The dust charging processes in the collections of electrons and ions in the nonequilibrium dusty plasma with power-law distributions are investigated on the basic of a new q-distribution function theory in nonextensive statistics. Electrons and ions obey the power-law distributions and are with q-parameters different from each other. We derive the generalized formulae for the dust charging currents in which the nonextensive effects play roles. Further we investigate the dust charging processes taking place in the homogeneous dusty plasma where only the particle velocities are power-law distributions and in the dust cloud plasma where the particle velocities and densities are both power-law distributions. By numerical analyses, we show that the nonextensive power-law distributions of electrons and ions have significant effects on the dust charging processes in the nonequilibrium dusty plasma.

The dust-acoustic waves and their stability driven by a flowing dusty plasma when it cross through a static (target) dusty plasma (the so-called permeating dusty plasma) are investigated when the components of the dusty plasma obey the power-law q-distributions in nonextensive statistics. The frequency, the growth rate and the stability condition of the dust-acoustic waves are derived under this physical situation, which express the effects of the nonextensivity as well as the flowing dusty plasma velocity on the dust-acoustic waves in this dusty plasma. The numerical results illustrate some new characteristics of the dust-acoustic waves, which are different from those in the permeating dusty plasma when the plasma components are the Maxwellian distribution. In addition, we show that the flowing dusty plasma velocity has a significant effect on the dust-acoustic waves in the permeating dusty plasma with the power-law q-distribution.

We study the secondary electron emissions induced by the impact of electrons on dust grains and the resulting dust charging processes in the nonequilibrium dusty plasma with power-law distributions. We derive new expressions of the secondary emitted electron flux and the dust charging currents that are generalized by the power-law q-distributions, where the nonlinear core functions are numerically studied for the nonextensive parameter q. Our numerical analyses show that the power-law q-distribution of the primary electrons has a significant effect on the secondary emitted electron flux as well as the dust charging currents, and this effect depends strongly on the ratio of the electrostatic potential energy of the primary electrons at the dust grain's surface to the thermodynamic energy, implying that a competition in the dusty plasma between these two energies plays a crucial role in this novel effect. a)

The dust-acoustic waves and their stability in the permeating dusty plasma with the Maxwellian velocity distribution are investigated. We derive the dust-acoustic wave frequency and instability growth rate in two limiting physical cases that the thermal velocity of the flowing dusty plasma is (a) much larger than, and (b) much smaller than the phase velocity of the waves. We find that the stability of the waves depend strongly on the velocity of the flowing dusty plasma in the permeating dusty plasma. The numerical analyses are made based on the example that a cometary plasma tail is passing through the interplanetary space plasma. We show that, in case (a), the waves are generally unstable for any flowing velocity, but in case (b), the waves become unstable only when the wave number is small and the flowing velocity is large. When the physical conditions are between these two limiting cases, we gain a strong insight into the dependence of the stability criterions on the physical conditions in the permeating dusty plasma. a) Corresponding