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.

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.

An electronic identity relation, relating capacitively coupled plasma sources to corresponding inductively coupled plasma sources, has been derived, starting from the Maxwell relations for matter and the characteristics of a capacitor and of an inductor. Furthermore, the breakdown conditions for both capacitively coupled plasmas and for inductively coupled plasmas as well as their optimal operation frequency ranges are discussed.

A combined Schamel's modified Korteweg–de Vries–Zakharov– Kuznetsov (S–KdV–ZK) equation efficiently describes the nonlinear behaviour of ion-acoustic waves in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons as prescribed by Cairns et al. (1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712), i.e. when the contribution of trapped electrons tends to zero. This combined S–KdV–ZK equation admits a double-layer solution propagating obliquely to the external uniform and static magnetic field. The condition for the existence of this double-layer solution has been derived. The three-dimensional stabilities of the double-layer solutions propagating obliquely to the external uniform and static magnetic field have been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands (1993 Determination of growth rate for linearized Zakharov–Kuznetsov equation. J. Plasma Phys. 50, 413–424; 1995 Stability obliquely propagating plane solitons of the Zakharov–Kuznetsov equation. J. Plasma Phys. 53, 63–73). It is found that the double-layer solutions of the combined S–KdV–ZK equation are stable at the lowest order, i.e. up to the order k, where k is the wave number of perturbation.

The operation of a free-electron laser (FEL) with electromagnetic wave wiggler in the presence of an ion-channel guiding as well as an axial guide magnetic field is considered and compared. Theoretical studies of electron trajectories and dispersion relations in a combined ion electrostatic field as well as large-amplitude backward-propagating electromagnetic waves are analyzed. The large-amplitude wave acts like a magnetostatic wiggler in a FEL. The results of a numerical study are presented and discussed. It is shown that in the wiggler pumped ion-channel free-electron laser (WPIC-FEL), electron orbits and dispersion relation are time-dependent, and over time, electron orbits while oscillating bear a periodic motion.

A quantum magnetohydrodynamic model is used to investigate the nonlinear propagation of dust ion-acoustic waves in a three-component quantum plasma composed of electrons, positively charged ions and immobile charged dust grains. Using the standard reductive perturbation technique, a Korteweg–de Vries equation is derived containing the quantum statistical and diffraction effects. There exists a critical value of the non-dimensional parameter H, proportional to the quantum diffraction, beyond which the bright soliton propagation is not possible with positive phase velocity. The effects of obliqueness, charged dust impurity and external magnetic field as well as the quantum mechanical effects are investigated numerically on the profiles of the amplitude and width of the solitary waves.

The width of a quasi-perpendicular collisionless shock front is smaller than the convective ion gyroradius so that ions become demagnetized in the ramp. An approach is proposed for derivation of approximate expressions for the magnetic compression ratio and cross-shock potential from the analysis of the ion motion across the ramp and pressure balance condition, without making assumptions about the ion equation of state. The cross-shock potential and magnetic compression ratio are found as functions of the Mach number for low-Mach-number perpendicular shocks.

Reconnection physics at micro-scales is investigated in an electron magnetohydrodynamics frame. A new process of collapse of the neutral current sheet is demonstrated by means of analytical and numerical solutions. It shows how at scales smaller than ion inertia length a compression of the sheet triggers an explosive evolution of current perturbation. Collapse results in the formation of a intense sub-sheet and then an X-point structure embedded into the equilibrium sheet. Hall currents associated with this structure support high reconnection rates. Nonlinear static solution at scales of the electron skin reveals that electron inertia and small viscosity provide an efficient mechanism of field lines breaking. The reconnection rate does not depend on the actual value of viscosity, while the maximum current is found to be restricted even for space plasmas with extremely rare collisions. The results obtained are verified by a two-fluid large-scale numerical simulation.

A vircator with a coaxial cavity has the potential to increase the beam–microwave conversion efficiency. According to the E-field distribution pattern of the modes in the anode cavity of a coaxial vircator, the resonant frequency band of the injected electron beam and the lowest two operating modes are derived. The main frequency of the virtual cathode is also deduced. The optimal operating frequency and high-efficiency designing method of a coaxial cavity vircator is discussed. An experimental setup is designed and built to test the high-power microwave (HPM) generation mechanism described by theoretical analysis as well as increase the power efficiency. HPM frequency obtained in the experiment is in good agreement with the analysis. The power and energy efficiencies obtained in the experiment are, respectively, 8.7% and 6.8% with 50 ns pulse width. Frequency and phase stable HPM radiation is observed as well as pulse shortening is evidently depressed.

The weakly nonlinear dynamics of dust ion-acoustic waves (DIAWs) are investigated in a dusty plasma consisting of hot ion fluid, variable charge stationary dust grains and non-thermally distributed electrons. The Korteweg–de Vries equation, as well as the Korteweg–de Vries–Burgers equation, are derived on the basis of the well-known reductive perturbation theory. It is shown that, due to electron non-thermality and finite ion temperature, the present dusty plasma model can support compressive as well as rarefactive DIA solitary waves. Furthermore, there may exist collisionless DIA shock-like waves which have either monotonic or oscillatory behavior, the properties of which depend sensitively on the number of fast non-thermal electrons. The results complement and provide new insights into previously published results on this problem (Mamun, A. A. and Shukla, P. K. 2002 IEEE Trans. Plasma Sci. 30, 720).

The analytic and numerical approaches to the investigation of the two-dimensional steady-state plasma flows are analyzed and compared with reference to a plasma accelerator channel in the presence of a longitudinal magnetic field. The present study continues a cycle of research into the plasma flows in the coaxial channels with the traditional azimuthal magnetic field. The additional longitudinal field opens new possibilities for controlling the dynamic processes and achieving the transonic flows. The research is based on the magnetohydrodynamic equations.