Low-frequency electromagnetic instabilities caused by a rotating dust flow
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LowFrequency Electromagnetic Instabilities Caused by a Rotating Dust Flow V. V. Prudskikh Research Institute of Physics, Southern Federal University, pr. Stachki 194, RostovonDon, 344090 Russia Received April 9, 2010; in final form, May 31, 2010
Abstract—Lowfrequency electromagnetic waves propagating obliquely to an external magnetic field in a plasma with an anisotropic dust component are considered. The cold dust is assumed to have considerable longitudinal and transverse velocity components with respect to the magnetic field. A dispersion relation demonstrating that both fast and slow waves can be unstable is derived in the framework of kinetic theory. Mechanisms and consequences of these instabilities are discussed in the context of the problem of plasma transition into a turbulent state behind the shock front of a supernova. DOI: 10.1134/S1063780X10120044
1. INTRODUCTION In recent years, electromagnetic waves propagating in a complex (dusty) plasma have attracted consider able interest. The dynamic properties of dust substan tially affect the spectra of lowfrequency oscillations, resulting, in particular, in the occurrence of a new cut off frequency and a dust–ion hybrid resonance [1–7]. In most cases, the properties of waves have been stud ied as applied to objects with a relatively high mass density of the dust component, when the effect of “loading” of oscillations with dust plays an important role. It was shown in [8] that plasma modes are sub stantially modified in the presence of even a small admixture of dust (the mass fraction of dust in the interstellar medium is about 0.01–0.02), provided that the dust component rotates with a substantial velocity about magnetic field lines. Such conditions occur in space plasma behind the shock fronts of supernovas. After the dust passes the shock front propagating per pendicularly to the external magnetic field, it begins to rotate at a speed of about threequarters of the shock front velocity (for a strong shock wave) [9]. Due to the high inertia of the dust component, the characteristic time of dust motion is substantially longer than the thermal relaxation times of electrons and ions behind the shock front and the period of dust grain gyration [8]. Such a plasma medium can be described in the framework of kinetic theory. The distribution func tions of electrons and ions can be assumed to be Max wellian, while the velocity distribution of dust grains can be approximated by the Dirac delta function, because the thermal motion of dust grains is negligible as compared to the velocity of directed (longitudinal or transverse) dust motion. It should be noted that the propagation velocity of strong shock waves and, con sequently, the velocity of dust behind the shock front can substantially exceed the Alfvén velocity. Under
these conditions, the energy density associated with the dust motion can be on the order of the thermal and magnetic energy of the plasma, thereby contributing considerably to its dynamic characteristics even if the dust dens
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