Transverse Instability of Dust Acoustic Solitary Waves in Magnetized Dusty Plasma composed of Vortex-like Distribution Ions

The dynamical behaviors of dusty plasma can be described by a (3+1)-dimensional modified Zakharov-Kuznetsov equation (mZKE) when the distribution of ions is vortex-like. The critical stable conditions for the line solitons are obtained by the linear stability analysis, which are also confirmed by the nonlinear dynamic evolution. An interesting phenomenon is found from the numerical results, maybe the first time, that the unstable line solitons of the mZKE will evolve into one or more completely localized soliton(s) after a long time evolution. Subsequently, we numerically studied the collision process of two line solitons. The results show that two stable line solitons can restore to their original states. However, if one of the two solitons or both of them are unstable, one or more completely localized solitons will appear during the collision. The results indicate that there are both elastic and inelastic collisions between line solitons.

Dissipative electrostatic wave modulation in warm multi-ion dusty plasmas with superthermal electrons

A theoretical investigation has been carried out to explore the modulational instability (MI) of electrostatic waves in a warm multi-ion dusty plasma system containing positive ions, negative ions and positively or negatively charged dust in presence of superthermal electrons. With the help of the standard perturbation technique, it is found that the dynamics of the modulated wave is governed by a damped nonlinear Schrödinger equation (NLSE). Regions of MI of the electrostatic wave are precisely determined and the analytical solutions predict the formation of dissipative bright and dark solitons as well as dissipative first- and second-order rogue wave solutions. It is found that the striking features (viz., instability criteria, amplitude and width of rogue waves, etc.) are significantly modified by the effects of relevant plasma parameters such as degree of the electron superthermality, dust density, etc. The time dependent numerical simulations of the damped NLSE reveal that modulated electrostatic waves exhibit breather like structures. Moreover, phase plane analysis has been performed to study the dynamical behaviors of NLSE by using the theory of dynamical system. It is remarked that outcome of present study may provide physical insight into understanding the generation of several types of nonlinear structures in dusty plasma environments, where superthermal electrons, positive and negative ions are accountable (e.g. Saturn’s magnetosphere, auroral zone, etc.).

Quantitative simulations of ratchet potential in a dusty plasma ratchet

Using a dusty plasma ratchet, one can realize the rectification of charged dust particle in a plasma. To obtain the ratchet potential dominating the rectification, here, we perform quantitative simulations based on a two-dimensional fluid model of capacitively coupled plasma. Plasma parameters are firstly calculated in two typical cross sections of the dusty plasma ratchet which cut vertically the saw channel at different azimuthal positions. The balance positions of charged dust particle in the two cross sections then can be found exactly. The electric potentials at the two balance positions have different values. Using interpolation in term of a double-sine function from previous experimental measurement, an asymmetrical ratchet potential along the saw channel is finally obtained. The asymmetrical orientation of the ratchet potential depends on discharge conditions. Quantitative simulations further reproduce our previous experimental phenomena such as the rectification of dust particle in the dusty plasma ratchet.

Propagation of dust-acoustic nonlinear waves in a homogeneous collisional dusty plasma

Nonlinear propagation of dust-acoustic waves DAWs in a weakly collisional dusty plasma comprising warm adiabatic fluid dust particles, isothermal electrons, and ions is investigated. We used the reductive perturbation theory to reduce the basic set of fluid equations to one evolution equation, namely damped Kadomtsev--Petviashivili (DKP). The analytical stationary solutions of the DKP equation are numerically analyzed, and the effect of various dusty plasma parameters on DAWs wave propagation is taken into account. We obtained, blast, anti-kink, periodic cnoidal and cnoidal waves. It is well known that explosive waves are a double edged sword. They can be seen, for example, in the atmosphere, or in engineering applications in metal coating. _______________________________________________