Some supplementary results and interpretations on the theory of Hall MHD solitons (McKenzie and Doyle 2002 Phys. Plasmas9, 55) are presented. It is shown that the Hall MHD soliton reduces, in the appropriate limit, to an electrostatic ion–cyclotron soliton. It is also shown how the dynamical equations governing the Hall MHD soliton can be obtained from a Hamiltonian H. Soliton solutions correspond to H = 0, periodic solutions to H < 0 and rotation-type solutions to H >0. Possible applications are discussed. A non-canonical Hamiltonian picture is developed and compared to the well-known example of a free rigid body.

We investigate the instability of obliquely propagating dust waves in a collisional, magnetized plasma containing negatively charged dust grains. It is assumed that the magnetic field strength is such that the ions and electrons are magnetized, while the dust is unmagnetized. We consider both modified two-stream and dust-acoustic instabilities that are driven by an ion cross-field drift and that occur for waves propagating obliquely to the magnetic field. We use parameters that may be representative of possible laboratory experimental conditions to illustrate the growth rates. We also compare our results with prior theoretical studies of a Hall current instability of perpendicularly propagating electrostatic waves. It is found that these obliquely propagating wave instabilities may also be important for representative laboratory parameters when the cross-field drift speed is a significant fraction of the ion thermal speed.

In this paper we generalize the classical Farley–Buneman (FB) instability to include space-charge effects and finite electron inertia. The former effect makes the ion-acoustic wave dispersive with the usual resonance appearing at the ion plasma frequency, but other than that the structure of the FB instability remains intact. However, the inclusion of the latter, finite electron inertia, gives rise to the propagating electron-cyclotron mode, albeit modified by collisions. In the presence of differential electron streaming relative to the ions, the interaction between this mode, attempting to propagate against the stream, but convected forward by the stream, and a forward propagating ion-acoustic mode, gives rise to a new instability distinct from the FB instability. The process may be thought of in terms of the coupling between negative energy waves (electron-cyclotron waves attempting to propagate against the stream) and positive energy waves (forward propagating ion-acoustic waves). In principle, the instability simply requires super-ion acoustic streaming electrons and the corresponding growth rates are of the order of one half of the lower hybrid frequency, which are faster than the corresponding FB growth rates. For conditions appropriate to the middle day-side E-region this instability excites a narrow band of frequencies just below the ion plasma frequency. Its role in the generation of electrojet irregularities may be as important as the classical FB instability.

An accretion disk with vertical structure around a young stellar object is investigated, considering anomalous magnetic viscosity. It was found that the I-mode was unstable in the outer disk, and sometimes turned stable in the inner disk, for the standard α model. However, we find that the I-mode is always unstable in the inner disk, owing to the anomalous magnetic viscosity.

A novel mechanism for the generation of large-scale zonal flows by small-scale Rossby waves in the Earth's ionospheric E-layer is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude magnetized Rossby waves. To describe this process a generalized Charney equation containing both vector and scalar (Korteweg–de Vries type) nonlinearities is used. The magnetized Rossby waves are supposed to have arbitrary wavelengths (as compared with the Rossby radius). A set of coupled equations describing the nonlinear interaction of magnetized Rossby waves and zonal flows is obtained. The generation of zonal flows is due to the Reynolds stresses produced by finite amplitude magnetized Rossby waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the magnetized Rossby pump wave. Explicit expression for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with existing results is carried out. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere.

Kinetic Alfvén waves are investigated in the presence of a general loss-cone distribution function including finite electron pressure and ion-gyroradius effects. The dispersion relation and damping/growth rate are evaluated for different electron to ion temperature ratios, Te/Ti, using a kinetic approach. The wave frequency ω and damping/growth rate γL are evaluated for two regimes of propagation, k⊥ρi < 1 and k⊥ρi > 1, where k⊥ is the perpendicular wave number and ρi is the ion-gyroradius. An enhancement of the wave frequency and a reduction in the damping rate are predicted by steep loss-cone distribution indices and Te/Ti. The growth of the wave is also noticed at higher values of the distribution index and lower Te/Ti. Plasma parameters appropriate to the plasma sheet boundary layer (PSBL) are used to discuss the propagation of kinetic Alfvén waves from the PSBL to the auroral ionosphere.

In recent years, much attention has been devoted to the electron-temperature-gradient (ETG) driven instability as a possible explanation for the high electron thermal conductivity found in most tokamaks. The present contribution assesses whether a specific three-dimensional fluid ETG model can reproduce the conductivity observed in the Tore Supra tokamak [Equipe Tore Supra (presented by R. Aymar) 1989 Plasma Physics and Controlled Nuclear Fusion Research (Proc. 12th Int. Conf., Nice, 1988, Vol. 1.) Vienna: IAEA, p. 9]. Although the model reproduces fairly well the observed critical gradient, a large discrepancy factor, of the order of 50, is found for the ratio between the experimental and the simulated conductivity. On the basis of this study, one must conclude that the electron heat transport cannot be explained only with a fluid ETG turbulence model.

The nonlinear propagation characteristics of dust ion acoustic waves in the presence of weak dissipations arising due to the low rates (compared to the ion oscillation frequency) of ionization, ion loss and dust charging are investigated. It is found that the ion acoustic solitary wave in such a dusty plasma is weakly dissipative in nature and is governed by a modified form of the Korteweg–de Vries equation. The analytical solution reveals that the ionization has a destabilizing effect, whereas ion loss and dust charge variation play a stabilizing role to control the ionization instability.

Scale interactions in Hall magnetohydrodynamics (MHDs) are studied using both the mean field theory derivation of transport coefficients, and direct numerical simulations in three space dimensions. In the magnetically dominated regime, the eddy resistivity is found to be negative definite, leading to large-scale instabilities. A direct cascade of the total energy is observed, although as the amplitude of the Hall effect is increased, backscatter of magnetic energy to large scales is found, a feature not present in MHD flows. The coupling between the magnetic and velocity fields is different than in the MHD case, and backscatter of energy from small-scale magnetic fields to large-scale flows is also observed. For the magnetic helicity, a strong quenching of its transfer is found. We also discuss non-helical magnetically forced Hall-MHD simulations where growth of a large-scale magnetic field is observed.

Radiation from a loosely constrained cyclotron motion of mono-energetic electrons on a common large orbit (LO) circle in a uniform axial magnetic field and in a right-hand circularly polarized field of plane electromagnetic waves has been studied numerically by particle simulation. A restoring force caused by neutralizing ions against the displacements of gyrating electrons from the original LO circle is introduced by a phenomenological potential well in the radial direction. It is shown that, in high-density beams such as ωb2 ≫~Ω2, Cherenkov instability in the azimuthal direction with ω <~ω+Vzkz leads to the excitation of microwaves. Here, ωb, ~ω, ω, Vz and kz are, respectively, relativistic beam plasma frequency, relativistic electron cyclotron frequency, oscillation angular frequency, axial component of beam velocity and axial wavenumber.

In the present research paper, the characteristics of dust-acoustic solitary waves (DASWs) and double layers (DLs) are studied. Ions are treated as non-thermal and variable dust charge is considered. The Korteweg–de Vries equation is derived using a reductive perturbation method. It is noticed that compressive solitons are obtained up to a certain range of relative density δ (=ni0/ne0) beyond which rarefactive solitons are observed. The study is further extended to investigate the possibility of DLs. Only compressive DLs are permissible. Both DASWs and DLs are sensitive to variation of the non-thermal parameter.

The components of the dielectric tensor for the distribution function given by Leubner and Schupfer have been obtained. The effect of the loss-cone index appearing in the particle distribution function in a hot magnetized plasma has been studied. A case study has been performed to calculate temporal growth rates of Bernstein waves using the distribution function given by Summers and Thorne and Leubner and Schupfer. The effect of the loss-cone index on growth rates is found to be quite different for the two distribution functions.

A theory for two-dimensional electron and ion Bernstein–Greene– Kruskal (BGK) modes in a magnetized space plasma is presented. The BGK modes are constructed using the energy and the canonical angular momentum of the particles, which are conserved in a cylindrically symmetric potential. The typical length scale of the BGK modes is of the same order or larger than the thermal gyroradius of the particles. The results are relevant for understanding the properties of observed localized structures in the Earth's magnetosphere and auroral zone, as well as in laboratory magnetoplasmas.

Large-amplitude electrostatic solitary structures are investigated in an unmagnetized charge-varying pair–ion–dust plasma in which electrons and positrons have equal masses. Their spatial patterns are significantly modified by the presence of the positron component. In particular, it may be noted that an addition of a small concentration of positrons abruptly reduces the potential pulse amplitude as well as the net negative charge residing on the dust grain surface. Under certain conditions, the solitary wave suffers the well-known anomalous damping leading to the development of collisionless shock waves. This investigation may be taken as a prerequisite for the understanding of the electrostatic solitary waves that may occur in space dusty plasmas.

Hall magnetohydrodynamics (HMHD) is a mono-fluid approximation extending the validity domain of the ordinary MHD system to spatial scales down to a fraction of the ion skin depth or frequencies comparable to the ion gyrofrequency. In the paper by Galtier (2006 J. Plasma Physics), an incompressible limit of the HMHD system is used for developing a wave turbulence theory. Nevertheless, the possibility and the consequences of such an approximation are different in HMHD and in MHD. Here, we analyse these differences by investigating the properties of the HMHD equations in the incompressible limit: the existence of linear modes, their dispersion relations and polarizations. We discuss the possibility of replacing the fluid closure equation of a complete HMHD system by an incompressibility hypothesis and determine the validity range.

We determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flat-topped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the first-order growth rate is not zero.

The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field is not nearly perpendicular to the direction of wave propagation, this allows us to use a multiple-scale expansion to demonstrate the existence and nature of nonlinear wave solutions. Such solutions are found to have a rapid oscillation of constant amplitude superimposed on the underlying large-scale variation. The approximate equations for the large-scale variation are obtained by making an adiabatic approximation and in one limit, new explicit solitary pulse solutions are found. In the case of a perpendicular magnetic field, conditions for the existence of solitary pulses are derived. Our results are consistent with earlier studies which were restricted to waves having a velocity close to that of long-wavelength linear magnetoacoustic waves.

Weakly nonlinear waves in strongly magnetized plasma with slightly non-isothermal electrons are governed by a modified Zakharov–Kuznetsov (ZK) equation, containing both quadratic and half-order nonlinear terms, which we refer to as the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation. We present a method to obtain an approximation for the growth rate, γ, of sinusoidal perpendicular perturbations of wavenumber, k, to SKdVZK solitary waves over the entire range of instability. Unlike for (modified) ZK equations with one nonlinear term, in this method there is no analytical expression for kc, the cut-off wavenumber (at which the growth rate is zero) or its corresponding eigenfunction. We therefore obtain approximate expressions for these using an expansion parameter, a, related to the ratio of the nonlinear terms. The expressions are then used to find γ for k near kc as a function of a. The approximant derived from combining these analytical results with the ones for small k agrees very well with the values of γ obtained numerically. It is found that both kc and the maximum growth rate decrease as the electron distribution becomes progressively less peaked than the Maxwellian. We also present new algebraic and rarefactive solitary wave solutions to the equation.

The breakdown characteristics of a low-frequency dielectric barrier discharge (DBD) at low pressure are investigated experimentally in He, Ne and Ar. The current waveform of this DBD, a series of pulses, is caused by the results of the electron avalanches under the action of the applied field and the quenching effect of the wall-charge field on the avalanches. Taking into consideration the diffusion loss of the charged particles in the breakdown processes, the experimental investigation and the theoretical analysis of its breakdown characteristics indicate that its breakdown voltage is higher than the calculation by the Paschen law and depends on the filled-gas pressure and the distance between the electrodes, instead of their product. The ion-induced secondary electron emission coefficient and the mean electron energy at the moment of breakdown can also be determined approximately by measuring the breakdown characteristics of the discharge tubes with different distances between the electrodes and combining the theoretical deductions. The experimental results and the theoretical analysis of the breakdown characteristics of this DBD are discussed.

A time-resolved diagnostic technique was used to investigate the emission spectra from the plasmas produced by 1.06 μm, 10 ns pulsed laser ablation of semiconductor GaAs. The characteristics of the species in plasma produced at different ambient pressure were analyzed. The full width at half maximum of the spectral line was measured and analyzed according to obtained spectra of the excited atoms; several line broadening factors were estimated according to our experimental conditions and the results indicate that the Stark broadening is the main broadening mechanism. Under the assumption of local thermodynamic equilibrium, the time evolution of electron number density was deduced from the Stark broadening measurements.