Stark broadening for simultaneous diagnostics of the electron density and temperature in atmospheric...

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Spectrochimica Acta Part B

Stark broadening for simultaneous diagnostics of the electron density and

temperature in atmospheric microwave discharges

J. Torres a, M.J. van de Sande b, J.J.A.M. van der Mullen a,c, A. Gamero a, A. Sola a,*

a Departamento de Fısica, Universidad de Cordoba, Campus Universitario de Rabanales (ed. C2), E-14071 Cordoba, Spainb Philips CFT, P.O. Box 218 5600 MD Eindhoven, The Netherlands

c Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513 5600 MD Eindhoven, The Netherlands

Received 5 July 2005; accepted 27 November 2005

Available online 18 January 2006

Abstract

In this paper we delimitate the use of the Stark broadening of lines spontaneously emitted by atmospheric-pressure plasmas as an indirect

method to determine both the electron density and temperature in discharges produced by microwaves. This method, previously presented in a

recent paper (J. Torres et al., J. Phys. D: Appl. Phys. 36 (2003), L55-59), allows us to obtain experimental results for these two parameters in argon

discharges in good agreement with other experimental results previously reported. The possibility of extending its use to a plasmogenic gas other

than argon is discussed, and the limitations of the method are pointed out.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Stark broadening; High-pressure discharge diagnostics; Electron density and temperature diagnostics; Microwave discharges

1. Introduction

Among the different aspects concerning Plasma Physics,

one of the most important deals with the possibility of

obtaining information about the principal characteristics in

the discharge. The knowledge of its relevant magnitude or

parameter values is achieved by means of experimental

methods or techniques as well as by any other available tools

(namely computational models). This field of Plasma Physics,

which receives the wide denomination of Plasma Diagnostic,

was developed from the beginning of the plasma studies

together with the Plasma Theory. Optionally, the methods of

Plasma Diagnosis can be organized in Electric and Magnetic

Probes (static or dynamic, simple or double) methods,

Electromagnetic (propagating, interferometric, resonant and

polarizing) methods, and Optical and Spectroscopic methods

(mass spectroscopy included). A much updated review on these

methods can be found in [1].

0584-8547/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.sab.2005.11.002

* Corresponding author.

E-mail address: [email protected] (A. Sola).

1.1. Direct and indirect techniques in Spectroscopic Plasma

Diagnostics (SPD)

Particularly, in Spectroscopic Plasma Diagnostics (SPD),

direct methods or techniques determine the electron density, ne,

and the electron temperature, Te, in plasmas without needing

any hypothesis about the type and degree of equilibrium

existing in the discharge. On the contrary, indirect methods or

techniques base their determination on hypotheses concerning

the particles that constitute the plasma, namely some specific

distributions for their different ionization and/or excitation

stages/states, as well as the distribution of the radiation

involved in these mechanisms [2,3].

Some qualitative differences affecting these two groups of

diagnostic techniques or methods can be pointed out in terms

of advantages and disadvantages. The advantages of the first

group of (direct) techniques versus the second group (indirect

ones) in SPD are quite evident. Except for a few occasions, the

distributions invoked above (i.e. distributions of translational,

excitation, ionization and radiation states) are not known

accurately enough or are only partially known, which could

invalidate their use. As examples, the well-known Boltzmann-

plot method to determine the excitation temperature, Texc, for

61 (2006) 58 – 68

ww

J. Torres et al. / Spectrochimica Acta Part B 61 (2006) 58–68 59

the excitation balance among atomic levels of the species in the

plasma, or the Saha-jump method to determine the ionization

temperature, Tion, for the ionization-recombination balance.

Both temperatures permit an estimation of the electron

temperature, Te, in the discharge and the use of these methods

requires the plasma to be close enough to the so-called Local

Thermodynamic Equilibrium (LTE). In this situation, proper

balances between microscopic processes at the same temper-

ature are guaranteed by the detailed balance principle. Also, the

method of molecular species rotational bands to determine the

so-called rotational temperature, Trot, (which is identified with

the heavy particle or gas temperature, Th or Tgas) implies a

certain special type of molecular excited state distribution as a

consequence of a particular excitation balance. And so do other

indirect methods such as measurement of the continuum part of

the plasma spectrum (for instance, the line-to- continuum ratio

method). Moreover, the use of Collisional-Radiative Models

(CRM) as complementary indirect tools is useful to determine

the populations of species in the plasma and their temperatures.

On the other hand, spectroscopic diagnostic techniques in

SPD exist which do not need any previous knowledge about

any distribution of particles or radiation in the discharge, or any

other requirement about particular balances among them to

determine the magnitudes or parameters of interest, ne and Te.

In this paper, we deal with these two groups of techniques.

Particularly, for determining both the electron density and the

electron temperature–probably the two main parameters in the

plasma–in the same experiment (that here is to say simulta-

neously), we invoke here two methods: a) the Thomson

scattering, or scattering of light by free electrons in the plasma

(an active and direct technique) and (b) the Stark broadening

of lines spontaneously emitted by the plasma (a passive and

indirect technique), these phenomena being affected by both

the electron density and the electron temperature.

1.2. Thomson scattering versus Stark broadening

The spectroscopic diagnostics method for determining at

the same time ne and Te known as Thomson scattering (in

both its versions coherent or incoherent) is a quite expensive

method and of critical implementation. This method has

numerous experimental difficulties, although it provides some

enviable performances such as precision, accuracy and spatial

and temporal definition [4–6]. An interesting review on

Thomson scattering can be found in Ref [7]. In turn, the Stark

broadening of certain spectral lines spontaneously emitted by

the plasma allows the determination of the electron density in

a rapid and non-expensive way provided the electron

temperature is known, although this emission spectroscopic

technique deals with a line of sight and not a particular

location in the plasma.

The basis of the diagnostic method determining at the same

time ne and Te by Stark broadening rests on the idea of the

study of two or more lines broadened under the same work

conditions. The results of applying this method of diagnosis to

one particular case were previously presented in a recent paper

[8] although the first idea about that was raised earlier [9]. By

superposing the information obtained for such lines, it is

possible to determine not only ne, but also Te in the discharge,

which in the end is a diagnostic equivalent to Thomson

scattering. In fact, it is a first, rapid and approximated

estimation of these magnitudes that can be sufficient for a

large number of cases in which only a rough value of these

magnitudes is needed. So, advantages and disadvantages are

reasonably balanced in this discharge diagnostic method versus

the more complicated, expensive and slow Thomson scattering.

However, for some specific cases in which accuracy and

precision in the measurements is needed, Thomson Scattering

will prevail over Stark broadening for the simultaneous

determination of ne and Te. A wider consideration about this

point can be found in the Introduction paragraph of the

previously mentioned paper [8].

In gaseous high-pressure discharges, microwave discharges

have been used more and more because such discharges are

very reproducible and stable, of easy handling and low cost

in most cases. In this paper we shall study the experiments

performed on the discharge produced by a TIA (Torch a

Injection Axiale) device [10] using argon and helium at

2.45 GHz at moderated HF powers (300–1000 W) in order

to compare with the already studied discharge produced by a

surfatron launcher [11] (surface-wave discharge, SWD) in a

capillary plasma column of argon at low HF powers, typically

less than 100 W [8]. It should be noted that in this kind of

microwave discharge we have a two-temperature (2-T) plasma,

that is characteristic of a non-equilibrium situation. The heavy

particle (gas) temperature, Tgas, is much less than the electron

temperature, Te. Of course, it is also possible to try our

diagnostic method in high-pressure discharges other than

microwave ones. In this way, the simultaneous measuring of

ne and Te by Stark broadening of spectral lines is extended to a

wider range of work conditions. This alternative direct method

presents not only advantages and disadvantages versus the

Thomson scattering, but also important limitations in its use

that will be pointed out and discussed.

Prior to the description of the experiments, we briefly

review the theories of the Stark broadening in the next section.

After that, we present the experimental aspects of the work

(setup and data treatment), the results and discussion for argon

and helium TIA discharges, and finally the conclusions.

2. Brief review on the Stark broadening theories

The profile of an emission line spontaneously emitted by

plasmas is broadened by different broadening causes, mainly

natural, Doppler, collisional (Stark) broadening as well as by

the instrumental function of the apparatus [2]. The Stark

broadening has its basis on the Stark effect and is a

consequence of radiating atoms interacting with free electrons

and ions in the plasma, through electric fields that these

particles create. The interaction between an atom emitting

electromagnetic radiation and an external electric field was

discovered in 1913 by the German scientist Johannes Stark in

the course of experiments on Doppler Effect. The occurrence of

the Stark effect is inherent to plasmas, since radiating atoms in

J. Torres et al. / Spectrochimica Acta Part B 61 (2006) 58–6860

plasmas are always subjected to the electric fields of the

charged particles that constitute the plasma.

The first statistical approach to explain the phenomenon,

initially developed by Holtsmark [12], is a quasi-static theory.

This theory mainly pays attention to the interaction caused by

the ions, of a more intense effect than that provoked by the

electrons during the time in which the emission takes place.

Historically, different theories have been developed later to

explain this broadening mechanism quantitatively better. Such

theories took into account the influence of the static ions and

also of the electron collisions. Some of them have a semi-

empirical character and/or apply to some specific spectral lines.

As an example, this was the case for the Hh line of the

hydrogen Balmer series. At present, the most important models

for this line are the merely quasi-static approach due to Hill

[13,14], as well as later approaches that also keep in mind the

electron impact contribution to some extent, namely the GKS

theory [15], the Greig’s theory [16], and the VCS theory [17].

For a measured Stark broadening concerning a line emitted by

the plasma, the different theories explaining this broadening

mechanism provide us different values for the electron density neat a given electron temperature Te in the discharge. If those values

of ne are historically sorted in the theories that provide them, the

result is a list of decreasing values. That is to say, the theoretical

values are refined with each new theoretical contribution taking

into account more and more causes of perturbation. In effect, by

adding the perturbation effect of the plasma free electrons to the

quasi-static theory, less density of ions will be necessary to

produce the same effect (broadening) on the same profile shape.

More recent microfield model methods (MMM) take into

account the ionic dynamics, which has supposed a new correction

and improvement of the theoretical predictions comparedwith the

experimental data. As was expected, by considering that the ions

also move during the interaction time, the result obtained for the

ion density is even lower. In this work, we use the computational

simulation (CS) theory due to Gigosos et al. (orGig-Card theory,

[18,19]), which includes the more relevant processes in the

plasma and constitutes one of themore accurate approximations at

the moment. It becomes a method for calculating line shapes with

the scheme of MMM, but with the electric microfield more

correctly obtained from an ideal experiment [20]. In this approach

the calculations have beenmade for three of the hydrogen Balmer

series lines, namely Ha, Hh and Hg, and their analogous lines of

the Lyman series. This ion-dynamic correction has not the same

relevance for each particular line.

In short, the Gig-Card model is based on the computational

numerical simulation of the behavior of all the particles in the

plasma. The electric field created by the charged particles,

electrons and ions, perturbing the emission of a hydrogen atom

is obtained. The plasma is considered as a globally neutral,

homogeneous and isotropic system in thermal equilibrium.

Atoms, ions and electrons are moving (quasi-) randomly in the

plasma, with rectilinear and uniform velocities given by the

Maxwell-Boltzmann distribution. These particles move in a

Debye sphere centered in the emitter, this sphere size being

related to the average distance between electrons, which is

controlled by the electron density. Inside this sphere of electric

influence that surrounds the central (emitter) atom, the position

(impact parameter) and the velocity (related to the temperature)

of each particle with respect to the central hydrogen atom are

calculated at each instant. In this situation, the time-dependent

electric microfield EY

tð Þ is obtained and introduced in the

evolution quantum equations of the system. The evolution in

time of the system is controlled by the evolution operator U(t)

obeying the time-dependent Schrodinger equation

ihd

dtU tð Þ ¼ V tð ÞIU tð Þ; ð1Þ

where V tð Þ ¼ H0 þ EY

tð ÞIdY

tð Þ is the Hamiltonian operator

including both the structure of the undisturbed states, H0, and

the effect of the charged perturbers on the emitters through the

dipole-field interaction energy term. The dipole moment

operator of the emitter atom dY

tð Þ ¼ qRY

tð Þ contains all the

information dealing with the considered electronic transition.

The emission profile of a spectral line concerning this transition

is obtained by the Fourier transform [21]:

I xð Þ ¼ 1

pRe

Z V

0

dtIeixtbC tð Þ�average

¼ 1

pRe

Z V

0

dtIeixtTr dY

tð ÞIdY

0ð Þqqh i

; ð2Þ

with dY

tð Þ ¼ Uþ tð ÞIdY

0ð ÞIU tð Þ, where U(t) is the already

mentioned evolution operator and Tr is the trace operation

calculating the average of the autocorrelation function C tð Þ ¼dY

tð ÞIdY

0ð Þ over the possible quantum states (statistic ensemble)

characterized by the density (matrix) operator q. All the

equations are numerically solved for given intervals of time

by means of numerical discretizing techniques under the

conditions described in [18,19]. Finally, the computational

Gig-Card model provides full emission profiles and data

concerning the Stark broadening of the studied line for certain

concrete conditions of electron temperature, electron density,

and mass of the perturbing ions.

The common way to determine ne by Stark broadening is to

experimentally measure the broadening of a line, and by

knowing approximately the value of Te (usually thanks to some

other complementary method of plasma diagnostics), to obtain

the corresponding value of ne. It is not easy to know Te in the

discharge accurately and, as a consequence, the calculated

values for ne are also affected by uncertainty. To some extent,

the temperature is a free parameter in the conventional Stark

broadening diagnostic method, i.e. once its value is fixed, ne is

determined.

The broadening of different spectral lines depends differ-

ently on ne and Te. Generally, the experimental broadening of

different lines corresponds to slightly different electron

densities depending on an arbitrary fixed Te. However, we

shall show that is possible to obtain coherent results (same

electron density) using different Balmer lines, by varying the

free parameter (electron temperature). In this way, all the nevalues related to different broadenings of different spectral

lines coincide at a specific Te. Finally we get a diagnosis of

these magnitudes in the plasma simultaneously from these

Fig. 2. Details of the studied plasma flame and its production device

(TIA’s tip).


lines. This cross-lines method for the diagnostic of both the

electron density and temperature that is proposed here lies in

the use of two (or more) lines at the same time in order to look

for a point (cross-point) in which the predicted electron density

and temperature are coincident for these lines.

3. Experimental aspects

3.1. Set-up used in the experiments

Let us now present some additional details concerning the

discharge used for diagnostics and its production device. This

spectroscopic method of diagnostic was already used in a

capillary argon plasma column produced by surfatron (SWD)

and its setup discussed in Ref. [8]. Now, we are interested in

testing the diagnostic method in other plasmas produced by

another device, namely the plasma produced in argon and

helium at atmospheric pressure by coupling microwave energy

at 2.45 GHz to the discharge with the aid of a TIA device [10].

This structure produces a plasma flame typically of 1 mm of

diameter and a few centimeters long expanding in the open air

in which the electron temperature and density are considerably

higher than in the surfatron plasma. As in the previous case, for

the spectroscopic diagnostics of this discharge standard optical

arrangements are used to increase the image size and focus the

light emitted by the brightest zone of the plasma flame into the

entrance slit of a THR 1000 (Jobin-Yvon) monochromator. At

its exit slit, a double optical detection system is mounted, that

alternatively permits us to use by means of a folding mirror: (a)

an iCCD (intensified Coupled Charge Device, FlameStar II,

LaVision), and (b) a phototube (Hamamatsu), both in the

visible region.

swercsgninut

wolf sag

daol

nortengamzHG 54.2

DC

circulator

emarfniamrewop

rotareneg

.A.I.T

wolf sag

tafruS

laixaoc-ediugevawnoitisnart

(a)

(b)

amsalp

Fig. 1. Optical arrangement for plasma spectroscopic diagnostics us

The light collected in the radial direction by the lens–that

focuses an image of the plasma of which a bright spot of about

one millimeter of diameter is at the entrance slit–comes from

different zones inside the plasma for a fixed axial position (see

Fig. 1, coupler (a) or TIA). For a proper diagnostics of the

discharge, in principle this is not a desirable feature spatially

speaking due to the existence of relevant radial gradients in the

discharge because the detection volume is rather large. The

light coming from different points with spectral profiles having

different widths is difficult to be treated. For that reason, the

diagnostic presented here is representative (or apparent) for a z

position in the plasma and not for any specific radial point

inside the plasma at this z. This position is measured from the

beginning of the discharge (z =0 at the tip of the TIA’s nozzle,

as appears in Fig. 2). Of course, we can move the system

regnulpelbavom

ROTAMORHCONOM

RELLORTNOC

knilartcepS

snel

DCC

nor

ed in this work with (a) TIA coupler and (b) surfatron coupler.

Fig. 3. Ar 500.02 nm line with and without extra-Hydrogen added to the

discharge.

Fig. 4. 3-D representation of the Hh Stark broadening as a function of Te and nemodeled by the Gig-Card theory.


properly to make the diagnostics at different z using the light

coming from different plasma positions (z heights).

Even when radially resolved diagnostic is needed, this

method is also suitable by using standard inversion techniques,

i.e. the Abel inversion for instance, provided that cylindrical

symmetry conditions are fulfilled by the discharge. This is the

usual situation when significant gradients exist in the dis-

charge, although at the moment this improvement is waiting to

be implemented in this experiment.

To properly observe the Balmer series lines, a small amount

of hydrogen is introduced in the argon discharge, about 1%.

We can control the amount of hydrogen introduced into the

discharge by using a flux meter (Tylan General, Dynamass

Flow System). So, when we say ‘‘gas’’, we mean plasmogenic

gas (i.e. argon) plus a small amount of H2. This amount is

enough to measure the intensities of the Balmer series

hydrogen lines, but does not disturb the discharge significantly.

This last point can be checked by observing and comparing the

argon spectral line intensities with and without the extra

hydrogen added to the discharge (see Fig. 3 for an example).

We can assume that our plasma is optically thin for radiation

of the Balmer lines, so the light from Balmer lines may go

through the whole plasma in its radial direction before it

escapes the plasma. Self-absorption is not a problem for these

hydrogen lines we are interested in because (i) the hydrogen is

a negligible perturbation for the plasma due to its low

concentration, (ii) they are non-resonant lines and (iii) the path

is really short.

3.2. Data treatment

Results of the Stark broadening by the computational model

arising from the Gig-Card theory are obtained at specific

values of electron temperature, electron density and reduced

mass parameter l. It is possible to perform an interpolation

between this data set to make a continuous function from the

discrete points directly calculated by the Gig-Card model. The

TIA plasma is typically a two-temperature (2-T) plasma: a

higher temperature for the electrons–that receive the energy

from the microwave field–and a lower temperature for the

heavy particles (ions and atoms), that mainly receive the energy

by electron collisional processes. This deviation from the

thermodynamic equilibrium can be taken into account using the

reduced mass l as a parameter (i.e., if the electron temperature

is twice the heavy particle temperature, a double reduced mass

must be used).

In Fig. 4, we can see this relationship in a 3-D representation

in which the Stark broadening versus the electron density and

the electron temperature is displayed for the case of Hh (at a

given l parameter).

For a given electron temperature, we can fit the dependence

of the Stark broadening on the electron density by using the

following logarithm form:

logne ¼ a� bln Dk þ cð Þ; ð3Þ

where in fact the parameters a, b and c are functions of the

electron temperature Te. Of course, they behave differently

with Te for each hydrogen line. For these parameters a

different fit function was found. Finally, the relative error of

the fit we have performed is below 1% with respect to the

original data, a very good fitting that makes it possible to use

this interpolation.

Aside from Stark broadening, any emission line spontane-

ously emitted by the plasma can be broadened by other

broadening causes such as the natural broadening (a conse-

quence of the Heisenberg’s principle of uncertainty), the

Doppler broadening (due to the thermal movement of the

emitter atoms), and the collisional broadening of pressure

(mainly caused by the interaction with neutral atoms of the

plasma). Moreover, the instrumental broadening (introduced by

the characteristic instrumental function of the monochromator)

should be separately considered as an external cause of line

broadening to be convoluted to real ones.

The total broadening of a line is caused by the combined

effect (convolution) of all causes contributing to the phenom-

enon. Each cause of broadening has its relative importance

with respect to the others according to the conditions of the

plasma, by causing a shift in the energy levels of the emitter

atoms and finally contributing to broaden the corresponding


line profile to a greater or lesser extent. The information needed

for our purposes is the part of the broadening profile only

corresponding to the broadening caused by Stark effect. This

part will be obtained by separating (deconvolution) the Stark

broadening from the total broadened profile, for which the

knowledge of broadening profiles other than the Stark one is

needed. But, under our working conditions (plasma at

atmospheric pressure with a moderate electron density and

temperature), the only relevant sources of broadening are the

Stark (FWHM around 1–10�1 nm), the instrumental (FWHM

around 10�1–10�2 nm) and the Doppler broadening (FWHM

around 10�2 nm). The effects of other less important causes of

broadening are neglected in our case [22] (the pressure

broadening FWHM is below 10�3 nm, and the natural

broadening and the effect of Van der Waals’ dipolar forces,

the resonant broadening induced by emissions of other similar

atoms and the broadening by reabsorption are even minor).

As good approximation, these profiles are of typically

Gaussian or Lorentzian forms and the combined contribution of

all of them (convolution) is a Voigt profile. The most useful

parameter used to measure the line broadening independently

of its intensity is the full width at half-maximum (FWHM) or

simply half-width. For two Gaussian profiles whose convolu-

tion product is a Gaussian profile too, the total FWHM is

Dktotal2 =Dk1

2+Dk22; in turn, for two Lorentzian profiles whose

convolution product is a Lorentzian profile too, the total

FWHM is simply Dktotal =Dk1+Dk2. However, the half-width

of the Voigt profile as a result of the convolution product of

Gaussian and Lorentzian profiles does not have a simple

analytic form in terms of the original profile FWHMs in the

convolution, although the following approach is considered

valid with high precision [23]:

DkVoigt,DkLorentz

2

� �2

þ Dk2Gauss

" #1=2

þ DkLorentz2

: ð4Þ

This equation allows us to obtain for example the Ha Stark

broadening, which is supposed to be a Lorentzian profile,

provided that both the Doppler and the instrumental broad-

enings are known. For determining the Doppler broadening,

the following equation is used:

DkDoppler ¼ 7:16I10�7k0ITgas

Matom

� �1=2

nmð Þ; ð5Þ

where Tgas is given in Kelvin and Matom in atomic mass units,

and k0 in nm is the central wavelength of the studied line.

This gas temperature is necessary to correctly evaluate the

Doppler broadening and can be measured by means of

different techniques. Its value is known under our working

conditions by previous works although its effect is relatively

unimportant for the gas temperature range characteristic of the

discharge (around 2000–3000 K). The instrumental broaden-

ing, being measured with a laser using the same experimental

set-up conditions, is finally assumed to be Gaussian (the

experimental broadening value is around 20% relative to the

total broadening).

4. Results and discussion

The experiments have been carried out repeatedly with two

different plasmogenic gases, namely argon and helium. As it

has already been explained before, it has been necessary to

add a controlled quantity of hydrogen to the discharge to

make the used lines of the hydrogen Balmer series

sufficiently visible. The gas flow remained constant at a liter

per minute with the addition of 1% of hydrogen into the main

gas flow.

Two different positions in the discharge have been checked:

(a) at approximately one centimeter above the tip of the TIA’s

nozzle, and (b) just above this tip, in order to compare the

results spatially. Since a radial study of the lines emitted by the

plasma has not been carried out, the obtained measurements are

apparent radial averages of the whole plasma in that position—

an adjusted average in which higher Te zones in the plasma are

more important, because there the emission are higher too. Two

different microwave powers, 600 and 800 W, have been used in

the experiments too.

After repeatedly recording spectral profiles of Ha, Hh and

Hg lines under given experimental conditions (HF power and

position in the flame), the different broadening mechanisms

other than Stark broadening were eliminated from the total

experimental profiles by using simplified de-convolution,

where Gaussian profiles were assumed for the non-Stark

contributions (thermal Doppler and instrumental broadening).

By applying the Gig-Card theory to the Stark broadenings

determined by this way, concerning the different studied lines

of the hydrogen Balmer series, we have obtained tables of

values for the electron density as a function of the electron

temperature. As was explained previously, from these points

we have performed a fit in order to interpolate more points, to

produce an almost continuous line of points (a parametric

function of the electron density vs. the electron temperature,

where the parameter is the full-width at half-maximum,

FWHM, Stark broadening).

This has been possible for the three first Balmer series

lines used in our study, but some problems have arisen with

Hg. Due to its intensity being very low, we have had a very

high dispersion in the Stark broadening values of Hg (that is

because its profile is not sufficiently different from the

background signal of the spectrum). The different measure-

ments concerning this line were not reproducible and they did

not arise as a set of homogeneous broadening values but

rather as a set of different values. Due to this difficulty, at

best we are able to obtain not a crossing point among these

three Balmer series lines (which is the ideal situation) but

rather a triangular-shaped crossing zone. This crossing zone

has a very small area (see Fig. 5) indicating a very low spread

of the obtained result. But in other cases, this area is much

larger and the results are not definitive by using three lines in

the crossing-point methods. In these same sets of measure-

ments however, Ha and Hh present a very stable behavior

with hardly any dispersion and providing a very stable value

of the Stark broadening of the line. At the moment, these two

lines will be the most useful tools for the simultaneous

Fig. 5. Illustrative case of diagnostic based on three lines, cross-point method. The used lines are Ha, Hh and Hg, and the result is rather a small cross-region than a

cross-point.


diagnostics of the electron density and temperature by means

of the crossing-point method.

The measurements including Hg provide coherent results

with those obtained with Ha and Hh, the other two lines, but

assuming a higher error range. The most desirable would be

to have a diagnostic based on the single-crossing point of

three lines, which has been achieved in a particular case as

illustrated in Fig. 5. But before, it should be necessary to

eliminate the great dispersion in the measurement of Hg. For

that, we believe that it will be necessary to add more

hydrogen to the discharge in future experiments in order for

the intensity of Hg to be higher. Furthermore, its profile

would be better defined and stand out against the background

signal. In this respect, let us remember that the quantity of

Fig. 6. Relationship of Te and ne values compatible with the measured Ha and

simultaneously determines Te and ne values in the TIA argon plasma.

hydrogen added to the discharge was fixed at 1% because that

value was shown valid in similar experiments in the surfatron

system. Indeed, this quantity has been sufficient to detect and

measure this line, but its intensity is too low to obtain

reproducible results.

4.1. Results on the TIA argon plasma

The results of the experiments on the TIA argon plasma are

shown in Fig. 6a and b at HF powers of 800 and 600 W,

respectively. For the experimental FWHM values obtained

concerning Ha and Hh indicated in the figures, the relationship

of the electron density and electron temperature values

compatible with these broadenings are depicted as two different

Hh Stark broadening at a power of (a) 600 W, (b) 800 W. The cross-point

Fig. 7. Detailed profile of Hh showing its main spectral components.


curves (position 1 cm approx. above the nozzle’s tip). As it is

known, the relationship of the electron density and the electron

temperature values at a given FWHM is practically flat in the

case of Hh (that is the reason to use preferably Hh if one is

interested in the electron density value only), the change of newith Te being extremely weak in the range of temperatures

shown in the figures. However, in the case of Ha this

relationship is more pronounced. By crossing both curves, it

is possible to find the values of ne and Te simultaneously at

which the Ha and Hh Stark broadenings predicted by the Gig-

Card theory coincide with those obtained experimentally. This

is the essence of the crossing-point method to determine ne and

Te at the same time. The results of the diagnostic for the

electron density and the electron temperature in this case are

1.51�1021 m�3 and 21100 K (800 W), and 1.46�1021 m�3

and 20800 K (600 W) respectively. These are reasonable

results compared with other works [24].

The electron densities predicted by the Stark broadening are

lower at 600 W than at 800 W, for each line separately. The

crossing-point in the simultaneous diagnostic is not very

different, although slightly inferior in both ne and Temagnitudes for the lower power. An error of T200 K in the

electron temperature (and its corresponding error in density

which is relatively lower) is estimated in this determination due

Fig. 8. Relationship of Te and ne values compatible with the measured Ha and Hh Sta

determines the Te and ne values in the TIA helium plasma.

to the fit process, the experimental dispersion in the measured

FWHM values concerning Ha and Hh profiles being very low.

In addition, we also assume in this work the possible error

inherent to the theory.

We think that the principal problem we have faced in this

determination is the de-convolution of the Hh line, which is

composed of many internal components, each one is separately

broadened by Stark, experimental and Doppler effects, etc. (see

Fig. 7, in which Hh line is approximated by two main internal

components). Usually, the top part with the central dip of Hh

profile is neglected in order to obtain measurements of Stark

broadening from FWHM to obtain ne [25]. The lack of a strong

central component is the reason to explain the existence of the

Hh central dip and its relative lesser dependence on the ion

dynamics with respect to the case of Ha. This last line is mainly

composed of a central component, with other lateral weak

components. In the future, we would like to perform a better

de-convolution of this experimental line profile, that would

make it possible to give a different value of full-width at half-

maximum (FWHM) from the same Hh measurements. Conse-

quently, the cross-point in the present diagnostic could change

slightly.

4.2. Results on the TIA helium plasma

For the case of the TIA helium plasma we have found an

added difficulty: in the region of interest, for all the studied

lines, the values of the electron density and the electron

temperature compatible with the measured Stark broadenings

concerning the involved lines are even less dependent than for

the argon Hh case. Therefore, in the corresponding repre-

sentations we obtain curves quasi-horizontal and quasi-

parallel to each other. To try a cross-point between these

lines with such a behavior is very difficult inside our error

range and is clearly nonsense, because in fact any temperature

inside a large range of values almost provides the same result

in density.

As illustrative of this, the results for the TIA helium plasma

at a microwave power of 600 W (position 1 cm approx. above

the nozzle’s tip) are represented in Fig. 8, in an identical scale

to that used in the TIA argon plasma. By comparing Figs. 6 and

8 for both cases, the difficulty of obtaining a diagnostic cross-

rk broadening at a power of 600 W. As in Fig. 6, the cross-point simultaneously


point is appreciated clearly. In this case, more appropriately we

could speak of a wide range of possible temperatures (19000–

24000 K), which is not interesting for our purposes. However,

the representation determines with high precision the value of

the electron density in the discharge, a considerable coinci-

dence existing between the values obtained by both Ha and Hh

lines. These experiments for the TIA helium plasma study were

also carried out at two different positions, 1 cm approx. above

the nozzle’s tip and just above this tip. The same difficulty was

found to have a diagnostic-cross point in both positions and

different powers.

By using the Hg line in this set of experiments, we could

not obtain satisfactory results (similarly to the argon case),

because the TIA helium plasma was more unstable, of

difficult and delicate setting-to-point due to the addition of

hydrogen, not being possible to measure this third line of the

hydrogen Balmer series with enough clarity. Furthermore, the

electron density obtained from Hg is almost independent of

the electron temperature in our range of interest. So, if we had

being able to measure the Stark Hg broadening in the right

way, we would have obtained another horizontal line (as in

Fig. 8), too difficult to use in the cross method. In summary,

the results for the TIA helium plasma were not satisfactory at

any axial position and/or different microwave powers (in a

similar way to Fig. 8). Improvements in Hg diagnostics seem

not to be useful in this case.

4.3. Comparison with the results on the surfatron plasma

As it was already commented, this diagnostic technique was

first tried in a high-pressure, argon-surfatron discharge, and the

experiment and results were reported in a previous paper [8].

Next, we shall compare the experiments and results on TIA and

surfatron argon plasmas.

In the surfatron experiment, a capillary plasma column of

typically 1 mm of internal diameter and a few centimeters

long depending on the HF power injected into the discharge

was produced inside a quartz capillary tube. This capillary

plasma column was sustained by a surface wave propagating

along the quartz–plasma interface, this kind of discharge

being recognized as Surface Wave Discharges (SWD) [26–

29]. The microwave frequency was also 2.45 GHz and the HF

Fig. 9. Relationship of Te and ne values compatible with the measured Hh and

power varied from 40 to 150 W. We focused the light axially

(not radially) emitted by the bright plasma using a standard

optical arrangement and the same spectroscopic equipment

that was explained before. The diagnostic was representative

for the whole discharge axially viewed and not for any

specific point inside the discharge (see Fig. 1, coupler (b) or

surfatron).

The TIA plasma has a larger electron density and electron

temperature than the surfatron plasma, in which we used a

lower microwave power (typically, 600 W in TIA vs. 120 W in

surfatron). At this relatively lower electron temperature (under

10000 K) it was possible to use the cross-point diagnostic too.

In fact, we found a cross point for the simultaneous diagnostic

of the electron density and the electron temperature using Hh

and Hg Balmer series lines. In surfatron plasma Hg could be

used because the hydrogen was easily introduced in the

discharge and its intensity was high enough to measure it in

the right way. On the contrary, Ha could not be used because

we found an electron density anomalously high when it was

used, and the cross-point with the other two lines did not exit.

Historically, the electron density obtained from Ha has been

larger than the electron density obtained from Hh or Hg in the

same experiment. That problem was partially resolved step by

step by the more modern Stark broadening theories. Particu-

larly, by using the Gig-Card theory (i.e. including ion

dynamic) it is possible to reconcile the results obtained from

Ha and its ‘‘sister’’ lines. But not always: for the range of

electron densities and temperatures existing in the surfatron,

experimental broadenings and theories lead to different

electron density if one uses Ha or Hh (this difference resulted

even more accused making use of the older theories). So, the

Stark broadening theory should be improved even more

because it is clear that the electron density must have a

univocal value independently of the lines used to determine the

plasma characteristics.

The results with the surfatron are shown in Fig. 9, for a

given microwave power of 120 W. The cross-point existed and

determined an electron temperature in the surfatron around

7000 K and an electron density of 6.6�1020 m�3. In the TIA

experiments, the microwave power feeding the discharge is

increased up to 600 W, and consequently the electron

temperature and the electron density were increased till

Hg Stark broadening at a power of 120 W for the surfatron experiment.


20000 K and 1.4�1021 m�3, respectively. Although it is not

the main purpose of this experimental work, these results

indicate that the argon plasma produced by TIA is closer to the

local equilibrium than the produced by surfatron. This

comparison has not been possible with the TIA helium plasma

because this plasmogenic gas was not used with the surfatron:

the capillary quartz tube melted with helium and its study was

not possible.

5. Conclusions

We have studied an experimental method to diagnose both

the electron density and temperature simultaneously in a high-

pressure, microwave-excited plasma. Compared with other

direct methods of simultaneous diagnostics (Thomson scatter-

ing, for instance), this method is really simpler and low-cost,

spectroscopic tools are used. It is based on an easy idea and

there are no assumptions about the plasma equilibrium state

and/or the distribution of the species existing in it. By studying

simultaneously different spectral lines spontaneously emitted

by the plasma in terms of their Stark broadenings, we have

shown that it is possible to determine the two main magnitudes

in the discharge (the electron density and the electron

temperature) at the same time, according to the Stark

broadening theories existing in the bibliography, namely one

of the most recent (the Gig-Card theory). This theory takes the

ion dynamics into account, whereas previous theories do not,

and that fact affects and is reflected in the results.

The experiments have been carried out to diagnose two

different discharges, namely the TIA plasma and the surfatron

plasma, and have been satisfactory in both cases. The method

is suitable under different working conditions and the results

are consistent if they are compared with previous works,

although a further comparison of this method with Thomson

scattering should be made in the future. Hydrogen gas must be

present in the discharge in order to make the Stark broadening

of Balmer series lines intense enough. We have shown that the

necessary amount of hydrogen gas is very low (around 1% of

the main gas flux in the plasma discharge), and does not change

the plasma conditions drastically.

It would be desirable to use more than two lines in order to

gain coherence in the diagnostics, which could cause the

existence of a small cross-region instead of a unique cross-

point, but at the moment we have found some difficulties to

obtain this in every case. This is an evident improvement in

which we shall continue working on. In this article, it has been

shown that such a possibility has been successfully performed in

a particular case.

No other elements are so well studied as the Balmer series

of hydrogen lines with respect to the Stark broadening of lines

spontaneously emitted by plasmas. Therefore, the possibility of

using any other lines (isolated argon or helium lines, for

example) is discarded at present. So, we are restricted to

hydrogen lines, but here we could have a future possibility with

the ultraviolet Lyman series of hydrogen lines, namely the

analogous Lyman-Ha, -Hh and -Hg lines which are also well

modeled by the Gig-Card theory.

Acknowledgments

The authors acknowledge Dr. Marco A. Gigosos for

valuable discussion on Stark broadening modeling. The

Bilateral Collaboration Framework signed between the Tech-

nical University of Eindhoven (NL) and the University of

Cordoba (E) to develop common research in Plasma Physics is

acknowledged too. Also, the Spanish Ministry of Science and

Technology for partially supporting this research under grant/

project No PPQ2001-2537, as well as the III PAI (Government

of Andalusia, Spain) and the University of Cordoba for

supporting the Group FQM136.

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