introduced. This factor is used to scale the theoretical Stark widths of each neutral and ion species to measured Stark widths found in the literature.

For singly charged positive ions Griem [START_REF] Griem | Semiempirical formulas for the electron-impact widths and shifts of isolated ion lines in plasmas[END_REF] gives the formula

∆λ Se = s r N e λ 2 ul 2πc ha 0 m e 16π 27
E H kT × u R 2 uu g se 3kT 2∆E uu + l R 2 ll g se 3kT 2∆E ll ( 38
)
where g se is an effective Gaunt factor plotted in [START_REF] Griem | Semiempirical formulas for the electron-impact widths and shifts of isolated ion lines in plasmas[END_REF]. Doubly and higher charged ions are treated according to Dimitrijević and Konjević [START_REF] Dimitrijević | Stark widths of doubly-and triply-ionized atom lines[END_REF] using

∆λ Se = s r N e λ 2 ul 2πc ha 0 m e 16π 27
E H kT × u R 2 uu |∆n =0 g se 3kT n * u,r 3
4E H z 2 r + l R 2 ll |∆n =0 g se 3kT n * l,r 3
4E H z 2 r + R 2 uu ˛∆n=0 u = u +1 gse 3kT 2∆E uu + R 2 uu ˛∆n=0 u = u -1 gse 3kT 2∆E uu + R 2 ll ˛∆n=0 l = l +1 gse 3kT 2∆E ll + R 2 ll ˛∆n=0 l = l -1 gse 3kT 2∆E ll (39)
where

gse (x) = 0.7 -1.1/z r + g se (x) ( 4 0 )
is a modified effective Gaunt factor. In order to use the above formulae, the coordinate matrix elements R ab have to be evaluated. For spectral lines with unknown transition probability, the coordinate matrix elements can be calculated using expressions based on the Coulomb approximation [START_REF] Griem | Semiempirical formulas for the electron-impact widths and shifts of isolated ion lines in plasmas[END_REF]. As the analysis includes only spectral lines with known transition probability the expression [43]

R 2 ab = 3hE 2 H 2πα 3 f ∆E 3 ab g a g b A ab for E a > E b A ba for E a < E b (41)
is used.

Basic data and numerical procedure

Comparison of the NIST [START_REF] Yu | NIST Atomic Spectra Database (version 3.1.5)[END_REF] and the Kurucz [START_REF] Kurucz | Atomic Line Data[END_REF] compilation of spectral lines showed that the first contains for all species except Fe + a higher number of energy levels while the second contains for each species a higher number of lines. Consequently, the composition calculations and the bound-free emission coefficients are based on the NIST data while the line emission coefficients are based on the Kurucz data.

The calculated electron Stark widths and the net emission coefficients are based on different subsets of lines from the Kurucz data base. In the calculation of the electron Stark widths the sum over the lines connected to upper or lower level of the considered line, e.g. [START_REF] Brum | Contiuum radiation in a high pressure argon-mercury lamp Plasma Sources[END_REF], was restricted to lines with transition wavelength λ ul below 10000 nm. The total number of these lines is close to the number of lines used by Menart et 2). The present net emission calculations include 5000 lines for each species. These were those lines with the highest line integrated emission coefficient. For comparison with earlier results the integral over wavelength in (3) was restricted to the range given in the corresponding reference. The wavelength integral in (3) was treated by Simpson integration using an inhomogeneous mesh. For each line a mesh was created so that the line integrated emission coefficient was reproduced with an accuracy better than 1 %. The meshes of all lines were superimposed on an additional homogeneous mesh with a wavelength step of 1 nm. Further mesh points were introduced at the cutoff wavelengths in the bound-free emission coefficients. Following Lowke [START_REF] Lowke | Predictions of arc temperature profiles using approximate emission coefficients for radiation losses[END_REF] G 1 (x) is evaluated by numerical integration of (4). Numerical integration was performed for arguments between 10 -3 and 500 with a relative error of 1 × 10 -6 . Outside this interval G 1 (x) is evaluated via its asymptotic expressions.

Results

Emission coefficients of pure argon and iron

Figures 2 and1 show the composition of argon and iron plasmas at a pressure of 0.1 MPa, respectively, and the wavelength integrated contributions to the emission coefficient of bound-bound, bound-free, and free-free transitions for each radiating species. For all but high temperatures the emission coefficient of iron is several orders of magnitude higher than the emission coefficient of argon. This excess of iron radiation is caused by the higher number of lines of Fe and their lower upper level energies leading to higher upper state population densities. Note that the ionization energy of Fe (7.90 eV) is lower than the energy of the first excited state of Ar (11.55 eV). For temperatures above 25000 K, where ions dominate the composition, both emission coefficients are of the same order of magnitude.

The figures show that the total emission coefficient of the plasma is dominated by line radiation. The temperature dependence of the different contributions can be understood considering the plasma composition. The temperature interval where a specific species dominates the line radiation is accompanied by a corresponding temperature interval where this species has the highest density. The total emission of each individual species is dominated by line radiation at low temperatures and by bound-free radiation at high temperatures. This behaviour is caused by ionization which decreases the radiator density and increases the density of the radiator ion with increasing temperature. Note however that at the temperatures where the shift from line to bound-free radiation occurs, e.g. 14000 K for Fe (figure 2), the total emission is dominated by the emission of the ion of the next ionization step. For argon corresponding temperatures are above 30000 K (figure 1).

Figure 3 shows a comparison of the emission coefficient of an argon plasma at different pressures with values given by Menart et al [START_REF] Menart | Line-by-line method of calculating emission ceofficients for thermal plasmas consisting of monatomic species[END_REF] and measurements done by Evans et al [START_REF] Evans | Measurement of emission and absorption of radiation by an argon plasma[END_REF]. The wavelength integration covers here the interval from 200 to 3500 nm corresponding to the sensitivity of the experiment [START_REF] Evans | Measurement of emission and absorption of radiation by an argon plasma[END_REF]. Both numerical results are identical to within 10 % and lie slightly above the experimental results. The optical path in the measurements includes windows made of vycor. The transmissivity of this material decreases rapidly for wavelengths below 280 nm. Menart et al [START_REF] Menart | Line-by-line method of calculating emission ceofficients for thermal plasmas consisting of monatomic species[END_REF] argue that the difference between the experimental values and their calculation results may be caused by an incomplete compensation of this reduced transmissivity.

Electron Stark width scaling factors

At atmospheric pressure van der Waals broadening is the strongest broadening mechanims only at low temperatures. With increasing temperature first Doppler broadening and then, with the onset of ionization, electron Stark broadening become the dominant broadening mechanism. At a given temperature the line-to-line differences of the electron Stark widths cover approximately two orders of magnitude. Thus the temperatures, where Stark broadening becomes the dominant broadening mechanism, depends on the considered line. While the emission coefficient is independent of the line widths the net emission coefficient for non-zero radius R depends on the absolute line widths and thus on the electron Stark width scaling factors s r introduced in ( 36), [START_REF] Suzuki | Momentum transfer cross section of argon deduced from electron drift velocity data[END_REF], and [START_REF] Kihara | Transport properties for gases assuming inverse power intermolecular potentials[END_REF].

The electron Stark width scaling factors s r for Ar, Ar + , Fe and Fe + used for the net emission coefficients presented below are determined by comparison of measured Stark widths with widths calculated here. The employed scaling factors are the mean ratios s r = ∆λ Se,exp /∆λ Se where the average is taken over all experimental line widths available for species r. This procedure was applied by Menart et al to argon and copper lines [START_REF] Menart | Line-by-line method of calculating emission ceofficients for thermal plasmas consisting of monatomic species[END_REF]. The experimental Stark widths must be specified together with independently measured electron density N e and temperature T . Appropriate values are taken from the reviews given by Konjević et al [START_REF] Konjević | Experimental Stark widths and shifts for spectral lines of neutral and ionized atoms (A critcal review of selected data for the period 1989 through 2000[END_REF] and Lesage [START_REF] Lesage | Experimental Stark widths and shifts for spectral lines of neutral and ionized atoms A critcal review of selected data for the period 2001[END_REF] containing measurements for 64, 210, 12 and 14 lines for Ar, Ar + , Fe and Fe + , respectively. The reviews summarize results from dedicated experiments in a temperature range from 6000 to 43000 K. As electron Stark widths for Ar 2+ and Fe 2+ are not given, the corresponding scaling factors are set to unity in this work.

Figure 4 shows the individual ratios ∆λ Se,exp /∆λ Se for Fe and Fe + lines given by Konjević et al [START_REF] Konjević | Experimental Stark widths and shifts for spectral lines of neutral and ionized atoms (A critcal review of selected data for the period 1989 through 2000[END_REF], the resulting electron Stark width scaling factors s r , and their standard deviation ∆s r . The provided Stark widths were measured on lines in the visible spectral range lying in regions covering approximately 6 and 30 nm for Fe and Fe + , respectively, except for three measurements given in [START_REF] Konjević | Experimental Stark widths and shifts for spectral lines of neutral and ionized atoms (A critcal review of selected data for the period 1989 through 2000[END_REF] and the one measurement given in [START_REF] Lesage | Experimental Stark widths and shifts for spectral lines of neutral and ionized atoms A critcal review of selected data for the period 2001[END_REF] for lines of neutral iron with wavelengths below 426 nm. The Stark width measurements for lines of Ar and Ar + cover wider ranges from 104 to 850 nm and from 250 to 720 nm, respectively. The resulting scaling factors have values between 0.48 for Ar and 3.21 for Fe. They are summarized in table 2. In expressions [START_REF] Brum | Contiuum radiation in a high pressure argon-mercury lamp Plasma Sources[END_REF], [START_REF] Suzuki | Momentum transfer cross section of argon deduced from electron drift velocity data[END_REF], and [START_REF] Kihara | Transport properties for gases assuming inverse power intermolecular potentials[END_REF] all transitions connected to upper or lower level of the considered line have a positive contribution to the electron Stark width. Thus, values of s r above unity as those for Ar + , Fe, and Fe + may be caused by a lack of lines in the underlying data. The scaling factor for Ar is smaller than unity because the employed theory on average overestimates the Stark width of Ar lines. The scaling factor s Ar = 0.32 ± 0.14 determined by Menart et al [START_REF] Menart | Line-by-line method of calculating emission ceofficients for thermal plasmas consisting of monatomic species[END_REF] does not differ significantly from the present value.

Figure 5 shows a comparison of the temperature dependency of the normalized electron Stark width ∆λ Se /N e deduced from experiments and calculated here for the neutral iron line at 538.337 nm. Additionally, an experimental fit of the electron Stark width of this line ∆λ Se /N e = 1.324 × 10 -33 m 4 (T /13000 K) 1.67 determined by Zielinska et al [START_REF] Zielinska | Investigations of GMAW plasma by optical emission spectroscopy Plasma Sources[END_REF] is given. The widths calculated here are approximately a factor two below the 'simple theoretical prediction' given by Freudenstein [START_REF] Freudenstein | Stark broadening of Fe I 5383 Å[END_REF]. Figure 5 indicates that for this line both theoretical calculations underestimate the increase of ∆λ Se /N e with temperature. A better agreement between theoretical and measured electron Stark widths is obtained when the scaling factor s Fe = 3.21 is applied.

Net emission coefficients

This section gives net emission coefficients for argon iron plasmas and comparisons with literature values. The net emission coefficients presented here use the electron Stark width scaling factors summarized in table 2. The wavelength integral in (3) covers the range from 30 to 2500 nm unless noted otherwise.

Figure 6 shows the net emission coefficient of argon plasmas at a pressure of 0.1 MPa for cylindrical geometry and values for spherical geometry given by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF]. The net emission coefficient rapidly increases with increasing temperature and decreases with growing plasma radius. The agreement of both net emission coefficients is better than approximately 10 %.

Figure 7 shows net emission coefficients of iron plasmas at a pressure of 0.1 MPa for cylindrical and for spherical geometry calculated here and values for spherical geometry given by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF]. It shows that the net emission coefficient for cylindrical geometry is smaller than values for spherical geometry. This is caused by the higher amount of irradiation and absorbed power at the arc axis when cylindrical geometry is considered. The results for spherical geometry are in good agreement with those given by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF] for all but the highest radius of 1 m. The difference between literature values and the present results in spherical geometry may be caused by deviations in the number of considered lines, transition probabilities and Stark widths. The present results for cylindrical geometry also show good agreement with the literature values for radii below 10 -3 m. For larger radii they show a faster decrease with increasing radius.

Figure 8 shows the influence of the electron Stark widths scaling factors s r on the net emissions cofficients of argon and iron plasmas at a pressure of 0.1 MPa in cylindrical geometry. The figure displays contour lines of net / net (s r = 1) -1 where net (s r = 1) is the net emission coefficient calculated with s r = 1 for all species. It shows that the scaling factors have no influence on net at low temperatures where Stark broadening is not the dominant broadening mechanism. For argon this region extends to higher temperatures than for iron, because iron has a smaller ionization potential. The influence of the electron Stark widths is small for small plasma radii because here the plasma remains optically thin for the emission lines. There is an intermediate range of radii where a scaling factor above unity leads to an increase of net and a scaling factor below unity to a decrease of net . In this intermediate range the net emission coefficient is dominated by the emission near the line centres. Enlarged line widths lead to reduced absorption coefficients near the line centres so that their contribution to net increases. In the line wings an increase of the line width leads to higher optical depths and a decrease of their contribution to net . With increasing plasma radius the optical depth near the line centre increases faster than in the line wings. Thus, when the line centres have reached high optical depth the influence of s r is weakened first and reversed in the limit of high plasma radius. The opposing behaviours of the absorption coefficient in the line centres and the line wings and the restriction of the influence of s r to the temperature region where species r has a high density lead to the formation of maxima and minima in net / net (s r = 1) -1. For the employed scaling factors these extrema are -17 and 12 % for argon and 11 and 37 % for iron. In the typical parameter range of GMAW processes (T = 5000-10000 K, R = 1-2 × 10 -3 m) [START_REF] Zielinska | Investigations of GMAW plasma by optical emission spectroscopy Plasma Sources[END_REF][START_REF] Rouffet | Spectroscopic investiagtion of the high-current phase of a pulsed GMAW process[END_REF] the scaling factors s r lead to an increase of net of an iron plasma by between 3 and 22 %.

The standard deviations ∆s r of the electron Stark width scaling factors give rise to an uncertainty ∆ net of the net emission coefficient. The variation of this uncertainty as a function of plasma temperature and radius has the same structure as the influence of the scaling factors on net shown in figure 8. The maximum absolute values of ∆ net in the intermediate range of radii are 12 and 14 % for argon, and 4 and 13 % for iron plasmas. In the GMAW range of parameters the uncertainty for iron plasmas has values between 0 and 8 %.

For the radius R = 1 m the net emission coefficients given by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF] decrease with increasing temperature for temperatures between approximately 6000 and 9000 K (figure 7). The present results in cylindrical and spherical geometry both reproduce this behaviour. There is good agreement between the present results for spherical geometry and the literature values for temperatures below 6000 K and above 13000 K, however at 9000 K the present results for spherical geometry are a factor of approximately 3.3 larger than the literature value. This descrepancy may be caused by differences in the employed Stark widths and continuous emission coefficients. The uncertainty ∆ net of the net emission coefficient of iron has its highest values in the region of the local minimum of net . It is 23 % at R = 1 m and T = 9000 K. Calculations where the continuous emission coefficient of Fe is increased by a factor of two show a decreases of the local minimum of net by 30 %.

Figure 9 shows the influence of the geometry on the net emission coefficient of an iron plasma at a pressure of 0.1 MPa. The figure displays contour lines of cyl net / sph net -1 where cyl net and sph net are the net emission coefficient for cylindrical and spherical geometry, respectively. For both geometries the electron Stark widths scaling factors in table 2 have been used. As expected from the geometry functions, the net emission coefficients are smaller for cylindrical geometry than for spherical geometry. For most temperatures the ratio of the net emission coefficient decreases monotonically with increasing plasma radius. The maximum reduction of 47 % induced by a change from spherical to cylindrical geometry in the considered parameter range lies at T = 9500 K and R = 1 m. In the region relevant for GMAW processes the net emission coefficient of iron plasmas for cylindrical geometry is 30 to 37 % smaller than values for spherical geometry. For argon plasmas the corresponding reduction is only between 5 and 9 %.

Figure 10 shows net emission coefficients of argon iron plasmas for different plasma radii and iron fractions from zero to unity for cylindrical geometry and values for spherical geometry given by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF]. It shows that for low temperatures the net emission of the plasma is determined by the radiation of iron as soon as small amounts of iron are contained in the plasma. For temperatures below 10000 K this is the case for iron fractions above 0.01 %. The differences between the values calculated here and in the literature [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF] seen in figure 7 reappear in figure 10. While the agreement between both results is good at small plasma radii the values calculated here decrease faster with plasma radius than those given by Menart et al [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF].

Figure 11 shows the contributions to the net emission coefficient for cylindrical geometry in the wavelength intervals 30-200 nm, 200-700 nm and 700-2500 nm representing the ultraviolet (UV), the visible and the infrared spectral range (IR), respectively. The net emission coefficients for R = 0 and 0.001 m are compared. The main contribution to the net emission coefficient comes from the visible spectral range for low temperatures and from the UV for high temperatures. The temperature where the shift between the spectral ranges occurs depends on the plasma radius and the iron mole fraction. At low temperatures the infrared contributes a higher fraction to the net emission coefficient than the ultraviolet. Due to the small absorption in the IR spectral range the percentage of the net emission coefficient originating from the infrared increases with increasing plasma radius. For 9000 K this fraction increases from 3 to 22 % when for radius increases from 0.001 to 0.01 m.

Conclusions

The net emission coefficient increases rapidly with increasing temperature and is dominated by the line radiation of iron, as soon as small amounts of iron are contained in the plasma. The net emission coefficient is dominated by radiation from the visible spectral range at low temperatures and dominated by radiation from the ultraviolet at high temperatures. The infrared radiation exceeds the ultraviolet only at low temperatures and its fraction of net emission coefficient increases with increasing plasma radius. The net emission coefficients for argon iron plasmas at atmospheric pressure calculated here are in good agreement with values from earlier investigations [START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF], even though the number of lines taken into account here is with 5000 lines per species considerably smaller. The semi-empirical Stark broadening theory [START_REF] Konjević | Experimental Stark widths and shifts for spectral lines of neutral and ionized atoms (A critcal review of selected data for the period 1989 through 2000[END_REF] was employed to calculate the Stark widths of the spectral lines. Additionally, the widths of the lines of Ar, Ar + , Fe and Fe + were scaled to experimental electron Stark widths. For temperatures and plasma radii typical of the iron containing core region of arcs occurring in the gas metal arc welding process (T = 5000-10000 K, R = 1-2 × 10 -3 m) [START_REF] Zielinska | Investigations of GMAW plasma by optical emission spectroscopy Plasma Sources[END_REF][START_REF] Rouffet | Spectroscopic investiagtion of the high-current phase of a pulsed GMAW process[END_REF] this scaling procedure leads to an increase of the net emission coefficient by between 2 and 23 %. The net emission coefficients of argon iron plasmas for cylindrical geometry presented in this work decrease faster with increasing radius R than earlier results where spherical geometry is considered. In the GMAW range of radii and temperatures the net emission coefficient of iron plasmas for cylindrical geometry is between 30 and 37 % smaller than corresponding values calculated for spherical geometry. (a) summarized in [START_REF] Konjević | Experimental Stark widths and shifts for spectral lines of neutral and ionized atoms (A critcal review of selected data for the period 1989 through 2000[END_REF], mean value (--), and standard deviation (---).

Figure 1 .Figure 2 .

 12 Figure 1. (a) Composition of an argon plasma at p = 0.1 MPa and (b) contributions of bound-bound (---), bound-free (-• -) and free-free (• • • • • •) transitions to the emission coefficient and their sum (--).

Figure 3 .Figure 4 .

 34 Figure 3. Emission coefficients of argon plasmas in the wavelength interval from 200to 3500 nm calculated here (--), in[START_REF] Menart | Line-by-line method of calculating emission ceofficients for thermal plasmas consisting of monatomic species[END_REF] ( ), and measured in[START_REF] Evans | Measurement of emission and absorption of radiation by an argon plasma[END_REF] (---).

1 Figure 5 .

 15 Figure 5. Normalized electron Stark widths ∆λ Se /N e of the Fe line at 538.337 nm: data from [48] (+), present results (--) with s Fe = 1 and resulting scaling factor s Fe = 3.21, 'simple theoretical prediction' from [50] (• • • • • •), experimental fit from [1] (---).

Figure 6 .

 6 Figure 6. Net emission coefficients of an argon plasma at P = 0.1 MPa: cylindrical geometry from this work (--), spherical geometry from [10] (---).

Figure 7 .Figure 8 .

 78 Figure 7. Net emission coefficient of an iron plasma at P = 0.1 MPa: cylindrical (--) and spherical geometry (• • • • • •) from this work, spherical geometry from [10] (---).

Figure 9 .

 9 Figure 9.Influence of the considered geometry on the net emission coefficient of an iron plasma at P = 0.1 MPa: contour lines of cyl net / sph net -1 (--), typical parameter range for GMAW processes (---).

Figure 10 .

 10 Figure 10. Net emission coefficients of argon iron plasmas at P = 0.1 MPa with iron mole fractions x Fe from 0 to 1 for (a) R = 0, (b) R = 1 × 10 -3 m, and (c) R = 1 × 10 -2 m: present work for cylindrical geometry (--), results from [10] for spherical geometry (---).

Figure 11 .

 11 Figure 11. Net emission coefficients for argon iron plasmas at P = 0.1 MPa for cylindrical geometry in different wavelength intervals and iron mole fractions (a) x Fe = 1 and (b) x Fe = 0.01: net emission coefficients for radius R = 0 (--), and R = 0.001 m (---).

  1 .

		E 0	σ 0	y a	P	y w	y 0	y 1
		eV	10 -22 m 2
	Ar	1.709+1 a) 2.106+1 2.645+2 4.706+0 4.185-1 1.688+0 8.943-1
	Ar +	2.494+1	2.503+1 1.272+2 4.288+0 5.108-1 9.299-1 7.195-1
	Ar 2+ 1.417+1	3.580+1 3.776+1 5.742+0 6.316-1 2.384+0 1.794+0
	Fe	1.407+2	1.083+4 4.458+0 1.691+1 4.039-1 0.000+0 0.000-0
	Fe +	1.933+1	3.679+4 3.564+0 1.566+1 4.144-1 0.000+0 0.000+0
	Fe 2+ 2.670+1	6.301+3 5.385+0 1.232+1 4.407-1 0.000+0 0.000+0

Table 2 .

 2 Resulting scaling factors s r for Stark widths, number of internal states N state and number of spectral lines N line extracted from[START_REF] Yu | NIST Atomic Spectra Database (version 3.1.5)[END_REF] and[START_REF] Kurucz | Atomic Line Data[END_REF], respectively, and number of spectral lines N MM line used in[START_REF] Menart | Net emission coefficients for argon-iron thermal plasmas[END_REF].

		s r	∆s r N state N line	N MM line
	Ar	0.47 0.27 497	3552	3553
	Ar +	1.65 0.90 417	6982	6959
	Ar 2+ 1.0	113	1008	996
	Fe	3.21 1.59 492	16739 15521
	Fe +	1.51 0.26 575	40180 41644
	Fe 2+ 1.0	564	22409 22243
	al [10] (table

Acknowledgment

This work was funded by the Deutsche Forschungsgemeinschaft (DFG) under grants UH 106/3-1. The author would like to thank H. Schneidenbach and D. Uhrlandt for helpful suggestions.


J H Van Helden

G Hancock

R Peverall
email: robert.peverall@chem.ox.ac.uk

G A D Ritchie

A 3 µm difference frequency laser source for probing hydrocarbon plasmas

The practicality of a compact solid-state laser based difference frequency generation (DFG) system is demonstrated as a tool for probing hydrocarbon based plasmas. The laser light of a cw Nd:YAG operating at 1064 nm and one of two DFB diode lasers operating at 1560 nm and 1620 nm were mixed in a periodically poled lithium niobate (PPLN) crystal producing mid-infrared radiation at 3.35 µm and 3.1 µm for the detection of CH 4 and C 2 H 6 at the first wavelength and C 2 H 2 and C 2 H 4 at the latter. The radiation was used to probe a rf capacitively coupled CH 4 plasma for a matrix of conditions, varying power (< 180 W) and pressure (< 1 Torr) in both direct absorption spectroscopy and wavelength modulation spectroscopy (WMS) experiments to achieve relatively high sensitivities while retaining accurate spectral information in the form of linewidths. A minimum detectable absorption coefficient α min of 2 × 10 -5 cm -1 was achieved for direct absorption spectroscopy which corresponds to a minimum detectable density for CH 4 of 1.7 × 10 12 cm -3 and an α min value of 2 × 10 -6 cm -1 was achieved for WMS measurements on C 2 H 2 . The depletion of CH 4 was measured to increase from 23% at 40 W to 40% at 180 W at a pressure of 0.84 Torr, and the depletion increased to 56% as the pressure decreases to 0.45 Torr.

Introduction

Tunable narrow band light sources in the mid-infrared (MIR) region (3 -20 µm) for molecular absorption spectroscopy are highly desirable for fundamental and applied plasma research. In this region, tunable lead salt diode lasers have been the most popular devices for tunable diode laser absorption spectroscopy (TDLAS), because they offer relatively high spectral intensity, narrow bandwidth and continuous tunability over an absorption profile [1]. However, these lasers have the drawback that they require cryogenic cooling. Furthermore, cheap tunable narrow-band optical sources operating in the 3 µm region where many molecules of fundamental and applied interest have strong C-H, N-H or O-H vibrational transitions are not readily available. Quantum cascade lasers are rapidly becoming the radiation source of choice for working in the MIR above 4 µm and will continue to do so as their emission wavelengths and that of interband cascade lasers (ICLs) decrease towards the 3 µm region [2]. In the meantime, there is an alternative method for the production of MIR radiation via nonlinear optical processes utilising widely available room temperature sources in the near-infrared (NIR). These lasers have the same advantageous features as the lead salt diode lasers but without the necessity of cryogenic operation making their use much simpler and because of their importance to telecommunications are based on mature technology. The NIR lasers are mixed in a non-linear cystal via a process called difference frequency generation (DFG) to produce a beam in the MIR with optical qualities directly related to those of the source lasers. The advent of the reliable production of periodically poled materials for applications in nonlinear optics in combination with widely tunable sources, such as external cavity diode lasers (ECDL), means that transitions can be accessed over a relatively large spectral range at high resolution ( 20 MHz). Primarily, periodically poled lithium niobate (PPLN) has been used either in a DFG or optical parametric oscillator arrangement to generate radiation in the MIR (∼ 3 µm) for gas detection applications [3,4,5,6,7].

In this paper, the practicality of a compact solid-state laser based DFG system is demonstrated as a tool for probing hydrocarbon based plasmas. These plasmas are frequently used for the deposition of diamond-like carbon (DLC) thin films which have attracted attention for many years now because of their excellent mechanical and optical properties. DLC films are nowadays used as protective coatings on magnetic storage discs, optical elements, razor blades and car parts [8] and as an intermediate layer for liquid crystal alignment during LCD production [9,10]. Furthermore, non-hydrogenated DLCs have a potential application in poly-LED and organic-LED devices [11,12]. Capacitively coupled rf plasmas of hydrocarbon/H 2 mixtures are frequently used for the deposition of these films. To obtain more insight into the diamond deposition process and so improve film quality and deposition rate(s), an understanding of the chemistry of the gas phase atoms, molecules, radicals and ions is required. Absolute number densities of key ground and excited species and their dependence on operating plasma parameters and spatial location within the reactor provide key information for models of the plasma chemistry [13]. DFG combined with direct absorption spectroscopy and wavelength modulation spectroscopy (WMS) provides an opportunity for sensitive detection of specific species in a plasma and therefore a means to investigate the chemical and physical properties of plasmas and to help unravel the complexity of such systems.

In this paper, we report on the generation of radiation around 3 µm produced by DFG and present measurements on CH 4 , C 2 H 2 , C 2 H 4 , and C 2 H 6 molecules in a rf capacitively coupled CH 4 plasma as a function of plasma input parameters. We employed a multi-track periodically poled PPLN crystal with poling periods between 29 and 32 µm capable of an extended wavelength coverage of 3.1 -4 µm with the appropriate pump/signal lasers. In the crystal, the laser light of a cw Nd:YAG operating at 1064 nm and one of two DFB diode lasers operating at 1560 nm and 1620 nm were mixed producing light at 3.35 µm and 3.1 µm. The laser light is then directed into the capacitively coupled rf plasma chamber using a multipass configuration to enhance the absorption signal. The signal to noise ratio is further improved by applying wavelength modulation spectroscopy (WMS), which transfers detection to a higher frequency regime to reduce noise.

Difference frequency generation

DFG relies upon the non-linear response of a material's induced polarisation when subjected to an intense electric field [START_REF] Boyd | Nonlinear Optics[END_REF]. More specifically, it is the second order nonlinear optical susceptibility term χ (2) of the induced polarisation P (t) within the material, that allows the generation of "difference frequency"light. The time-dependent induced polarisation in a material is given by

P (t) = ǫ 0 (χ (1) E a (t) + χ (2) E a (t) 2 + χ (3) E a (t) 3 + . . .), (1)
where E a (t) is the applied electric field, χ (n) are the non-linear susceptibilities and ǫ 0 is the vacuum permittivity. DFG is one of the three second order nonlinear interactions which generate light through the application of two different electric fields to a material; the others are second harmonic generation (SHG) and sum frequency generation (SFG), which occur simultaneously but with varying degrees of efficiency. In DFG, the ouput radiation or idler radiation, i, is produced by mixing two input radiation sources, the signal, s, and the pump, p. For the DFG process, the conservation of energy provides the following relationship between the pump, signal and idler radiation frequencies: ω p -ω s = ω i , where ω p > ω s > ω i by convention. Since nonlinear processes are phase-sensitive, both pump and signal radiation should have a constant phase relationship in order to maximise the efficiency in generating the idler radiation such that the phase mismatch ∆ k is

∆ k = kp -ks -ki = 0, (2)
where kp , ks and ki are the wave vectors of the pump, signal and idler radiation, respectively, and k j = (n j ω j )/c, where n j is the refractive index and c is the speed of light in vacuum. To achieve this the polarisation and focussing of the incident laser beams, the geometry and temperature of the crystal all need to be optimised to ensure a proper phase relationship is maintained between the interacting beams along the propagation direction. Due to chromatic dispersion (the frequency dependence of the refractive index of a material) each wave travels at a different speed through the material and ∆ k becomes non-zero, reducing the efficiency of the nonlinear interaction. Therefore phase matching is required for the incident and produced light rays and this is usually conducted within a birefringent medium in which the refractive index is polarisation dependent. However, in cases where it is not possible to achieve efficient phase matching with birefringent crystals, quasi-phase matching (QPM) can be used; this is achieved by using periodically-poled materials, such as PPLN, where a periodic change in the local polarity of χ (2) between the layers in the crystal corrects for the phase mismatch. The periodically-poled crystal is made by producing a series of individual crystal 'slices' (each a few tens of microns in thickness) with alternating slices being rotated by 180 • C. This leads to a periodic alternation of the optical axis, changing the sign of χ (2) , allowing efficient generation of the idler radiation. The optimal physical conditions for quasiphase matching in a periodically-poled crystal are achieved when △k QP M (T ) is zero,

∆k QP M (T ) = 2π n p (T ) λ p - n s (T ) λ s - n i (T ) λ i - 1 Λ(T ) , (3)
where λ p , λ s and λ i are the pump, signal and idler wavelengths, respectively, and Λ(T ) is the temperature-dependent crystal poling period. Finally, n p (T ), n s (T ) and n i (T ) are the temperature-and wavelength-dependent extraordinary refractive indices, respectively, described by the Sellmeier equations for PPLN [START_REF] Jundt | [END_REF] n 2 e,x (λ x , T ) = A 1 +B 1 f (T )+

A 2 + B 2 f (T ) λ 2 x -(A 3 + B 3 f (T )) 2 + A 4 + B 4 f (T ) λ 2 x -A 2 5 -A 6 λ 2 x (4)
where λ x is the wavelength in µm for the i, p and s radiation, and A z and B z are the optimised parameters given in table 1. The temperature parameter, f (T ), is defined as

f (T ) = (T -24.5) × (T + 570.5), ( 5
)
where T is the crystal temperature in • C.

Wavelength modulation spectroscopy

In WMS (see for example [16]) the detection frequency is raised to a higher frequency domain where technical noise sources are less likely to interfere with the signal and hence a higher signal-to-noise ratio (SNR) can be achieved compared to conventional absorption spectroscopy. Experimentally, this entails applying a relatively fast sinusoidal modulation to the diode laser current to modulate its wavelength usually in the kHz regime, while slowly scanning the laser to cover the spectral region of interest. The interaction between the absorbing species and the spectrally modulated light leads to the generation of signals at the modulation frequency and various harmonics thereof. Signals can then be demodulated at these frequencies, to obtain higher sensitivity signals, which are however no longer absolute and thus a calibration is needed.

In WMS, the overall instantaneous angular frequency of the electric field of the laser, ω, is the combination of the central laser frequency ω L which is slowly ramped and traverses the absorption profile and ω m which is the rapid modulation superimposed on ω L , with amplitude △ω m as described by

ω = ω L + △ω m cos(ω m t). (6)
The interaction between absorbing species and the spectrally modulated light leads to changes in the time-dependent intensity of the modulated radiation which can be expressed as a cosine Fourier series

I(ω L , t) = ∞ n=0 A n (ω L ) cos(nω m t), (7)
where A n (ω L ) (where n > 0) are the harmonic components of the series. To record a WMS spectrum the detector signal is demodulated, generally by a lock-in amplifier, where only signals that are at the same frequency and phase as the applied modulation frequency, ω m , are filtered by the lock-in amplifier for signal averaging.

Assuming that I 0 , the baseline signal, is independent of frequency in the absence of an absorber, and by substituting ω m t with θ, each individual harmonic component in the presence of a frequency-dependent absorption cross-section, σ(ω), is given by:

A n (ω L ) = 2 π π 0 I 0 (ω L + △ω m cos θ) exp[-σ(ω L + △ω m cos θ)cl] cos(nθ) dθ = 2I 0 π π 0 exp[-σ(ω L + △ω m cos θ)cl] cos(nθ) dθ. (8)
For small absorptions, when σcl ≪ 1, the expression simplifies to

A n (ω L ) = 2I 0 cl π π 0 -σ(ω L + △ω m cos θ) cos(nθ) dθ, (9)
hence the magnitude of the harmonic component is directly proportional to the sample concentration, c.

A special case occurs when △ω m is much smaller than the halfwidth Γ of the absorption line being probed, resulting in the so-called derivative limit. Using a Taylor series expansion of σ(ω), the expression for this limit is derived from (9) and is given by,

A n (ω L ) = I 0 2 1-n cL n! △ω n m d n σ dω n ω=ω L (10)
In the derivative limit, the magnitude of the n th harmonic component is therefore proportional to the n th derivative of σ(ω). In practical applications the use of △ω m ≪ Γ produces a signal with a small amplitude. The signal size can be increased by applying a larger value of △ω m , and this value is often chosen to be of the order of Γ to maximise signal amplitude. Even at this magnitude of △ω m , the signal is qualitatively similar to the n th derivative of the absorption lineshape. In general, it is possible to monitor signals at all harmonics of the modulation frequency, however only the first and secondharmonic signals are commonly used [START_REF] Hutchinson | Diode laser studies of trace species and their reactions[END_REF].

Although WMS is good for removing technical noise, the WMS spectrum obtained is not self-calibrating, unlike direct absorption. Hence a calibration of the obtained spectra using techniques such as direct absorption spectroscopy or measurements against standard gas mixtures are required in order to determine absolute concentrations. Recent publications report that WMS spectra may be calibrated directly from the residual amplitude modulation (RAM) signal [START_REF] Duffin | [END_REF]19].

Experimental details

The characteristics of the DFG source have been described previously [3] and so only a brief description follows. The experimental setup used for the work at 3.1 µm is depicted schematically in figure 1. Here, the compact (3 × 3 × 12 cm) ∼ 400 mW Nd:YAG laser (Crystalaser) operating at 1064.73 nm acts as the pump laser and the distributed feedback (DFB) fibre coupled diode laser (Furukawa FOL15DCWD series, ∼ 30 mW), tunable between 1618.5 nm and 1622.3 nm, as the signal laser. For the work at 3.35 µm, an equivalent DFB laser (JDSU CQF474708 series) operating between 1559 nm and 1561 nm is used. The resulting laser beam has an instrumental line width of 2 MHz. Wavelength tuning of the system was possible by temperature and current tuning of the diode lasers. A fraction of the DFB laser light is directed onto a spectrum analyser (Melles Griot), with a free spectral range of 2.33 GHz and a finesse of 100, for wavelength calibration. Both beams are co-aligned using a dichroic mirror and focused by lenses prior to the dichroic mirror through a multitrack PPLN crystal in order to generate the difference frequency radiation. The PPLN crystal (HC Photonics, 30 × 7.9 × 0.5 mm) is AR coated for 1064 and 1550 nm and has 7 tracks with poling periods between 29 and 32 µm in 0.5 µm increments of which the 30 µm track was used to generate 3.1 µm radiation and the 30.5 µm track to generate 3.35 µm radiation. The crystal was mounted inside an HC Photonics oven which was optimally aligned using a three-axis micrometer stage and enabled temperature control, via resistive heating, between room temperature and 130 • C, to within 0.1 • C. With the 7 tracks an extensive wavelength range from 3.1 to 4 µm can be covered upon changing the diode laser and tuning the crystal temperature. The relatively low power radiation (≈ 18µW) around 3 µm was decoupled from the high power diode and YAG radiation using a germanium filter anti-reflection coated for 3 µm; the ∼ 3 µm radiation was transmitted whereas the diode and Nd:YAG beams were absorbed or reflected into a beam dump. The ∼ 3 µm radiation was collimated using a 50 mm focal length CaF 2 biconvex lens and passed through the plasma chamber.

As discussed previously, the poling period of the PPLN crystal is chosen to optimise phase matching given the pump and signal wavelengths and the properties of the crystal. The refractive index of the crystal varies with temperature and so, with control and stabilisation of crystal temperature, the efficiency of the DFG generation can be optimised for the desired mixing process. In figure 2(a) the measured MIR signal is shown as a function of the crystal temperature for two values of the signal wavelength.

At λ s = 1620.97 nm the maximum output power for the MIR radiation is observed at 80 • C. This optimal crystal temperature changes when the DFB laser is scanned across a range of wavelengths due to changes in the QPM conditions inside the PPLN. For example, at λ s = 1619.5 nm the optimal temperature is shifted down to 78 • C. The shape of the tuning curves has the characteristic asymmetry associated with focused Gaussian beams and matches the expected tuning curve as shown in ref. [3]. Efficient MIR generation over 15 cm -1 was achieved for crystal temperatures of 80 • C and 68.6

• C to produce the 3.1 and 3.35 µm radiation, respectively. In figure 2(b) the measured MIR output versus the wavelength of the diode laser at 1620 nm is plotted for a crystal temperature of 80 • C. This shows that the conversion efficiency changes dramatically as a function of the signal wavelength at a fixed temperature.

Details of the plasma chamber have been previously published [20] and are summarized here. Experiments were carried out in a capacitively-coupled parallel plate rf plasma reactor (Plasma Technology RIE 80) (also shown in figure 1). The rf power at 13.56 MHz was supplied by an analogue power supply (ENI HF 300) to a 170 mm diameter aluminum lower electrode, separated from a similar grounded electrode by 55 mm; the entire electrode assembly of the chamber is water cooled. The power applied varied between 0 and 180 W, with less than 5% reflected power controlled with a matching network. This planar plate configuration is surrounded by a quartz vacuum vessel with an inner diameter of 280 mm, and an alloy box which acts as a Faraday cage to prevent interference of the rf plasma with the electronics of the DFG system. CH 4 gas (BOC 99.5%) entered the chamber via a mass flow controller through a shower-head arrangement imbedded in the upper grounded electrode (typical flow rates ∼ 1000 sccm), and were pumped through a 50 mm aperture located below the driven electrode using a roots blower backed by a rotary pump (Edwards EH250 and E2M40, respectively). The working pressure was varied between 0.17 and 2 Torr and was monitored by two capacitance manometers (Ceravac, 0 -1 Torr and 0 -10 Torr). The chamber was fitted with two side arms with CaF 2 windows, transparent in the 3 µm region, to allow the MIR beam through the plasma chamber. To increase the absorption path length, the beam was passed through the reactor three times by silver mirrors in a multipass configuration. The total path length was 160 cm of which 51 cm was in the plasma region. After multipassing, the light was focused by an off-axis paraboloid mirror, onto a liquid nitrogen cooled InSb detector (New Brunswick).

During direct absorption measurements the laser was scanned over ∼ 0.5 cm -1 by applying a triangular voltage ramp with at a frequency of 10 Hz to the laser. The 1064 nm beam was modulated using an optical chopper (Bentham, ∼ 2.8 kHz) and the detector signal was then demodulated using the lock-in amplifier (Stanford Research Systems, SR510) before being displayed on the oscilloscope (LeCroy WaveSurfer 434); 500 averages were taken for each spectrum. WMS was conducted by applying a low ramping frequency of 2 Hz scanning over ∼ 0.5 cm -1 to the laser in a similar fashion as for direct absorption measurements. A function generator (TTi TG1304) was used to produce the fast sinusoidal modulation frequency, ω m , of ∼ 22 kHz with a modulation depth, △ω m , of ∼ 257 MHz. The corresponding absorption spectra were obtained by demodulating the detected signal at the desired harmonic using the lock-in-amplifier, before being displayed on the oscilloscope; again 500 averages were taken for each spectrum.

Results and discussion

For the measurements of the densities either direct absorption spectroscopy or WMS was used. In figure 3, example spectra of CH 4 taken at 0.17 Torr are shown obtained with both methods without the plasma on. Table 2 contains the details of the transitions probed, such as line position and assignment. In the direct absorption spectrum, the four strong transitions absorbed a considerable amount of the laser intensity and they suffer from line broadening. However, the weaker transitions have an absorption of < 10% and are not affected in this way. For example, the measured Doppler width of the transition labeled J = 3, A 2 is (9.99 ± 0.17) × 10 -3 cm -1 which is in relatively good agreement with the theoretical Doppler width of 9.23 × 10 -3 cm -1 at 298 K, but outside the statistical error quoted. This discrepancy is most likely due to a slight broadening of the line as a result of laser instabilities over the time the spectra were taken (50 seconds). This implies that with direct absorption spectroscopy the temperature of species in the plasma can be determined with a precision of 50 K. The sensitivity of direct absorption spectroscopy can be described by an α min value which is independent of sample and a value of 2 × 10 -5 cm -1 recorded in 50 seconds was achieved in these experiments determined from the CH 4 data. This corresponds to a minimum detectable density for CH 4 of 1.7 × 10 12 cm -3 . In figure 3(b), the WMS spectra using 1f -harmonic detection is shown. Absorption signals detected using WMS always have linewidths that are wider than their corresponding Doppler-limited linewidth due to modulation broadening, but using a fitting routine, the linewidth and therefore temperature can be determined. The magnitude of the absorption is proportional to the species concentration and after calibration the densities can be easily deduced. The main advantage of WMS is that it is less susceptible to baseline variations and noise and here it has typically a 10 times higher signal-to-noise ratio (SNR) than the direct absorption spectroscopy data.

In figures 4(a) -4(g), WMS spectra are shown for the region 3211.7 -3218.7 cm -1 obtained using 2f -harmonic detection in a CH 4 plasma; the operating power of the plasma was 180 W and the pressure was 1.57 Torr. In the same figures, spectra are plotted recorded for a reference cell containing 115 Torr of C 2 H 2 . Although 1f -harmonic detection gave larger signal amplitudes, 2f -harmonic detection was used throughout these experiments to reduce baseline variation. Analysis of the spectra presented in figures 4(a) to 4(f) provides information on several vibrationally excited species in C 2 H 2 . Transitions from the ground state and numerous transitions from hot bands were observed: various transitions from 22 different vibrational bands were successfully assigned by comparing the obtained spectra to Rinsland's study [21] on C 2 H 2 in the 3 µm region. The assignments are shown in the spectra and the vibrational bands they belong to are listed in table 3. Part of the unassigned transitions in the plasma spectra must be C 2 H 2 transitions as they are also observed in the gas cell. The other unassigned transitions could be from C x H y molecules, or radicals like CH 3 and C 2 H. The 2fharmonic detection sensitivity is 2 ×10 -6 cm -1 recorded in 250 seconds corresponds to a minimum detectable density of 10 12 cm -3 when using integrated transition cross sections of ∼ 10 -22 cm 2 cm -1 molecule -1 , typical of hydrocarbon molecules, and indicates the potential of this methodology for probing radical species such as CH 3 , which densities are reported to be of this order of magnitude [22,23].

C 2 H 2 has two low lying vibrational states which are significantly populated at room temperature (also probed and relevant transitions shown in the figures) corresponding to the ν 4 and ν 5 bending modes at 612 cm -1 and at 730 cm -1 , respectively. Taking the spectrum recorded at room temperature with a C 2 H 2 cell containing 115 Torr of gas as a benchmark for the relative heights of absorption lines, and adjusting the observed heights for a change in rotational temperature from 298 to 400 K (see further on), an estimate of the degree of vibrational excitation with the plasma on can be obtained. It should be noted that the an apparent increase in vibrational population due to a temperature increase to 400 K has not been included here, as quite often in plasma systems the vibrational and rotational modes are decoupled. The spectra indicate that populations in the ν 4 and ν 5 levels are being depleted with respect to the ground state, but with populations in the 2ν 4 and 2ν 5 levels enhanced, pointing towards a non-Boltzmann vibrational distribution. Further work is required on other higher lying vibrational states in order to determine the vibrational energy distribution, and whether or not it is perhaps well described by a two temperature Boltzmann function.

According to the Beer-Lambert law, the absorption signal due to a species with a particular density is proportional to the cross-section of that species. The cross-sections relating the absorption to the density of a species are temperature dependent because they depend upon the temperature dependent populations of individual quantum states. Hence knowledge of the plasma temperature is needed for total density measurements. By measuring the rotational temperature, T rot , of the C 2 H 2 in the plasma, total densities for a particular vibrational level can be calculated assuming that the rotational populations are described by a Boltzmann distribution for all the species. The rotational temperature is obtained by taking the ratio of the integrated absorptions of two transitions that originate from the same lower vibrational state as this cancels the dependence of the line intensity on the total internal partition function, Q(T ), and the ratio becomes temperature-dependent only. In order to increase the SNR, strong C 2 H 2 transitions in the region 3212 -3218 cm -1 were measured with direct absorption spectroscopy; their line positions and assignments are given in table 4. In the extraction of T rot as a function of plasma power and pressure, the average of the ratios of P27/P31 and P31/P26 were determined. Of the transitions that are in the accessed spectral region, these two sets of transitions have intensity ratios that are most sensitive to a change in T rot (a factor of 1.3 over 100 K) because they involve rotational levels that are furthest apart (in energy) and hence have the largest rotational population differences for a given set of conditions. The measured T rot was essentially invariant to the change in plasma pressure or rf power within the experimental error. Thus, an averaged value of T rot = 400 ± 55 K was assumed and the rotational, vibrational and translation temperature were all assumed to be equal in order to calculate the integrated cross-sections for the observed transitions. These assumptions probably result in an underestimation of the densities as the C 2 H 2 spectra indicate a non-Boltzmann vibrational distribution for C 2 H 2 . All of the measurements are also spatial averages and assume a uniform density distribution and temperature distribution through the chamber. In tables 4 -6, the details of the transitions probed such as line position, the integrated cross section at 400 K and the assignments obtained from the HITRAN 2008 database [24] are given. At the reported plasma temperature, the absorption crosssections of C 2 H 4 in the accessible wavelength range are at least an order of magnitude smaller than those of C 2 H 2 . Due to its low detection limit, we were not able to detect C 2 H 4 by direct absorption spectroscopy under all the conditions investigated. Hence the C 2 H 4 density was determined from WMS spectra. Since the peak height of an absorption profile in a WMS spectrum is proportional to the density of the absorbing species, the ratio of peak heights between transitions of C 2 H 4 and C 2 H 2 allows the C 2 H 4 density to be estimated, given that the ratio is corrected for the difference in the absorption cross-sections of the two species, and the WMS data on C 2 H 2 have been calibrated from direct absorption spectroscopy measurements. The C 2 H 6 densities could be obtained by direct absorption spectroscopy under all experimental conditions.

The densities reported are the averaged densities determined using the transitions listed in the tables 4 -6 for C 2 H 2 , C 2 H 4 , and C 2 H 6 . The obtained densities of C 2 H 2 , C 2 H 4 , and C 2 H 6 were insensitive to changes in plasma pressure and rf power within the experimental error and were around 7.9 ± 0.3 × 10 14 cm -3 , 9.5 ± 1.5 × 10 14 cm -3 , and 7.9 ± 2.2 × 10 14 cm -3 for C 2 H 2 , C 2 H 4 , and C 2 H 6 , respectively. The uncertainty in the temperature and thus integrated cross section results in an error of 20% for C 2 H 2 , 10% for C 2 H 4 , and 32% for C 2 H 6 . We note that the C 2 H 2 density was found to vary between 7.8 × 10 14 cm -3 and 8.4 × 10 14 cm -3 for repeated measurements on different days under the same conditions (0.84 Torr and 180 W). The recorded densities hence show a very good agreement between measurements, despite the large possible error estimated. These densities are of the same order of magnitude as observed in rf CH 4 plasmas assuming a Boltzmann density distribution over the rotational and vibrational states [22,23].

We also determined the CH 4 depletion under the conditions investigated. From the spectra, we determined the rotational temperature of the CH 4 molecules in the plasma to be 330 ± 25 K and used this temperature to calculate the integrated cross-sections for the transitions assuming a Boltzmann density distribution. In the process of calculating the CH 4 density, it has to be remembered that the plasma is confined between the electrodes and that the plasma region is only one third of the total optical pathlength. Therefore, a line-of-sight radiation beam measures the averaged properties of CH 4 , and the obtained T rot is thus the averaged rotational temperature of a third of CH 4 at plasma temperature (400 K) and the rest being at presumably a lower temperature resulting in 330 K. The rotational temperatures of 400 K for species in the center of the chamber and 330 K for CH 4 molecules is in agreement with previous measured temperatures in rf CH 4 plasmas [23,25]. In table 2, the details of the transitions probed such as line position, the integrated cross section at 330 K and the assignments obtained from the HITRAN 2008 database [24] are given. The deduced CH 4 depletion is presented in figures 5(a) and 5(b) for varying CH 4 pressure and plasma power. The depletion of CH 4 increased from 23% at 40 W to 40% at 180 W, and increased to 56% as the pressure decreases to 0.45 Torr. This conforms to the intuitive notion that an increase in the rf power driving the plasma increases both the electron temperature and number density and therefore more dissociation takes place in the plasma (as is always found in these systems). The C 2 H 2 , C 2 H 4 , and C 2 H 6 densities are however relatively insensitive to the plasma conditions compared with the methane loss resulting in a discrepancy in the carbon balance. The missing carbon atoms could be related to the deposition of carbon films on the walls of the plasma chamber but we note however that it is impossible to deduce exactly the chemical balance of the plasma without knowledge of the vibrational population distribution.

Conclusion

This paper demonstrates the practicality of a compact solid-state laser based DFG system as a tool for probing hydrocarbon based plasmas. The production of midinfrared radiation has been successfully achieved by combining 1064 nm radiation from a cw Nd:YAG laser with 1560/1620 nm radiation from distributed feedback (DFB) fibre coupled diode lasers in a PPLN crystal. The resultant 18 µW of radiation around 3.2 µm has been used to probe a rf capacitively couple CH 4 plasma for a matrix of conditions, varying power (< 180 W) and pressure (< 1 Torr) in both direct absorption spectroscopy and WMS experiments to achieve relatively high sensitivities while retaining accurate spectral information in the form of linewidths. An α min value of 2 × 10 -5 cm -1 was achieved for direct absorption spectroscopy which corresponds to a minimum detectable density for CH 4 of 1.7 × 10 12 cm -3 . The conversion of CH 4 to other species was determined by measuring the densities of C 2 H 2 , C 2 H 4 , and C 2 H 6 which were respectively around 7.9 ± 0.3 × 10 14 cm -3 , 9.5 ± 1.5 × 10 14 cm -3 , and 7.9 ± 2.2 × 10 14 cm -3 . Finally, the depletion of CH 4 was measured to increase from 23% at 40 W to 40% at 180 W at a pressure of 0.84 Torr, and the depletion increased to 56% as the pressure decreases to 0.45 Torr.

List of figure captions:

(1) Schematic of the DFG experimental setup.

(2) (a) Experimentally measured tuning curves for two signal wavelengths, 1620.97 nm ( ) and 1619.52 nm (• ), as a function of crystal temperature. (b) The measured MIR signal as a function of the wavelength of the diode laser at 1620 nm at a temperature of 80 • C.

(3) (a) Direct absorption spectrum and (b) Wavelength modulation spectrum of 0.17 Torr of CH 4 without the plasma on. In the direct absorption spectrum, the four strong transitions absorbed a considerable amount of the laser intensity and they suffer from line broadening. The details of the transitions probed are given in table 2.

( (5) The depletion of CH 4 as a function of (a) CH 4 pressure at a power of 180 W and (b) plasma power at a pressure of 0.84 Torr.

Figure 1 .Figure 2 .Figure 4 .

 124 Figure 1. van Helden et al.

Figure 5 .

 5 Figure 5. van Helden et al.

  ) WMS spectra of C 2 H 2 in the region 3211.7 -3218.7 cm -1 as measured in a reference cell of 115 Torr of C 2 H 2 (top) and of the CH 4 plasma (bottom) using 2f -harmonic detection; the operating power of the plasma was 180 W and the pressure was 1.57 Torr. Marked in the spectra are transitions which could be assigned in both the 115 Torr cell and in the plasma and the vibrational bands they belong to are listed in table3. The other lines observed are not assigned, but part of them are from C 2 H 2 transitions as they are observed in both spectra. The other unassigned transitions could be from C x H y molecules, or radicals like CH 3 and C 2 H.

Table 1 .

 1 The A z and B z parameters of the Sellmeier equation for PPLN[START_REF] Jundt | [END_REF]. B 4.629 × 10 -7 3.862 × 10 -8 -0.89 × 10 -8 2.657 × 10 -5

	z	1	2	3	4	5	6
	A 5.35583	0.100473	0.20692	100	11.34927 1.5334 × 10 -2

Table 2 .

 2 Details of the transitions of the ν 3 asymmetric stretch mode of CH 4 , where J is the rotational quantum number and C gives the symmetry[24].

	Transition

Table 3 .

 3 Assignments of the C 2 H 2 bands in the 3 µm region observed in our WMS spectra[21].

Table 4 .

 4 Details of the C 2 H 2 transitions[24].

	Line position Integrated cross-section, T = 400 K Upper vibrational Lower vibrational Transition
	(cm -1 )	(cm 2 cm -1 molecule -1 )	level	level
	3212.640735	8.82 × 10 -21	010(11) 0 + (Σ + u )	0000 0 0 0 (Σ + g )	P28e
	3215.253045	3.21 × 10 -20	010(11) 0 + (Σ + u )	0000 0 0 0 (Σ + g )	P27e
	3217.066339	9.69 × 10 -21	0010 0 0 0 (Σ + u )	0000 0 0 0 (Σ + g )	P31e
	3217.853528	1.29 × 10 -20	010(11) 0 + (Σ + u )	0000 0 0 0 (Σ + g )	P26e

Table 5 .

 5 Details of the transitions of the ν 9 asymmetric CH 2 stretch mode of C 2 H 4 , where J, K a and K c are the rotational quantum numbers[24]. Transition Line position Integrated cross-section, T = 400 K (cm -1 ) (cm 2 cm -1 molecule -1 ) J' K a ' K c ' ← J" K a " K c "

	3217.359364	8.17 × 10 -22	14 12	3	13 11	2
	3217.359364	8.17 × 10 -22	14 12	2	13 11	3
	3217.585582	2.735 × 10 -22	27 9	18	26 8	19
	3217.585582	6.381 × 10 -22	27 9	19	26 8

Table 6 .

 6 Details of the transitions of the ν 7 band of C 2 H 6[24].

	Transition

Acknowledgments

The authors would like to thank the EPSRC for the award of an Advanced Research Fellowship (R.P.)

Label

Upper Level Lower Level 12 C 2 H 2 I 010 (11) 0 + (Σ + u ) 0000 0 0 0 (Σ + g ) II 010( 21)