Hostname: page-component-5c6d5d7d68-pkt8n Total loading time: 0 Render date: 2024-08-22T22:40:25.122Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalization of the perturbation theory by using a repeating equation: A case that reveals the plasma chaotic state

Published online by Cambridge University Press:  23 October 2012

C. L. XAPLANTERIS ,
E. D. FILIPPAKI  and
L. C. XAPLANTERIS
C. L. XAPLANTERIS
Affiliation:
Plasma Physics Laboratory, IMS, NCSR “Demokritos”, Athens, Greece Hellenic Army Academy, Vari Attica, Greece
E. D. FILIPPAKI
Affiliation:
Plasma Physics Laboratory, IMS, NCSR “Demokritos”, Athens, Greece
L. C. XAPLANTERIS
Affiliation:
School of Physics, National and Kapodistrian University of Athens, Greece ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Among the theoretical and experimental situations of interest in plasma physics are the waves that rise into the plasma and are strongly affected from the plasma parameters. Therefore, the development of strong relations between unperturbed and perturbed quantities is proved to exist both experimentally and theoretically. In the present paper, the mathematical solution ended in a relation between drift and perturbed velocities, which presupposes the perturbed velocity value to be very small in comparison with the drift velocity. However, the experiment has shown that the presupposition of the small value of the perturbations is not satisfied in many laboratory instances; as a result the use of the perturbation theory is limited. To surpass this difficulty, the big perturbed quantity was divided into small and equal parts, and by using the equation between unperturbed and perturbed velocities as a repeating relation, the perturbed theory may be extended and generalized beyond the small disturbances. In addition, calculations with a little change in the initial conditions were carried out, to determine when the plasma obtains chaotic behavior.

Type
Papers
Information
Journal of Plasma Physics , Volume 79 , Issue 2 , April 2013 , pp. 221 - 231
Copyright
Copyright © Cambridge University Press 2012

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

Anastassiades, A. and Xaplanteris, C. L. 1983 Drift wave instability in the presense of an RF-field in a magnetized plasma. J. Phys. Soc. Jpn 52, 492–500.CrossRefGoogle Scholar
Block, D., Piel, A., Schröder, C. H. and Klinger, T. 2001 Phys. Rev. E 63, 056401.Google Scholar
Braginskii, S. I. 1965 Transport Processes in a Plasma. New York: Reviews of Plasma Physics.Google Scholar
Chen, F. 1964 Phys. Fluids 7, 949–955.CrossRefGoogle Scholar
D' Angelo, N. and Motley, R. 1963 Phys. Fluids 6 (3), 422–425.CrossRefGoogle Scholar
D' Angelo, N. 1963 Phys. Fluids 6 (4), 592–593.CrossRefGoogle Scholar
Drummond, J. 1961 Plasma Physics. New York: McGraw-Hill.Google Scholar
Ellis, R., Marden-Marshall, E. and Majeski, R. 1980 Plasma Phys. 22, 113–132.CrossRefGoogle Scholar
Gravier, E., Caron, X. and Bonhomme, G. 1999 Phys. Plasmas 6, 1670.CrossRefGoogle Scholar
Hendel, H. W., Coppi, B., Perkins, F. and Politzer, P. A. 1967. Phys. Rev. Lett. 18, 439–442.CrossRefGoogle Scholar
Klinger, T. 1998 Control of chaos in plasmas. In: Handbook of Chaos Control (ed. Schuster, H. G.). Weinheim, Germany: Wiley–VCH, ch. 20, pp. 513–562.Google Scholar
Koepke, M. E., Klinger, T., Seddighi, F. and Piel, A. 1996 Phys. Plasmas 3, 4421–4426.CrossRefGoogle Scholar
Krall, N. and Trivelpiece, A. 1973 Principles of Plasma Physics. Tokyo: McGraw-Hill Kogakusha.CrossRefGoogle Scholar
Lakhina, G. S. and Shukla, P. K. 1987 Astrophys. Space Science 139, 275–279.CrossRefGoogle Scholar
Lieberman, M. and Lichtenberg, A. 1994 Principles of Plasma Discharges and Materials Processing. New York: John Wiley.Google Scholar
Marden-Marshall, E., Ellis, R. F. and Walsh, J. E. 1986 Plasma Phys. 28, 1461–1482.Google Scholar
Okamoto, A., Hara, K., Nagaoko, K., Yoshimura, S., Vranjes, J., Kono, M. and Tanaka, M. Y. 2003 Phys. Plasmas 10, 2211–2216.CrossRefGoogle Scholar
Sen, A. K. 2000 Phys. Plasmas 7, 1759.CrossRefGoogle Scholar
Shukla, P. K., Birk, G. and Bingham, R. 1995 Geophys. Res. Lett. 22, 671–674.CrossRefGoogle Scholar
Spitzer, L. 1967 Physics of Fully Ionized Gase, 2nd edn.New York: John Wiley.Google Scholar
Vranjes, J., Saleem, H. and Poedts, S. 2004 Phys. Rev. E 69, 056404.Google Scholar
Wesson, J. 1997 Tokamaks, 2nd edn.Oxford: Clarendon Press.Google Scholar
Xaplanteris, C. L. 2009 J. Plasma Phys. 75, 395–406.CrossRefGoogle Scholar
Xaplanteris, C. L. and Filippaki, E. 2011 J. Plasma Phys. 77, 679–692.CrossRefGoogle Scholar
Xaplanteris, C. L., Filippaki, E. and Mistakidis, I. S. 2012 Chaotic modeling and simulation (CMSIM), 1, 157–162.Google Scholar