Hamiltonian and variational formulations of equations describing weakly nonlinear magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension are discussed. For wave propagation in uniform media, the wave interactions of interest consist of (a) three-wave resonant interactions in which high-frequency waves may evolve on long space and time scales if the wave phases satisfy the resonance conditions; (b) Burgers self-wave steepening for the magnetoacoustic waves, and (c) mean wave field effects, in which a particular wave interacts with the mean wave field of the other waves. The equations describe four types of resonant triads: slow–fast magnetoacoustic wave interaction, Alfvén–entropy wave interaction, Alfvén–magnetoacoustic wave interaction, and magnetoacoustic–entropy wave interaction. The formalism is restricted to coherent wave interactions. The equations are used to investigate the Alfvén-wave decay instability in which a large-amplitude forward propagating Alfvén wave decays owing to three-wave resonant interaction with a backward-propagating Alfvén wave and a forward-propagating slow magnetoacoustic wave. Exact solutions of the equations for Alfvén–entropy wave interactions are also discussed.

The condition for the validity of the orbital motion limited (OML) theory is reviewed, with reference to the calculation of the floating potential attained by a spherical body immersed in a plasma. It is shown that the OML theory is never satisfied in Maxwellian plasmas, even in the case of very small bodies, i.e. those with radii much smaller than the plasma Debye length. The case considered is that where the ion temperature is less than or equal to the electron temperature. The results are relevant to the theory of dusty plasmas, where the OML theory has been much employed.

The temperature profiles in wall-stabilized atmospheric-pressure arcs in pure argon and in argon–carbon dioxide mixtures have been obtained at currents of 5–40 A and for molar percentages of CO2 ranging from 0.9% to 25% using spectroscopic techniques. With the addition of CO2 to a pure-Ar arc, we show the formation of a core of higher temperatures with a larger gradient of the radial temperature distribution at the arc centre. These investigations show that the addition of even a few percent of CO2 to Ar has a marked effect both upon extinction of the arc according to current values and upon the temperature profiles. Few measurements have been done in Ar–CO2 mixtures in a wall-stabilized arc.

A magnetohydrodynamic (MHD) wave, incident on the boundary between two MHD media in relative motion, may be amplified or attenuated by exchanging energy with the kinetic energy of the background flow. The conventional treatment of this problem uses a definition of the wave energy such that energy is conserved at the boundary. An amplified reflected wave then leads to the requirement of a transmitted wave carrying negative energy. Such an approach, while producing correct results, obscures the nature and location of the energy interchange. In this paper, the proper definitions of energy density and flux in a moving plasma are discussed, and the relationship of the group velocity and the energy flow is clarified. The mechanism by which energy is exchanged between streaming plasma and wave is through the work done by the Maxwell and Reynolds stresses on the gradient of velocity at the boundary. The location of the energy exchange is identified as the active boundary, with no need to invoke ideas of negative energy. The relationship between the two approaches is critically discussed.

In this paper, a point of view is assumed where the tokamak is treated as a thermodynamic system open to external interactions. Those stationary states of the plasma are considered that are associated with a stationary entropy, i.e. with equilibrium between the entropy produced by the plasma and the entropy injected into it through the auxiliary heating. By means of the concept of magnetic entropy (a quantity that measures, in the framework of information theory and under suitable constraints, the probability of coarse-grained current density configurations), the responses can be analysed of the equilibrium magnetic configuration and of the related pressure profile to the intensity and to the deposition profile of the auxiliary heating when a condition of stationary entropy is attained. These factors are found to have considerable bearings on the magnetic equilibrium – in particular on the generation of states with negative magnetic shear. Moreover, the existence of a thermodynamic relation between entropy production and thermal conductivity involves a connection between magnetic structure and transport properties, and implies a strong reduction of the heat flow in the region of low or negative shear. Examples of practical interest are discussed both in the case of a homogeneous and that of a sharply localized power deposition.

The equations of magnetohydrodynamics (MHD) are written for non-uniform viscosity and resistivity – the latter in the cases of Ohmic and anisotropic resistivity. In the case of Ohmic (anisotropic) diffusivity, there is (are) one (two) transverse components of the velocity and magnetic field perturbation(s), leading to a second-order (fourth-order) dissipative Alfvén- wave equation. In the more general case of dissipative Alfvén waves with isotropic viscosity and anisotropic resistivity, the fourth-order wave equation may be replaced by two decoupled second-order equations for right- and left-polarized waves, whose dispersion relations show that the first resistive diffusivity causes dissipation like the viscosity, whereas the second resistive diffusivity causes a change in propagation speed. The second resistive diffusivity invalidates the equipartition of kinetic and magnetic energy, modifies the energy flux through the propagation speed, and also changes the ratio of viscous to resistive dissipation. If the directions of propagation and polarization are equal (i.e. for right-polarized upward-propagating or left-polarized downward-propagating waves), the magnetic energy increases relative to the kinetic energy, the resistive dissipation increases relative to the viscous dissipation, and the total energy density and flux increase relative to the case of isotropic resistivity; the reverse is the case for opposite directions of propagation, i.e. upward-propagating left-polarized waves and downward-propagating right-polarized waves, which can lead to the existence of a critical layer. The role of the viscosity and first and second resistive diffusiveness on the dissipation of Alfvén waves is discussed with reference to the solar atmosphere.

We provide a revised, and substantially enriched, version of an old study of ours, dealing with the theory of the slow evolution of a strictly dissipative, cylindrical plasma column in vacuum [J. Plasma Phys.43, 217–237 (1990)]. After correcting a technical mistake made in our previous formulation of the model of the physical system under consideration, we develop a fully amended version of the associated theory, paying special attention to the problem's well-posedness. A number of comments, generalizations and further details have also been added.

We derive a weak turbulence formalism for incompressible magnetohydrodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic field B0ê∥. Numerically and analytically, we find energy spectra E± ∼ kn±⊥, such that n+ + n− = −4, where E± are the spectra of the Elsässer variables z± = v ± b in the two-dimensional case (k∥ = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made.

This paper reports the first experimental results in which the kinetic energy of cold fog, generated in a water arc plasma, exceeds the electrical energy supplied to form and maintain the arc. The cold fog explosion is produced by breaking down a small quantity of liquid water and passing a kiloampere current pulse through the plasma. The 90-year history of unusually strong water arc explosions is reviewed. Experimental observations leave little doubt that internal water energy is being liberated by the sudden electrodynamic conversion of about one-third of the water to dense fog. High-speed photography reveals that the fog expels itself from the water at supersonic velocities. The loss of intermolecular bond energy in the conversion from liquid to fog must be the source of the explosion energy.

Kinetic Alfvén waves in the presence of an inhomogeneous electric field applied perpendicular to the ambient magnetic field in an anisotropic, inhomogeneous magnetoplasma are investigated. The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of a kinetic Alfvén wave. Expressions are found for the field-aligned current, the perpendicular current, the dispersion relation and the particle energies. The growth rate of the wave is obtained by an energy- conservation method. It is predicted that plasma density inhomogeneity is the main source of instability, and an enhancement of the growth rate by electric field inhomogeneity and temperature anisotropy is found. The dispersion relation and growth rate involve the finite-Larmor-radius effect, electron inertia and the temperature anisotropy of the magnetoplasma. The applicability of the investigation to the auroral acceleration region is discussed.

The properties of plasma sheaths developed along plasma boundaries are investigated analytically, assuming that dielectric slabs are present between electrodes. A collisionless plasma is confined by two planar electrodes. Planar dielectric slabs with finite thickness partition the plasma into many pieces. The sheath electric field is inversely proportional to the sum of 2(1+l)+Δ/ελ, where Δ and ε are the total thickness and the relative dielectric constant respectively of the dielectric slabs, l is the number of slabs and λ is the Debye length of the high-density plasma. In this context, the plasma sheaths may easily be controlled by appropriate choices of dielectric materials and their size.

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in resonant slow-wave layers developed by Ruderman et al. [Phys. Plasmas4, 75 (1997)] is used to study the interaction of sound waves with a one-dimensional planar magnetic plasma configuration. The physical problem studied here is the same as that considered by Ruderman et al. [Phys. Plasmas4, 91 (1997)]. The difference is in the description of the wave motion in the resonant layer. Ruderman et al. assumed that dissipation dominates non-linearity in the resonant layer and considered the nonlinear term in the governing equation for the wave motion in the resonant layer as a perturbation. In contrast, it is assumed in the present paper that nonlinearity dominates dissipation in the resonant layer. The solution to the governing equation for the wave motion in the resonant layer is obtained in the approximation of strong nonlinearity, and it is shown that the amplitude of the wave motion saturates when the Reynolds number tends to infinity. This solution is then used to derive the nonlinear connection formula that determines the jump across the resonant layer in the velocity component in the direction of inhomogeneity. The nonlinear connection formula is, in turn, used to obtain a nonlinear one- dimensional integral equation describing the outgoing sound wave, which appears owing to partial reflection of the incoming sound wave from the inhomogeneous plasma. The solution to this integral equation is obtained in the form of a sinusoidal wave under the assumption that an incoming sound wave contains the fundamental harmonic only. The coefficient of wave-energy absorption is calculated analytically in the long-wavelength approximation and numerically for arbitrary wavelengths.

An analysis is made of the phenomenon of self-induced erosion and spectral breaking of ionizing high-power microwave pulses propagating in a gas. The analysis describes in an analytically explicit and physically clear way the consistent interaction between the microwave pulse and the self-induced breakdown plasma. In particular, it clarifies, both qualitatively and quantitatively, the mechanisms behind the pulse erosion and the spectral breaking phenomenon, i.e. the splitting of the pulse spectrum into a redshifted and a blueshifted peak as observed in numerical simulation results as well as in experiments.

The effect of Coulomb correlations on the spectrum of electromagnetic waves propagating in a non-ideal magnetized fully ionized hydrogen plasma is studied. We employ the dielectric tensor constructed by means of the classical theory of moments without using perturbation theory.

Dispersion characteristics of surface waves in a semibounded plasma flow with relativistic velocity u0 parallel to the plasma–vacuum interface are presented. The plasma is considered to be cold and collisionless, which allows us to take into account only the electron motion. It is shown that – in contrast to the bulk waves, which are invariant with respect to Lorentz transformations and whose spectrum is independent of the flow velocity – the surface waves are not invariant, which leads to a dependence of their spectrum on the flow velocity and, correspondingly, to non-reciprocity. The latter peculiarity is due to the fact that the boundary conditions are not invariant.

Cylindrical ion-acoustic solitons are investigated in a warm plasma with negative ions and multiple-temperature electrons through the derivation of a cylindrical Korteweg–de Vries equation using a reductive perturbation theory. The results are compared with those for the corresponding planar solitons.

Higher-order contributions in reductive perturbation theory are studied for small- but finite-amplitude ion-acoustic solitary waves in a warm plasma with negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures and pressures). The basic set of fluid equations are reduced to a Korteweg–de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potential. At the critical negative-ion density, the coefficient of the nonlinear term in the KdV equation vanishes. A new set of stretched coordinates is then used to derive a modified KdV equation and a linear inhomogeneous modified KdV-type equation at the critical density of negative ions for the second-order perturbed potential. Stationary solutions of the coupled equations, for both cases, are obtained using a renormalization method.

Surface eigenmodes in a dusty plasma, where the dust is confined to a particular region, modelled as a uniform slab with non-uniform smooth boundary layers, are discussed. Inside this region, electron depletion occurs, while outside it, the plasma is just a normal uncontaminated plasma. In addition, the dust component can flow with respect to the background plasma, as a first approximation to cometary tails, where there is a notable difference between the fast flowing solar wind and the slow moving dust tail, viewed in the comet frame. The equilibrium densities and flow are non-uniform and the description involves a space-dependent dielectric function, which indicates the possibility of singular points, where eigenmodes resonate with local plasma oscillations. Surface eigenmodes on the slab are obtained analytically in the limit of long wavelengths, and these give rise to two distinct frequency domains, both having three different wave solutions. One of these refers to plasma surface waves, unaffected by the dust flow. The other two lead to convective surface modes, which become unstable for large flow speeds, akin to Buneman-type instabilities. A detailed study is made of the resonant processes in the boundary layers, including damping and growth rates.

Plasma screening effects on elastic electron–ion collision processes in a Lorentzian (kappa)-distribution plasma are investigated using the eikonal method. The electron–ion interaction potential is obtained by introducing a plasma dielectric function εκ. The semiclassical straight-line trajectory method is applied to the path of a projectile electron in order to investigate the variation of the eikonal phase as a function of impact parameter and spectral index κ. In the first-order eikonal approximation, the dynamic plasma screening effect on the eikonal phase is found to be a static screening effect, and depends only on the Debye length and spectral index. The position of the maximum of the differential elastic eikonal cross-section recedes from the ion core with increasing spectral index. The plasma screening effect on the eikonal cross-section increases with decreasing spectral index.

The influence of a highly energetic electron beam on the electron distribution function (e.d.f.) in a hot dense plasma is investigated by solving the Boltzmann equation analytically. A plateau is obtained in the tail of the e.d.f. over an energy range between the excitation threshold and an energy value half that of the monoenergetic electrons. The importance of this plateau is discussed for a dense He-like argon plasma.