Skip to main content
Log in

Gas-dynamic approach in the nonlinear theory of ion acoustic waves in a plasma: An exact solution

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

An exact solution of the problem of the acoustic wave structure in a plasma is obtained. Both plasma component are treated as gases with specified initial temperatures and adiabatic exponents. The system of equations describing the wave profile is solved using an original method consisting of reducing the system to the Bernoulli equation. A numerical example of the obtained general solution of the problem of the wave profile for arbitrary parameters is given. Curves are constructed that bound the region of existence of a stationary solitary ion acoustic wave in the parameter space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. A. Vedenov, E. P. Velikhov, and R. Z. Sagdeev, “Nonlinear vibrations of a rarefield plasma,” Yadern. Sintez, 1, 82–100 (1961).

    Google Scholar 

  2. R. Z. Sagdeev, “Collective processes and shock waves in a rarefield plasma,” in: Questions of Plasma Theory [in Russian], No. 4, Atomizdat, Moscow (1964), pp. 20–187.

    Google Scholar 

  3. A. E. Dubinov and I. D. Dubinova, “How can one solve exactly some problems in plasma theory,” J. Plasma Phys., 71, No. 5, 715–728 (2005).

    Article  ADS  Google Scholar 

  4. I. D. Dubinova, “Theory of nonlinear ion acoustic waves in a plasma with the inertia of electrons taken into account,” Vopr. Atom. Nauki Tekh., Ser. Teor. Prikl. Fiz., 3, 18–23 (2005).

    Google Scholar 

  5. J. F. McKenzie, “The ion-acoustic soliton: A gas-dynamic viewpoint,” Phys. Plasma, 9, No. 3, 800–805 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  6. J. F. McKenzie, F. Verheest, T. B. Doyle, and M. A. Hellberg, “Compressive and rarefactive ion-acoustic solitons in bi-ion plasmas,” Phys. Plasma, 11, No. 5, 1762–1769 (2004).

    Article  ADS  Google Scholar 

  7. J. F. McKenzie, T. B. Doyle, M. A. Hellberg, and F. Verheest, “Compressive and rarefactive ion-acoustic solitons in a two component electron plasma,” J. Plasma Phys., 71, No. 2, 163–176 (2005).

    Article  ADS  Google Scholar 

  8. S. Maitra and R. Roychoudhury, “Gas dynamical approach to study dust acoustic solitary waves,” Phys. Plasma, 12, No. 6, 064502?1–064502?4 (2005).

    Google Scholar 

  9. Ch. Sack and H. Schamel, “Evolution of a plasma expanding into vacuum,” Plasma Phys. Control. Fusion, 27, No. 7, 717–749 (1985).

    Article  ADS  Google Scholar 

  10. C. R. Johnston and M. Epstein, “On the exact amplitude, velocity and shape of ion-acoustic waves,” Phys. Plasma, 7, No. 3, 906–910 (2000).

    Article  ADS  Google Scholar 

  11. M. Ya. Ivanov, “On analysis of ion solitons in a plasma without a magnetic field,” Fiz. Plazmy, 8, No. 2, 384–389 (1982).

    Google Scholar 

  12. M. Ya. Ivanov, “One class of soliton solutions of the hydrodynamic equations of motion of ions in a homogeneous plasma in the absence of external fields,” Fiz. Plazmy, 8, No. 3, 607–612 (1982).

    Google Scholar 

  13. A. E. Dubinov, “Theory of nonlinear waves of a spatial charge in neutralized electron flows: A gas-dynamic approach,” Fiz. Plazmy, 33, No. 3, 239–246 (2007).

    Google Scholar 

  14. A. I. Akhiezer, I. A. Akhiezer, and R. V. Polovon, Plasma Electrodynamics [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  15. V. F. Zaitsev and A. D. Polyanin, Handbook on Ordinary Differential Equations [in Russian], Fizmatlit, Moscow (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 3–11, September–October, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dubinov, A.E. Gas-dynamic approach in the nonlinear theory of ion acoustic waves in a plasma: An exact solution. J Appl Mech Tech Phys 48, 621–628 (2007). https://doi.org/10.1007/s10808-007-0078-8

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10808-007-0078-8

Key words

Navigation