Jpn. J. Appl. Phys. 45 (2006) pp. 5189-5196  |Previous Article| |Next Article|  |Table of Contents|
|Full Text PDF (383K)| |Buy This Article|

Equality of Higher-Order Diffusion Coefficients between Component and Composite Electron Swarms in Gas

Hirotake Sugawara and Yosuke Sakai

(Received December 15, 2005; accepted February 22, 2006; published online June 8, 2006)

When an electron swarm in gas is composed of component electron swarms individually in drift equilibrium, the higher-order diffusion coefficients (HDCs) of the composite electron swarms are equal to those of the component electron swarms. We have derived this equality theoretically and have examined it by numerical simulation. The HDCs are the time derivatives of higher-order cumulants, which are quantities characterizing the shape of a spatial electron distribution. This fact seemingly indicates the dependence of the HDCs of the composite electron swarms on the arrangement of the component electron swarms. However, the equality holds irrespective of the relative positions and electron populations of the component electron swarms. We have given a consistent explanation to these facts. We have also discussed electron swarm development from dispersed or multiple electron sources that may appear in practical experiments.

KEYWORDS: electrical discharge, plasma, simulation, transport parameter, electron swarm, diffusion coefficient, drift equilibrium, cumulant, moment
URL: http://jjap.ipap.jp/link?JJAP/45/5189/
DOI: 10.1143/JJAP.45.5189

References

1. H. Tagashira, Y. Sakai and S. Sakamoto: J. Phys. D 10 (1977) 1051[IoP STACKS].
2. K. Kumar, H. R. Skullerud and R. E. Robson: Aust. J. Phys. 33 (1980) 343.
3. H. A. Blevin and J. Fletcher: Aust. J. Phys. 37 (1984) 593.
4. J. H. Whealton and E. A. Mason: Ann. Phys. (N.Y.) 84 (1974) 8[CrossRef].
5. J. H. Whealton: J. Phys. B 7 (1974) 1602[IoP STACKS].
6. H. Sugawara, Y. Sakai, H. Tagashira and K. Kitamori: J. Phys. D 31 (1998) 319[IoP STACKS].
7. J. de Urquijo, C. A. Arriaga, C. Cisneros and I. Alvarez: J. Phys. D 32 (1999) 41[IoP STACKS].
8. J. de Urquijo: Plasma Source Sci. Technol. 11 (2002) A86[IoP STACKS].
9. J. de Urquijo, J. L. Hernández-Ávila, E. Basurto and F. Ramírez: J. Phys. D 36 (2003) 1489[IoP STACKS].
10. D. M. Xiao, L. L. Zhu and Y. Z. Chen: J. Phys. D 32 (1999) L18[IoP STACKS].
11. D. M. Xiao, L. L. Zhu and X. G. Li: J. Phys. D 33 (2000) L145[IoP STACKS].
12. Y. Nakamura: J. Phys. D 20 (1987) 933[IoP STACKS].
13. Suugaku Jiten (Encyclopedia of Mathematics), ed. Mathematical Society of Japan (Iwanami, Tokyo, 1985) p. 853 [in Japanese].
14. W. C. Rinaman, C. Heil, M. T. Strauss, M. Mascagni and M. Sousa: in Standard Mathematical Tables and Formulae: Probability and Statistics, ed. D. Zwillinger (CRC Press, Boca Raton, 1996) 30th ed., Chap. 7, p. 574.
15. E. W. Weisstein: in CRC Concise Encyclopedia of Mathematics, ed. E. W. Weisstein (CRC Press, Boca Raton, 1999) p. 370.
16. H. Sugawara and Y. Sakai: J. Phys. D 32 (1999) 1671[IoP STACKS].
17. M.-C. Bordage, P. Ségur, L. G. Christophorou and J. K. Olthoff: J. Appl. Phys. 86 (1999) 3558[AIP Scitation].
18. H. Date, K. Kondo and H. Tagashira: J. Phys. D 26 (1993) 1211[IoP STACKS].
19. K. Kitamori, H. Tagashira and Y. Sakai: J. Phys. D 13 (1980) 535[IoP STACKS].