Synchronization mechanism and Arnold tongues for dust density waves

The nonlinear phenomenon of synchronization is characterized experimentally for dust density waves, i.e., dust acoustic waves, which are self-excited due to an ion streaming instability. The waves propagate in a dust cloud with a natural frequency of 22 Hz. We synchronize these waves to a different frequency using a driving electrode that sinusoidally modulates the ion density. We study four synchronized states, with frequencies that are multiples of 1, 2, 3, and 1/2 of the driving frequency. Comparing to phenomena that are typical of the van der Pol paradigm, we find that synchronization of our waves exhibit the signature of the suppression mechanism but not that of the phaselocking mechanism. Additionally, synchronization of our waves exhibits three characteristics that differ from the van der Pol paradigm: a threshold amplitude that can be seen in the Arnold tongue diagram, a branching of the 1:1 harmonic tongue at its lower extremity, and a nonharmonic state. The latter state appears to be a nonlinear oscillation; it is neither at the natural frequency nor a synchronized state.

Ion temperature gradient instability in a dusty plasma

An analysis of the temperature-gradient-driven ( eta(i) ) instability of drift waves in dusty plasma is presented. Various limits that allow for the coupling of the drift wave with the dynamics of dust grains are discussed. In particular, the cases of tiny (magnetized) and relatively heavy (unmagnetized) grains are studied. It is shown that in both limits the behavior of the eta(i) mode is considerably affected by the dust dynamics. The growth rate turns out to be higher in the presence of dust, and the instability threshold is lower, resulting in a more unstable plasma.

Effects of dust charge fluctuations on current-driven dust-ion-acoustic waves

The effects of fluctuating grain charge on current-driven dust-ion-acoustic modes are investigated in the presence of various physical parameters which are varied in order to describe the behavior of the mode in detail. Variation of the charge clearly influences the ion-acoustic mode by changing of its frequency and growth rate. We report here the existence of a dust charge fluctuation mode in the system, and it is shown that the mode is unstable for a negative charge on the dust per unit volume not exceeding some critical value.

Kinetic approach to low-frequency waves in dusty self-gravitating plasmas

A kinetic model is derived for the propagation of low-frequency waves in a dusty plasma containing very heavy dust particles, when the self-gravitational interaction due to these grains is included in the analysis. Analytical expressions for the dispersion function are used to examine the instability and damping of the modes. The stability regions of low-frequency waves are compared in the kinetic and the analogous hydrodynamic models, showing that there are only slight differences. However, the kinetic analysis modifies the growth rates of the Jeans instability and can considerably alter the conditions for the propagation of stable dust modes.