In plasmas with electron drift (current) relative to static ions, the ion acoustic wave is subject to the kinetic instability which takes place if the directed electron speed exceeds the ion acoustic speed. The instability threshold becomes different in the case of one quasi-neutral electron-ion plasma propagating through another static quasineutral (target) plasma. The threshold velocity of the propagating plasma may be well below the ion acoustic speed of the static plasma. Such a current-less instability may frequently be expected in space and astrophysical plasmas.

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The effects of nonsteady dust charge variations and weak magnetic field on small but finite amplitude nonlinear dust acoustic wave in electronegative dusty plasma are investigated. The dynamics of the nonlinear wave are governed by a Korteweg–de Vries Burger equation that possesses dispersive shock wave. The weak magnetic field is responsible for the dispersive term, whereas nonsteady dust charge variation is responsible for dissipative term, i.e., the Burger term. The coefficient of dissipative term depends only on the obliqueness of the magnetic field. It is found that for parallel propagation the dynamics of the nonlinear wave are governed by the Burger equation that possesses monotonic shock wave. The relevances of the findings to cometary dusty plasma, e.g., Comet Halley are briefly discussed.

The problem of nonlinear Landau damping of helicon waves in dusty plasma in particular emphasis to the acceleration of soliton is presented here. This in the framework of a collisionless, anisotropic homogeneous dusty plasma in one dimension, can be well described by two coupled dynamical equations of the generalized Zakharov type, with one extra nonlocal term coming from Landau damping. Nonlinear-nonlocal term gives rise to essential contributions relative to the local term. Then under different conditions, kinetic nonlinear Schrödinger equation is constructed and nonlinear decrement is obtained for two cases. It is noticed that the time dependant term in the ponderomotive force plays a significant role for this kind of damping. Additionally, it is shown that nonlinear Landau damping leads to the amplitude modulation of dust helicon waves, further modulational instability, and maximal growth rate is obtained when the group velocity of the helicon wave reaches the dust-acoustic speed. It is demonstrated that how the nonlinear Landau damping leads to the acceleration of soliton, which is eventually slowed down after transferring some of its energy to the wave. Emission of dust-acoustic wave by accelerated soliton is discussed briefly.

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Nonlinear screening of the dust grains immersed in a homogenous fully ionized electron-ion plasma is investigated. Assuming conservation of entropy, an important relation is obtained between the maximum potential (and therefore the charge) of the dust grain and the temperature of the electrons. The Thomas-Fermi equation is derived for the potential of a dust grain in a nondegenerate plasma suggesting the existence of dust atom with a well defined atomic radius. Furthermore, based on the Born-Oppenheimer approximation, the notion of a dust-grain molecule is introduced in which the protons act like a kind of “glue” which binds two negatively charged dust grains together, and the motion of the grains have little influence on that binding force. Finally, considering the weak interaction between the proton clouds of two dust grains, an expression of exchange energy is obtained.

Positive and negative ions forming so-called pair plasma differing in sign of their charge but asymmetric in mass and temperature support a new acoustic-ike mode. The condition for the excitation of ion sound wave through electron beam induced Cherenkov instability is also investigated. This beam can generate a perturbation in the pair ion plasmas in the presence of electrons when there is number density, temperature and mass difference in the two species of ions. Basic emphasis is on the focusing of ion sound waves and we show how, in the area of localization of wave energy, the density of pair particles increases while electrons are pushed away from that region.Further, this localization of wave is dependent on the shape of the pulse. Considering the example of pancake and bullet shaped pulses, we find that only the former leads to compression of pair ions in the supersonic regime of the focusing region. Here possible existence of regions where pure pair particles can exist may also be speculated which is not only useful from academic point of view but also to mimic the situation of plasma (electron positron asymmetric and symmetric ) observed in astrophysical environment.

The propagation pattern of electromagnetic waves (EMWs) in dusty plasmas is quite different from that in electron-ion plasmas. For instance, here the ponderomotive force acts on dust grains as a negative pressure, and a nonlinear Schrödinger equation with an additional nonlinear term is obtained. Based on this equation, the modulation instability is examined and it is shown that the growth rate becomes maximum when that additional term compensates the diffraction term. The main part of this work is devoted to the localization of the grains by the EMW. Considering both subsonic and supersonic regimes, it has been shown that under certain conditions the grains are localized and the ions circumnavigate the grains, whereas the electrons escape from the region of localization. Further, the localization of grains by the EMW is found to be shape-dependent of the pulse. Comparing pancake and light bullet shaped pulses in the supersonic regime, and it is shown that only the light bullet shape leads to the compression of grains. Finally, investigating nonstationary solution, it is shown that for some parameters, the nonlinear wave breaking and the formation of a shock wave can take place.