Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-09T06:29:23.809Z Has data issue: false hasContentIssue false
  • English
  • Français

On the inertia term in the momentum equation in the free-fall regime of discharge maintenance

Published online by Cambridge University Press:  27 October 2010

ST. ST. LISHEV ,
A. P. SHIVAROVA  and
KH. TS. TARNEV
ST. ST. LISHEV
Affiliation:
Faculty of Physics, Sofia University, BG-1164 Sofia, Bulgaria ([email protected])
A. P. SHIVAROVA
Affiliation:
Faculty of Physics, Sofia University, BG-1164 Sofia, Bulgaria ([email protected])
KH. TS. TARNEV
Affiliation:
Department of Applied Physics, Technical University-Sofia, BG-1000 Sofia, Bulgaria
Get access Rights & Permissions [Opens in a new window]

Abstract

The study, being on two-dimensional modelling of low pressure discharges, suggests an approach to the nonlinear inertia term in the momentum equation of the positive ions needed to be accounted for in the free-fall regime of the discharge maintenance. On the basis of conclusions that the inertia term acts in the wall sheath, where the ions fly perpendicularly to the walls, it is shown that (i) the parallel – to the walls – velocity component can be neglected, and (ii) the rest of the convective derivative can be determined by using the energy conservation law in the collisionless case. In a way, the inertia term acting as a retarding force is joined to the momentum loss term by introducing effective collision frequencies. The validity of the procedure is proved in a model of a low pressure argon discharge by comparison with the exact solutions for the two-dimensional spatial distribution of the discharge characteristics (ion velocity, electron density and temperature and DC electric field and its potential). The conclusion is that (i) ignoring the velocity component that is parallel to the walls does not cause deviation from the exact solution, and (ii) the approximation of using the energy conservation law in the collisionless case is good enough.

Type
Papers
Information
Journal of Plasma Physics , Volume 77 , Issue 4 , August 2011 , pp. 469 - 478
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Tonks, L. and Langmuir, I. 1929 Phys. Rev. 34, 876.CrossRefGoogle Scholar
[2]Self, S. A. and Ewald, H. N. 1966 Phys. Fluids 9, 2486.CrossRefGoogle Scholar
[3]Self, S. A. 1967 Phys. Fluids 10, 1569.CrossRefGoogle Scholar
[4]Ilić, D. B. 1973 J. Appl. Phys. 44, 3993.CrossRefGoogle Scholar
[5]Kouznetsov, I. G., Lichtenberg, A. J. and Lieberman, M. A. 1996 Plasma Sources Sci. Technol. 5, 662.CrossRefGoogle Scholar
[6]Franklin, R. N. 2000 Plasma Sources Sci. Technol. 9, 191.CrossRefGoogle Scholar
[7]Pejović, M. M., Ristić, G. S. and Karamaković, J. P. 2002 J. Phys. D: Appl. Phys. 35, R91.CrossRefGoogle Scholar
[8]Paunska, Ts., Shivarova, A. and Tarnev, Kh. 2004 Vacuum 76, 377.CrossRefGoogle Scholar
[9]Paunska, Ts., Schlüter, H., Shivarova, A. and Tarnev, Kh. 2006 Phys. Plasmas 13, 023504.CrossRefGoogle Scholar
[10]Salabas, A., Gousset, G. and Alves, L. L. 2002 Plasma Sources Sci. Technol. 11, 448.CrossRefGoogle Scholar
[11]Richards, A. D., Thompson, B. E. and Sawin, H. H. 1987 Appl. Phys. Lett. 50, 492.CrossRefGoogle Scholar
[12]Gogolides, E. and Sawin, H. H. 1992 J. Appl. Phys. 72, 3971.CrossRefGoogle Scholar
[13]Makasheva, K. and Shivarova, A. 2001 Phys. Plasmas 8, 836.CrossRefGoogle Scholar
[14]Kolev, St., Schlüter, H., Shivarova, A. and Tarnev, Kh. 2006 Plasma Sources Sci. Technol. 15, 744.CrossRefGoogle Scholar
[15]Kolev, St., Lishev, St., Shivarova, A., Tarnev, Kh. and Wilhelm, R. 2007 Plasma Phys. Control. Fusion 49, 1349.CrossRefGoogle Scholar