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.

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.

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

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.

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.

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.

Starting from a set of equations that lead to a linear dispersion relation coupling kinetic Alfvén waves and ion-acoustic waves, three-dimensional KdV equations are derived for these waves. These equations are then used to investigate the three-dimensional stability of solitary kinetic Alfvén waves and ion-acoustic waves by the small-k perturbation expansion method of Rowlands and Infeld. For kinetic Alfvén waves it is found that there is instability if the direction of the plane-wave perturbation lies inside a cone, and the growth rate of the instability attains a maximum when the direction of the perturbation lies in the plane containing the external magnetic field and the direction of propagation of the solitary wave.

The transverse spreading of magnetic field lines in a turbulent plasma is investigated analytically in order to obtain a statistical characterization at large spatial scales. We develop a functional-integral method that allows us to calculate in a systematic way statistical averages of physical quantities that depend on the fluctuating field. The known magnetic diffusion coefficient for the shear-free case is corrected with a term arising from the assumption of a finite transverse correlation length. For the case with magnetic shear the functional method provides the appropriate framework for a perturbative approach based on diagram series.

In this work we investigate the nonlinear dynamical interaction of magnetized electrons and ordinarily polarized electromagnetic modes. We show that when either the mode amplitude is sufficiently large or the electronic longitudinal momentum along the external magnetic field is sufficiently small, non-integer harmonics originating from higher-order terms in the expansion of the Hamiltoniari in powers of the electromagnetic field become important, and the relevant action-angle phase space ceases to be well described by standard nonlinear pendulum approximations. We develop appropriate resonance overlap studies in order to determine the conditions to be satisfied at the transition from regular to chaotic orbits, checking the accuracy of the results with numerical integrations of the full dynamical equations. We verify that chaotic orbits occur within a ‘window’ among the possible values of the longitudinal momentum. The width of this window and the degree of overlap between neighbouring resonances within it are both shown to grow with particle action and wave frequency. We also show that once overlap has occurred for a particular value of the action, it persists for larger values of this quantity, a circumstance that leads to a large amount of particle energization.

This paper presents a paraxial theory of relativistic self-focusing of a Gaussian laser beam in plasma for a time-harmonic plane wave at arbitrary beam intensity. Since the relativistic mechanism is instantaneous, the theory is also applicable to self-focusing of laser pulses. The analysis leads to two values for the critical beam power for self-focusing, Pcr1 and Pcr2. When P < Pcr1 < Pcr2, the beam diverges. When Pcr1 <P <pcr2, it first converges, then diverges, and so on. When P > Pcr2 it first diverges, then converges, and so on.

A model of a cylindrically symmetric, force-free magnetic field consisting of a sequence of concentric layers with piecewise-constant α is used to construct models of the surface currents on isolated, force-free magnetic flux tubes. Two boundary conditions are considered: a current-neutralized flux tube (Bφ = 0, Bz φ 0, Bz ≠ O at r > r0), and an isolated current-carrying flux tube (Bφ ≠ 0, Bz = 0 at r > r0). A single-a model that is current-neutralized is a reverse-field pinch, and is unacceptable as a model for a solar flux tube. Examples of two-α models for a current-neutralized flux tube are presented. The models of the surface currents satisfying either boundary condition are shown to simplify considerably when the surface layer is thin. A model consisting of several layers, with piecewise-constant α, may be used to find an approximate solution for a force-free flux tube with an arbitrarily specified current profile.