Measurement of temperature and electrons density ...

Optics and Lasers in Engineering 51 (2013) 382–387

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Measurement of temperature and electrons density distribution of atmospheric arc plasma by moire´ deflectometry technique Fatemeh Salimi Meidanshahi a, Khosro Madanipour b,c,n, Babak Shokri a,d a

Shahid Beheshti University, G.C., Department of Physics, Tehran, Iran Optics, Laser and Photonics Institute, Amirkabir University of Technology, Hafez Street, Tehran, Iran c Optical Measurement Central Laboratory, Amirkabir University of Technology, Hafez Street, Tehran, Iran d Shahid Beheshti University, G.C., Laser and Plasma Research Institute, Tehran, Iran b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 September 2012 Received in revised form 11 November 2012 Accepted 30 November 2012 Available online 25 December 2012

In the present paper, the refractive index, electron density and temperature distribution of atmospheric arc plasmas are measured by moire´ deflectometry. The deflection angle of rays passing through the plasma is obtained by moire´ fringe analysis. Then by using inverse Abel transform integral for this axisymmetric plasma, the refractive index distribution is obtained in different points of plasma and environment. Considering the relation between plasma temperature and refractive index, the spatial temperature distribution of the arc plasma is evaluated. Also, in contrast to conventional models to obtain electron number density, in which the refractive index of plasmas is approximately assumed equal to the electron refractive index, a model is used for accurate and absolute measurement of the electron density profile. This technique is especially suitable for measuring axially symmetric plasma parameters. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Moire´ deflectometry Atmospheric arc plasma Electron Ion and molecule number density

1. Introduction The spatial distributions of temperature and electron concentration are important characteristics in optimum design and application of variety of plasmas. So it is desirable that a technique applied for plasma diagnostics is non-interfering and capable of in-situ and online measuring the probe volume. Plasma diagnostic techniques can be divided into two categories: the method based on the electric probes and the optical methods. In the first method, several difficulties in use of electrical probes, as a simple method, restrict the advantage of this method. For example, the dimensions of the probes perturbing the plasma and the need for complicated analysis for some plasma conditions are essential restrictions. Several optical diagnostic methods give very high accuracy due to non-intrusive probes [1,2]. Among them, holographic interferometry [3–6,9], Schlieren and shadowgraphy techniques [7–11], optical emission spectroscopy and laser absorbtion [8,9,12–15], Thomson scattering [9], Michelson, Mach–Zehnder and Nomarski polarization interferometry [16–20], laser beam deflectometry [21] and digital holography [22–24] can be mentioned. Moire´ deflectometry is a method of wave front analysis in which both Talbot effect [25] and moire´ technique is applied for measuring

phase objects or reflection surfaces [26–29]. Moire´ deflectometry in contrast to interferometry methods is simple and is not sensitive to vibration with no complicated and expensive measurement set-up. Also, interferometric methods are not efficient at high gradient temperature and density due to decreasing fringe spacing and difficulty of recording and analyzing of the fringes. The main advantage of moire´ deflectometry technique is that the spatial profile of considerable parameter can be obtained by one time measurement but laser beam deflectometry and spectroscopic methods provide only pointwise data. Also plasma diagnostics by moire´ deflectometry in contrast to spectroscopic methods does not need restricting assumption of the local thermodynamic equilibrium (LTE) state of plasmas. In the present paper, moire´ deflectometry technique is applied to determine the electron density and temperature distribution of atmospheric arc plasma. In contrast to conventional models to obtain electron number density, in which the refractive index of plasmas are approximately assumed to be equal to the electron refractive index and ignore the ions and neutral particles contributions, a model is used for accurate and absolute measurement of the electron density profile.

2. Theory n

Corresponding author at: Optics, Laser and Photonics Institute, Amirkabir University of Technology, Hafez Street, Tehran, Iran. Tel.: þ 98 9122498819; fax: þ 98 21 64543140. E-mail addresses: [email protected], [email protected] (K. Madanipour). 0143-8166/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlaseng.2012.11.018

When a plasma is transparent with respect to a probe light, it can be assumed as a phase object. The light beam passing through the plasma medium is deflected due to the refractive index

F.S. Meidanshahi et al. / Optics and Lasers in Engineering 51 (2013) 382–387

According to the dispersion relation in the plasma and phase velocity definition, the electron density distribution can be evaluated in terms of contribution of electrons to the plasma refractive index [32]:

Y δd

α rf

Y0 P1

x0

xf

yf P2

2pme c2

Ne ¼

X

G1

Z

G2

Fig. 1. Light beam deflection, passing through the phase object and gratings G1 and G2.

2

e2 l

ð1nÞe ;

dd Xk

¼

d ddM ðy,zÞ Xk dM

ð1Þ

where d and dM are the pitch of gratings and moire´ fringes 2 spacing, Xk is kth Talbot distance given byX k ¼ kd =l where l is the wavelength of the probe beam. Eq. (1) shows that the resolution of moire´ deflectometry in diagnosing the refractive index can be increased by using the gratings with smaller pitches and higher Talbot distances. For an axially symmetric object, where n(x,y,z)¼n(r,z) and ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ x2 þ y2 , the refractive index can be written in cylindrical coordinates as [20] Z nf rf aðy,zÞ pffiffiffiffiffiffiffiffiffiffiffiffiffi dy; nðr,zÞnf ¼ ð2Þ p r y2 r 2 where n(x,y,z) and nfs are the refractive index of the phase object and air (ambience), respectively; x0 and xf are the limits of the phase object in the propagation direction. Therefore, the sensitivity of this technique is proportional to the accuracy of measuring the deflection angle. So the sensitivity can be increased by optimizing the pitch of gratings and Talbot distance and by increasing the moire´ spacing. By numerical solution of this inverse Abel integral [30], the refractive index distribution is determined. Edlen equation can be used to calculate the air refractive index, nf, by measuring the ambient atmospheric conditions including air temperature, pressure, and relative humidity [26]. To determine the plasma temperature distribution, the relation between the refractive index and temperature should be calculated. The refractive index of the plasma as an ionized gas including the contribution of neutral molecules, ions and electrons is equal to [31] ðn1Þ ¼ ðn1Þe þ ðn1Þi þ ðn1Þm :

ð3Þ

Three right terms of Eq. (3) correspond to the refractive index of electrons, ions and molecules, respectively.

ð4Þ

where me and e are electron charge and mass; n, c, l and Ne are the refractive index, light velocity in vacuum, probe wavelength and electron number density, respectively. The contribution of electrons to the plasma refractive index can be rewritten as 2

gradient. By measuring the deflection angle, the refractive index and subsequently, different parameters such as electron, ion and molecule concentrations and also temperature distribution can be obtained. Among the different optical techniques for temperature measurement, Moire´ deflectometry is a technique of wave front analysis based on geometrical optics. Deflection of the light beam passing through the inhomogeneous medium is utilized to obtain the different parameters distribution. As it is shown in Fig. 1, a coherent collimated light beam propagates through a phase object (plasma) as the probe beam and the beam is deflected due to the refractive index gradient in the object. For simplicity, the pitches of two gratings should be the same (d). So the selfimage of grating G1 lines on grating G2 is displaced by dd. Ultimately moire´ pattern is shifted by ddM. According to Fig. 1, the ray deflection angle a can be calculated by [20]

aðy,zÞ ¼

383

ðn1Þe ¼

e2 l N e 2 4:46 1014 l N e 2pme c2

l : cm,Ne : cm3 :

ð5Þ

The refractive index of neutral molecules can be expressed as [33] 1 B A þ 2 Nm ; ðn1Þm ¼ ð6Þ L l where, L is the Loschmidt number (L¼2.687 1019 cm 3), Nm is the molecule number density and A and B are constant quantities depending on molecules or atoms for oxygen and nitrogen that are A¼2.83 10, 4 B ¼2.03 10 6 [33]. Mostly, the contribution of ions to the refractive index can be neglected but one can consider the contribution of ions in the refractive index of the plasma as follows: 1 B A þ 2 Ni ; ðn1Þi ¼ Z ð7Þ L l where Z is the relative specific refractivity (specific refractivity of ions with respect to molecules). It is well known that the refractive index of a gas depends on its microscopic properties and mass density distribution. So the refractive index of the plasma can be rewritten as 1 B 2 n1 ¼ Aþ 2 N m þ ZN i 4:46 1014 l N e l : cm,N e : cm3 : L l ð8Þ As air contains roughly (by volume) 78.09% nitrogen and 20.95% oxygen, for atmospheric plasmas by substituting A ¼2.83 10, 4 B¼ 2.03 10 6, and Z ¼0.8143 for air [34], and the probe wavelength 632.8 nm into the above equation, we obtain: n ¼ 1:0709 1023 ðNm þ0:8143N i Þ1:7859 1022 Ne :

ð9Þ

Eqs. (8) and (9) show the negative effect of the electron number density on the refractive index and indicate that n is a function of probe wavelength, and electron, molecule and ion number densities. The contribution of an electron is almost 17 times than the contribution of a molecule and 20.5 times than the contribution of an ion. It should be mentioned that Ne and Ni and Nm can be calculated by considering the first and second ionization of the dominant substances in the atmospheric arc plasma and solving the Saha equation. Assuming quasi-neutrality of plasmas and making use of the ideal gas state equation, the final relations are [34]: K 1P 2K 1 K 2 P N3e þ 2K 1 N2e þ 3K 1 K 2 Ne ¼ 0; ð10Þ kT kT Ni ¼

K 2 þ Ne Ne ; 2K 2 þ Ne

Nm ¼

P 2N2e þ 3N e K 2 ; kT Ne þ 2K 2

where P is the plasma pressure.

ð11Þ

ð12Þ

384


According to Eq. (9) and above equations, the relation between the refractive index and electron number density can be calculated. Fig. 2 indicates the dependence of the refractive index on electron density which is a useful criterion to determine the plasma region. Corresponding to plasma definition, even partially ionized gas as few as 10 electrons per cubic centimeter can have the characteristics of plasma [35]. When the refractive index distribution versus distance is evaluated experimentally from Eq. (2), the plasma region can be determined. The relation between temperature and electron density can be obtained by solving Eq. (10). Moreover, by measuring the electron density distribution, the temperature distribution can be calculated.

3. Experiments and results In this section, the temperature distribution and electron number density of the atmospheric arc plasma are measured by moire´ deflectometry method according to the approach described in Section 2. The schematic of the experimental set-up is presented in Fig. 3. A He–Ne laser with wavelength 632.8 nm is the probe light source and lenses L1 and L2 are used as a beam expander. A precision pin hole (PH) with diameter 8 mm is positioned at the intermediate focal point of lenses for spatial filtering. Two Ronchi gratings with the pitch d ¼0.1 mm are used in the measurement set-up. Grating G2 is placed on the 12th Talbot distance of grating G1. In this distance which is about 190 mm, the visibility of moire´ fringes are maximum.

By focusing lens L3 with 200 mm focal length, a CCD camera records reference fringes and deformed fringes. For eliminating the lines of gratings and recording only moire´ pattern, a diaphragm placed at the focus of L3 serves as a spatial filter that can let only the zero spatial frequency pass through. As seen in Fig. 4, the measured atmospheric arc plasma is produced by using a power supply with 12 kV voltage. The distance between the two electrodes is 3.20 mm and the electrodes are made of non-magnetic stainless steel. When the plasma is generated, temperature and refractive index gradient is created in the plasma medium and the air around the plasma. These gradients cause the deformation of moire´ fringes. Fig. 5 shows two images recorded by the CCD camera before and after temperature gradient: (a) shows the reference deflectogram; (b) shows the deformed moire´ deflectogram after generating the plasma. The deflection of moire´ pattern is obvious in Fig. 5b. By image analysis, the moire´ fringes position is found. This position is shown in Fig. 6; the moire´ fringe deflection versus the moire´ fringe spacing ddM =dM is obtained in each point of the image. The ray deflection angle data, a, is evaluated from Eq. (1) as illustrated in Fig. 7. The amount of the moire deflection, ddM, is the difference between reference and deflected fringes position. The laboratory temperature, pressure and relative humidity was recorded 29.2 1C, 660.65 mmHg and 38.4%, respectively. Therefore, the ambient refractive index is calculated from Edlen equation as nf ¼1.000228570.000000039 [36]. The refractive index distribution versus distance from the arc plasma center is shown in Fig. 8. As can be seen, the refractive index reaching to a fix value is compatible with the ambient refractive index 1.0002285. By the described approach, since plasma density can range from just a few electrons (approximately 10 electrons) present in a cubic centimeter for Lab plasmas, the plasma region

Fig. 2. Distribution of refractive index (n 1) versus the logarithm of the electron density.

Fig. 4. Moire´ deflectometry experimental set-up. ARC

PH Laser

PC

L1 CCD

D L3

G2

G1

L2

Fig. 3. Schematic diagram of moire´ deflectometry. L1, L2 and L3 are three convex lenses. G1 and G2 are two gratings with a pitch of 0.1 mm. PH, TO, D, CCD and PC stand for pin hole, test object, diaphragm, camera and computer, respectively.


385

Fig. 5. (a) Reference fringes, and (b) deflected fringes by temperature gradient of the measured atmospheric arc plasma and the air around it.

Fig. 7. The ray deflection angle versus distance from the arc plasma center.

Fig. 6. The found position of moire´ deflectogram.

can be determined. It means that according to Fig. 2, the plasma region is valid when the number of electron carriers per cubic centimeter is higher than 10 (cm 3). Fig. 9 shows the spatial distribution of the refractive index of the plasma. The plot of the electron number density versus distance is presented in Fig. 10. By inserting the laboratory pressure as the plasma pressure and the electron density of the plasma into Eq. (10), the temperature profile versus distance from the arc plasma center is evaluated, shown in Fig. 11. Both plots in Figs. 10 and 11, show an approximately symmetrical distribution of the arc plasma. From Fig. 10, the highest number density of electrons is 3.37 1016 cm 3 and from Fig. 11, the highest temperature of

the plasma is 111111 K in the center of the plasma. Also, diameter of the plasma is obtained approximately as 2.53 mm. As expected, the measured ne and T profiles are not the same at different r positions and both of them decrease with the increasing distance from the plasma center.

4. Conclusion The work presented in this paper concerns atmospheric arc plasma diagnostics. The refractive index, electron number density and temperature distribution of the plasma is obtained by calculating the temperature dependence of the arc plasma refractive index and the relation between electron density and the refractive index of the plasma. It appears that this optical

386


Fig. 8. Refractive index distribution versus distance from the arc plasma center. Fig. 11. The temperature distribution of the arc plasma versus distance from the arc plasma center.

consequently to determine the optimum condition for every plasma application. This confirms that the present method has several advantages with respect to the most popular methods in plasma diagnostics such as Longmuir probe, spectroscopy and Mach–Zehnder interferometry. This technique, with no complicated and expensive setup, is simple and not sensitive to vibration. Also the test object should be transparent with respect to the wavelength of the probe light. The advantage of moire´ deflectometry with respect to interferometry is the direct evaluation of the refractive index gradient and its simplicity. Also for large temperature gradients, interferometry is limited and can produce erroneous information while moire´ deflectometry is able to be used with more certainty. The accuracy and the sensitivity of moire´ deflectometry technique can be increased by varying the Talbot distance and the pitch of moire´ fringe.

Fig. 9. The dependence of the refractive index of the plasma region on distance from arc plasma center evaluated experimentally.

Acknowledgments Authors would like to acknowledge Mr. Mohhamad Reza Khani for his great help in the plasma laboratory. References

Fig. 10. The electron density profile of the atmospheric arc plasma versus distance from the arc plasma center.

deflectometry as an accurate and automatic method can be one of the best way to experimentally study the transparent axially symmetric plasmas with high temperature gradient and

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