Waves in an inhomogeneous plasma with Hall dispersion
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The evolution of steady-state periodic solutions of the Korteweg-de Vries equation (the socalled cnoidal waves), propagating along the direction of the gravitational force with an arbitrary orientation of the magnetic field, is studied for plasma characterized by Hall dispersion and Joule dissipation, using the magnetohydrodynamic approximation. The wavelength is regarded as much shorter than the characteristic scale of the inhomogeneity. The dependence of the wave amplitude on the distance to the source of the wave is considered for various limiting cases. The behavior of the wave depends on the temperature distribution in the medium. In the particular case of an isothermal atmosphere, the problem is solved analytically for a cold plasma in the absence of dissipation. The amplitude of both fast and slow waves increases when the wave travels upward and diminishes when the wave travels downward. The nonlinearity of the wave (i.e., the parameter characterizing the deviation of the wave from sinusoidal form) diminishes in the case of fast magnetoacoustic waves when the wave travels upward and increases when the wave travels downward. The situation is reversed for slow magnetoacoustic waves.
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- 1.L. A. Ostrovskii and N. R. Rubakha, “Nonlinear magnetic sound in a gravitational field”, Izv. Vyssh. Uchebn. Zaved., Radiofiz.,15, No. 9 (1972).Google Scholar
- 2.V. B. Baranov and M. S. Ruderman, “Waves in plasma with Hall dispersion”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3 (1974).Google Scholar
- 3.V. B. Baranov and M. S. Ruderman, “On waves in plasma with the Hall dispersion”, in: Rarefied Gas-dynamics, Proceedings of the Ninth International Symposium, Göttingen, 1974, Vol. 1, Porz-Wahn (1974).Google Scholar
- 4.V. I. Karpman, Long Waves in Dispersing Media [in Russian], Nauka, Moscow (1973).Google Scholar
- 5.L. A. Ostrovskii and E. N. Pelinovskii, “On approximate equations for waves in media with slight non-linearity and slight dispersion”, Prikl. Mat. Mekh.,38, No. 1 (1974).Google Scholar
- 6.M. S. Ruderman, “Method of obtaining the Korteweg-de Vries-Burgers equation”, Prikl. Mat. Mekh.,39, No. 4(1975).Google Scholar
- 7.L. A. Ostrovskii and E. N. Pelinovskii, “Nonlinear waves in inhomogeneous media with dispersion”, in: Problems on the Diffraction and Propagation of Waves [in Russian], No. 12, Izd. LGU, Leningrad (1973).Google Scholar
- 8.R. L. Wiegel, “A presentation of cnoidal wave theory for practical application”, J. Fluid Mech.,7, Pt. 2 (1960).Google Scholar
- 9.L. A. Ostrovskii and E. N. Pelinovskii, “Method of averaging and generalized variational principle for nonsinusoidal waves”, Prikl. Mat. Mekh.,36, No. 1 (1972).Google Scholar