We have investigated how the presence of an electromagnetic beam and a static magnetic field influences the ion-acoustic solitons in a plasma. A modified KdV equation is derived in which the electromagnetic field plays the role of a source term. By using the perturbation analysis technique, it is shown that a homogeneous electromagnetic beam does not destabilize the ion-acoustic solitons; it reduces the amplitude, but not the velocity, of the solitons. However, any inhomogeneity in the electromagnetic field intensity does destabilize the ion-acoustic solitons; albeit not to an appreciable extent for typical cases.

This work presents a systematic investigation and comparison of electromagnetic ion-cyclotron (e.m.) and electrostatic ion-cyclotron (e.s.) instabilities in uniform mixed warm and cold plasmas for magnetospheric-like plasma parameters. The following main aspects are included: Analytical: (i) we derive simple approximate expressions for the maximum growth rate, γmax for the quasi-electrostatic instability in the regime ωr » …p, к┴ » к∥ (к∥ ≠ 0) with the protons being described by mixed loss-cone and cold populations and with inclusion of electromagnetic coupling effects due to electrons; (ii) we analyse another regime in which electrostatic instalilities first increase with addition of cold plasma and decrease only after having reached a maximum, namely a regime with ωr » …p, к = к≠; (iii) we summarize the corresponding analytical results for parallel propagating electromagnetic ion-cyclotron unstable waves and discuss their validity range.

The influence of a static electric field on electron oscillations of (i) a cold beam of electrons and (ii) a hot non-drifting plasma is investigated. The importance of the relative strength of the field is emphasized. In the weak field limit the oscillations are adiabatic, manifested by the existence of adiabatic invariants, preservation of eigenmodes and absence of reflexion. If the field is strong, however, interesting new features, such as mutual coupling of eigenmodes and wave reflexion, appear. Possible stability properties of a monotonic electrostatic transition (shock, double layer) are also discussed.

Kinetic theory of the self-modulation of a quasi-monochromatic ordinary wave propagating across an external magnetic field is presented. Explicit expressions of the dispersion and the nonlinear coupling coefficients are given for a Maxwellian plasma. In the limit of zero-temperature, a Karpman–Kruskal linear stability of the O-mode envelope is discussed.

We have described previously the evolutionary process of magnetic field-line reconnexion by a localized enhancement of resistivity. In this paper, it is demonstrated by numerical experiment that the evolution is eventually checked, with the system attaining a quasi-steady state. On the basis of the quasi-steady configuration, established from an initially antiparallel magnetic field, we can now clarify the MHD properties that are characteristic of the diffusion, field reversal and external regions, respectively, and then the mutual dependence among them. Especially, the physical processes in the diffusion region are noteworthy, since the ultimate cause for the present reconnexion process is the bending of the field lines towards the magnetic neutral point, which results from the locally enhanced resistivity assumed in the diffusion region. The present numerical results generally agree with the analytical results for the steady reconnexion, although some discrepancies exist owing to the differences of the postulated basic situations between them. It is pointed out that changes in flow properties across the boundary of the field reversal region agree well with those required for a slow mode compression wave and that the dominant process in the external region corresponds to a fast mode expansion.

In contrast to the electronic heat conduction losses which for a tamped thermonuclear micro-explosion are minimized by a spherical target shape, the adiabatic temperature rise can be larger for a non-spherical implosion geometry, whereas for a given plasma volume and density the bremsstrahlung losses are independent of the particular geometry. The enhancement of the adiabatic temperature rise results from the ‘scissors effect’ in non-spherical implosions by which a cavity wedge can assume a larger geometric implosion velocity than the physical implosion velocity of the cavity wall. The net effect of the enhanced adiabatic temperature rise by the 'scissors effect' and enhanced electronic heat conduction losses for non-spherical cavity shapes results in an optimal non-spherical implosion geometry. For the special case of an imploding oblate ellipsoid the optimal eccentricity is derived from an exact analytical solution. The predicted effect leads to a reduction in required beam power density, permitting less beam focusing than is necessary for spherical targets, which is of special importance for electron- and ion-beam induced micro-explosions, and may even make possible the attainment of thermonuclear temperatures by chemical explosives.

One possible mechanism for ring current proton losses is the electrostatic ioncyclotron instability. Since typical ring-current parameters involve values of β of the order of one, the electron response must be treated electromagnetically. To this end, the effect of electromagnetic corrections on the electrostatic ioncyclotron instability is discussed. It is shown that the electromagnetic response of the electrons has been only partially included in previous studies. A relatively simple expression for the growth rate, including all relevant corrections, is derived. On the basis of this expression, growth rates for typical ring-current parameters are calculated and compared with previous results. Flute-like modes are shown not to be affected by these corrections.

This paper is concerned with the propagation of one-dimensional nonlinear waves in the relatively simple physical situation of a cold, collisionless, field-free, slightly non-uniform plasma comprising a stream of oscillating electrons and a stream of ions whose oscillatory motion is neglected. The waves are considered as a small perturbation from the corresponding uniform periodic solution. The equations which govern the slow variation of certain gross quantities associated with the waves are obtained by applying the ‘two-timing’ technique to the basic plasma equations. The properties of the resulting modulation equations are discussed and an exact solution of an initial value problem for them is given.

The acceleration of trapped particles by a Langmuir wave in an inhomogeneous plasma is investigated for different density profiles. In particular the important case of a wave moving towards its refiexion point is considered both analytically and numerically. To obtain estimates of the energy gain of the trapped particles, their stability is investigated. Our findings differ from those of previous authors. The effect of wave damping, and a slowly varying frequency (whistler-like phenomena), on the stability of trapping is estimated.

General equations are derived for the interaction of four waves to second order (i.e. two triplets with two waves common to both). The solutions are analysed under various initial conditions and it is shown that the weaker triplet (as measured by the coupling constraints) is stabilized by the stronger one against explosive instabilities, whereas the converse does not happen. It is further found that under certain circumstances one of the common waves may act as a ‘catalyst’, remaining fixed in amplitude, while the other waves oscillate or even grow exponentially. This work extends the treatment of Karplyuk, Oraevskii & Pavlenko to include the possibility of negative energy waves.

The second order elliptic differential equation which describes the static equilibrium of an axisymmetric ideally conducting plasma toroid, in the magnetohydrodynamic approximation, may be transformed into an equivalent equation which admits at least one class of exact analytic solutions for which the original equation is essentially nonlinear. Necessary and sufficient conditions are given for the existence of systems in this category having closed toroidal flux surfaces and a result is proved which gives some insight into the mathematics by which the spatial variation of the hydrodynamic pressure can be represented by families of nested closed curves.

This paper presents an investigation of the effect of self-focusing on the absolute growth rates of parametric back-scattering (e.g. stimulated Raman and Brillouin scatterings) and absorptive instabilities (e.g. two-plasmon decay and ion–plasmon decay) in a homogeneous and collisionless plasma. Gaussian intensity distribution of the pump laser beam causes the redistribution of carriers in the plane transverse to the beam propagation on account of the ponderomotive force, and leads the beam to propagate in an oscillatory wave guide mode. The modifications in plasma frequency and intensity of the beam cause the growth rates of the above parametric instabilities to show an oscillatory behaviour with the distance of propagation.