It is shown that electrostatic ion-cyclotron (EIC)-like modes can be excited by the pre-existing electron density ripple across the external magnetic field in a dusty magnetoplasma. For this purpose, we use the ion continuity and momentum equations, together with the Boltzmann-distributed electrons, and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that the EIC-like modes in dusty magnetoplasmas can be driven due to the free energy in the electron density ripple.

Typically a magnetohydrodynamical model for neutral plasmas must take into account both the ionic and the electron fluids and their interaction. However, at short time scales, the ionic fluid appears to be stationary compared to the electron fluid. On these scales, we need consider only the electron motion and associated field dynamics, and a single fluid model called the electron magnetohydrodynamical model which treats the ionic fluid as a uniform neutralizing background applies. Using Maxwell's equations, the vorticity of the electron fluid and the magnetic field can be combined to give a generalized vorticity field, and one can show that Euler's equations govern its behavior. When the vorticity is concentrated into slender, periodic, and nearly parallel (but slightly three-dimensional) filaments, one can also show that Euler's equations simplify into a Hamiltonian system and treat the system in statistical equilibrium, where the filaments act as interacting particles. In this paper, we show that, under a mean-field approximation, as the number of filaments becomes infinite (with appropriate scaling to keep the vorticity constant) and given that angular momentum is conserved, the statistical length scale, R, of this system in the Gibbs canonical ensemble follows an explicit formula, which we derive. This formula shows how the most critical statistic of an electron plasma of this type, its size, varies with angular momentum, kinetic energy, and filament elasticity (a measure of the interior structure of each filament) and in particular it shows how three-dimensional effects cause significant increases in the system size from a perfectly parallel, two-dimensional, one-component Coulomb gas.

A Korteweg–de Vries (KdV) equation is derived here, that describes the nonlinear behaviour of long-wavelength weakly nonlinear dust acoustic waves propagating in an arbitrary direction in a plasma consisting of static negatively charged dust grains, non-thermal ions and isothermal electrons. It is found that the rarefactive or compressive nature of the dust acoustic solitary wave solution of the KdV equation does not depend on the dust temperature if σdc < 0 or σdc > σd*, where σdc is a function of β1, α and μ only, and σd*(<1) is the upper limit (upper bound) of σd. This β1 is the non-thermal parameter associated with the non-thermal velocity distribution of ions, α is the ratio of the average temperature of the non-thermal ions to that of the isothermal electrons, μ is the ratio of the unperturbed number density of isothermal electrons to that of the non-thermal ions, Zdσd is the ratio of the average temperature of the dust particles to that of the ions and Zd is the number of electrons residing on the dust grain surface. The KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σdc < 0 or σdc > σd*. When 0 ≤ σdc ≤ σd*, the KdV equation describes the rarefactive or the compressive dust acoustic solitary waves according to whether σd > σdc or σd < σdc. If σd takes the value σdc with 0 ≤ σdc ≤ σd*, the coefficient of the nonlinear term of the KdV equation vanishes and, for this case, the nonlinear evolution equation of the dust acoustic waves is derived, which is a modified KdV (MKdV) equation. A theoretical investigation of the nature (rarefactive or compressive) of the dust acoustic solitary wave solutions of the evolution equations (KdV and MKdV) is presented with respect to the non-thermal parameter β1. For any given values of α and μ, it is found that the value of σdc completely defines the nature of the dust acoustic solitary waves except for a small portion of the entire range of the non-thermal parameter β1.

The basic features of obliquely propagating dust-ion-acoustic (DIA) solitary waves, and their multi-dimensional instability in a magnetized multi-ion dusty plasma containing hot adiabatic inertia-less electrons, cold positive and negative ions, and negatively charged static dust have been theoretically investigated by the reductive perturbation method, and the small-k perturbation expansion technique. The combined effects of electron adiabaticity, external magnetic field (obliqueness), and negative ions, which are found to significantly modify the basic properties (speed, amplitude, width, and instability) of small but finite-amplitude DIA solitary waves, are explicitly examined. It is also found that the instability criterion and the growth rate are significantly modified by the external magnetic field, the propagation directions of both the nonlinear waves and their perturbation modes, and the presence of negative ions. The implications of our results in space and laboratory dusty plasmas are briefly discussed.

We present a kinetic theory analysis of the electrostatic ion cyclotron (EIC) instability in a plasma containing positive ions, electrons, and negative ions that are much more massive than the positive ions. Conditions are investigated for exciting the fundamental and the higher harmonic EIC waves associated with each ion species. We find that as the concentration of heavy negative ions increases, the wave frequencies increase, the unstable spectrum in general shifts to longer perpendicular wavelengths, and the growth of higher harmonic EIC waves tends to increase within certain parameter ranges. Applications to possible laboratory plasmas are discussed.

The implosion dynamics and fusion parameters of a high density D-T fibre plasma driven by Z-pinch with current stepping technique is investigated. Our numerical results demonstrate that a current-stepping technique reduces the minimum pinch radius, and as a result high density, high temperature plasma can be formed. Thus a staged pinch device with current-stepping technique can be used as an alternative approach to achieve fusion conditions with relatively small values of discharge current and with a long pulse duration.

We study the propagation and damping of small-amplitude prominence oscillations invoking steady flow and radiative losses due to Newton's cooling with constant relaxation time. We find that the strength of steady flow has a large influence on the propagation (e.g. period, phase velocity) of wave modes. In the presence of steady flow, the thermal mode is a propagating wave and hence it can be observed in solar prominences. The thermal mode contributes to the non-thermal line broadening in the solar atmosphere. The steady flow does not affect the damping time of the wave modes. The damping of slow and thermal modes is highly dependent on the radiative relaxation time. The thermal perturbation, in the presence of steady flow, is found to be larger in the case of the thermal mode than in the slow and fast modes. The energy flux (~300 W m−2) associated with the thermal mode is sufficient to heat the quiet regions of the Sun. The slow mode contribution to non-thermal broadening has been estimated. The non-thermal broadening is found to be large in the case of the prominence with large characteristic length. The steady flow, in the presence of Newton's cooling, breaks the symmetry between the forward and backward propagating modes. No modes with negative energy have been found. For strong flows (above 10 km s−1), the canonical backward wave propagates in the forward direction, which can play an important role in wave detection and prominence seismology.

Counterstreaming plasma systems with intrinsic temperature anisotropies are unstable against the excitation of Weibel-type instabilities, namely, filamentation and Weibel instabilities, and their cumulative effect. Here, the analysis is extended to counterstreaming plasmas with weakly relativistic bulk velocities, while the thermal velocities are still considered to be non-relativistic. Such plasma systems are relevant for fusion plasma experiments and the more violent astrophysical phenomena, such as jets in gamma-ray burst sources. Simple analytical forms of the dispersion relations are derived in the limit of a small transverse temperature or a large temperature anisotropy of the beams. The aperiodic growing solutions are plotted systematically for the representative cases chosen in Paper I (Lazar et al. 2009 J. Plasma Phys. 75, in press). In the limit of slow non-relativistic plasma flows, the numerical solutions fit well with those obtained in Paper I, but for weakly relativistic streams an important deviation is found.

In this paper we present a theoretical investigation of the growth/propagation of a ring ripple, superposed on a Gaussian electromagnetic beam propagating along the direction of magnetic field in a magnetoplasma. The nature of propagation of the ripple is analysed in a paraxial-like approximation by radial expansion of the dielectric function, corresponding to the composite (Gaussian and ripple) electric field profile of the beam around the position of the maximum of the ripple. The two cases of collisional plasmas (with negligible thermal conduction) and collisionless plasmas (dominant ponderomotive nonlinearity) are considered. The effect of the magnetic field on the critical curves and focusing/defocusing of the ripple are studied and discussed.

This paper presents an analysis of the spatial growth of a transverse instability, corresponding to the propagation of an electromagnetic beam, with uniform irradiance along the wavefront in a collisional plasma, along the direction of a static magnetic field; expressions have been derived for the rate of growth, the maximum value of the rate of growth and the corresponding value of the wave number of the instability. The instability arises on account of the ejection of electrons from regions where the irradiance of the perturbation is large. The energy balance of the electrons taking into account ohmic heating and the power loss of electrons on account of (i) collisions with ions and neutral species and (ii) thermal conduction has been taken into account for the evaluation of the perturbation in electron temperature, which determines the subsequent growth of the instability. Further, the relationship between the electron density and temperature, as obtained from the kinetic theory, has been used. The filamentation instability becomes enhanced with the increase of the static magnetic field for the extraordinary mode while the reverse is true for the ordinary mode. Dependence of growth rate on irradiance of the main beam, magnetic field and a parameter proportional to the ratio of power loss of electrons by conduction to that by collisions has been numerically studied and illustrated by figures. The dependence of the maximum growth rate and the corresponding optimum value of the wave number of the instability on the irradiance of the main beam has also been studied. The paper concludes with a discussion of the numerical results, so obtained.