Splitting of the modes of a low-frequency magnetosonic wave in a polydisperse dusty plasma
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Splitting of the Modes of a LowFrequency Magnetosonic Wave in a Polydisperse Dusty Plasma V. V. Prudskikh Research Institute of Physics, Southern Federal University, pr. Stachki 194, RostovonDon, 344090 Russia Received April 9, 2010
Abstract—The properties of magnetosonic waves that propagate perpendicularly to the external magnetic field in a polydisperse dusty plasma and the frequencies of which are about the dust cyclotron frequency are analyzed. A dispersion relation containing integrals of functions of the dust grain radius is derived and inves tigated as a function of the parameters characterizing the polydisperse properties of dust. It is found that, in a polydisperse dusty plasma, the lowfrequency magnetosonic mode splits into two branches. The first, lower frequency branch has a cutoff, while the higher frequency branch has a resonance. Between the two branches, there is a forbidden frequency range within which electromagnetic waves cannot propagate perpendicular to the magnetic field. The width of the forbidden frequency range is determined as a function of the slope of the distribution function of dust grains over radii and the interval within which the dust grain radii lie. DOI: 10.1134/S1063780X10120032
1. INTRODUCTION Charged dust grains substantially affect the proper ties of electromagnetic modes in a magnetized plasma. Immovable dust grains produce a charged back ground, which modifies the electromagnetic spectra, whereas the dust dynamics, which plays a significant role at frequencies much lower than the ion gyrofre quency, gives rise to new plasma modes [1–5], includ ing dust Alfvén waves, dust magnetosonic waves, and dust whistlers. In many laboratory experiments and astrophysical objects (such as comets tails, planetary rings, and molecular clouds), the mass density of dust substantially exceeds that of the ion component. The properties of lowfrequency hydromagnetic waves with frequencies lower or about the dust grain gyrofre quency are mainly determined by the parameters and dynamics of the dust component, whereas the plasma electrons and ions contribute only via their drift under the action of the external magnetic field and the elec tric field of the wave. In this case, the inertia forces acting on the electrons are much weaker than the Lorentz forces and can thus be ignored. The properties of magnetosonic waves in dusty plasma were studied in many papers (see, e.g., [3, 4, 6]). In particular, it was shown that, in the presence of dust, a magnetosonic wave propagating perpendicular to the external magnetic field splits into the lower and higher frequency modes. The frequency of the former is lower than the ion–dust hybrid frequency, whereas the latter can exist in the frequency range between the dust cutoff frequency (which is zero in the absence of dust) and the electron–ion hybrid frequency. On the other hand, it was reported in [7] that dust magneto sonic waves propagating perpendicular to the external
magnetic field in a plasma containing two kinds of dust grains
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