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We study the dispersion relation for parallel propagating ion-cyclotron (IC)waves in a dusty plasma, considering situations where the velocity dispersionalong perpendicular direction is greater than along the parallel direction, andconsidering the use of product-bi-kappa (PBK) velocity distributions for theplasma particles. The results obtained by numerical solution of the dispersionrelation, in a case with isotropic Maxwellian distributions for electrons andPBK distribution for ions, show the occurrence of the electromagneticion-cyclotron instability (EMIC), and show that the decrease in the kappaindexes of the PBK ion distribution leads to significant increase in themagnitude of the growth rates and in the range of wavenumber for which theinstability occurs. On the other hand, for anisotropic Maxwellian distributionfor ions and PBK distribution for electrons, the decrease of the kappa index inthe PBK electron distribution contributes to reduce the growth rate of the EMICinstability, but the reduction effect is less pronounced than the increaseobtained with ion PBK distribution with the same $\kappa$ index. The resultsobtained also show that, as a general rule, the presence of a dust populationcontributes to reduce the instability in magnitude of the growth rates andrange, but that in the case of PBK ion distribution with small kappa indexesthe instability may continue to occur for dust populations which wouldeliminate completely the instability in the case of bi-Maxwellian iondistributions. It has also been seen that the anisotropy due to the kappaindexes in the ion PBK distribution is not so efficient in producing the EMICinstability as the ratio of perpendicular and parallel ion temperatures, forequivalent value of the effective temperature.

Electromagnetic ion-cyclotron instability in a dusty plasma with product-bi-kappa distributions for the plasma particles