Electromagnetic waves in a polydisperse dusty plasma

The properties of low-frequency electromagnetic waves in a polydisperse dusty plasma are studied. The dispersion relation for the waves propagating at an arbitrary angle to the external magnetic field is derived, with the coefficients explicitly determined by the dust-size distribution function. The dependence of wave dispersion on properties of the dust-size distribution function is analysed. It is shown that the cutoff for an oblique propagation in plasma with a wide scatter of dust sizes takes place at a much lower frequency than in a plasma with monosized dust particles. It is found that dispersion properties of a transversal magnetosonic wave mode around dust-cyclotron frequencies considerably differ from those in a plasma with monosized dust. In a plasma with low mass fraction of dust particles, the dispersion is smooth without the cutoff and the resonance intrinsic for a plasma with monosized dust. Increase of the dust fraction results in splitting of the dispersion curve on to two branches. Further increase of the dust fraction leads to emergence of the third branch located between the cutoffs and restricted from the lower and higher frequencies by two resonances. The dependence of the frequencies of cutoffs and resonances on the width of the dust-size distribution, its slope and the dust mass fraction are analysed. It is shown that the transparency frequency windows in a plasma with polydisperse dust are wider for transversal elecromagnetic waves, but narrower for longitudinal or oblique waves. (C) 2013 AIP Publishing LLC.