Advertisement

Technical Physics

, Volume 63, Issue 3, pp 347–353 | Cite as

Two Modes of the Self-Similar Evolution of Charged Plasma

  • V. A. Pavlov
Plasma

Abstract

Two self-similar modes of evolution of charged particles’ high-current beam are described analytically. The situation being considered falls within the field of nonneutral plasma electrodynamics. The process is considered in terms of the nonlinear 1D evolution of the charge density w(x, t) in the channel of a longdistance transmission line with nonlinearly distributed resistance R, capacitance C, and inductance L: R = R(w), C = C(w), and L = 0. It is shown that initially the front of w(x, t) accelerates and then slows down. The description of the process in the channel is based on the charge conservation law. An idealized “kinematic” approach is used according to which an equation in two unknowns (charge density and current density in the channel) can be reduced to an equation in one unknown w(x, t). A strongly nonlinear wave process is studied. A discontinuous solution w(x, t) is constructed with a zero boundary condition at infinity. Such a model description can apply only for revealing the main qualitative features of a complex process. Analytical expressions for the variation in the evolution of the front velocity and perturbed area length are derived. An interrelation between the nonlinearity parameter of the process and the amount of charge in the interelectrode gap is suggested based on the experimental data for the evolution of streamers.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. M. Bazelyan and Yu. P. Raizer, Phys.-Usp. 43, 701 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    E. M. Bazelyan and Yu. P. Raizer, The Physics of Lightning and Lightning Protection (Fizmatlit, Moscow, 2001).Google Scholar
  3. 3.
    E. M. Bazelyan and Yu. P. Raizer, Spark Discharge (Mosk. Fiz.-Tekh. Inst., Moscow, 1997).Google Scholar
  4. 4.
    S. I. Yakovlenko, Tech. Phys. 49, 1150 (2004).CrossRefGoogle Scholar
  5. 5.
    E. D. Lozanskii and O. B. Firsov, Spark Theory (Atomizdat, Moscow, 1975), Chap. 6–7.Google Scholar
  6. 6.
    P. A. Vitello, B. M. Penetrante, and J. N. Bartsley, Phys. Rev. E 49, 5574 (1994).ADSCrossRefGoogle Scholar
  7. 7.
    N. L. Aleksandrov and E. M. Bazelyan, J. Phys. D: Appl. Phys. 29, 740 (1996).ADSCrossRefGoogle Scholar
  8. 8.
    A. A. Kulikovsky, Phys. Rev. E 57, 7066 (1998).ADSCrossRefGoogle Scholar
  9. 9.
    N. Y. Babaeva and G. V. Naidis, J. Phys. D: Appl. Phys. 29, 2423 (1996).ADSCrossRefGoogle Scholar
  10. 10.
    N. Yu. Babaeva and G. V. Naidis, Tech. Phys. Lett. 25, 91 (1999).ADSCrossRefGoogle Scholar
  11. 11.
    M. Arrayas, U. Erbert, and W. Hundsdorfer, Phys. Rev. Lett. 7, 174 (2002).Google Scholar
  12. 12.
    I. Gallimberti, J. Phys. D: Appl. Phys. 5, 2179 (1972).ADSCrossRefGoogle Scholar
  13. 13.
    K. N. Schneider, Electra, No. 53, 31 (1977).Google Scholar
  14. 14.
    N. Goelian, P. Lalande, A. Bondiou-Clergerie, and G. L. Bacchiega, J. Phys. D: Appl. Phys. 30, 2441 (1997).ADSCrossRefGoogle Scholar
  15. 15.
    K. N. Schneider, IEE Proc. A 133 (7), 3 (1986).Google Scholar
  16. 16.
    A. Bondiou and I. Gallimberti, J. Phys. D: Appl. Phys. 27, 1252 (1994).ADSCrossRefGoogle Scholar
  17. 17.
    P. Ortega, in Proc. 7th Int. Symp. on High Voltage Engineering, Dresden, Germany, 1991, Ed. by W. Kleber (Dresden Univ., Dresden, 1991), p. 105.Google Scholar
  18. 18.
    J. Y. Won and P. F. Williams, J. Phys. D: Appl. Phys. 35, 205 (1972).Google Scholar
  19. 19.
    G. B. Whitham, Proc. R. Soc. London, Ser. A 203, 571 (1950).ADSCrossRefGoogle Scholar
  20. 20.
    G. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).zbMATHGoogle Scholar
  21. 21.
    V. A. Pavlov, J. Appl. Mech. Tech. Phys. 51, 800 (2010).ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Ya. B. Zel’dovich and A. S. Kompaneets, in Collected Volume Dedicated to the 70th Birthday of Academician A. F. Ioffe (Akad. Nauk SSSR, Moscow, 1950), p. 61.Google Scholar
  23. 23.
    G. I. Barenblatt, Prikl. Mat. Mekh. 16 (31), 67 (1952).Google Scholar
  24. 24.
    G. I. Barenblatt, Similarity, Self-Similarity, and Intermediate Asymptotics (Gidrometeoizdat, Leningrad, 1978), Chap. 2.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of PhysicsSt. Petersburg State UniversityPeterhof, St. PetersburgRussia

Personalised recommendations