Interpretation of Stark broadening measurement s on a spatially integrated plasma spectral line J. Tho uin M. Benmouffok P. Freton J. -J. Gonzalez

2025-05-05 0 0 1.93MB 16 页 10玖币

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Interpretation of Stark broadening measurements on a spatially integrated

plasma spectral line

J. Thouin, M. Benmouffok, P. Freton, J.-J. Gonzalez

LAPLACE, Université de Toulouse, UMR 5213 CNRS, INPT, UPS, Toulouse, France

Email : thouin@laplace.univ-tlse.fr

Key words: Spectroscopy; Stark; Thermal Plasma; Hα

1 Abstract:

In thermal plasma spectroscopy, Stark broadening measurement of hydrogen spectral lines is

considered to be a good and reliable measurement for electron density. Unlike intensity based

measurements, Stark broadening measurements can pose a problem of interpretation when

the light collected is the result of a spatial integration. Indeed, when assuming no self-

absorption of the emission lines, intensities simply add up but broadenings do not. In order to

better understand the results of Stark broadening measurements on our thermal plasma

which has an unneglectable thickness, a Python code has been developed based on local

thermodynamic equilibrium (LTE) assumption and calculated plasma composition and

properties. This code generates a simulated pseudo experimental (PE) Hα spectral line

resulting from an integration over the plasma thickness in a selected direction for a given

temperature profile. The electron density was obtained using the Stark broadening of the PE

spectral line for different temperature profiles. It resulted that this measurement is governed

by the maximum electron density profile up until the temperature maximum exceeds that of

the maximum electron density. The electron density obtained by broadening measurement is

70% to 80% of the maximum electron density.

2 Introduction:

For the experimental characterisation of an electric arc, emission spectroscopy is the

diagnostic method of choice for the measurement of the plasma temperature or species

densities. Among the different spectroscopic diagnostic methods, those based on the

measurement of the Stark broadening of a spectral line are widely used [1–6].

In order to perform a spatially resolved spectroscopic measurement within the plasma there

are several methods. When an assumption of plasma axisymmetry can be made, methods

based on Abel inversion can be used [6, 7]. When this assumption is no longer valid and the

optical system allows simultaneous acquisitions in different directions, tomographic

reconstruction methods can be considered [8].

However, when none of these methods can be applied, because the plasma is not

axisymmetric, the time constraints are too great, the intensity of the discharge is not sufficient

to allow the selection of light rays or because the experimental setup does not allow a complex 
optical setup, it is common to collect the light emitted by the plasma using a focusing optical 
setup or selecting a direction with pinholes [1, 3, 5, 9]. In this case the light is collected over 
the entire thickness of the plasma and the broadening measurement is made on the spectral 
line  resulting  from  the  integration  over  the  thickness  of  the  plasma.  For  inhomogeneous 
plasma and depending on the measurement performed, it can be complex if even possible to 
interpret the measured quantity. 
The  presented  study  was  performed  in  order  to  interpret  experimental  results  of  Stark 
broadening  measurements  on  𝐻𝛼 spectral  line  emitted  by  a  water  thermal  plasma.  This 
plasma,  considered  at  local  thermodynamic  equilibrium  (LTE),  is  generated  by  a  ten 
milliseconds electric arc in a water tank which vaporizes the water. The light is collected in a 
direction  selected  using  a  couple  of  pinholes.  We  are  interested  in  the  theoretical 
determination of the electron density by measurement of the broadening of a spectral line. 
We are interested in the hydrogen spectral line Hα for which we consider the Stark effect as 
the dominant source of broadening in the presence of a high electron density [2].  
In order to study the relevance of the broadening measurement to obtain the electron density, 
we will first define the context of our study. Then, we will present the parameters that govern 
the profile of a spectral line: (1) the emissivity of the transition associated with the Hα spectral 
line which will be calculated from the plasma composition and (2) the Stark broadening of the 
Hα line determined by simulation from the work of Gigosos et al. [10] We will then perform a 
parametric study using different temperature profiles for the water thermal plasma. We will 
focus on the electron density determined from the reconstructed Hα pseudo experimental 
(PE) spectral line for these different profiles assuming that the broadening is only due to Stark 
effect. Finally, we will conclude on the meaning of the obtained measurements. 
3 Context of this study: 
 
We performed experimental emission spectroscopy measurements on a water plasma. This 
plasma was generated between two vertical sharpened rods of tungsten (see fig. 1). In order 
to generate the arc, a half sine wave of current is applied through a fuse wire. The wire is 
vaporized  by  Joule  effect  and  generates  a  water  vapour  bubble  which  gradually  expands 
before  collapsing. The duration  of  the discharge is  10ms and the  sinusoidal current  wave 
(f=50Hz) has an amplitude of about 1kA. A theoretical study of the phenomenon was carried 
out in our team [11] in order to understand the behaviour of the plasma. A water plasma 
bubble was simulated using the commercial @Fluent software based on the finite volume 
method. Plasma properties have been calculated for water, the theory is presented in Harry-
Solo et al. [12]. First instants of the bubble formation are not described; the simulation begins 
with  a  conducting  channel  already  established.  Using  the  experimental  variations  of  the 
measured voltage and current intensity, a source term is applied within a volume defined by 
a boundary temperature of 7kK. This arbitrary temperature defines the conducting channel. 
Naturally, this volume changes during the deposition of energy. The phase transition between 
vapour and liquid was handled using a model based on that of Lees [13]. This study gave us a 

homogenous value for the pressure inside the vapour bubble close to 3 bar at very early times

of the expansion (t<0.5ms). Therefore, in this article the plasma will be considered to be pure

water and its properties calculated for a pressure of 3 bar.

To illustrate, fig. 1 shows the observed bubble with the plasma contained in the saturated

zone. This image was obtained using a Photron FASTCAM SA5 high-speed camera, the

exposure time was 1/25000s and three neutral density filters were fitted on the lens with an

attenuation factor respectively of 64, 32 and 16. The acquisition method is described with

more details in [14]. The circle in the foreground corresponds to the shape of the observation

window. A halogen lamp is used as backlighting, its filament is visible horizontally in the

background. Backlighting is only necessary to improve the observation of the edge of the

water vapour bubble. Two copper electrode holders support the tungsten rods of 1.6 mm

diameter vertically. Between the two electrodes is placed a 0.13 mm copper wire.

Figure 1: Image of a water vapour bubble. The image is saturated in the centre by the

emission of light from the arc.

The light emitted by the plasma is collected through two irises which select a beam of light.

When considering no self-absorption, the light collected is the sum of all emissions on the line

of sight selected by the two pinholes, see fig. 2:

Figure 2: Plasma light selection and acquisition.

Figure 2 shows the light being collected on the line of sight I(X0). We can consider that the

profile of one emission spectral line, at a given wavelength, integrated over this string of

plasma is the sum of the local emissions at that same wavelength along the string. These local

emission spectral lines can be characterized using the local conditions of emission. We will

describe this process in sect. 4.

4 Spectral emission line description:

The shape of a spectral line profile can be characterized using different parameters such as its

amplitude or its broadening. The area covered by the profile of the spectral line is dependent

on those two previous parameters but also on the shape of the profile. These different

parameters are illustrated on fig. 3. The full width half area FWHA of the spectral line is the

width of the hatched area. The full width at half maximum FWHM is plotted as well.

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摘要：

InterpretationofStarkbroadeningmeasurementsonaspatiallyintegratedplasmaspectrallineJ.Thouin,M.Benmouffok,P.Freton,J.-J.GonzalezLAPLACE,UniversitédeToulouse,UMR5213CNRS,INPT,UPS,Toulouse,FranceEmail:thouin@laplace.univ-tlse.frKeywords:Spectroscopy;Stark;ThermalPlasma;Hα1Abstract:+Inthermalplasmaspect...

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Interpretation of Stark broadening measurement s on a spatially integrated plasma spectral line J. Tho uin M. Benmouffok P. Freton J. -J. Gonzalez

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