A two-dimensional double simple wave solution is given for both weakly and highly magnetized non-relativistic plasmas moving across the magnetic field. The dependence of the density and the magnetic field on the two independent phases, namely, components of the fluid velocity, is derived. It is shown that initial spatial distributions must satisfy a definite equation whose solution determines a special category for initial conditions. The time of blow up for any fixed value of the pair phase is found. A large general class of solutions for initial distributions is obtained. For any chosen initial distribution, the physical plane of flow at any instant of time splits into two regions, one forbidden and the other permitted. These regions are obtained numerically at a typical time for a special initial distribution. For this double wave solution, differential equations for streamlines and fluid trajectories are derived. Only for the simplest cases can the corresponding curves be completely integrated and these are given in this paper. The results are qualitatively similar to the one-dimensional case derived by Stenflo and Shukla.

We evaluate the correlated stopping power of a swift chain of N charges aligned with its (non-relativistic) velocity. We find that the distance required between two charges for the chain to act as a separated set of isolated charges is much larger than the dynamical screening length because the wake effect is very important when the chain elements are situated close to each other.

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 filamentation of the resistive instability in a weakly ionized quasi-neutral current-carrying plasma in the diffusion frequency region in the nonlinear regime is investigated. By using the magnetohydrodynamics equations and Ampere's law and assuming that the plasma is non-isothermal and inhomogeneous, the evolution of the magnetic field diffusion into the plasma is described by the Lienard nonlinear differential equation. Furthermore, it is shown that the departure of the profiles of the magnetic field and electron density variation from a sinusoidal shape in the nonlinear regime and a transverse filamentation and density steepening can occur in the static limit. Also, it is shown that the shape of the transverse filamentation can vary in this regime depending on the gradient of the magnetic field.

In this paper the focusing/defocusing of (i) a single Gaussian electromagnetic beam and (ii) a number of coaxial Gaussian electromagnetic beams, propagating in the extraordinary mode along the Earth's magnetic field in the ionosphere has been investigated in the paraxial approximation. The growth of a sinusoidal instability on account of self-focusing has also been studied. The nonlinearity in the dielectric function, responsible for the focusing/defocusing arises from the redistribution of the electron density, caused by the non-uniform distribution of the electron temperature. The electron temperature is determined by the energy balance for electrons/ions taking into account the Ohmic heating, the collisions and the radiation from the sun. The wave frequency has been assumed to be greater than the plasma frequency. The electron cyclotron frequency due to the Earth's magnetic field in the ionosphere is much larger than the electron collision frequency. This is specifically true for a height of 150 km. Numerical results have been presented for a range of parameters and a discussion of the same has been presented.

Reconnection is believed to be responsible for plasma acceleration in a large number of space and astrophysical objects. Onset of reconnection is usually related to instabilities of current sheet equilibria. Analytical self-consistent models of an equilibrium current sheet (Harris equilibrium) are known for non-relativistic plasmas and some special cases of relativistic plasmas. We develop a description of generalized Harris equilibria in collisionless non-relativistic and relativistic plasmas. Possible shapes of the magnetic field are analyzed.

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.

Axisymmetric equilibria with incompressible flows of arbitrary direction are studied in the framework of magnetohydrodynamics under a variety of physically relevant side conditions consisting, for example, in that the plasma temperature or the magnetic field modulus are uniform on magnetic surfaces. To this end a set of pertinent nonlinear ordinary differential equations (ODEs) are transformed to quasilinear ODEs and the respective initial value problem is solved numerically with appropriately determined initial values near the magnetic axis. Several equilibrium configurations are then constructed surface by surface. It turns out that in addition to the usual configurations with a magnetic axis, the non-field aligned flow results to novel toroidal shell equilibria in which the plasma is confined within a couple of magnetic surfaces. In addition, the flow affects the elongation and triangularity of the magnetic surfaces and opens up the possibility of changing the magnetic field topology by creating double toroidal shell-like configurations.

By means of kinetic fluctuation theory, the relaxation process between the electron and ion temperatures in a magnetized homogeneous plasma is considered. The cases when the external upper-hybrid pump wave excites modified convective cells and ion-acoustic waves are analysed. The inverse relaxation time in the regime where the turbulent fluctuations are developed is calculated for these cases and its dependence on the pump wave and plasma parameters is deduced.

The existence of magnetosonic solitons in dusty plasmas is investigated. The nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus derived. A solution of the nonlinear equations is presented. It is shown that, owing to the presence of dust, static structures are allowed. This is in sharp contrast to the formation of the so-called shocklets in usual magnetoplasmas. A comparatively small number of dust particles can thus drastically alter the behavior of the nonlinear structures in magnetized plasmas.

We present the results of three-dimensional self-consistent multi-fluid simulations of magnetic reconnection in a dusty plasma. We ballistically relax a Harris-like current sheet into a fluid pseudo-equilibrium. We then perturb the current sheet with typical inflow and outflow velocities associated with classical models of reconnection. We find a 20% decrease in magnetic energy for the case of a locally enhanced resistivity. For a parameter-dependent resistivity we find a 26% decrease in magnetic energy in the current sheet. We find dust-neutral relative flow velocities that are a factor of two greater than the dust Alfvén velocity. We then explore the implications of these flows on aerodynamic drag heating of the dust particles.

We present results from a particle–fluid simulation of auroral electrons and discuss the distribution of parallel electric fields along auroral field lines and the processes occurring during the build up of these electric fields. Neglecting field-aligned ion dynamics, the main potential drop has a width of about 5000, km and is centered at an altitude of roughly 5000, km. We find that the gradient in the potential becomes steeper and the build up of the potential drop becomes faster if the temperature of the magnetospheric electrons is lower.

The Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation describes the nonlinear behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external uniform (space independent) static (time independent) magnetic field in a plasma consisting of warm adiabatic ions and a superposition of two distinct population of electrons, one due to Cairns et al. (1995 Geophys. Res. Lett.22, 2709), which generates the fast energetic electrons, and the other the well-known Maxwell–Boltzman distributed electrons. It is found that the compressive or rarefactive nature of the ion-acoustic solitary wave solution of the KdV-ZK equation does not depend on the ion temperature if σc<0 or σc>1, where σc is a function of β1, nsc and σsc. This β1 is the non-thermal parameter associated with the non-thermal velocity distribution function of electrons (Cairns et al.), nsc is the ratio of the unperturbed number density of the isothermal electrons to that of the non-thermal electrons and σsc is the ratio of the average temperature of the non-thermal electrons to that of the isothermal electrons. The KdV-ZK equation describes compressive or rarefactive ion-acoustic solitary wave according to whether σc<0 or σc>1. When 0 ≤ σc ≤ 1, the KdV-ZK equation describes compressive or rarefactive ion-acoustic solitary wave according to whether σ>σc or σ<σc, where σ is the ratio of the average temperature of ions to the effective temperature of electrons. If σ takes the value σc with 0 ≤ σc ≤ 1, the coefficient of the nonlinear term of the KdV-ZK equation vanishes and for this case the nonlinear evolution equation of the ion-acoustic wave is a modified KdV-ZK (MKdV-ZK) equation. It is found that the four-dimensional parameter space, originated from the physically admissible values of the four-parameters β1, σ, σsc and nsc of the present extended plasma system, can be decomposed into five mutually disjoint subsets with respect to the critical values of the different parameters, and the nonlinear behaviour of the same ion acoustic wave in those subsets can be described by different modified KdV-ZK equations. A general method of perturbation of the dependent variables has been developed to obtain the different evolution equations. The applicability of the different evolution equations and their solitary wave solutions (along with the conditions for their existence) have been investigated analytically and graphically.

Low-frequency magnetic field fluctuations are observed in space plasmas, e.g. as upstream waves at the Earth's bow shock. Such upstream waves can steepen into very large amplitude wave phenomena, e.g. short large-amplitude magnetic structures (or SLAMS for short), shocklets or discrete wave packets. Such observations motivated us to study the nonlinear behavior of low-frequency and large-amplitude plasma waves in terms of the full nonlinear Hall–MHD framework. In the case of stationary (nonlinear) waves, the Hall–MHD equations can be rewritten in the so-called Sakai–Sonnerup system of equations that describe this plasma state and provide oscillatory and solitary types of solutions. An overall parameter study on the polarization characteristics, together with the magnetic field components and density variations of the different ranges of solutions, is presented here. These results can be further on applied to the theoretical treatment of particle interaction with such waves, e.g. at shocks in space plasmas, possibly leading to particle acceleration.

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.

In this paper the concept of negative energy waves facilitates the analysis of instability in a magnetized bi-ion plasma with differential ion streaming. There are three frequency regimes in which instability may arise. For frequencies less than the alpha particle gyrofrequency, a negative energy alpha ion-cyclotron mode can interact with a positive energy proton-cyclotron mode. In the intermediate frequency regime lying between the alpha and proton gyrofrequencies, a negative energy alpha-acoustic mode interacts with a positive energy proton-cyclotron mode. In the high-frequency regime above the proton-cyclotron frequency a negative energy alpha-acoustic mode interacts with a positive energy proton-acoustic mode. The resonance (or coalescence) condition which lends itself to a simple geometrical interpretation as the intersection between the proton and alpha mode wave normal diagrams with differential streaming permits the evaluation of the instability growth rate in each frequency regime, which is calculated for both subsonic and supersonic differential streaming.

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.

Monte Carlo simulation is conducted for a strongly coupled one-dimensional confined-particles system. We deal with an infinite chain of positively charged dust particles. The particles interact through the Yukawa screened potential. It is found that a critical value exists for the number of closest neighbors that are involved in the interaction. The inter-particle distance at equilibrium is found. Using these results, we study the dust-acoustic as well as the dust-lattice modes for two situations. In the first we neglect the friction force while in the second situation the presence of an ambient gas in plasma is considered.

The dispersion relation for superluminal waves in degenerated and isotropic electron–positron plasmas is investigated. The dispersion equation of linear waves is derived from the relativistically correct form of the dielectric function and the Fermi distribution function. Analytical dispersion laws for the real part of the wave frequency are derived by applying the long-wavelength approximation and the short-wavelength approximation. Using the numerical simulation method, we obtain the full dispersion curve which cannot be given by an analytic method.

The plasma temperature in a new plasma source shows unusual behaviour at low pressures (about 1 mTorr) and high absorbed powers. In Ar plasma at pressures of about 1 mTorr, the electron temperature shows a pronounced maximum inside an electromagnetic accelerator, which is followed by a rapid drop at the boundary between the accelerator region and the main chamber. In this paper a neoclassical thermo-conductivity model based on the analysis of the electron trajectories is proposed to describe the sharp electron temperature profile. Quantitative agreement of the calculated temperature profile with the experiment is observed.