A standard theory of strong scintillations in an isotropic medium is extended to the case of polarized radiation propagating through a weakly anisotropic, randomly inhomogeneous, magnetized plasma. A hierarchy of moments of the radiationfield is defined, with an nth-order moment being an nth-rank polarization tensor, and the tensor equation for the evolution of an arbitrary moment is derived. Emphasis isplaced on the mutual coherence function (a second moment), which is rewritten in terms of the Stokes parameters. The evolution of the polarized radiation through the randomly inhomogeneous, weakly anisotropic medium is described in terms ofa matrix equation for the Stokes vector. It is shown that the theory implies that a depolarization occurs as a result ofsuch propagation. This corresponds to a decrease in the degree of linear polarization for propagation through a weakly anisotropic plasma. The rate of depolarization is estimated, and an interpretation is suggested. The polarization dependence of the angular size of the apparent image is determined. Two counter-intuitive results are found: that the image canhave a circularly polarized component even for an unpolarized source, and that the angular size of the linearly polarized source can decrease. These are interpreted in terms of random variations in the ray path with opposite signs for the two natural modes, resulting in a separation of the centroids of the images in the two circular polarizations.

The theory of strong scintillations in a weakly anisotropic plasma is used to derive an equation satisfied by the correlation functions for the Stokes parameters. The coefficients that describe these correlation functions are determined explicitly in terms of a matrix generalization of the standard phasestructure function. In discussing implications of the theory, emphasis is placed on terms that have no counterpart in an isotropic plasma. It is shown that the decay of the linear polarizaiton that results from differential Faraday rotation is different in the mean squares and the square means of the Stokes parameters. In principle, this allows one to determine properties relating to the fluctuations of the magnetic field along the ray path. A formal treatment of polarization dependent intensity fluctuations in a magnetized plasma is presented and discussed briefly.

We use the general Fokker–Planck coefficients derived in the first paper of this series, which describe the interaction of energetic charged particles with weak plasma turbulence in a magnetized plasma, to calculate the mean free path λ of cosmic-ray particles along the uniform background magnetic field. This quantity is a key parameter for confining energetic charged particles in cosmic plasmas, and can be experimentally inferred from interplanetary in-situ observations of solar particle events

Nonlinear MHD waves propagating obliquely to the external magnetic field in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts are treated without imposing the customary quasi-neutrality between the different species or neglecting the displacement current in Ampère's law. The wave magnetic field obeys a vector nonlinear evolution equation, which in the limits of parallel propagation or of both the neglect of the displacement current and the imposition of quasi-neutrality reduces to the vector formulation of the well-known derivative nonlinear Schrödinger equation.

This study treats the system of Vlasov and Maxwell equations for the Fourier transform in space and time of a plasma referred to Cartesian co-ordinates with the z co-ordinate parallel to the uniform equilibrium magnetic field; the equilibrium plasma density depends on ηχ, where η is a parameter, and goes to zero as │χ│ → ∞. The component ky of the wave vector is taken to be zero, whereas kz is non-zero, thereby allowing for Landau damping. Coupling of the components of the electric field parallel and perpendicular to the equilibrium magnetic field (the ordinary and extraordinary waves in a homogeneous plasma) is neglected.

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

The asymptotic theory of flows of high-pressure plasmas past biased bodies (electrostatic probes) is extended to relatively low charge densities, where the Debye radius h is comparable to or exceeds the thickness ▴ of the viscous near- probe boundary layer. Various orders of magnitude of h with respect to a dimension of the probe and various ranges of the probe potential are considered. The governing physical mechanism of current transfer in the perturbation region is identified in each regime, and simple formulae for the probe current–voltage characteristic are obtained whenever possible. In particular, it is shown that an earlier conclusion, valid for h ≪ Δ, on the existence of a linear segment on the electron branch of current-voltage characteristic with a slope depending on the electron density, is also valid in the present situation. It h ≫ Δ, a similar conclusion holds for the ion branch; at large enough probe potentials the jon branch saturates —although for a different physical reason than in the case h ≪ Δ

The spatial factor Φ(x) of the vibratory-state MWB (‘multiple water-bag’) plasma potential Φ = Φ(x) exp (- iwt) in the vicinity of its generating electric charge rgr;(x) exp (- iwt) is proved to be the Poisson potential U(x) of ρ plus an error function ξ(x) whose magnitude can be rendered as small as desired, in relation to │Φ(x)│, by locating the recording point sufficiently close to the charge. How close this should be is independent of ρ, but depends quantitatively on the MWB model and the frequency ω, and qualitatively on whether the frequency of the vibrations is greater or less than the plasma frequency. A high vibration frequency reinforces accuracy in the Poissonian approximation. The question as to whether Φ is weaker or stronger than U(x) is tacked. Shielding efficiency is explored in the vibratory state.

Cross–field transport coefficients for the electric current and heat flux have been calculated for an equal–mass plasma for various values of the Hall parameter Ωr in the range Ωr ≥ 1. Coefficients have also been calculated for parallel transport. These have been obtained using the linearized Fokker–Planck equations for both particle species, taking advantage of the mass symmetry, which leads to remarkable cancellations in the collision terms.

Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long-wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of warm ion-fluid and hot isothermal electrons is investigated using reductive perturbation theory. A Korteweg-de Vries-type equation, with temperature- and relativistic-parameter-dependent coefficients is obtained. The renormalization method is applied to the equations obtained from the different orders of perturbation theory to obtain a stationary solution. Relativistic cold and non-relativistic warm plasma limits are considered in order to make comparisons with previous results.

The expansion of a quantum electron gas (non-relativistic, no spin) is investigated via the one-particle Schrödinger–Poisson model. Classically, the nonlinear term enhances the formation of a very regular asymptotic state. By means of rescaling methods, we conjecture that the quantum asymptotic solution is identical to the classical one. Subsequent numerical simulations confirm the above conjecture and define precisely the way in which the classical limit is approached.

The generation of a quasi-stationary nonlinear magnetization current in a plasma in the presence of high-frequency electromagnetic waves is considered. A kinetic theory is developed that takes the velocity dependence of the collision frequency into account. The results show that even a small collision term can have a significant effect on the generation mechanism.

A helical ion beam propagating through a plasma cylinder drives electrostatic ion-cyclotron waves to instability via cyclotron interaction. Higher harmonics of the beam cyclotron frequency can be generated in this way. The growth rate increases with the harmonic number. The efficiency of beam energy transfer to the wave can be of the order of a few per cent.

The following property is shown of the entropy functional constructed in previous work and associated with a Vlasov electrostatic or magnetostatic collective equilibrium (a static solution of the Vlasov equation): the vanishing of the first variation of the functional is equivalent to Hamilton's principle applied to a Lagrangian describing motion of the underlying system of particles compatible with the collective equilibrium, provided that the variations are associated with reversible processes. This property is shown in two cases: (i) a system of particles in Coulomb interaction admitting a collective (Vlasov) equilibrium in the presence of a scalar pressure; and (ii) a system of independent electrons in a background of fixed ions subject to an external electric field and to a magnetic field (created in part by electron currents) associated with a cylindrically or toroidally symmetric equilibrium in the presence of the electron–ion friction force and an anisotropic pressure.

This paper presents the theory of an inhomogeneous source of cyclotron emission from a three-branch mode-conversion layer in a non-uniformly magnetized plasma. The physical formulation of the problem is based on the generalized Kirchhoff's law that relates, branch by branch, the emission to the absorption. General integral expressions for both absorbed and emitted energy fractions along each wave branch are obtained. A discrete multi-point model of absorbers and emitters is analysed. A variational principle for the integral of the emitted power is formulated.

A study is made of electrostatic waves in a cold equal-mass plasma. Numerical simulation reveals that cold equal-mass plasmas are fundamentally unstable to such oscillations, in contrast to the behaviour of these waves in electron-ion plasmas. A quasi-linear analysis of the problem is performed and an analytic solution found that duplicates the early evolution of the plasma.

A high-power millimetre wave (w1, k1) propagating through a magnetized plasma in the presence of a wiggler magnetic field (0, k0) produces density perturbations at (w1, K1 +K0). The density perturbations couple with the oscillatory velocity at (wl, K1) to produce a nonlinear current at (2w1, 2K1 +K0) driving second-harmonic electromagnetic radiation. The amplitude of the generated wave is sensitive to cyclotron resonance.