The existence of Bernstein–Greene–Kruskal (BGK)-like trapped ion modes in dusty plasmas is investigated by means of the pseudo-potential method applied to the Vlasov–Poisson system. The nonlinear dispersion relation, determining the phase velocity, and the pseudo-potential, representing the wave form and hence its spectral decomposition, are derived and analysed with respect to the effect of dust. Dust is found to diminish the region in ω, k-space, where periodic wave solutions of fast and slow mode character exist. Localized wave solutions in the form of solitary ion holes, owing their existence to the presence of dust, coexist as well, but turn into slow ion acoustic double layers in the limit of vanishing dust.

The existence of localized ion waves in a dense quantum plasma is established. Specifically, ion solitary waves are stationary solutions of the equations composed of the nonlinear ion continuity and ion momentum equations, together with the Poisson equation and the inertialess electron momentum equation in which the electric force is balanced by the quantum force associated with the Bohm potential that causes electron tunneling at nanoscales. The solitary ion waves are characterized by a large-amplitude electrostatic potential and ion density maxima and smaller amplitude minima on the flanks of the solitary waves. We identify the speed interval for the existence of the ion solitary waves around a quantum Mach number that is of the order of unity.

Nonlinear quantum Hall-MHD equations for a warm dense magnetoplasma with an anisotropic electron pressure are derived. The nonlinear equations include the quantum force associated with electron tunneling effects. The newly found equations can be used to investigate the dense plasma stability, as well as different types of waves, instabilities, and nonlinear structures in a warm dense magnetoplasma.

The quantum effect on the Weibel instability in an unmagnetized plasma is presented. Our analysis shows that the quantum effect tends to stabilize the Weibel instability in the hydrodynamic regime, whereas it produces a new oscillatory instability in the kinetic regime. A novel effect called the quantum damping, which is associated with the Landau damping, is disclosed. The new quantum Weibel instability may be responsible for the generation of non-stationary magnetic fields in compact astrophysical objects as well as in the forthcoming intense laser–solid density plasma interaction experiments.

The nonlinear coupling between high-frequency surface plasmons (SPs) and low-frequency ion oscillations on metallic plasma surfaces with charged nanoparticles is considered. It is shown that a finite-amplitude SP wave is modulationally unstable against the excitation of non-resonant ion oscillations. The growth rates and thresholds of the modulational instabilities are presented.

It is shown that a nonlinear surface plasma wave at a plasma–vacuum interface can propagate in the form of a dark/grey envelope soliton. The latter is associated with a subsonic density cavity, which traps the complex surface wave electric field.

In this work we show that a repulsive force between nearby dust grains in a plasma can exist, due to scattering of the incident radiation. Two types of forces are discussed, one of them being formally identical to electrostatic repulsion. This leads to the definition of an effective dust charge of the dust grain, which only depends on the scattering process. Our discussion shows that such a repulsive interaction occurs in quite general physical conditions.

The equivalent charge of photons in dense unmagnetized and magnetized Fermi plasmas is determined through the plasma physics method. This charge is associated with the polarization of the medium caused by the ponderomotive force of the electromagnetic waves. Relations for the coupling between the electron plasma density perturbation and the radiation fields are derived for unmagnetized and magnetized plasmas, taking into account the quantum force associated with the quantum Bohm potential in dense Fermi plasmas. The effective photon charge is then determined. The effects of the ion motion are also included in the investigation.

It is shown that purely growing magnetic fields in a two-component dusty plasma can e generated due to the equilibrium drift of positive and negative dust grains. For this purpose, a linear dispersion relation has been derived by using the hydrodynamic equations for the charged dust fluids, the Maxwell equation and Faraday' law. The dispersion relation admits a purely growing instability, the growth rate of which is proportional to the equilibrium streaming speeds of positive and negative dust grains. A possible physical explanation for the instability is offered. Applications of our investigation to magnetic fields in the thin Martian environments, interplanetary spaces and dense molecular clouds are mentioned.

We consider a kinetic modulational instability of broadband (random phase) magnetic-field-aligned circularly polarized dispersive Alfvén waves in plasmas. By treating random phase Alfvén waves as quasi-particles, we consider their nonlinear interactions with ion quasi-modes within the framework of the wave-kinetic and Vlasov descriptions. A nonlinear dispersion relation governing such interactions is derived and analyzed. An explicit expression for the kinetic modulational instability growth rate is presented. Our results can be of relevance to the nonlinear propagation of incoherent Alfvén waves, which have been frequently observed in interstellar media, in the solar corona and in the solar wind, as well as in the foreshock regions of planetary bow-shocks and laboratory plasmas.

An improvement of an existing three-dimensional analytical model describing the solar wind flow near a reconnection site at the dayside magnetopause is reported. Introducing an arbitrary orientation of the reconnection line, general solutions for the plasma velocity and magnetic field during the transition of the magnetopause are presented, together with the development of the magnetopause transition layer away from the reconnection site.

The resonant coupling between Alfvén waves is reconsidered. New results are found for cold magnetoplasmas where temperature effects are negligible.

We consider the nonlinear interactions between upper-hybrid (UH) and Alfvén modes in a magnetized electron–ion plasma containing a fraction of stationary charged dust grains. The interaction is governed by a pair of equations for the UH wave envelope including the relativistic electron mass increase and the density and compressional magnetic field fluctuations associated with the Alfvén modes that are, in turn, driven by the ponderomotive force of the UH waves. The coupled mode equations are then Fourier analyzed to obtain a new dispersion relation, which admits new classes of modulational instabilities. The existence of a cusp-shaped UH envelope soliton is also predicted. The result can have relevance to the electron acceleration by sharply localized UH waves in the dusty magnetosphere of Saturn.

In a recent study [1] the effect of ionization and losses on the propagation of ion acoustic solitary waves is investigated. For that purpose the corresponding source and sink terms of the form $$\begin{equation} Q_{\rm i}- \nu_{\rm L}n_{\rm i}, \label{ss}\end{equation}$$ are included in the right-hand side of the ion continuity equation. The related contribution of the source–sink effects in the ion momentum equation is then given as the above source–sink term multiplied by the ion velocity, so that the ion momentum equation used in [1]becomes $$\begin{equation}n_{\rm i} \biggl(\frac{\partial v_{\rm i}}{\partial t} + v_{\rm i}\frac{\partial v_{\rm i}}{\partial x}\biggr)= - n_{\rm i}\frac{\partial \phi}{\partial x} - \sigma_{\rm i} \frac{\partial n_{\rm i}}{\partial x} - \nu_{\rm i} n_{\rm i} v_{\rm i} - (Q_{\rm i}- \nu_{\rm L} n_{\rm i}) v_{\rm i}.\end{equation}$$ The objective of this Comment is to show that the last term in (2) cancels out exactly, as will be shown in the further text, so that any effect originating from this term is spurious. In addition, this term implies that the velocity of the neutrals that become ions, before the impact ionization (or whatever the cause of its ionization may be), is equal to the velocity of ions that become neutrals, since this source–sink term is multiplied by the same velocity. A similar improper model has been used previously in the literature (see the references cited in [1]). It is remarked that the proper inclusion of the source–sink effects has been described in the literature before, although it seems to remain unnoticed. Therefore, it is timely to address this issue in order to provide a formally correct model for future studies.

The main objective of the Comment made by J. Vranjes et al. is that the source–sink approach in studying physical phenomena, such as the ionization instability, is suspect. Also the term $(Q_{\rm i}-\nu_{\rm L} n_{\rm i})v_{\rm i}$ in the ion momentum conservation equation of the source–sink model used by [1] is improper.

This issue of the Journal of Plasma Physics is dedicated to Radu Balescu on the occasion of his 65th birthday.

Of the more than 170 articles published worldwide by Professor Balescu to date, more than 25 have been published in this journal. Readers of the Journal of Plasma Physics will thus be well acquainted with his contributions to the study of the interplay between plasma turbulence and the theory of transport phenomena in magnetically confined plasmas. A vast community of students, teachers and researchers will also have read or consulted the many monographs, five to date, written by Balescu and world-famous for their clarity. In his first monograph, Statistical Mechanics of Charged Particles (Interscience, New York), published in 1963, the whole of plasma physics, including the transport equation to which his name will remain attached, was put into the broader context of statistical physics. The monograph Equilibrium and Non-Equilibrium Statistical Mechanics (Wiley-Interscience, New York) followed in 1975, and still inspires many teachers today.