A contribution to the theory of streamer breakdown

  • A. I. Zakharov
  • I. G. Persiantsev
  • V. D. Pis'mennyi
  • A. V. Rodin
  • A. N. Starostin


The development of a systematic theory of streamer breakdown of a gas requires the consideration of the transport of the region of ionization toward the ionized gas in an electric field depending on the form of the streamer, which in turn is determined by the transport mechanisms [1–3]. In this form the problem is very complicated,and the theory takes the path of investigation of different qualitative models of a streamer [4]. It is assumed in [4] that the rates of anode-directed and cathode-directed streamers are determined by the drift velocity of the electrons. The mechanism of propagation of anode-directed streamers is taken to be the development of avalanche from the leading front of the electrons traveling to the anode. On the side of the cathode, electrons before the front of the cathodedirected streamer are produced due to the transport of radiation from the ionized region [1]. It is shown in [5] that direct photo-ionization is ineffective because of the small range of the quantas, and a mechanism of development of cathode-directed streamer related to the associative ionization of excited atoms is proposed. These atoms are formed by long-span resonance photons from the wings of the spectral line. An interesting prediction of the theory [4] was a linear dependence of the velocity of the streamers on their length. This dependence was confirmed in experiments on the study of streamer breakdown initiated at the center of the discharge gap in spark chambers [6, 7]. At the same time, for streamers developing from avalanche initiated at one of the electrodes the velocity of propagation of the “breakdown wave” remains constant with a good accuracy in gaps having lengths of the order of 1 m. In the present work a qualitative theory is developed which permits one to calculate the velocity of the an ode-directed streamer in the case where it is independent of the length. Since for pressures of the order of atmospheric pressure the diffusion coefficient of excited atoms [8] is comparable with the electron diffusion coefficient, the effect of radiation transport is disregarded. The stability of the front of the streamer to infinitely small perturbations is investigated. It is shown that, when the finite thickness of the front is taken into consideration, the streamer is stable. It is unstable in the approximation of infinitely thin leading fronts.


Diffusion Coefficient Spectral Line Small Perturbation Transport Mechanism Small Range 
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Literature cited

  1. 1.
    L. Leb, Basic Processes of Electrical Discharges in Gases [in Russian], Gostekhizdat, Moscow (1950).Google Scholar
  2. 2.
    D. Meek and D. Craggs, Electrical Breakdown in Gases [Russian translation], IL, Moscow (1960).Google Scholar
  3. 3.
    G. Reter, Electron Avalanche in Gases [Russian translation], Mir, Moscow (1968).Google Scholar
  4. 4.
    É. D. Lozanskii and O. B. Firsov, “Qualitative theory of streamers,” Zh. Éksp. Teor. Fiz.,56, No. 2 (1969).Google Scholar
  5. 5.
    É. D. Lozanskii, “Natureof photoionizing radiation in streamer breakdown of a gas,” Zh. Tekhn. Fiz.,38, No. 9 (1968).Google Scholar
  6. 6.
    V. A. Davidenko, B. A. Dolgoshein, and S.V. Somov, “Experimental investigation of development of steamer breakdown in neon,” Zh. Éksp. Teor. Fiz.,55, No. 2 (1968).Google Scholar
  7. 7.
    N. S. Rudenko and V. I. Smetanin, “Investigation of development of streamer breakdown of neon in large gaps,” Zh.Éksp. Teor. Fiz.,61, No. 1 (1971).Google Scholar
  8. 8.
    V. I. Myshenkov and Yu. P. Raizer, “lonization wave propagating due to diffusion of resonance quanta and sustained by microwave radiation,” Zh.Éksp. Teor. Fiz.,61, No. 5 (1971).Google Scholar
  9. 9.
    E. P. Velikhov and A. M. Dykhne, Wave of Nonequilibrium lonization in Gas, Proc. VII Intern. Conf. on Phenomena in Ionized Gases, Belgrade, 1965.Google Scholar
  10. 10.
    Ya. B. Zel'dovich, “Theory of propagation of flames,” Zh. Fiz. Khim.,22, No. 1 (1948).Google Scholar
  11. 11.
    A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, “Investigation of diffusion equation associated with the increase of amount of matter and its application to a biological problem,” Byull. MGU, Sec. A,1, No. 6 (1937).Google Scholar
  12. 12.
    D. L. Turcotte and R. S. B. Ong, “The structure and propagation of ionizing wave fronts,” J. Plasma Phys.,2, No. 2 (1968).Google Scholar
  13. 13.
    N. W. Albright and D. A. Tidman, “Ionizing potential waves and high-voltage breakdown streamers,” Phys. Fluids,15, No. 1 (1972).Google Scholar
  14. 14.
    S. Brown, Elementary Processes in Gas Discharge Plasma [Russian translation], Atomizdat, Moscow (1961).Google Scholar
  15. 15.
    A. F. Volkov and Sh. M., Kogan, “Physical phenomena in semiconductors with negative differential conductivity,” Uspekhi Fiz. Nauk,96, No. 4 (1968).Google Scholar
  16. 16.
    G. I. Barenblatt and Ya. B. Zel'dovich, “On the stability of propagation of flames,” Prikl. Matern, i Mekhan.,21, No. 6 (1957).Google Scholar
  17. 17.
    L. D. Landau and E. M. Lifshits, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow-Leningrad (1954).Google Scholar
  18. 18.
    G. I. Barenblatt, Ya. B. Zel'dovich, and A. G. Istratov, “On thermal-diffusion stability of a laminar flame,” Zh. Prikl. Mekhan. Tekhn. Fiz., No. 4 (1962).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • A. I. Zakharov
    • 1
  • I. G. Persiantsev
    • 1
  • V. D. Pis'mennyi
    • 1
  • A. V. Rodin
    • 1
  • A. N. Starostin
    • 1
  1. 1.Moscow

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