Plasmadynamical equations for a two-component plasma are obtained starting from the linearized Vlasov–Landau kinetic equation. Explicit formulae are given for the frequency dependent transport coefficients. Eigenvalues of ten plasmadynamical modes are also discussed.

This paper is the first part of a work concerning a statistical theory of Langmuir turbulence in which the destabilization of an ensemble of plasmons by self- modulation is considered as a critical phenomenon. The first part is devoted to a discussion of the existence of a statistical equilibrium for the ensemble of modes. A transition curve, which separates equilibrium from non-equilibrium, is found. Several properties of the plasma, when the self-modulation instability is saturated, are derived in the neighbourhood of the critical Langmuir energy density Wc. In particular, the Langmuir energy spectrum is found to be proportional to kd-3, the correlation length is found to diverge as üW–Wcü–half, and the anomalous conductivity at the plasma frequency is found to diverge as üW – Wcü-1.

The stability of a self-consistent, large-amplitude, circularly polarized wave in a warm plasma is investigated. For perturbations to the system propagating normal to the plane of circular polarization, a dispersion relation is derived employing an expansion in the nonlinear wave amplitude and the momentum of the plasma particles in the plane of polarization. Instability results both in the absence and presence of a large-scale magnetic field with a growth rate of the order of the nonlinear wave amplitude.

The theory of electrostatic plasma turbulence is considered. The basic equations for the dynamics of the hierarchy of the moment equations are derived and the difficulty of the closure problem for strong plasma turbulence is discussed. The characteristic functional in phase space is introduced and its relations to the correlation functions are described. The Hopf functional equation for dynamics of the characteristic functional is derived, and its equivalence to the hierarchy of the moment equations is established. Similar formulations were carried out in velocity-wave vector space. characteristic functional are considered and their relationships are studied. An approximate solution for Hopf's equation for the nearly normal turbulence is obtained which is shown to predict diffusion of the mean distribution function in velocity space.

The structure of transverse MHD shock waves in an initially partly ionized plasma is studied using a three-fluid model with collisional transport coefficients. This model includes the effects of non-equilibrium ionization and of ion velocity slip. A closed set of structure equations is obtained and it is shown that they have a saddle-point – saddle-point topology which prohibits direct integration. In distinction from previous MHD shock structure studies, it is not possible to reduce the number of variables in a realistic manner to allow direct integration, nor is it possible to use the method of matched asymptotic expansions. An iterative solution method is presented in this paper, based on a detailed analysis of the integral curve topology.

The properties of certain wave modes excited in a weakly ionized plasma placed in an external d.c. electric field are analyzed from the standpoint of the linearized kinetic equation, the electron steady-state distribution function being taken in the form of the extended Margenau–Davydov and, in particular, Druyvesteinian. The presence of absolute stability cones formed by certain propagation directions is found. The corresponding critical values of the electron drift, destabilizing each of the modes considered, is also evaluated for a plasma with a Druyvesteinian distribution.

Under the assumption of a general symmetry (dependency on two space variables only), a generalized Grad–Shafranov equilibrium equation is derived and discussed. An elementary formulation of the boundary conditions is given and the existence of solutions is investigated. It emerges that from the equilibrium requirements almost no restrictions follow for the two arbitrary functions appearing in the equilibrium equation.

The structure of transverse MHD shock waves in a partly ionized hydrogen plasma is studied using a three-fluid model with collisional transport coefficients developed in Part 1. The morphology of the various sublayers in the shock front is analyzed in detail and it is shown that strong shock waves have a characteristic viscous structure. Weak to moderate strength shock waves display a resistive structure in which the enhanced transverse resistivity due to ion-slip plays a significant role, leading to a pronounced peak in the ion temperature profile. Calculated shock structure profiles are also compared with experimental temperature data. Results in the form of tables and figures are presented for shock waves with fast Mach number ranging from 1–10 in hydrogen plasma with initial degree of ionization ranging from 5–100%.

Using a simpler formalism than in the original paper on this subject, we verify the earlier result that, for a pump frequency separation Δ approximately equal to twice the ion acoustic frequency Ω, the use of two long-wavelength pumps can reduce the threshold for parametric excitation of ion-acoustic waves when, and only when, the Langmuir wave damping rate γ is much larger than Ω. The threshold is then reduced by a factor of order Ω/Ω, the optimum value of t being ▵ 2Ω –Γ for equal pump amplitudes, where Γ is the ion-acoustic wave damping rate and Γ ≪ Ω. The analysis presented in a recent paper is shown to be valid only for γ ≪ Ω, where the threshold reduction is quite small, vanishing in the limit of weak ion-acoustic wave damping (Te/Ti≫ 1).

Ideal MHD equilibria with an ignorable space variable are investigated. It is shown that only three classes of these symmetric equilibria exist: the systems with a straight, a (cylindric) helical, and a circular magnetic axis.

The plasma response to electrostatic travelling wave packets with a slowly varying envelope is investigated, including dynamical friction between electrons and ions. A kinetic diffusion equation and, therefrom, a new set of macroscopic equations is derived which includes current and magnetic field generation due to friction and wave momentum transfer.

Many different problems, associated with the propagation of electromagnetic waves in an inhomogeneous isotropic plasma and governed by second-order differential equations, are reformulated so as to be brought within the scope of a common analytical procedure. Refiexion coefficients, energy considerations, approximation procedures, slab refiexion, and other theorems are considered, the investigations of different physical processes all being attributable to one underlying mathematical method involving integrals, whose integrands contain quadratic products of the field variables and their derivatives in two different arrangements.

The cold-plasma model of the radio wave scattering from spatially random fluctuations of electron density in an anisotropic plasma is extended to the warmplasma model, in which the effect of electron pressure is taken into account. Since the medium is compressible as well as anisotropic, there is the additional possibility of mode conversion from an incident electromagnetic wave to a scattered electron plasma wave. Some numerical results are also included.

A nonlinear Alfvén wave structure with axial symmetry about the line of force of an ambient magnetic field is presented. The solitary wave forms a ‘ring’ shaped waveguide along the magnetic field line.

Langmuir probe measurements have been carried out which confirm the occurrence of double-layers in an argon positive column. Pulsing the discharge current permitted probe measurements to be performed in the presence of the double- layer. Supplementary evidence, obtained from d.c. and pulsed discharges, indicated that the double-layers formed in the two modes of operation were similar. The double-layers observed were weak and stable; their relation to other classes of double-layers is discussed, and directions for future work are suggested.

A class of magnetostatic solutions is obtained for the magnetic field and current in a toroid. The solutions are characterized by nested toroidal flux surfaces whose cross-sections are concentric circles. The model distribution of the magnetic field and current allows a correct calculation of the typical self-induced magnetic force exerted by a current interacting with its own magnetic field in a toroidal configuration.

A brief review of resonance cones in magnetized plasmas and their relationship with guided wave modes in bounded plasmas is given. It is shown that these two concepts are related mathematically by a Watson transformation, and physically by being complementary descriptions of waves in a warm bounded plasma. A detailed summary of the complementary nature of these two wave descriptions is given.

Recently a spatially uniform expression for the time asymptotic binary correlation function of a Landau-stable plasma was derived from the BBGKY hierarchy equations. In this paper, the high-frequency (Vei ≪ ‖w‖ ≪ ωpe) electrical conductivity of a spatially homogeneous, unmagnetized Lorentz plasma

is calculated from this expression; the result is compared with those obtained from other convergent collision integrals.

Propagation of electron-acoustic waves in a strongly nonlinear magnetoplasma with two ion species is investigated. The presence of the second ion component affects the dynamics of these solitary waves in a variety of ways. Besides solitons, supersonic holes (density depressions) are produced by sufficiently large- amplitude perturbations. Heavier and hotter ions are more favourable to the holes. Applications of the present investigations to space plasmas are pointed out.