Dependence of electron energy distribution function

JCBPS; Section C; May.2015–July.2015, Vol. 5, No. 3; 4355-4367.

E- ISSN: 2249 –1929

Journal of Chemical, Biological and Physical Sciences An International Peer Review E-3 Journal of Sciences Available online atwww.jcbsc.org Section C: Physical Sciences CODEN (USA): JCBPAT

Research Article

Dependence of electron energy distribution function and transport parameters for SF6, CO2 and (SF6 - CO2) gases mixture discharge Enas. A. Jawad* Department of Physics, College of Education for Pure Sciences (Ibn Al-Haitham)/ University of Baghdad, Iraq. Received: 4 August 2015; Revised: 18 August 2015; Accepted: 03 September 2015

Abstract: We use a binary gas mixture Monte Carlo simulation model EEDF program for the numerical solution of the Boltzmann equation to calculate the electron energy distribution function and the transport parameters in pure SF6, CO2 and their mixtures. The electron swarm parameters are evaluated in the range (50 Td ≤ E/N ≤ 900 Td) at the temperature273K and Pressure 0.1 Mpa. These parameters, namely are: mean electron energy, characteristic energy, mobility of electron, Diffusion Coefficient and drift velocity. The calculated distribution function is found to be remarked non-Maxwillian that has energy variations which reflect the import electron-molecule energy exchange processes. Also, the mixtures have different energy values depending on transport, energy between electron and molecule through the collisions. Behaviour of electron transport parameters is nearly from the experimental results in references.After CO2 was added to SF6 the drift velocity of electron in SF6–CO2 increases. The mean electron energy, characteristic energy and Diffusion Coefficient to the mixture are increasing at sulphur hexafluoride ratios increased. Keyword: SF6–CO2 gas mixture, Plasma and Electron Discharges, Swarm Parameter, drift velocity, mobility of electron, diffusion coefficient, kinetic and Transport Theory of Gases dielectric properties INTRODUCTION By transport equation (Boltzmann equation) is completely described the motion of particles of plasma or gas considered as pure or as a mixture. We can get the normalized distribution function that's 4355

J. Chem. Bio. Phy. Sci. Sec. C, May 2015 – July 2015; Vol.5, No.3; 4355-4367.

Dependence of electron…

Enas. A. Jawad

playing important roles in calculation the electron swarm parameters by solving the Boltzmann equation. There are many classes of computational techniques that are used to solve the transport equation. One of these the Monte Carlo methods. The physics of electron swarms has been attracting considerable attention during the past decades because of the interest in the various physical effects taking place in these settings and by the need for accurate input data in discharge modeling1,2. The computational resources and numerical techniques made it possible to develop a detailed picture of the physics of particle swarms. Most of the efforts have been devoted to electron swarms, the electron energy distribution function and the transport properties have been determined for a wide variety of gases and gas mixtures3–13. EEDF the software package allowing investigates kinetic and transport properties of plasma in the mixture of gases for the numerical solution of the Boltzmann equation for the Electron Energy Distribution Function in low-ionized plasma in an electric field. It is used for calculations of electron transport and kinetic coefficients in gas mixtures. Sulphur hexafluoride (SF6) is almost exclusively used in the transmission and distribution of electrical energy because of its high dielectric strength and outstanding interruption. Replacement gases for use in high-voltage electrical equipment14-16. Considering the relatively poor dielectric strength of environment-friendly pure gases and gas mixtures such as air, an alternative solution is to mix these with electronegative gases, including SF6, at partial concentrations of a few percent as possible substitute gases for pure SF6, which can effectively reduce the adverse impact on the environment. From a practical view, the candidates for pure gases mixed with SF6 are required to have adequate insulation and current interruption capability. Chemical stability and no flammability or explosiveness. Eventually, the possible candidates that can be used are limited to N2 and CO2. Of these, CO2 mixture seems to be a good candidate as a result of a superior dielectric strength. As a matter of fact, CO2 has started to attract attention as an arcquenching medium, and full-scale 72 kV prototype circuit breakers using CO2 have been manufactured17. However, CO2 cannot completely replace SF6 due to its relatively poor current interruption performance compared to that of pure SF6, especially at higher voltage levels. As a result, SF6–CO2 mixtures are becoming one of the most promising candidates to substitute SF6 gas. For circuit breakers, the fast thermal and dielectric recovery of SF6 (short time constant for an increase in resistivity) which contributes to its high interruption capability is closely connected with its properties such as excellent thermal cooling ability and high dielectric strength. THEORY The fundamental equation governing the electron distribution function is the Boltzmann equation. For spatially uniform gas in the presence of steady electric field. The Boltzmann equation for electrons in collisions, state is given by18: 𝜕𝑓 𝜕𝑡

+ V

𝜕𝑓 𝜕𝑟

−

𝑒 𝐸 𝜕𝑓 𝑚 𝜕𝑉

𝜕𝑓 𝜕𝑡 𝑐

=� �

(1)

Where (𝜕𝑓/𝜕𝑡)𝑐 represents the rate of change of f ( r, v ,t) due to collision, thus, when collisions are considered. The total derivative (𝜕𝑓/𝜕𝑡)𝑐 represents all particles moving in the phase space, where, the partial derivative (𝜕𝑓/𝜕𝑡)𝑐 represents the change in the number of electrons at a given point in the phase space. 4356



Enas. A. Jawad

Solution of the transport Boltzmann equation for the electron –velocity distribution function 𝑓 (𝑟 , 𝑣, 𝑡) is approximated by 𝑓 ( 𝑣), since it is assumed that electron fields is independent of space and time and the problems of electron interactions are spatially uniform, so that the velocity dependence distribution function can be written by Legendre series expansion as follow19. 𝑓 (𝑟 , 𝑣, 𝑡) = 𝑓 + ∑∞ 𝑙=0 𝑓𝑙 (𝑟 , 𝑣, 𝑡) 𝑝𝑙 (cos θ)

(2)

𝑓 (𝑣) = 𝑓(𝑣) + ∑∞ 𝑙=0 𝑓𝑙 (𝑣) 𝑝𝑙 (cos θ)

(3)

Or, in terms of the velocity dependence approximation

The drift velocity is a nonlinear function with an electric field, and the mobility depends on strength field. At sufficiently low E/N, where an electron loses all equal to the gain from the electric field at one elastic collision, the drift velocity is proportional to E/N. The relation between drift velocity (cm /s) and distribution function of energy is given by20: 𝑣𝑑 = −

𝐸 2e 1/2 ∞ 𝑢 𝑑𝑓0 � � ∫0 𝑑𝑢 3 𝑚 𝑁 𝑄𝑚 (𝑢) 𝑑𝑢

(4)

Where 𝑄𝑚 is momentum transfer cross section (cm-2), the mobility is defined as the proportionally coefficient between the drift velocity of charged particle and electric field . The mobility of electrons is: 𝜇𝜇𝑒 =

𝑒 𝑚 𝑣𝑚

=

𝑣𝑑 𝐸

(5)

Where 𝑣𝑚 represent the electron momentum- transfer collision frequency. The electron mobility decreased with E/N increase, these occur energy loss result of electrons through the collisions between electrons and neutral molecules. From the relation between the drift velocity and mobility, we can calculation electron mobility equation21: 𝜇𝜇𝑒 = −

1 2𝑒 ∞ 𝑢3/2 𝜕𝑓0 𝑑𝑢 ∫ 3 𝑚 0 𝑣𝑚 (𝑢) 𝜕𝑢

(6)

The mean energy (eV) is: ∞

3

ε = ∫0 𝑢2 𝑓0 (𝑢) 𝑑𝑢

(7)

The relation between diffusion coefficient and electron energy distribution function is given by22: 𝐷𝑒 =

1 2 ∞ 𝑢3/2 ∫ 3 𝑚 0 𝑣𝑚 (𝑢)

𝑓0 𝑑𝑢

(8)

Characteristics energy (eV) gives by relation: 𝑢𝑐ℎ = 𝑒

𝐷𝑒 𝜇𝑒

(9)

The primary ionization coefficient is a basic parameter in discharge physics and is defined as the number of ionizing collisions made by an electron in moving 1cm in the direction of the applied 𝛼 electric field. The coefficient is used in describing the behaviour of a swarm of electrons travelling 𝑁

through a gas23. The ionization coefficient is calculated from the relation: 𝛼 𝑁

𝜂 𝑁

= =

1 1 ∞ ∫ 𝑄 𝑢2 𝑓0 (𝑢) 𝑑𝑢 𝑣𝑑 𝑢 𝑖 𝑖

1 1 ∞ 2 𝑓 (𝑢) 𝑑𝑢 𝑢 𝑄 ∫ 𝑎 0 𝑣𝑑 𝑢 𝑎

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(10) (11)


Enas. A. Jawad

Where α (in cm-1) the ionization coefficient, 𝜂 (in cm-1) the attachment coefficient, 𝑄𝑖,𝑎 (in cm2) the ionization and attachment cross section, 𝑢𝑖,𝑎 the ionization and attachment potential. 𝛼 𝑁

The breakdown criterion of gases = electronegative gases.

𝜂 𝑁

gives the value E/N at which breakdown occurs in highly

In this work using a mathematical technique for solving the Boltzmann transport equation by using the Monte Carlo method and involving the calculation of the electron transport or swarm parameters24 ,25 The electron energy distribution function and transport parameters was calculated for range (50900) Td with EEDF program by input data for this program such as collision cross section, the number density of gases, number and types of gases, concentration of gas, distribution density, E/N represent the ratio between electric field intensity to the number density of gas, molecular Weight, gas temperature, electron density. Electron energy distribution Function dependent of collision cross sections. The EEDF software package for calculations of the Electron Energy Distribution Function in gas mixtures26. RESULTS AND DISCUSSION The Boltzmann transport was equation solved for SF6, CO2 andSF6 – CO2 mixtures of different ratios. The electron swarm parameters in different mixtures have been analyzed for range of E/N values (50 Td ≤E/N≤900 Td) the different ratios mixtures of SF6 – CO2 gases are listed in Table (1-5). Table 1: The data of the mean electron Energy (eV) as a function E/N in different ratio SF6 – CO2 mixtures. ε(eV)

ε(eV)

pure SF6

SF6–CO2

SF6–CO2

SF6–CO2

SF6–CO2

(15/85)%

(25/75)%

(50/50)%

(75/25)%

50

3.65

1.85

1.92

2.34

2.91

100

4.81

3.51

3.68

4.1

200

6.73

5.62

5.74

300

8.2

6.92

400

9.38

500

ε(eV)

ε(eV)

SF6–CO2

SF6 CO2

(85/15)%

(90/10)%

Pure CO2

3.19

3.34

1.69

4.4

4.62

4.69

3.25

6.06

6.39

6.52

6.59

5.44

7.05

7.38

7.66

7.93

8.02

6.74

8.01

8.14

8.5

8.9

9.08

9.17

7.83

10.33

9.01

9.14

9.09

9.89

10.06

10.15

8.84

600

11.2

9.96

10.08

10.42

10.79

10.96

11.04

9.78

700

11.99

10.88

11

11.3

11.63

11.77

11.84

10.72

800

12.75

11.81

11.9

12.16

12.45

12.57

12.63

11.67

900

13.49

12.73

12.8

13.01

13.24

13.34

13.39

12.62

Electric field/ gas density E/N (Td=10-17 V.cm2 )

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ε(eV)

ε (eV)

ε(eV)

ε(eV)



Enas. A. Jawad

Table 2: The data of the Characteristic energy of electron uch (eV) as a function E/N in different ratio SF6 – CO2 mixtures. Electric field/ gas density E/N

uch (eV)

uch (eV)

uch (eV)

uch (eV)

uch (eV)

uch (eV)

uch (eV)

uch (eV)

SF6–CO2

SF6–CO2

SF6–CO2

SF6–CO2

SF6–CO2

SF6 CO2

pure SF6

(15/85)%

(25/75)%

(50/50)%

(75/25)%

(85/15)%

(90/10)%

Pure CO2

50

3.28

1.78

1.89

2.09

2.5

2.75

2.91

1.63

100

4.27

3.04

3.14

3.45

3.82

3.99

4.08

2.88

200

5.76

4.66

4.74

5.02

5.32

5.5

5.58

4.54

300

6.85

5.66

5.75

6.02

6.38

6.55

6.65

5.54

400

7.65

6.46

6.56

6.84

7.19

7.36

7.45

6.34

500

8.24

7.18

7.27

7.53

7.85

8.06

8.08

7.06

600

8.75

7.83

7.92

8.13

8.43

8.55

8.62

7.72

700

9.18

8.45

8.52

8.71

8.93

9.03

9.08

8.35

800

9.59

9.04

9.1

9.24

9.41

9.48

9.52

8.97

900

9.99

9.62

9.65

9.75

9.89

9.91

9.94

9.57

(Td=10-17 V.cm2 )

Table 3: The data of Mobility 𝜇𝜇 (cm2/V.s) of electron as a function E/N in different ratio SF6 – CO2 mixtures. Electric field/ gas density E/N

𝜇𝜇 ×102

𝜇𝜇 ×102

𝜇𝜇 ×102

𝜇𝜇 ×102

𝜇𝜇 ×102

𝜇𝜇 ×102

𝜇𝜇 ×102

𝜇𝜇 ×102

pure SF6

SF6– CO2

SF6– CO2

SF6– CO2

SF6– CO2

SF6–CO2

SF6 –CO2

(15/85)%

(25/75)%

(50/50)%

(75/25)%

(85/15)%

(90/10)%

50

4.44

8.18

7.65

6.75

5.62

5.15

4.91

8.92

100

3.59

4.77

4.60

4.20

3.88

3.76

3.70

5.07

200

2.89

3.24

3.20

3.10

3.00

2.95

2.93

3.30

300

2.57

2.78

2.70

2.71

2.64

2.61

2.60

2.81

400

2.40

2.51

2.50

2.48

2.44

2.42

2.41

2.53

500

2.30

2.33

2.33

2.32

2.31

2.30

2.30

2.33

600

2.23

2.19

2.20

2.20

2.21

2.22

2.22

2.19

700

2.17

2.09

2.09

2.11

2.14

2.15

2.16

2.07

800

2.13

2.00

2.01

2.04

2.08

2.10

2.11

1.98

900

2.10

1.92

1.94

1.98

2.04

2.06

2.07

1.90

(Td=10-17 V.cm2 )

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Pure CO2


Enas. A. Jawad

Table 4: The data of Diffusion Coefficient 𝐷𝑒 (cm2/s) of electron as a function E/N in different ratio SF6 – CO2 mixtures. Electric field/ gas density E/N

De×103

De×103

De×103

De×103

De×103

De×103

De×103

De×103

pure SF6

SF6–CO2

SF6–CO2

SF6–CO2

SF6–CO2

SF6–CO2

SF6 CO2

(15/85)%

(25/75)%

(50/50)%

(75/25)%

(85/15)%

(90/10)%

Pure CO2

(Td=10-17 V.cm2) 50

1.46

1.46

1.44

1.41

1.41

1.42

1.43

1.45

100

1.53

1.45

1.44

1.45

1.48

1.50

1.51

1.46

200

1.66

1.51

1.52

1.55

1.60

1.62

1.64

1.50

300

1.76

1.57

1.59

1.63

1.69

1.71

1.73

1.55

400

1.83

1.63

1.64

1.69

1.76

1.78

500

1.89

1.67

1.69

1.75

1.81

1.84

1.86

1.65

600

1.95

1.72

1.74

1.80

1.86

1.90

1.91

1.69

700

2.00

1.76

1.78

1.84

1.91

1.94

1.96

1.75

800

2.50

1.80

1.83

1.89

1.96

1.99

2.01

1.77

900

2.09

1.85

1.87

1.93

2.01

2.04

2.06

1.82

1.80

1.60

Table 5: The data of Drift velocity vd (cm/s) of electron as a function E/N in different ratio SF6 – CO2 mixtures. Vd×106

Vd×106

Vd×106

Vd×106

Vd×106

Vd×106

Vd

6

SF6–CO2

SF6–CO2

SF6–CO2

SF6–CO2

SF6–CO2

SF6 –CO2

×106

pure SF6

(15/85)%

(25/75)%

(50/50)%

(75/25)%

(85/15)%

(90/10)%

Pure CO2

50

5.96

10.9

10.3

9.07

6.56

6.92

6.60

12.0

100

9.0

12.8

12.4

11.3

10.5

10.1

9.90

13.6

200

15.5

17.4

17.2

16.6

16.1

15.9

15.8

17.7

300

20.7

22.4

22.2

21.8

21.3

21.1

20.9

22.6

400

25.7

27.0

26.9

26.6

26.0

26.0

26.0

27.2

500

38.0

31.3

31.3

31.2

31.0

30.9

30.9

31.4

600

35.9

35.4

35.4

35.5

35.7

35.7

35.8

35.3

700

40.9

39.2

39.4

39.8

40.3

40.5

40.6

39.0

800

45.8

42.9

43.2

43.9

44.8

45.2

45.4

42.5

900

50.7

46.0

46.9

48.0

49.2

49.8

50.1

45.9

Electric field/gas density E/N (Td=10-17 V.cm2 )

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Vd ×10



Enas. A. Jawad

The influence of different discharge parameters on the electron distribution function is shown in figures (1 -3). The electron energy distribution function strongly affected by changing the parameter E/N or gas mixtures. The distribution functions are clearly non- Maxwillian having distinct varying curvatures at all electron energies. Because the electron lose energy in inelastic collisions with atom in the mixture.

Fig. 1: The EEDF as a function of electron Energy for several value of E/N in pure SF6

Fig. 2: The EEDF as a function of electron Energy for several value of E/N in pure CO2

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Enas. A. Jawad

Fig. 3: The EEDF as a function of electron Energy for several value of E/N in SF6 – CO2 (50/50)% gases mixture. Figure (4) shows the change of distribution function for different ratios of SF6 – CO2 gases mixture at constant value of E/N = 200 Td. The electron energy distribution function is minimum at low ratio of CO2 and the probability of collisions is small and increase in electrons energy from the electric field. The energy gain from the electric field will be distributed on number of electrons and therefore the electron energy is higher in less collisions region.

Fig. 4: The EEDF as a function of electron Energy for different ratio gases mixture of mixtures where E/N is constant. In figure (5) the variation of the mean electron energy with E/N for different of the mixtures components is shown. Which have been calculated using the software package EEDF pro26. The mean electron energy of SF6 is higher than other gases and mixtures (number of collision is lower). And it is 4362



Enas. A. Jawad

show clearly that the mean electron energy is increases from E/N (50-900) Td this is because that the growth of the inelastic collisions of electrons.

Fig. 5: The mean electron Energy as a function E/N in different ratio SF6 – CO2 mixtures. The characteristic energy for different ratio of mixtures is shows in figure (6), the higher value of thermal energy occurs in pure SF6 compared with other ratios and is lower than the value in pure CO2.

Fig. 6: The characteristic energy of E/N in different ratio of gas mixtures (SF6-CO2 ). The mobility of electron as a function of E/N is shown in figure (7), we denote at Sulfur hexafluoride gas the mobility is lower than that of SF6 - CO 2 gases mixture because the electron energy in SF6 gas is higher than that with mixture,and therefore the probability of collisions is larger in Sulfur hexafluoride gas and the mobility in mixture is very few at higher E/N value .and process is reversed in weak electric fields with low probability of collisions. 4363



Enas. A. Jawad

Fig. 7: The Mobility of electron as a function of E/N in different ratio of gas mixtures (SF6-CO2 ). In figure (8) is shows The Diffusion Coefficient for different ratio of mixtures, the lower value of thermal energy occurs in pure CO2 compared with other ratios and is higher than the value in pure SF6.

Fig. 8: The Diffusion Coefficient as a function of E/N in different ratio of gas mixtures (SF6-CO2). Figure (9) is represents the drift velocity of pure SF6 ,CO2 and SF6- CO 2 different mixing ratios as a function of E/N which have been calculated using The software package EEDF pro26 . The data have been recorded in Table (5). The drift controlled by inelastic collisions and proportional to E/N, and it takes higher value with increasing of E/N, since the elastic scattering cross section decreases strongly with the energy in this range of E/N.As shown in this figure, E/N increases rapidly for wide E/N range (50 Td ≤E/N≤ 900 Td), which is due to the reduction of the number of collisions as the energy of the swarm coincides with the sharply decreasing part of momentum transfer cross section. 4364



Enas. A. Jawad

Fig. 9: The drift velocity as a function of E/N in different ratio of gas mixtures (SF6-CO2). Electron in an ordinary case, have an ordinary movement that is define as thermal motion, but with increasing E/N value, the speed of electrons will increase too ; this will lead to another kind of motion known as the drift motion. It also shows that after CO2 was added to SF6, drift velocity in SF6–CO2 increases; thus the growth of the avalanche becomes more severe. This may be the reason for the fact that with an increase in SF6 content in the gas mixture, the electrical strength of the gas mixture increases. From figure (10) shows the suitable agreement between our calculated results with the corresponding experimental results27, 28.

Fig. 10: The drift velocity of electrons versus E/N in SF6-CO2gas mixture various percentages. CONCLUSION The calculating electron energy distribution function and the transport parameters for pure SF6, CO2 and their mixtures with different concentrations by using the numerical solution of Boltzmann equation EEDF program. The behavior of the swarm parameters, which are drift velocity, mean kinetic electron energy characteristic energy, mobility of electron, and Diffusion coefficient dependence on the ratio of the 4365



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mixture components, can very probably, be explained by a preferential weighting of the elastic and inelastic scattering of the electrons on sulfur hexafluoride and Carbon dioxide molecules at different values of E\N, also the results were in good agreement with the computational work. This work shows that CO2 in SF6–CO2 mixtures can change the transport properties. After CO2 was added to SF6 the drift velocity of electron in SF6–CO2 increases. The mean electron energy, characteristic energy and Diffusion Coefficient to the mixture are increasing at sulphur hexafluoride ratios increased. REFERENCE 1. S. Pancheshnyi, S. Biagi, M. C. Bordage, G. J. M. Hagelaar, W. L. Morgan, A. V Phelps, L. C. Pitchford, Chemical Physics, 2012, 398, 148. 2. L. L. Alves, K. Bartschat, S. F. Biagi, M. C. Bordage, L. C. Pitchford, L. C. M. Ferreira, G. J. M. Hagelaar, W. L. Morgan, S. Pancheshnyi, A .V. Phelps, V. Puech and O. Zatsarinny, J. Phys. D: Appl. Phys., 2013 ,46, 334002. 3. R. E. Robson, R. Winkler, F. Sigeneger, Phys. Rev. E., 2002, 65, 056410. 4. D. Loffhagen, G. L. Braglia and R. Winkler, Contrib. Plasma Phys., 2006, 38, 527. 5. R. E. Robson, P. Nicoletopoulos, Li B and R. D. White, Plasma Sources Sci. Technol., 2008, 17, 024020. 6. Z. Lj. Petrović, S. Dujko, D. Marić, G. Malović, Z Nikitović, O. Saˇsić, O Jovanović, V Stojanović and M. Radmilovi´, J. Phys. D: Appl. Phys., 2009, 42, 194002. 7. S. Dujko, R. D. White, Z. Lj. Petrović and R. E. Robson, Plasma Sources Sci. Technol., 2011, 20, 024013. 8. N. R. Pinhão, Z. Donkó, D. Loffhagen, E. A. Pinheiro Mand Richley, Plasma Sources Sci. Technol., 2004,13, 719. 9. D. Trunec, Z. Bonaventura and D. Neˇcas, J. Phys. D: Appl. Phys., 2005, 39, 2544. 10. R. D. White, M. J. Brunger, N. A. Garland, R. E. Robson, K. F. Ness, G. Garcia, J. de Urquijo, S. Dujko and Z. Lj. Petrović , European Physical Journal D bf., 2014, 68, 125. 11. D. Yunkun, Lu. Chengdong and X. Dengming, IEEE Trans. Plasma Sci., 2012, 40, 2671. 12. S. Dujko, Raspopović, R. D. White, T. Makabe and Z. Lj. Petrović , Eur. Phys. J. D., 2014, 68, 166. 13. A. P. Napartovich and I. V. Kochetov, Plasma Sources Sci. Technol., 2011, 20, 025001. 14. L. G. Christophorou, J. K. Olthoff and D. S. Green, Gases for electrical insulation and arc interruption: possible present and future alternatives to pure SF6; NIST Tech. Note., 1997, 1– 44, 1425. 15. Y. Cressault, V. Connord, H. Hingana, Ph. Teulet and A. Gleizes, Transport properties of CF3I thermal plasmas mixed with CO2, air or N2 as an alternative to SF6 plasmas in highvoltage circuit breakers, J. Phys. D: Appl. Phys., 2011, 44, 495202. 16. Y. Yokomizu, R. Ochiai and T. Matsumura, Electrical and thermal conductivities of hightemperature CO2–CF3I mixture and transient conductance of residual arc during its extinction process, J. Phys. D: Appl. Phys., 2009, 42, 215204. 17. T. Uchii, Y. Hoshina, K. Miyazaki, T. Mori, H. Kawano, T. Nakano and Y. Hirano, Development of 72 kV class environmentally-benign CO2 gas circuit breaker model, IEEJ Transactions on Power and Energy, 2004, 47–84, 124. 18. Z. D. Niktovic and V. D. Stojanovic, Modeling of high E/N in mixtures of CF4 and its radicals, Publ. Astron. obs, Belgrad., 2008, 84, 103-106. 19. K. Smith and R. W. Thomson, Computer Modeling of Gas, Plenum Press, New York, 1978. 4366



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* Corresponding author: Enas. A. Jawad Dept. of Physics /College of Education for Pure Sciences (Ibn Al-Haitham)/ University of Baghdad, Iraq.

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