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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v52.i12.10
pages 1-6

Problems of Evolution in Magnetohydrodynamics

Alevtina Alexandrovna Aleksandrova
Kharkov National University of Radio Engineering and Electronics, 14, Lenin Ave, Kharkov, 61166, Ukraine
Yu. N. Aleksandrov
Kharkov National University of Radio Engineering and Electronics, 14, Lenin Ave, Kharkov, 61166, Ukraine

RÉSUMÉ

We consider low-frequency oscillations that can be excited and propagate in plasma. We restrict our study to the case of sufficiently slow macroscopic processes. We need this assumption in order to use the hydrodynamic description of these processes, which, as well as the electromagnetic description of the field, is contained in the magnetohydrodynamics equations [1] for the velocity of the medium u(r, t), the strength of the magnetic field b(r, t), and the density of the medium ρ(r, t). In linear magnetohydrodynamics, a wave packet consists of characteristic waves of the following seven types: two accelerated magnetoacoustic, two decelerated magnetoacoustic, two Alfen, and one entropic waves. In Alfen waves, we have zero perturbations of medium density and entropy and of the components of the medium and the magnetic field that lie in the plane passing through the directions of the unperturbed magnetic field Bo and wave propagation. In magnetoacoustic waves, we have zero perturbations of the entropy and components of the medium and of the magnetic field that are perpendicular to the direction of wave propagation and to Bo. Hence magnetoacoustic waves are isoentropic and plane polarized. Finally, in the entropic wave, only the density and entropy are perturbed. The above wave packet is described by the state vector ψ, which, at each point M(x, y, z) in space and at each time instant t, can be determined by the domains of the initial and boundary conditions for these waves.