Magnetohydrodynamic wave interactions in a linear shear flow are investigated using the Lagrangian fluid displacement ξ and entropy perturbation Δ S, in which a spatial Fourier solution is obtained in the frame of the background shear flow (Kelvin's method). The equations reduce to three coupled oscillator equations, with time-dependent coefficients and with source terms proportional to the entropy perturbation. In the absence of entropy perturbations, the system admits a wave action conservation integral consisting of positive and negative energy waves. Variational and Hamiltonian forms of the equations are obtained. Examples of wave amplification phenomena and sharp resonant-type wave interactions are obtained. Implications for the interaction of magnetohydrodynamic waves in the shear flow between fast, polar coronal-hole solar wind and slow, streamer belt solar wind are discussed.

We present results of quantitative multi-fluid simulations of the nonlinear dynamics of Kelvin–Helmholtz modes in the partially ionized dusty plasma of noctilucent clouds. Noctilucent clouds are a typical example of dusty plasmas in the Earth's mesosphere/lower thermosphere. A specific feature observed in noctilucent clouds is wavy, turbulent structure. Possible explanations for these structures, which are discussed in the literature, are based on hydrodynamical models. The dusty plasma aspect has been widely neglected, so far. In this paper we examine the nonlinear dynamics of Kelvin–Helmholtz modes in noctilucent clouds from the viewpoint of dusty plasma dynamics. The corresponding results are in good qualitative and quantitative agreement with observations.

The dispersion relation of azimuthal electromagnetic surface waves on a magnetized annular plasma surrounded by a metallic cylindrical coaxial anisotropic dielectric lined waveguide is obtained. The thickness of the dielectric and its location in the waveguide are studied with respect to their effects on the number of spectra observed. The graphs of frequency spectra against the ratio of radii of the annular plasma and η = ωpe/Ωe are plotted. Finally, surface E-modes for coaxial anisotropic and isotropic dielectrics have been investigated.

The octic fluid dispersion equation, the kinetic Boltzmann–Vlasov equation and the MHD (scalar pressure) analysis, programmed for a two-species collisionless magnetoplasma in a form permitting direct comparison between them, have been applied to the study of the Alfvén modes in both low- and high-β plasmas. In the low-βregime all methods give essentially the same solutions for the isotropic fast magnetosonic and the field-guided shear Alfvén modes. The real part of the refractive index of the field-guided slow magnetosonic acoustic mode is almost identical in the fluid and kinetic analyses, but is 50% too high in the MHD analysis owing to neglect of the trace-free part of the pressure tensor which drives almost half of the acoustic energy flux. The strong damping of the acoustic mode in both low- and high-β plasmas is drastically reduced by increase of electron temperature, whereas a moderate increase in the perpendicular ion temperature is sufficient to eliminate shear Alfvén damping in high-β plasmas and even to produce wave growth, the effect being more pronounced the higher the plasma β. The fluid analysis shows the electromagnetic energy flux to be negligible in the acoustic mode, in which the acoustic flux is driven both by the trace-carrying and trace-free parts of the pressure tensor, but is usually the dominant component in the (fast) magnetosonic mode.

Mode converted Bernstein waves potentially allow the implementation of local heating and current drive in spherical torus devices, which are not directly accessible to low-harmonic cyclotron waves. The mode conversion method of Cairns and Lashmore-Davies previously used to study the usual mode conversion in non-planar geometry is extended to include the effect of the high-magnetic-field-side cutoff, and is solved analytically. The analytic solutions to the triplet, cutoff–resonance–cutoff, equations give the reflection and conversion coefficients in terms of parameters defining the local behavior of the dispersion relation. The variation of mode conversion efficiency depends not only on the coupling parameter but also on the phasing effect introduced by the high-field-side cutoff. The change in characteristic phases, which are concerned with the coupling parameter, brings an additional degree of freedom allowing optimization via the position of the high-field cutoff. A discrete spectrum of phases exists for which complete mode conversion of the incident wave for a transit of the resonance region can be achieved. The results we obtain here give the general conditions for efficient Bernstein wave heating in two-dimensional geometry.

A dipole-like rotating magnetic field was produced by a pair of circular, orthogonal coils inside a metal vacuum chamber. When these coils were immersed in plasma, large currents were driven outside the coils: the currents in the plasma were generated and sustained by the rotating magnetic dipole (RMD) field. The peak RMD-driven current was at roughly two RMD coil radii, and this current (60 kA m−) was sufficient to reverse the ambient magnetic field (33 G). Plasma density, electron temperature, magnetic field and current probes indicated that plasma formed inside the coils, then expanded outward until the plasma reached equilibrium. This equilibrium configuration was adequately described by single-fluid magnetohydrodynamic equilibrium, wherein the cross product of the driven current and magnetic filed was approximately equal to the pressure gradient. The ratio of plasma pressure to magnetic field pressure, β, was locally greater than unity.

We present an in depth study of the fluid limit of a kinetically derived collisional, current-driven instability that includes shears in the field-aligned currents as well as collisions. We show how the theory presented here generalizes other theories, including the collisionless current-driven electrostatic ion acoustic instability and its sheared collisionless version. We offer a low-frequency generalization of the zero frequency ion shear driven instability by minimizing the relative drift magnitude as well as the shears themselves. We discuss the implication of our theoretical framework both for strongly field-aligned modes and modes where the wavevectors have arbitrary angles with respect to the ambient magnetic field. We discuss the results in terms of F-region irregularity observations of coherent echoes by ionospheric radars.

Langmuir waves excited by transverse pumping plasmons near the critical surface in a laser-plasma may collapse, leading to the formation of a density cavity owing to the ponderomotive force. The collapse behavior of electromagnetic waves, Langmuir waves and ion-sound waves are studied numerically. The interactions of the three-wave system will lead to the tendency for an equilibration of energy over both the transverse and Langmuir plasmons with the same frequency near ωpe, which is shown in our numerical analysis.

Collisionless magnetic reconnection dynamics is considered by including the effects of electron inertia as well as parallel electron compressibility. A fluid treatment is adopted for both electrons and ions. Collisionless plasma dynamics properties near a two-dimensional X-type magnetic neutral line in the steady state are explored. The effects of electron inertia and parallel electron compressibility on the hyperbolicity (or lack thereof) of the magnetic field lines in the neutral layer are discussed. A unified linear tearing-mode formulation incorporating both electron inertia and parallel electron compressibility is given. The parallel-electron-compressibility branch is shown to couple in general to the electron-inertia branch in the presence of resistivity. A sufficient condition for linear stability in the Lyapunov sense for steady states of this collisionless plasma system signifying current confinement is deduced. Bounds on the equilibrium current gradient are shown to constitute sufficient conditions for nonlinear stability in the Lyapunov sense for steady states via nonlinear bounds for a suitable perturbation norm.

The propagation of circularly polarized electromagnetic beams along the magnetostatic field in an electron plasma is investigated. As a consequence of a strong interaction with the medium, the beam spreads rapidly on propagation near the cutoff frequencies and the cyclotron resonant frequency of the corresponding plane waves, as well as near the plasma frequency. The power absorption for unit length near the cyclotron frequency and the plasma frequency are determined. For tightly focused beams, there is significant power absorption near the plasma frequency as compared with that at the cyclotron resonant frequency.

A compressible model of the magnetosheath plasma flow is considered. Magnetic reconnection is assumed to occur in a region stretching from the sub-Solar point to the north. Two locations of the reconnection site are treated: two and four Earth radii from the sub-Solar point, respectively. By treating the transition layer as very thin, we solve the governing equations approximately using the method of matched asymptotic expansions. The behavior of the magnetic field and the plasma velocity close to a reconnection site during the transition from the magnetosheath to the magnetosphere is investigated. We also obtain the development of the transition layer thickness north and south of the reconnection point. The magnetopause transition layer is represented by a large-amplitude Alfvén wave implying that the density is approximately the same across the magnetopause boundary. In order to match the solutions we consider a compressible ideal magnetohydrodynamic model describing density, velocity and magnetic field variations along the outer magnetopause boundary. We also compare the analytical results with solutions from a numerical simulation. The compressible effects on the structure of the magnetic field and the total velocity evolution are visible but not dramatic. It is shown that the transition layer north of the reconnection point is thinner than to the south. The effect is stronger for reconnection at higher latitudes.

The structure of a stationary electrostatic plasma wave propagating at a right angle to a weak magnetic field is studied. It is shown that the periodic finite amplitude wave is close in its physical structure to Bernstein–Greene–Kruskal wave of a perfectly definite type. The distinguishing feature of such a nonlinear wave is the absence of the resonant particles trapped by the wave. The electron distribution function, density perturbation and the shape of the wave electrostatic potential are found. The nonlinear dispersion relation is derived to determine the frequency shift due to the perturbation of the distribution function in the resonant region.

The solitary structures of the ion-acoustic waves have been considered in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having a vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field. The nonlinear dynamics of ion-acoustic waves in such a plasma is governed by the Schamel's modified Korteweg–de Vries–Zakharov–Kuznetsov (S-ZK) equation. This equation admits solitary wave solutions having a profile sech4. When the coefficient of the nonlinear term of this equation vanishes, the vortex-like velocity distribution function of electrons simply becomes the non-thermal velocity distribution function of electrons and the nonlinear behaviour of the same ion-acoustic wave is described by a Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. This equation admits solitary wave solutions having a profile sech2. A combined S–KdV–ZK equation more efficiently describes the nonlinear behaviour of an ion-acoustic wave when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons, i.e. when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits an alternative solitary wave solution having a profile different from either sech4 or sech2. The condition for the existence of this alternative solitary wave solution has been derived. It is found that this alternative solitary wave solution approaches the solitary wave solution (the sech2 profile) of the KdV-ZK equation when the contribution of trapped electrons tends to zero. The three-dimensional stability of these solitary waves propagating obliquely to the external uniform and static magnetic field has been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of the instability have been derived at the lowest order. It is also found that the instability condition and growth rate of instability of the alternative solitary waves are exactly the same as those of the solitary waves as determined from the KdV-ZK equation (the sech2 profile) when the contribution of trapped electrons tends to zero.

The nonlinear propagation of the dust-acoustic wave is investigated in a weakly non-ideal plasma comprising Boltzmann electrons, non-thermal ions characterized by a non-thermal parameter α and a negatively charged dust fluid. The non-ideal dust fluid is represented by the van der Waals equation of state. Arbitrary amplitude soliton solutions are found to occur for both supersonic and subsonic values of the Mach number. Upper and lower limits of the range of values of α for which solitons exist are examined as a function of the non-ideal parameters associated with the effects of volume reduction and the cohesive forces, for both the supersonic and subsonic cases.

The analytic solution for the time stationary non-monotonic double layers in multi-species plasma is presented. This solution is the analytic extension of the monotonic double layer and the solitary hole. We have derived the modified Korteweg–de Vries equation in plasmas, taking account of negative ion effects. The effects of negative ion and density on the properties of the non-monotonic double layer are discussed.

A numerical investigation is presented to show the existence, formation and possible realization of large-amplitude solitary potentials in a charge varying dusty plasma with trapped ion particles. These nonlinear localized structures are self-consistent solutions of the Vlasov equation representing saturated states of a three-stream unstable collisionless dusty plasma. The saturation is provided by an interplay between ion trapping and dust charging. It is found that under certain conditions the effect of dust charge variation can be quite important. In particular, it may be noted that the dust charge variation leads to an additional enlargement of the nonlinear localized structure. Furthermore, our results show that the dust charge variation provides an alternate physical mechanism causing dissipation and as a consequence causes the wave amplitude to decay and transfer to the so-called noise tail.

Small-amplitude electrostatic solitary waves are investigated in unmagnetized dusty plasmas with variable charge resonant trapped dust particles. It is found that under certain conditions spatially localized structures, the height and nature of which depend sensitively on the plasma parameters, can exist. The effects of dust grain temperature, equilibrium dust charge, trapping parameter, and dust size on the properties of these solitary waves are briefly discussed. A neural network with a given architecture and learning process, and which may be useful to interpret experimental data, is outlined. Our investigation may be taken as a prerequisite for the understanding of the solitary dust waves that may occur in space as well as in laboratory plasmas.

Relativistic effects on dispersion in a degenerate electron gas are discussed by comparing known response functions derived relativistically and non-relativistically. The main distinguishing feature is one-photon pair creation, which leads to logarithmic singularities in the response functions. Dispersion curves for longitudinal waves have a similar tongue-like appearance in the relativistic and non-relativistic case, with the main relativistic effects being on the Fermi speed and the cutoff frequency. For transverse waves the non-relativistic treatment has a non-physical feature near the cutoff frequency for large Fermi momenta, and this is attributed to an incorrect treatment of the electron spin. We find (with two important provisos) that one-photon pair creation is allowed in superdense plasmas, implying relatively strong coupling between transverse waves and pair creation.

The aim of the present work is to investigate tokamak equilibria with reversed magnetic shear and sheared flow, which may play a role in the formation of internal transport barriers (ITBs), within the framework of the two-fluid model in cylindrical geometry. The study is based on exact self-consistent solutions by means of which the impact of the magnetic shear, s, and the ‘toroidal’ (axial) and ‘poloidal’ (azimuthal) ion velocity components, viz and viθ, on the radial electric field, Er, its shear, |dEr/dr|, and the shear of the E×B velocity, ωE×B≡|d/dr(E× B/B2)|, is examined. For a wide parametric regime of experimental concern it turns out that the contributions of the viz, viθ and pressure gradient (∇ Pi) terms to Er, |Er′| and ωE×B are of the same order of magnitude. The contribution of the ∇ Pi term is missing in the framework of magnetohydrodynamics (MHD) (G. Poulipoulis et al. 2004 Plasma Phys. Control. Fusion46, 639). The impact of s on ωE×B through the ∇ Pi term is stronger than that through the velocity terms; in particular for constant Bz the ion pressure gradient contribution to ωE×B at the point where dEr/dr=0 scales as (1−s)(2−s), whereas the ion flow contributions to ωE×B scale as (1−s). The results indicate that, like MHD, the magnetic shear and the sheared toroidal and poloidal velocities act synergetically in producing electric fields and therefore ωE×B profiles compatible with the ones observed in discharges with ITBs; owing to the ∇ Pi term, however, the impact of s on Er, |Er′| and ωE×B is stronger than that in MHD.

This paper presents the effect of ripple on the plasma wave excitation process and acceleration of electrons in a laser produced plasma. The plasma wave is generated by the beating of two coaxial lasers of frequencies ω1 and ω2, such that ω1-ω2≅ωp. One of the main laser beams also has intensity spikes. The nonlinearity due to the relativistic mass variation depends not only on the intensity of one laser beam but also on the second laser beam. Therefore the behavior of the first laser beam affects the second laser beam, hence cross-focusing takes place. Owing to the interaction of ripple and the main laser beams, the ripple grows inside the plasma. The behavior of the ripple in the plasma affects the excitation of the electron plasma wave as well as the electron acceleration. The amplitude of the electron plasma wave and the electron energy are calculated, in the presence of ripple.