Analysis of the radial profile of the electron density in the thin capillary on the basis of OES measurements 

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Reconstruction of radial profiles of active species

Plasma is an object with plenty of various species such as electrons, positive and negative ions, atoms and molecules either in ground or electronically excited state. Measurements of concentration of these various species are, in fact, records of their temporal and spatial profiles. Therefore, it was necessary to gather information not only about temporal dependence of concentrations of active species but about the discharge spatial structure as well. As soon as the experiments were conducted in a capillary where a fast ionization wave was propagating, it was assumed that plasma profile is homogeneous along the whole length of the capillary. The problem was therefore to restore the 1D-structure of the radiation (as a function of radius) which is related to the radial distribution of species of interest such as electrons and positive ions.

Experimental procedure

First, it should be noted that the experiments were conducted both in pure CO2 and in a CO2:N2=10:1 mixture.
To collect the information about the discharge radial distribution, an ICCD camera with an optical system was required. If the image is obtained by a lens, the data cannot be treated as a spatial distribution of the excited species since plasma isn’t a volumetric object, and a set of photons come to the ICCD detector from different regions of the discharge. If each pixel comes to the ICCD matrix from parallel beams only, the reconstruction of radial profile becomes possible. The signal F(y) can therefore be considered as a result of direct Abel transform of the radial profile f(x; y) = f(r) which is the object of our interest. Thereby, in order to restore the f(r) it was necessary to apply inverse Abel transform (IAT) to the signal acquired by the ICCD camera. The details of the procedure can be found in [65, 95].
To gather the data which were consequently treated by the IAT, it was necessary to place the ICCD camera in such a way that the beams coming from the discharge cell could be considered as parallel. This goal could be reached by placing the camera at a distance equal to > 20 radii of the discharge cell. The camera should have been placed in a horizontal and stable way and should have been able to record the entire vertical of the discharge. The gate and delay of the camera could be monitored by the WinSpec software. The gate of the camera should have been as small as possible (<5 ns) and the gate delay was selected according to the time instant of interest. To choose a wavelength of interest corresponding to an atomic or molecular transition representing the distribution of active species in plasma, a narrow bandpass filter was used. Finally, it was essential to take a photo of the lightened discharge cell (see Figure 2.12). It was necessary for image scaling (in the current case, 1 mm was equal to 18.66 pixels). As soon as the image had recorded, it was necessary to select a vertical line for slicing (see Figure 2.13, red line). The F(y) is the light intensity function along the red line. An input file which was treated by the code was therefore a column with numbers designating the emission intensity. A number of an element in the column is the number of pixel along the vertical line.

Applied voltage and electric current

The first electric characteristics which were recorded in both capillaries were the waveformes of the applied voltage and electric current flowing through the discharge cell. The measurements have been down with the help of back current shunts connected to a digitizing oscilloscope. The details of the acquisition procedure of applied voltage has been described in details in the Chapter 2; as it has been mentioned in the Chapter, both values are related by the equation (2.1). It should be reminded that the main difference between the acquisition procedure in the thin and FTIR capillaries was the number of used back current shunts. Two BCSs were used in the experiments with the thin capillary and a single BCS was used in the experiments with the FTIR one. As it will be seen further, this difference implies slightly different procedures of data treatment.

FTIR capillary

As it was mentioned before, the main difference between the thin capillary and FTIR capillary consisted on the fact that the latter had its low voltage electrode grounded. Consequently, it was possible to measure the electric current and applied voltage by one back current shunt only. The waveform of the voltage applied to the FTIR capillary and recorded by the BCS is given in the Figure 3.4. The first incident pulse (1st INC) was the same as it has been just described for the thin capillary. It can be seen between 0 and 40 ns.
The most important pecularity of the applied voltage waveform consists on the fact that the incident pulse reflects both from high voltage and low voltage electrodes.

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Dissociation fraction and energy efficiency at different pressures at low pulse frequency regime

First, dissociation fraction and its efficiency was measured at low frequency pulse regime at different pressures. The values of pressure were varied varied between 5 mbar and 35.4 mbar. The flow rate and peak voltage of the incident high voltage pulse were constant and equal to 7.4 sccm and 9.4 kV, respectively. The purpose of these measurements was to find the optimal pressure for both parameters with the least possible change of number of pulses N treating a portion of gas in the discharge cell. Another requirement to the pulse frequency was to maintain N close to unity. The value N can be found in several steps. First, the actual flow rate can be calculated from the standard flow rate according to the following equation: Q = Qst pstT pTst : (4.1).
Here, pst = 1000 mbar and Tst = 273 K are pressure and temperature corresponding to standard conditions. p is pressure taken as average between values of two pressure gauges installed upstream and downstream and was varied between 5 mbar and 35.4 mbar. The most interesting value which is an object of discussions is gas temperature T. The simplest way to assume its value is to take the temperature T equal to room temperature. Let’s verify the validity of the assumption. Since it is gas density which influences the N value, it is necessary to calculate the characteristic time per of propagation of an acoustic perturbation in the discharge cell which characterizes the time of change of gas density in the discharge cell. It can be found in the following way [99]: per = l c = l q RT .

Table of contents :

Acknowledgements
R´esum´e de th`ese
Abstract
1 Literature review 
1.1 State of the art of conversion of carbon dioxide
1.1.1 Actual state of the CO2 problem
1.1.2 Different techniques of CO2 conversion
1.1.3 Theoretical aspects of conversion of carbon dioxide in low temperature plasma
1.1.4 Experiments on conversion of carbon dioxide in low temperature plasma
1.2 Nanosecond discharges. Fast ionization waves. Dissociation of gases in nanosecond discharges
1.2.1 Fast ionization waves
1.2.2 Dissociation of molecular nitrogen and oxygen in nanosecond discharges
1.2.3 Dissociation of carbon dioxide in nanosecond discharges
1.3 Numerical modeling of CO2 discharges
1.4 Conclusions of the literature review
2 Experimental methods 
2.1 Discharge cell
2.1.1 General observations
2.1.2 Thin capillary
2.1.3 FTIR capillary
2.2 Electric measurements
2.2.1 Back current shunts and high voltage cables
2.2.2 Capacitive probe
2.3 Optical emission spectroscopy
2.4 Fourier Transform Infrared Spectroscopy(FTIR)
2.4.1 Basic principles of FTIR
2.4.2 Experimental procedure and data treatment
2.5 Reconstruction of radial profiles of active species
2.5.1 Experimental procedure
2.5.2 Inverse Abel transform
3 Electric characteristics of the discharge 
3.1 Applied voltage and electric current
3.1.1 Thin capillary
3.1.2 FTIR capillary
3.2 Electric field
3.2.1 Thin capillary
3.2.2 FTIR capillary
3.3 Deposited energy
3.3.1 Thin capillary
3.3.2 FTIR capillary
3.4 Conclusions
4 Measurements of CO2 dissociation fraction and its energy efficiency by FTIR 
4.1 Dissociation fraction and energy efficiency at different pressures at low pulse frequency regime
4.2 Dissociation fraction and energy efficiency at high pulse frequency regime
4.3 Dissociation fraction and energy efficiency at different parameters
4.3.1 Different flow rates
4.3.2 Different applied voltages
4.4 Conclusions
5 Study of the discharge by optical emission spectroscopy 
5.1 Optical emission spectra
5.1.1 Thin capillary
5.1.2 FTIR capillary
5.2 Temporal behaviour of the main electronically excited species in the thin capillary
5.3 How big is the electron energy?
5.4 Behaviour of the Swan band in the FTIR capillary
5.4.1 Variable pressures
5.4.2 Varied delay between pulses
5.5 Conclusions
6 Measurements of the temporal profile of the electron density in the thin capillary 
6.1 Description of the technique
6.2 Experimental results
7 Analysis of the radial profile of the electron density in the thin capillary on the basis of OES measurements 
7.1 Experimental setup
7.2 Experimental results
7.3 Relation between the emission profiles and the electron density. Validity of gas temperature measurements
7.4 Conclusions
8 Measurements of the gas temperature as the function of time by the means of optical emission spectroscopy 
8.1 FTIR capillary
8.2 Thin capillary
8.3 Conclusions
9 Numerical modeling of the discharge 
9.1 Principles of 0D modeling
9.2 Kinetic scheme
9.2.1 Set of reactions
9.2.2 Vibrational kinetics
9.2.3 Vibrational distribution function
9.3 Validation of the model
9.3.1 Calculations of gas temperature profile
9.3.2 Electron density
9.3.3 Predictions of CO2 dissociation fraction and energy efficiency .
9.3.4 Temporal profiles of the electronically excited species
9.4 Conclusions
10 General conclusions 
List of Figures
Bibliography

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