Skip to main content Accessibility help
×
Home

Study of the electron kinetics in cylindrical hollow cathodes by a multi-term approach

  • F. Sigeneger (a1) and R. Winkler (a1)

Abstract

The non-local kinetics of the electrons in a cylindrical, axially symmetric hollow cathode discharge is theoretically investigated. A new multi-term method for solving the inhomogeneous Boltzmann equation in cylindrical coordinates has been developed to adequately describe the pronounced anisotropy of the electron velocity distribution function expected in the cathode fall region. This method is based on a tensorial representation of the expansion of the electron velocity distribution function in spherical harmonics. The resultant hierarchy of component equations has been specified to cylindrical geometry with rotational symmetry and axial uniformity. A subset of component equations could be separated which determines the relevant distribution parts needed to analyze the radial behaviour of important electron properties in the hollow cathode. Using measured profiles of the electric field, this subset has numerically been solved for a helium plasma at a discharge current of some mA and a pressure of few torr. Based on this approach in addition to the radial variation of the energy distribution, that of important transport properties and collision rates is studied and the non-local particle and power balance of the electrons are analysed. Some theoretical results are compared with available experimental ones.

Copyright

Corresponding author

References

Hide All
[1] Adamowicz, T.M., Donkó, Z., Szalai, L., Rózsa, K., Kwasniewski, W., Appl. Phys. B 65, 613 (1997)
[2] Petrov, G.M., J. Phys. D: Appl. Phys. 30, 67 (1997)
[3] Donkó, Z., Szalai, L., Pockl, M., IEEE J. Quantum Electron. 34, 47 (1998)
[4] Tobin, R., IEEE J. Quantum Electron. 36, 1053 (2001)
[5] Csillag, L., Janossy, M., Appl. Phys. B 73, 55 (2001)
[6] Mills, R.L., Int. J. Hydrogen Energy 26, 579 (2001)
[7] Chen, Y.M., Yu, G.P., Huang, J.H., Surf. Coating Technol. 141, 156 (2001)
[8] Nakamura, M., Korzec, D., Aoki, T., Engemann, J., Hatanaka, Y., Appl. Surf. Sci. 175, 697 (2001)
[9] D'Couto, G.C., Tkach, G., Ashtiani, K.A., Hartsough, L., Kim, E., Mulpuri, R., Lee, D.B., Levy, K., Fissel, M., Choi, S., J. Vac. Sci. Technol. B 19, 244 (2001)
[10] Koltypin, E.A., Nastyukha, A.I., Smirnov, P.A., Sov. Phys.-Tech. Phys. 15, 1703 (1971)
[11] K.H. Schoenbach, A. El-Habachi, W. Shi, M. Ciocca, Proc. of the XXIIIth Int. Conf. on Phenomena in Ionized Gases, Toulouse, 1997, Vol. 5, p. 22
[12] Günter-Schulze, A., Z. Phys. 19, 313 (1923)
[13] Helm, H., Z. Naturforsch. 27a, 1812 (1972)
[14] Stockhausen, G., Kock, M., J. Phys. D: Appl. Phys. 34, 1683 (2001)
[15] Hashiguchi, S., Hasikuni, M., Jpn. J. Appl. Phys. 28, 699 (1989)
[16] Kolobov, V.I., Tsendin, L.D., Plasma Sources Sci. Technol. 4, 551 (1995)
[17] R. Arslanbekov, A. Kudryavtsev, Electron kinetics in the cathode region of glow discharges. Plane and hollow cathodes, in Electron Kinetics and Application of Glow Discharges, edited by U. Kortshagen, L.D. Tsendin (New York and London, Plenum Press, 1998), Vol. 367 of NATO ASI Series B, p. 161
[18] Hashiguchi, S., Hasikuni, M., Jpn. J. Appl. Phys. 27, 1010 (1988)
[19] Hashiguchi, S., IEEE Trans. Plasma Sci. 19, 297 (1991)
[20] Donkó, Z., Z. Naturforsch. 48a, 457 (1993)
[21] Donkó, Z., Rózsa, K., Tobin, R.C., J. Phys. D: Appl. Phys. 29, 105 (1996)
[22] Fiala, A., Pitchford, L.C., Boeuf, J.P., Phys. Rev. E 49, 5607 (1994)
[23] A. Fiala, L.C. Pitchford, J.P. Boeuf, in Proc. of the XXIIth Int. Conf. on Phenomena in Ionized Gases, Hoboken, 1995,Vol. 4, p. 191
[24] Donkó, Z., Phys. Rev. E 57, 7126 (1998)
[25] Kutasi, K., Donkó, Z., J. Phys. D: Appl. Phys. 33, 1081 (2000)
[26] Baguer, N., Bogaerts, A., Gijbels, R., Spectrochim. Acta Part B 57, 311 (2002)
[27] Petrov, G.M., Zhechev, D., Phys. Plasmas 9, 1815 (2002)
[28] Sigeneger, F., Winkler, R., Contrib. Plasma Phys. 36, 551 (1996)
[29] Sigeneger, F., Winkler, R., Plasma Chem. Plasma Process. 17, 1 (1997)
[30] Sigeneger, F., Golubovskii, Y.B., Porokhova, I.A., Winkler, R., Plasma Chem. Plasma Process. 18, 153 (1998)
[31] Leyh, H., Loffhagen, D., Winkler, R., Comput. Phys. Commun. 113, 33 (1998)
[32] Loffhagen, D., Winkler, R., J. Phys. D: Appl. Phys. 29, 618 (1996)
[33] Petrov, G., Winkler, R., J. Phys. D: Appl. Phys. 30, 53 (1997)
[34] S. Pfau, R. Kozakov, M. Otte, J. Rohmann, Proc. of XXIVth Int. Conf. on Phenomena in Ionized Gases, Warsaw, 1999, Vol. 3, p. 33
[35] Otte, M., Pfau, S., Sigeneger, F., Winkler, R., Europhys. Conf. Abstracts 24F, 272 (2000)
[36] Wilhelm, J., Winkler, R., Beitr. Plasmaphys. 8, 167 (1968)
[37] Johnston, T.W., J. Math. Phys. 7, 1453 (1966)
[38] Castellvi, P., Comput. Phys. 9, 335 (1995)
[39] Sigeneger, F., Sukhinin, G.I., Winkler, R., Plasma Chem. Plasma Process. 20, 87 (2000)
[40] Loffhagen, D., Braglia, G.L., Winkler, R., Contrib. Plasma Phys. 38, 527 (1998)
[41] Hagstrum, H.D., Phys. Rev. 104, 672 (1956)
[42] Winkler, R., Braglia, G.L., Wilhelm, J., Il Nuovo Cimento 10D, 1209 (1988)
[43] Fon, W.C., Berrington, K.A., Hibbert, A., J. Phys. B: At. Mol. Opt. Phys. 14, 307 (1981)
[44] M. Hayashi, Electron collision cross sections, in Plasma Material Science Handbook, edited by Japan Society for the Promotion of Science (Tokyo, Ohmsha, 1992), p. 748
[45] H. Cohen, Mathematics for Scientists and Engineers (Englewood Cliffs, Prentice-Hall, 1992)

Keywords

Related content

Powered by UNSILO

Study of the electron kinetics in cylindrical hollow cathodes by a multi-term approach

  • F. Sigeneger (a1) and R. Winkler (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.