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.
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References
A. A. Vedenov, E. P. Velikhov, and R. Z. Sagdeev, “Nonlinear vibrations of a rarefield plasma,” Yadern. Sintez, 1, 82–100 (1961).
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.
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).
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).
J. F. McKenzie, “The ion-acoustic soliton: A gas-dynamic viewpoint,” Phys. Plasma, 9, No. 3, 800–805 (2002).
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).
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).
S. Maitra and R. Roychoudhury, “Gas dynamical approach to study dust acoustic solitary waves,” Phys. Plasma, 12, No. 6, 064502?1–064502?4 (2005).
Ch. Sack and H. Schamel, “Evolution of a plasma expanding into vacuum,” Plasma Phys. Control. Fusion, 27, No. 7, 717–749 (1985).
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).
M. Ya. Ivanov, “On analysis of ion solitons in a plasma without a magnetic field,” Fiz. Plazmy, 8, No. 2, 384–389 (1982).
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).
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).
A. I. Akhiezer, I. A. Akhiezer, and R. V. Polovon, Plasma Electrodynamics [in Russian], Nauka, Moscow (1974).
V. F. Zaitsev and A. D. Polyanin, Handbook on Ordinary Differential Equations [in Russian], Fizmatlit, Moscow (2001).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 3–11, September–October, 2007.
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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
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DOI: https://doi.org/10.1007/s10808-007-0078-8