The problem of linear conversion of an ordinary polarized electromagnetic wave in a magnetized plasma with density gradient parallel to the magnetic field is considered. An expression for the conversion coefficient as a function of angle of incidence, WKB parameter and magnetic field is obtained. The magnetic field leads to a narrowing of the range of angles of incidence leading to linear conversion, compared with the unmagnetized case.

Nonlinear Rayleigh-Taylor instability of a heavy, infinitely conducting fluid, supported against gravity by a uniform magnetic field in the vacuum, is studied for three-dimensional disturbances using the method of multiple time-scales. The three-dimensional problem can be reduced to two dimensions as it is found that an instability present for a three-dimensional disturbance of a given wavelength, for a given equilibrium magnetic field, is also present for a two-dimensional disturbance of the same wavelength propagating along an equilibrium magnetic field of lower strength. The instability is studied for both standing and progressive waves. Although in the linear stability problem the instability growth rate for a progressive wave of a given wavelength is equal to that for a stationary wave of the same wavelength, in the nonlinear instability problem studied here these waves are found to have different growth rates. Our results are compared and contrasted with those for the two-dimensional instability problem studied earlier.

The effect of finite spectral width on the modulational instability of Langmuir waves has been investigated applying a method developed by Alber to derive a transport equation for the spectral density. The numerical results presented show that the spectrum is stable against modulational perturbation when the spectral width exceeds some critical value. For a Gaussian spectrum, the maximum growth rate is less than that for a monochromatic wave but the domain of modulational instability is extended. For a uniform distribution the shift in the growth rate curve towards the region of shorter wavelength is more pronounced and, for a certain range of spectral width, the maximum growth rate exceeds that for a monochromatic wave.

The effect of the ponderomotive depression of the plasma density on the power reflexion coefficient is calculated in the first space harmonic approximation. Numerical results demonstrate a considerable growth of the reflexion coefficient when increasing the RF power. Exceptionally, the reflexion coefficient can be almost invariable up to high RF power densities (≃ 10kW cm-2), if the unperturbed plasma density gradient is high (≳ 5 × 1012 cm-4). The relation of the present theory to experiments is discussed.

A retarded time superposition principle is formulated and proved for the two particle correlation function in a multi-species relativistic, and fully electro-magnetic, plasma. This principle is used to obtain the relativistic collision operator. Starting from the relativistic Klimontovich equation, the statistical (Liouville) average of the Klimontovich equation yields an expression for the collision operator in terms of the two-time two-point correlation function for two particles, G12(1, t12, t2). It is proved that G12(1, t12, t2) can be written in a retarded time superposition form in terms of the self-correlation W11(1, t12, t2) and the discreteness response function P(1, t12, t2). The equation for the pair correlation function G12(1, t12, t2), excluding triplet or higher-order correlations, is thus replaced by the simpler equation for P(1, t12, t2). This is the test particle problem which relates P(1, t12, t2) to the discreteness source term W11(1, t12, t2). The equations for P(1, t12, t2). and W11(1, t12, t2) are solved for stationary, homogeneous plasmas without external fields. With these solutions, the collision operator is expressed in terms of the relativistic dielectric properties of the plasma.

The negative resistance of double layers has been invoked to explain instability in diode currents, and the flickering aurora phenomenon. In this paper the theory of the negative resistance is extended by a more detailed account of the constraints that are imposed on the electron distributions in the double layer. Attention is concentrated on the energetic trapped electrons which originate at the high potential side of a double layer.

The existence of a non-trivial free boundary solution of the nonlinear Grad-Shafranov equation is studied. In the case of axisymmetric toroids, the existence of the solution is proved by the standard variational approach using assumptions which are not physically restrictive. Also, the existence of a cylindrically symmetric solution is proved in the case of straight cylinders with circular cross-section.

The structure of driven electrostatic oscillations is determined for a cold plasma with a zero-order density gradient along the magnetic field. A set of well-behaved structures, bounded at plasma resonance, exists for discrete values of the perpendicular wavenumber. A Green's function suitable for sources located in the overdense region of the plasma is constructed. The driven medium responds as a loss free guide.

We present the first detailed experimental study of the plasma response to movement of a plane ion-rich sheath. The results show clearly that ion rarefaction waves are associated with sheath expansion while ion enhancement (‘compressive’) waves are formed on sheath collapse. The data are compared successfully with a nonlinear theory which includes the presence of a presheath prior to the sheath motion.

The first-order CGL fluid equations for electrons including the first-order heat fluxes are applied to the propagation of whistler waves. The dispersion relation of whistler waves is derived for two types of equilibrium electron distribution functions with cold and hot components. The effect of electron temperature anisotropy and the existence of cold electrons on the field-aligned propagation of whistler waves is analysed. It is shown that the electron temperature anisotropy intensifies the tendency of whistler waves to follow the lines of force of static magnetic field, that the existence of cold electrons in an anisotropic plasma further intensifies this tendency, and that under certain conditions the waves propagate only along the static magnetic field.

For the solution of Petschek's problem of field-line reconnexion, a new method is elaborated which is based on the introduction of a special co-ordinate system in which the streamlines and the magnetic lines of force become co-ordinates simultaneously. We have constructed the zero-order and the first-order approximation (for small Alfvén Mach numbers) for the solution of Petschek's problem in the steady-state, compressible, two-dimensional symmetric case. It is shown that the density across the slow shock wave increases by a factor

and the pressure by

(β = 8πρ0/B20, γ being the adiabatic exponent), and the plasma accelerates up to the Alfvén velocity. On the bases of the results obtained and of the analysis of numerical experiments on the reconnexion problem we draw the conclusion that during the initial phase of the process there develops a current sheet as described by Syrovatskii and that simultaneously there is a development of the tearing mode instability whose nonlinear phase creates the condition for the reconnexion process in the sense of Petschek.

A detailed mathematical analysis of plane steady-state reconnexion is given for the case when the plasma parameters and the magnetic fields are not identical on both sides of the current sheet. Asymptotic solutions in the sense that the inflow velocity is much less than the local Alfvén velocity as well as the arrangement of shock waves are obtained. Rotational (Alfvén) waves, slow shock waves, rarefaction waves (expansion fans), and a contact discontinuity may occur. Four different types of solution, corresponding to different shock wave configurations, are possible. They depend on the parameters of the inflow regions in a unique way.