The presence of the immobile charged dust in the plasma modifies the scale over which the Hall effect becomes important. For a positively charged dusty background this scale can become arbitrarily large. It is shown that the emergence of the Hall effect in an immobile charged background is related to the presence of an electric field that operates over the plasma gyration period. The generalized flux, which is a combination of the magnetic and fluid vortex flux, can decay due to the presence of the charge or the density inhomogeneities. The normal mode behavior of such a dusty plasma could be very different for positively and negatively charged grains. Whereas for negatively charged grains the usual magnetohydrodynamic (MHD) modes are present in the system, for positively charged grains, the Alfvén mode may not exist if Znd~ne, where Z is the charge of the dust and nd(ne) are the dust (electron) number densities. In the presence of the inhomogeneities, inertialess dusty plasma is subject to the Hall instability. It is shown that the growth rate of the Hall instability is proportional to the whistler frequency. Since Hall drift is nondissipative in nature, this instability can play important role in redistributing the magnetic energy from the large to small scales.
Copyright 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of plasmas, Vol. 13, Issue 12, pp.122106-1-122106-6 and may be found at http://link.aip.org/link/?php/13/122106.