IEEE Transac t ions on Electr ical In su la t ion Vol. 28 No. 1 , F e b r u a r y 1993

CO M M U N I C A T 10 N

Electron Swarm Parameters in Nitrogen Oxygen and Air

Jianfen Liu and G. R. Govinda Raju University of Windsor,

Department of Electrical Engineering, Windsor, Ontario, Canada

A B S T R A C T A comprehensive set of data of electron swarm parameters in nitrogen, oxygen and air are calculated by the Monte Carlo technique. It is shown that for mixtures of gases the calcu- lated values differ considerably from those obtained using the simplified procedure of partial addition of the parameters of the constituent gases.

1. I N T R O D U C T I O N

1.1 PURE GASES

OR obvious engineering purposes a study of the break- F down strength of gases is important and involves the electron drift velocity W , the mean energy ( E ) and Towns- end’s first ionization coefficient a. These quantities are referred to generally as the electron swarm parameters and depend upon the ratio of the electric field E to gas pressure p . Two different parameters are used in the liter- ature; E / p where E is the electric field in V/cm and p the gas pressure in Pa, E / N where N is the number density of gas molecules a t 0°C. In this communication we use E / N which has the dimension of Vcm’. To avoid large negative powers of 10, a unit of 1 Td=10-17 Vcm2 is used. The conversion factor from E / N to E / p is 2 . 6 9 ~ 1 0 - ~ V/cm Pa-’ = 1 Td. In this brief note we use the T d unit.

A large volume of data have been published in the lit- erature [l] on the electron transport coefficients in several gases over a wide range of E / N . The data required for engineering purposes generally fall over a wide range of E / N . For partial discharge studies the E / N values lie in the range 750 to 1200 Td. For high pressure break- down the same parameter lies in the range of 90 to 150 Td. Data in the intermediate range are often required for theoretical analysis of leader and streamer propaga- tion ahead of an electron avalanche.

In choosing an appropriate value for the transport co- efficients, one is confronted with a bewildering set of da- t a obtained under different conditions, using a variety of experimental techniques. Furthermore the range of E / N covered by individual investigators are restricted to a nar- row range and preclude general applicability. Hence a set of comprehensive data for the three gases N2, 0 2 and air is considered to be valuable and in this brief Communica- tion the values calculated using Monte Carlo Simulation are reported.

1.2 AIR AND OTHER Oz/Nz M IXTU RES

Several empirical formulas have been suggested in the literature for the calculation of swarm parameters in mix- tures of gases. Since their applicability is very limited, the parameters are sometimes calculated using the fractional sum approach. For example the ionization coefficient in a mixture of gases is calculated [2] as

amiz = za1 + (1 - z)a2 (1)

in which a is the first ionization coefficient and x is the fraction of a component in the mixture. As a further refinement in the theoretical approach, the collision cross section of the mixture Q m may be derived from individual cross sections as [3,4]

NQm = N l Q l + N2Q2 (2)

0018-9367 $3.00 @ 1993 IEEE

IEEE Transactions on Electrical Insulation Vol. 28 No. 1, February 1993

N2 0 2 air W [7,8] [5,7,9-111 [12-151‘

[5i7I [I61 e

155

where l /NQm is the number of collisions per cm drift of the electron. This approach has the advantage that all Table 2. Published studies in three gases. transport coefficients may be calculated using the same set of cross sections and therefore there is self consistency. Both these formulas are empirical. In our calculations we have adopted a basically new approach. When an electron collides with a molecule in a gas mixture, the result of that particular collision will depend upon the collision cross sections appropriate to that species. The Monte Carlo simulation is a more realistic way of tracing the motion of electrons in the gas mixture.

Table 1. Electron swarm parameters in Nz, 0 2 and air.

a / ~ (10-17 c”+ w (I 106 cms”) i (ev)

-

20

40

60

80

100

130

200

300

400

500

600

700

800

900

1000

1300

2000

E/N(Td) N2 0 2 Alr N2 0 2 Alr N2 0 2 Alr

3.72 5.7 4.33 0.96 2.61 0.97

5.36 7.8 6.25 1.10 3.31 1.20

6.96 9.4 7.76 1.38 3.60 1.63

8.85 11.3 9.71 2.06 3.85 2.45

0 0.07 0 10.80 14.7 11.28 2.67 4.52 3.13

a i r - ”[ 1.1 7 0 % 5 0 % O2 0 2

2 0

0.07 0.17 0 08 12.86 16.5

0.39 0.92 0.50 18.60 22.82

1.80 2.70 1.94 28.35 29.98

3.56 4.79 3 59 38.84 38.76

4.99 6.57 5.93 45.17 47.78

7.05 9.19 6.99 57.78 51.39

8.49 10.81 8.17 67.76 59.29

9.55 1227 1034 84.34 63.52

11.34 14.07 11.23 88.25 67.02

11.20 15.63 12.35 108.29 69.48

15.11 20.67 16.60 129.01 84.63

19.72 26.43 20.32 177.13 106.41

14.06

21.00

30.96

38.36

49.62

55.67

65.05

72.60

78.83

85.99

110.34

156.65

II 3.71 4.60 3.90 8 5.16 5.96 5.70

7.16 7.50 7.28 I 1 8.56 9.54 8.61 1 10 5 0

E I N X l O o T d ) 10.07 11.10 10.11

11.34 12.33 11.73

13.01 13.55 13.47 Figure 1. Difference in the values of ionization coefficients calculated using Equation (1) and Monte Carlo approach expressed as a percentage of the latter.

as shown in Figure 1, clearly demonstrates that the frac-

14.98 15.09 14.51

16.39 16.07 16.10

17.38 17.41 17.36

22.54 21.08 22.42

35.66 28.61 33.51 -

tional additional methods result in considerable errors.

may be as high as 15%o. For purpos- es of comparing our theoretical results with the previous- ly published results the references given in Table have been used:

In the Monte L511 we have adopted The magnitude of the error depends upon E / N and in a mean collision time approach in which the mean colli- sion time is divided into smaller time intervals. For each interval the event of a collision is simulated by generat- ing a random number and comparing it with the collision probability. The nature of this collision is determined by a similar process. The electron swarm parameters are sampled a t a certain time interval. The collision cross sections in 0 2 and N2 are the same as adopted in [5,6].

the

2. CONCLUSIONS

Table 1 shows the ionization coefficient, drift velocity and mean energy in Nz, 0 2 and air (78% N2 + 22% 0 2 ) .

The highest difference between previously published data and the present values is within 3~6%.

comprehensive set of da t a for swarm parameters for A Nz, oxygen and air over a wide range of E / N values are calculated using the Monte-Carlo simulation.

The magnitude of the transport coefficients in these gases are distributed in the following way (with E / N in T d units):

Two other mixtures with 50% and 70% oxygen are also investigated. A comparison of results for these mixtures

156 Liu et al.: Electron Swarm Parameters

[8] H. Schulumbohm, “Stoflionisierungskoeffizienten A. Mittlere Elektronenenergien und die Beweglichkeit von Elektronen in Gasen”, Z. Physik, Vol. 184, pp.

[9] H. Ryzko, “Drift Velocity of Electrons and Ions in Dry and Humid Air and in Water Vapor”, Proc. Phys. Soc., London, Vol. 85, pp. 1283-1295, 1965.

WO, > WaiT > WN,

WO, < WaiT < WN, E / N > 400 492-505, 1965.

E / N < 400

Co2 > Fair > C N ~ E / N < 900 CoZ < < C N ~ E / N > 900

[ $1 o2 > [$] air > [ $ I N a

(3)

20 < E / N < 2000

[lo] M. S. Naidu and A. N. Prasad, “Mobility, Diffusion and Attachment of Electrons in Oxygen”, J . Phys. D., Vol. 3, pp. 957-964, 1970.

The approximate fractional sum method for the cal- culation of these parameters is applicable in 0 2 and Nz mixtures only in a certain range of E / N ; for certain Val- ues of E / N , the errors may be as high as 15%.

[I11 M. A. Harrison and R. Geballe, m simultaneous Measurement of Ionization and Attachment Coeffi-

REFERENCES

E. C. Beaty, J . Dutton and L. C. Pitchford, “A Bibli- ography of Electron Swarm Data”, JILA (Joint Insti- tute for Laboratory Astrophysics) Information Cen- ter Report No. 20, 1979.

A. Wieland, “Breakdown Mechanisms in Electroneg- ative Gases (SF6) and in Gas Mixtures”, ETZ-A, Vol. 94, pp. 370-373, 1973.

G. R. Govinda Raju and R. Hackam, “Breakdown Field Strength of SF6, N 2 0 , SF6 + Nz and SF6 + NzO”, Journal of Appl. Phys., Vol. 52, pp. 3912- 3920, 1981.

L. Frommhold, “Uber Verzogerte Elektronen in Elektronenlawinen” , Insbesondere in Sauerstoff un Luft, durch Bildung und Zerfall Negative Ionen 0-”, Fortschr. Physik., Vol. 12, pp. 597-643, 1964.

J . Liu and G. R. Govinda Raju, “Evaluation of Transport Coefficients in Nitrogen by Monte-carlo Method”, J . Franklin Institute, Vol. 329, no. 1, pp. 181-194, 1992.

J . Liu and G. R. Govinda Raju, “Calculation of Elec- tron Swarm Parameters in Oxygen Using a Rigorous Boltzmann Equation Analysis”, Canadian Journal of Phys., Vol. 70, pp. 216-224, 1992.

S. C. Haydon and 0. M. Williams, “Combined Spa- tial and Temporal Studies of Ionization Growth in Nitrogen”, J . Phys. D., Vol. 9, pp. 523-536, 1976.

cients”, Phys. Rev., Vol. 91, pp. 1-7, 1953.

[12] J . A. Rees, “Electron Drift Velocities in Air”, Austr. J . Phys., Vol. 26, pp. 427-431, 1973.

[13] H. Hessnauer, “Anlagerungskoeffizienten und Drift- geschwindigkeiten von Elektronen in Luft” , Z. Phys. Vol. 204, pp. 142-154, 1967.

[14] J . L. Morzzi and D. A. Price, “Ionization, Attach- ment and Detachment in Air and Air-CO2 Mix- tures”, J . Phys. D., Vol. 7, pp. 1434-1440, 1974.

[15] C. Raja Rao and G. R. Govinda Raju, “Growth of Ionization Currents in Dry Air a t High Values of E / n ” , J . Phys. D., Vol. 4, pp. 494-503, 1971.

[16] R. D. Hake Jr. and A. V. Phelps, “Momentum- transfer and Inelastic-collision Cross Sections for Electrons in 0 2 , CO and COz”, Phys. Rev., Vol. 158, pp. 70-84, 1967.

[17] C. Raja Rao and G. R. Govinda Raju, “The Ratio of Diffusion Coefficient to Mobility for Slow Electrons in Dry Air”, J . Phys. D., Appl. Phys., Vol. 4, pp. 769-772, 1971.

[18] A. E. D. Heylen, “Calculated Electron Mobility in Nitrogen, Oxygen and Air for 0.1 < E / p < 100 Vcm-’ m m Hg-”’, Proc. Phys. Soc., London, Vol. 79, pp. 284-292, 1962.

Manuscript was received on 20 September 1991, in final form 31 August 1992.