The stability of localized solitary wave solutions of simultaneous nonlinear Schrödinger equations describing different types of interacting waves in a plasma has been investigated. It is found that the stability depends on the nature and strength of the interaction potential between the two waves. The possible results of interactions between two colliding solitary waves have been discussed using the conservation laws.

Using the Bhatnagar–Gross–Krook collision model, the effects of charge-transfer and elastic ion-neutral collisions on the crossfield beam-driven ion-acoustic instability in a double plasma device are studied. Elastic collisions cause a slowing of the beam, while charge exchange gives rise to an exponential decay in ion beam density. The resultant damping of the instability is calculated and compared with experiment.

Analytic forms for the MHD continuous spectra in axisymmetric tokamak equilibria are derived using an expansion scheme in powers of the small inverse aspect ratio. Resulting formulae for the shear Alfvén continuum have been evaluated for the shear Alfvén wave heating experiment on the Tokapole II device at the University of Wisconsin-Madison. Mode coupling, induced by toroidicity or non-circularity, is shown to occur, in first order, on and near rational surfaces for particular poloidal and toroidal mode numbers. The coupling is shown to produce gaps in the spectrum, analogous to the gaps which appear in the energy spectrum of a single electron in a periodic potential lattice.

Petschek's model of compressible reconnexion developed in part 1 is extended to include an additional transverse magnetic field. Part of the incoming Poynting flux is degraded into kinetic energy at an intermediate wave (rotational) discontinuity. Yet more is degraded into heat and kinetic energy at a slow shock lying downstream of it. Everywhere downstream of the rotational discontinuity, the transverse magnetic field exceeds its upstream value. As a result, the total release of magnetic energy from the antiparallel components of the incoming magnetic field calculated in part 1 is decreased by a factor lying between a half and unity. The weak radial inhomogeneity exemplified by the ‘local’ similarity solution is determined by consideration of the fast and slow magneto-acoustic and Alfvén waves emitted at the neutral point. The Alfvén waves lead to a weak singularity in the vicinity of the rotational discontinuity, while a similar singularity is found in the vicinity of the outflow axis of symmetry associated with an entropy wave.

Generalized expressions for the rates of change of the momentum, energy and thermal anisotropy of fast, charged particle beams interacting with non-Maxwellian multi-species plasmas are derived. The results hold for the case of spherically symmetric systems and, therefore, are relevant for inertial confinement fusion schemes driven by fast charged particle beams and for various astro-physical situations. The calculations are based on the Fokker-Planckformalism. The effects connected with the departures from the Maxwellian distribution functions are expressed in terms of their fifth moments, , which reflect the role of the non-Maxwellian tails. The familiar stopping power expression holding for Maxwellian targets is recovered as a particular case.

It is shown that the asymptotic evolution of a finite-amplitude Alfvén wave propagating parallel to the uniform magnetic field in a warm homogeneous collisionless plasma is governed by the modified nonlinear Schrödinger equation. The dispersion is provided by the ion finite Larmor radius (FLR) effects in the momentum equation and the Hall current and electron pressure corrections to the generalized Ohm's law. In the cold plasma limit the equations reduce to those available in the literature. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in the solar wind.

Nonlinear ion-acoustic waves in magnetized plasmas are investigated. In strong magnetic fields they can be described by a Korteweg-de Vries (KdV) type equation. It is shown here that these plane soliton solutions become unstable with respect to bending distortions. Variational principles are derived for the maximum growth rate γ as a function of the transverse wavenumber k of the perturbations. Since the variational principles are formulated in complementary form, the numerical evaluation yields upper and lower bounds for γ. Choosing appropriate test functions and increasing the accuracy of the computations we find very close upper and lower bounds for the γ(k) curve. The results show that the growth rate peaks at a certain value of k and a cut-off kc exists. In the region where the γ(k) curve was not predicted numerically with high accuracy, i.e. near the cut-off, we find very precise analytical estimates. These findings are compared with previous results. For k≥kc, stability with respect to transverse perturbations is proved.

The interaction of an electron with two electromagnetic waves propagating in an isotropic plasma is studied. It is shown, by numerical calculations, that the electron behaves stochastically, above a given threshold of the wave field amplitudes. The numerical threshold is compared with those given by analytical criteria. The results might be relevant to the laser-plasma interaction problem.

Linear stability of doublets against axisymmetric modes in the approximation of resistive MHD was studied earlier; two modes were identified as those most likely to be unstable, namely the ‘up-down’ mode, which tends to move the plasma up or down and the ‘droplet-ellipse’ mode which tends to deform the doublet into either a droplet or an ellipse. In the treatment described in this paper, quadratic terms in the perturbation are retained. For an equilibrium which is symmetric about the midplane it is easy to see that the quadratic terms vanish for the ‘up-down’ mode. For the ‘droplet-ellipse’ mode this is not the case. This mode allows two different deformations according to linear theory; the effect of the quadratic terms is found always to be stabilizing for one of these deformations, and destabilizing for the other. Thus, owing to the effects of such nonlinear terms, one may expect in experiments to observe unstable developments in a preferred direction, namely that of destabilization, and one expects to observe a faster deterioration of an equilibrium than that predicted from linear theory. These tendencies have been observed in doublet experiments. In this paper the formalism for including quadratic terms in the perturbation is discussed and results from numerical examples are given.

The amplification of fast extraordinary mode waves with frequencies very close to the electron cyclotron frequency is investigated for a plasma which consists of a weakly relativistic electron component with a loss-cone type distribution and a cold background electron component. The basic mechanism of the amplification is attributed to a relativistic cyclotron resonance between the wave and the energetic electrons. The method employed in the present analysis enables us to solve the dispersion relation in a self-consistent manner for arbitrary ratio of the densities of the energetic and background electrons. It is found that the maximum growth rates occur at certain values of ω2pe/Ω2e and the angular dependence of the growth rate is sensitive to the ratios ω2pe/Ω2e and ne/nb. Here ωpe and Ωe are the electron plasma frequency and the electron cyclotron frequency, respectively, and ne and nb denote the number densities of the energetic and background electrons, respectively.

The stability of lower-hybrid waves in a collisional, fully ionized plasma carrying a field-aligned current is investigated. From the two-fluid equations in the cold-plasma approximation, a generalized dispersion relation and formulae for the real frequency ωI and growth rate ωR are derived. The results of a numerical study are presented showing the dependence of ωR and ωI on the angle between the direction of propagation and the magnetic field, the ratio of the electron drift velocity to the parallel phase velocity, and other plasma parameters. Lower-hybrid instability with electron drift velocity small compared with the parallel phase velocity is predicted.

The nonlinear interaction of two HF electromagnetic spherical waves is studied in a homogeneous isotropic plasma. Due to space variations in the k vectors of the mother waves, the interaction is localized. The structure and the amplitude of the generated Langmuir wave are calculated and a possible experiment is discussed.

The linear Vlasov dispersion equation for electrostatic plasma instabilities driven by gravity and weak density gradients perpendicular to a uniform magnetic field is derived and solved numerically. Two interchange instabilities emerge: the well-known fluid mode at long wavelengths and a kinetic mode at wavelengths short compared with the ion gyroradius. The properties of both instabilities are studied, as well as the effects of gravity on the universal and lower-hybrid density drift instabilities. The results show that the kinetic interchange generally has a larger growth rate than the fluid interchange instability, indicating that, whenever the latter is present in a collisionless plasma, the former may also be found.

An extension of the method of characteristics for parabolic equations is proposed that allows the integration of the energy equation for a static, heated and radiating, heat-conducting, optically thin plasma in a magnetic field. The invariance of all physical quantities is assumed, throughout the work, to occur along an arbitrary curvilinear direction. Finally, an example is presented to illustrate how the algorithm actually works.