The nonlinear Rayleigh—Taylor instability of viscous magnetic fluids is considered under the influence of gravity and surface tension in the presence of a constant tangential magnetic field. The method of multiple-scales expansion is employed. A nonlinear Schrödinger equation with complex coefficients is imposed from the solvability conditions and used to analyse the stability of the system. A quadratic dispersion relation with complex coefficients is obtained. The Hurwitz criterion for a quadratic polynomial with complex coefficients is used to control the stability of the system. It is found that an increase in the viscosity increases the extent of the stable region in the presence of a magnetic field. Finally it is shown that the magnetic permeability of the fluid affects the stability conditions.

Extremely large-amplitude Langmuir waves are investigated on the basis of relativistic kinetic theory. Analytical formulae for the electron density and the electric field of the wave differ essentially from earlier results obtained using the cold-hydrodynamical equations.

Obliquely propagating ion-acoustic nonlinear periodic waves in a magnetized plasma consisting of warm adiabatic ions and two Maxwellian electron species are studied. Using the reductive perturbation method, the Korteweg–de Vries (KdV) equation is derived and its cnoidal wave solution is discussed. It is found that as the amplitude of the cnoidal wave increases, so does its frequency. The effects of variations in the density and temperature ratios of the two electron species, the ion temperature, the angle of obliqueness and the magnetization on the characteristics of the cnoidal wave are discussed in detail. When the coefficient of the nonlinear term of the KdV equation, a1, vanishes, the modified Korteweg–de Vries equation is derived, and its periodic-wave solutions are discussed in detail. In the limiting case these periodic-wave solutions reduce to soliton or double-layer solutions.

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

Reflection and excitation of ion-acoustic waves by a bipolar potential structure consisting of a grid and a metallic plate have been investigated experimentally in a multi-component plasma with negative ions. Reflection is observed owing to the presence of the negative ions, even if both the grid and the plate are biased negatively with respect to the plasma potential so as to collect positive ions. Reflection coefficients and excitation efficiencies are measured as a function of the bias voltage of the electrodes. The reflection coefficient becomes larger for a negative bias of the grid, and is almost constant for a positive bias of the grid as the partial pressure of SF6 gas is increased.

A pair of quasi-linear-like equations is derived to describe the effect of three-wave interactions between high-frequency photons and Langmuir waves in a differential approximation. Induced photon decay leads to terms analogous to those for spontaneous emission, but involving the square of the photon occupation number. The effect on the Langmuir waves is evaluated for axisymmetric photons. The effect on the photons is shown to be similar to but weaker than induced Compton scattering by thermal electrons. The absorption coefficient for the Langmuir waves is evaluated for an axisymmetric distribution of photons, and used to discuss a photon-beam-induced instability. Possible astrophysical applications to solar ‘spike’ bursts, the eclipse of a radio pulsar and the variable low-frequency emission from some active galactic nuclei are discussed briefly, and it is concluded that the process can account for the observed properties of the eclipse of PSR 1957 + 20.

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.

In the theory of tearing modes analytical expressions for the growth rate y are only known for large y > 1/TR. However, since resistive instabilities cannot be externally stabilized, they will rather be observed at small growth rates, which are also the ones that matter in a bifurcation analysis. In this paper the described gap in the tearing theory is closed for the model of a convected resistivity in a sheet pinch. The analytical expressions obtained from an asymptotic perturbation analysis for small growth rates are as simple as those for large growth rates. However, they differ from them appreciably, and also show a marked difference between symmetric and asymmetric perturbations. Specifically, for asymmetric modes in contrast to the symmetric ones, no stability threshold exists, i.e. all asymmetric modes are at least weakly unstable. In addition to the results for small growth rates, an implicit analytical formula is presented that bridges the regime between small and large growth rates. The high quality of the analytical results is confirmed by numerical solution of the full tearing equations

Parametric decay of an upper-hybrid pump into another upper-hybrid wave and a low-frequency lower-hybrid mode is considered in a two-electron temperature plasma. Expressions for the nonlinear dispersion relation and growth rate are obtained. It is found that the growth rate is quite sensitive to the hot-electron temperature and the density ratio of the hot and the cold components only when the side-band frequency is close to the second or third harmonic of the cyclotron frequency. The relevance of our investigation to Q machines and the ELMO bumpy torus is pointed out.

MHD instabilities are governed by the transport-determined plasma profiles, and the transport process is affected in turn by the instabilities. Using a one-dimensional code, we have investigated the inter-relationship between instabilities, transport and plasma profile in a tokamak discharge. The results show that the global energy confinement becomes strongly dependent on the boundary transport condition owing to strong coupling between them, and a higher edge temperature would ensure a higher core temperature and hence greater global energy confinement.

The hydromagnetic Kelvin–Helmholtz instability is relevant in many complex situations in astrophysical and laboratory plasmas. Many cases of interest are very complicated, since they involve the combined roles of velocity shear, density and magnetic field stratification, and various geometries in compressible plasmas. The present work is part of a systematic investigation of the influence of the various physical and geometrical parameters characterizing the plasmas on the Kelvin–Helmholtz modes. The general dispersion relation for ideal compressible MHD modes localized near a velocity discontinuity between two uniform plasmas is derived. The existence and characteristics of the modes and their stability are studied analytically for any relative orientation of B, u and k, for continuous B and ρ. It is shown that the stability of a given configuration cannot be determined by considering only special orientations of k (say flute or parallel modes). The results obtained here may serve as a guide to interpret results in more complicated and realistic situations, such as those occurring in experiments and natural plasmas.

A family of three-dimensional models of reconnection is presented in which the different members of the family are characterized by the vorticity with which plasma flows towards the reconnection site. The nature of this inflow also determines the size and speed of the outflow jet that carries reconnected field lines away from the reconnection site, and the shape of the MHD shocks that bound it. Flows with positive vorticity are of a flux pile-up type, for which the outflow jet is fastest and narrowest. Among those with negative vorticity is the three-dimensional analogue of Petschek reconnection. Not all combinations of vorticity and reconnection rate are possible; for those solutions with negative vorticity, there is a maximum reconnection rate. As the magnetic Reynolds number Rme or the current density is increased, this maximum is reduced and the possible types of solution become more polarized towards the two extremes of flux pile-up and slow compression regimes. Given a distribution of vorticities and inflow speeds, these models give the corresponding distribution of possible steady-state reconnection rates. As an illustrative example, we take Gaussian distributions of both to show that the resulting distribution is dominated by the flux pile-up regime.

The characteristics of the specularly reflected laser light (1.06 μm) from a copper plasma have been studied experimentally. The diffusivity and depolarization of specularly reflected radiation can be explained by the density contours and self-generated magnetic field at the radiation turning point in the plasma layer.

Dynamical equations are derived for the evolution of weakly nonlinear electron plasma waves when the electron distributions are characterized by more than one temperature component. The presence of electron-acoustic modes in multi- temperature plasmas opens a new decay channel. By considering an explicit example, it is demonstrated that these distributions imply significant modifications of the standard models for the decay spectrum of electron plasma waves. In particular, long-wavelength Langmuir waves can decay to shorter wavelengths. The results can have implications for ionospheric heating experiments.

The interaction of electromagnetic filamentation instability and electrostatic Langmuir parametric instabilities (parametric decay instability and oscillating two-stream instability) driven by an intense laser in a plasma is examined. Near the critical layer of an underdense plasma, where the incident laser frequency is close to the local plasma frequency, coupling of unstable electromagnetic and electrostatic modes may occur. The transition from purely electromagnetic and purely electrostatic instabilities to hybrid instabilities is analysed using the generalized Zakharov equations.

At lower-hybrid frequencies in tokamaks, ponderomotive forces at fast-wave launching typically lead in the vicinity of the launching structure to a boundary plasma density increase. This results in a decrease in the reflection coefficient, and, in detached plasmas, to the appearance of a local electric field maximum at several centimetres from the launching grill structure; this electric field maximum is connected to the reversal of the plasma density gradient near the grill mouth because of ponderomotive force effects.

Motivated by the need to explain observed elliptically polarized emission from Jupiter, the mechanism of electron-cyclotron maser emission is considered for drifting electron distributions, where the electrons stream with a non-zero mean velocity parallel to the magnetic field lines. An analytical expression for the semirelativistic growth rate is derived and its properties analysed in detail for waves generated in the magneto-ionic modes. The main features of the growth rate are discussed, on the basis of a geometric analysis using resonant ellipses.

The theory of linear magneto-acoustic surface waves is investigated for current sheets across which the magnetic field has an arbitrary change of direction: in the first place discontinuously, and in the second place via a narrow transition region in which the magnetic field rotates with constant amplitude, so that the gas pressure remains constant. It is found that the effect of non-zero pressure is to eliminate the surface wave for certain angles of propagation and to allow the existence of an additional, slower, surface wave for other angles of propagation. The resonance damping of the surface waves when the current sheet is of small non-zero width is considered, and it is found that Alfvénresonance damping always occurs, as well as (for high β and certain angles of propagation) compressive- or cusp-resonance damping.

We present the results of a theoretical investigation of the conditions for the existence of a stationary, strong, monotonic double layer. A model that includes finite temperatures both of the particle species accelerated by the double layer and of those reflected by it is developed on the basis of the general theory of double layers due to Andrews and Allen. A numerical solution of the model equations is presented and analysed. Explicit approximate formulae for the electron-to-ion current ratio (i.e. the Langmuir factor) and for the initial velocities (i.e. directional energies of the accelerated particles at the double-layer boundaries before acceleration) are also derived that fit almost exactly the exact numerical solution over a wide range of double-layer potentials. It is shown that in the cases in which the standard results of Langmuir and Bohm are an oversimplification, approximate formulae may be used instead of exact numerical solutions to obtain quite accurate results in a simple manner.

Large-amplitude relativistic nonlinear Langmuir waves are analysed using the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two- fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ratio of ion mass to electron mass. The constant energy depends on the ratio of electron velocity to that of light. In the non-relativistic limit large-amplitude relativistic Langmuir waves do not exist. This investigation predicts new findings of large-amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important.