Quantum field theory is used to investigate the nonlinear effects of two modified ordinary monochromatic waves propagating across a uniform magnetic field. Amplitude-dependent wavelength and frequency shifts are derived. Unlike previous work that employs the Krylov–Bogoliubov–Mitropolskii method, the investigation uses the diagrammatic technique of field theory. The calculations show that increase of the above-mentioned physical parameters due to nonlinear interaction and drifting electrons depends upon the ratio of drifting to phase velocity.

The nonlinear interaction between two Alfvén waves and a sound wave is studied, using the normal-mode approach. This leads, in a simple way to a set of coupled equations, and consequently to a dispersion relation for the waves under consideration. It is shown that a large-amplitude Alfvén wave can give rise to two distinct types of parametric instabilities, namely the oscillating and the purely growing waves. In each case, the expressions for the threshold pump intensity, the frequency shift and the growth rate of the excited waves are obtained. In particular, the results for a propagating pump under perfect frequency matching conditions are compared with those of Sagdeev & Galeev.

Wave propagation in a cold, collisionless, two-component plasma is analyzed by considering, first, the frame of reference in which the field has no space dependence, and then applying a Lorentz transformation to obtain a wave whose space-time dependence is a function of t — nz / c only, where n is a constant. Exact (nonlinear, relativistic) results for known special cases, and some others, are given; and it is shown that, when there is no ambient magnetic field, the general problem in essence reduces to the solution of one second-order, nonlinear differential equation. The desirabifity of introducing a free parameter representing a stream velocity in the direction of wave propagation is emphasized; and the significance of the choice of this parameter is discussed.

An effect of an axial current on the propagation of low-frequency axisymmetric magnetohydroclynamic waves in a radially non-uniform plasma column was investigated theoretically and experimentally. It was found that the axial current and the density gradient cause a coupling between the torsional and compressional waves.

The weak-coupling approximation takes stochastic perturbations of orbits into account, but neglects a part of mode coupling. This approximation, which is non-trivial, is discussed here. Its domain of validity appears to be T E ≪Tt provided the turbulence is strong enough so that γNL- γL ñ γL. If γL ≪ a stronger condition is required. It is shown that the growth rate γNL can be calculated either from the nonlinear dispersion equation εNL =0, or from the energy equation, provided thepropagator conserves particles. Dupree's propagator U does not do this; but it gives a correct approximation of γNL, provided Δv≫vth.

We consider the possibility of modifying the Sonnerup solution for incompressible fluid flow about an X-type re-connexion line, to include fields and flows parallel to the X line. We find that such fields and flows may change across the discontinuities of the Sonnerup solution. By considering the requirements imposed by a proper matching across the various regions of flow, and by the integral conservation properties of the diffusion region, we seek to find the restrictions that are imposed on this parallel field and flow, and on the arrangement of the discontinuity planes around the diffusion region. We find that four types of such arrangements are possible, each corresponding to a different set of restrictions on the parallel field and flow. In one case, where all the discontinuity planes intersect at a common line, the ‘ parallel’ parameters of the in-flow and out-flow regions may be arbitrarily and independently chosen. Of the remaining three cases, one contains solutions with uniform parallel fields ad flows, while the other two depend for their existence on large fluid flow or magnetic field shears across the two in-flow regions.

Collision integrals of excited hydrogen atoms were calculated in the temperature range 10000–25 000 ˚K. These values were used for calculating the viscosity and έ the contribution of the heavy components λH to the translational thermal conductivity of a LTE hydrogen plasma. The results show a dependence of έ and λH on the calculated transport cross-sections.

We consider the flow of a highly conducting incompressible fluid in the convection region surrounding an X-type neutral line. The Sonnerup solution is generalized to include cases in which the in-flowing anti-parallel magnetic fields are of unequal magnitude, and in which the plasmas of the two in-flow regions have unequal density. It is found that there exists no unique solution for a given set of in-flow plasma parameters, but that the out-flowing plasma may exit within a certain range of angles with respect to the in-flow direction, depending on in-flow parameters.

The purpose of the paper is to investigate, by means of kinetic theory, the wave—wave couplings that may occur in a magnetized and partially ionized plasma medium containing neutrals (or ions) with inverted population levels. We study the interaction of three monochromatic waves which propagate parallel to the direction of a magnetic field in the medium. Transverse as well as longitudinal waves are considered. The present paper, which represents a generalization of previous contributions to the subject, offers several new interesting processes of interaction, which may be basic to the description of phenomena occurring in astrophysics. Furthermore, it is of interest in connexion with laboratory plasma and laser experiments.

With electrostatic probes, the electric field component E∥ along the magnetic field B was comprehensively investigated in a collisionless plasma, the density of which was of the order of 1010 cm-3. The plasma in the experiment has several properties in common with the plasma of the ionosphere/magnetosphere scaled to laboratory dimensions. It is produced by means of electron cyclotron resonance in a microwave cavity located in the magnetic field gradient in one half of a magnetic mirror field. The magnetic field strength is 3600G in the resonance zone and 1800G in the middle of the mirror field. The measurements show that a stationary E∥ exists everywhere in the plasma, where the magnetic field gradient grad11 B in the direction of the field is different from zero. The direction of E‖ is opposite to that of grad‖B. The total potential drop along B between the resonance zone and the midplane of the mirror field is of the order of kilovolts. E‖ accelerates ions along B to energies of the order of kilo electron volts. Experimental parameters of importance for the production of E‖ are the neutral gas pressure p (normally a few times 10− Torr), the microwave power (usually about 2kW), and the mirror ratio γ in the mirror region opposite to the cavity side, γ was normally <2. For γ>2·3, an instability develops and no stationary E‖ remains. As p is increased, E‖ decreases successively. In terms of the mean free path λ, it is found that λ>5−10L is a necessary condition for the existence of E‖. L is twice the distance between the cavity and the midplane of the mirror field. In the experiment, the ion and electron pitch angle distributions are forced to be different; the ion velocity is mainly parallel to B, and the electron velocity essentially perpendicular to JB, and as consequence E‖ is created. In this way an experimental demonstration is presented of the theoretically predicted relation between E‖ and the pitch angle distributions. When imposing sufficiently strong radial electric fields Er (fields perpendicular to B), the distribution of the potential along B is deformed, probably due to changes in the particle distributions caused by E‖. We think that our results strongly support the idea that Et is produced in the magnetosphere, and is at least sometimes an important mechanism for the acceleration and precipitation of auroral particles.

We present a procedure to solve the Vlasov–Poisson equations for electrostatic wave packets. We obtain a Schrödinger type of wave equation, taking the wave– particle interaction into account. We use this equation to study the propagation of one finite-amplitude wave packet. We find a change in amplitude caused by interaction between the packet and particles propagating near to the group velocity. Also, we find a modulation of the plasma in the front of the packet, caused by trapping effects.

It is emphasized that the dispersion relation for surface waves at a vacuum—plasma interface can be obtained by setting the reflexion coefficient to zero The relations for warm, collisional and hot, collisionless plasmas are derived in this way, and shown to be inagreement with previous results. The former relation is expressed explicitly as a cubic equation for y = 2c2k12/ω2p, as a function of x = 2ω2/ω2p − 1, where k1 is thecomponent of the wave vector along the interface, a is the frequency and w the plasma frequency; and the nature of the three branches of the y(x) curve is analyzed in detail. The rotation of the vacuum wave vector as the frequency runs from 0 to ∞ is displayed, and it is established that one and only one branch corresponds, in the collisionlesscase, to pure surface waves.

It is argued that the use of quasi-normality or ‘random phase’ approximations in the kinetic theory of the two-dimensional guiding-centre plasma gives rise to unphysical and inconsistent results.

The oblique echo model for the resonance near the local upper hybrid frequency fT observed by topside sounders involves the propagation of slow waves away from the sounder, which later return as echoes after refiexion due to an electron density gradient. The model is investigated by using ray tracing techniques. Use of Poeverlein constructions gives some idea as to the qualitative nature of the rays which contribute to the resonance. A quantitative description requires the use of ray-trajectory equations. By using a simple approximate warm electromagnetic dispersion relation (which, nevertheless, retains all the important features of the exact dispersion relation), the ray-trajectory equations are integrated analytically for the case of a stratified plasma with a linear density gradient. These equations are used to investigate the behaviour of the frequency of the received echoes as a function of delay time. The resonance exhibits strikingly different characteristics for fT<2fH and fT>2fH respectively, where fH is the electron gyrofrequency. For fT<2fH the resonance is ‘strong’, the receiver observing a continuous response consisting of two echoes which interfere to give a fringe pattern. Some typical ray paths are illustrated. For fT<2fH the resonance is ‘weak’ and without fringes. A condition is derived for the existence of intercepting ray paths and for the maximum time delay that occurs when they do exist.

The Charybdis apparatus is designed to produce parallel and oblique shock waves in a magnetized plasma. An initial hydrogen plasma (nel 7 × 1020 m-3, T1 ˜ 1.3 eV) is produced in a Pyrex chamber (0.46 m cia., 1 2 m long) containing an axial magnetic field (B1 up to 0.2 T). A diffuse current front is produced in a fast-rising radial discharge between a central electrode and an annular outer electrode at one end of the chamber. The Lorentz force on the current sheet causes axial motion, and a quasisteady shock proffle propagates ahead. A clear shock separation is achieved across almost the complete radial extent for a wide range of initial parameters. The shock propagation angle to the initial field ranges from 0Ú to 40Ú. The Alfvén Mach number MA of the flow is varied by changing the initial field strength. Switch-on shock behaviour is demonstrated at a point of parallel propagation for low MA. For higher MA cases, no separated point of parallel propagation occurs in the shock profile.

This paper presents an idealized, one-dimensional theoretical model of a novel method of launching a slow-mode hydromagnetic shock wave. The reduction of the transverse magnetic field component, at the boundary of a semi-infinite plasma containing a uniform oblique magnetic field, results in the propagation of a fast-mode expansion wave followed by a slow-mode shock. An experiment designed to test this launching method is described. An initial hydrogen plasma containing axial and azimuthal magnetic field components is set up in a large annular apparatus. The azimuthal field is then reversed at one end of the device, by a fast-rising radial discharge. Diagnosis of the resulting flow, with small magnetic and electric probes, shows the propagation of the fast expansion wave and the slow shock; but there also follows a third wave, having the properties of a ‚piston’. When the theory is extended to include a moving boundary (i.e. ‚piston’), good quantitative agreement is obtained with the experimental results. The annular geometry of the experiment leads to centrifugal effects not considered in the one-dimensional theory; but these are not sufficient to disrupt seriously the main flow pattern. Detailed measurements of the shock indicate a dispersive structure.