This paper is a theoretical and experimental study of the propagation of longitudinal electron waves in a collisionless, homogeneuos, isotropic plasma, composed of Maxwellian and supra-thermal electrons. Assuming the supra-thermal electrons are mono-energetic, the velocity distribution function is chosen as a Maxwellian plus water-bag distribution; then, using the method of residues (inverse Fourier–Laplace transform), the behaviour of the electric field is found to be in good agreement with experimental results obtained for a plasma of Maxwellian and quasi-mono-energetic electrons. The plasma parameters can be deduced from the theoretical dispersion curves matching the experimental points; they are found to agree well with those measured by electrostatic probes. Experimental values of damping and excitation coefficients are also compared with the theoretical. The results suggest that a longitudinal electron wave propagation experiment may be used as a powerful diagnostic tool to examine non-Maxwellian plasmas.

The interaction between an ion wave and its second harmonic is discussed theoretically, on the basis of coupled-mode equations derived from the Korteweg–de Vries equation. Using an exact solution of the coupled-mode equations, we give a numerical analysis of the properties of the solutions; and we show that superposition of two waves can describe the formation of two solitons, the interaction between them, and the recurrence of an initial state. Our theory can explain completely recent experimental results on ion wave solitons excited by a continuous sine wave.

The propagation of a nonlinear wave in a dispersive medium has been extensively studied in the last decade. In a plasma, a finite-amplitude ion wave can form solitons in the course of its evolution, if wave damping is neglected.

Wave propagation in a hot, collisionless electron plasma (without ambient magnetic field) is analyzed by coisidering the frame of reference in which the field has no space dependence. It is shown that the governing equations are of the same form as those for a cold plasma, and are likely to have corresponding exact (nonlinear, relativistic) solutions. In particular, it is shown that there exists a solution representing a purely transverse, circularly polarized, monochromatic wave. Three approximate forms of the dispersion relation of this wave are obtained explicitly, the first being valid when the temperature correction is small, the second applying to weak waves, and the third to strong waves. Purely longitudinal waves are also discussed.

A re-examination of the linear E x B instability problem for infinite stratified media gives results differing from those published. The main point is to warn against the application to inhomogeneous media of the usual instability criterion, as developed for homogeneous media. The fact that the dispersion relation gives complex values of ω for real k does not always indicate the existence of an instabifity. It could also describe propagation of a constant wave energy through an inhomogeneous medium. It is demonstrated that in certain situations it is possible to choose dependent variables in such a way that these two effects disentangle, allowing for a definite solution of the instability problem.

In this paper the linear stability' problem for an infinite inhomogeneous, partially ionized gas penetrated by crossed electric and magnetic fields, is re-examined. Several authors (e.g. Reid 1968; Whitehead 1967, 1971; Cunnold 1969; Chimonas 1969; Linson & Workman 1970; looper & Walker 1971; Sato 1971; Sato & Tsuda 1972; Kato 1972) have considered the possibility that the so-called cross-field instability exists in the ionosphere. Our reason for treating the problem again is to point out a deficiency in the literature.

We calculated relative and absolute maximum linear growth rates of the electromagnetic ion–cyclotron instability produced by the addition of cold plasma to an infinite uniform anisotropic plasma. In this, both accurate numerical solution of the linearized dispersion relation, and approximate analytic calculations, were carried out, and the results were compared critically.

Qualitatively, results similar to those obtained in the past for the right-hand polarized electron–cyclotron electromagnetic (whistler) waves (Cuperman & Landau 1974) are found also for the left-hand polarized waves considered in this paper. Specifically, the electromagnetic ion–cyclotron instability in a warm, anisotropic proton plasma, characterized by Pp ≡ βP,A2p(Ap + 1) ≲ 1, may be significantly enhanced by addition of cold plasma.

This paper investigates the fluctuation spectrum of the surface waves in a semi-infinite plasma, and in a plasma cylinder, with an inhomogeneous boundary layer. It is shown that the correlations of the surface waves are dependent on temperature and density distributions in the boundary layer. The correlation function is determined by temperature values in the points of transition layer, where the longitudinal dielectric permeability becomes equal to zero. Dependence of the obtained correlation function on co-ordinates, in the electrostatic limit, is characterized by the complex correlation length, which is fully determined by the inhomogenity of the plasma density near the boundary.

In this paper, the electrostatic resonance properties of an inhomogeneous plasma column are treated by the Rayleigh–Ritz method. In contrast to Parker, Nickel & Gould (1964), who carried out an exact computation, we use a description of the RF equation of motion and pressure term that allows us to express the system of equations in Euler–Lagrange form. The Rayleigh–Ritz procedure is then applied to the corresponding Lagrangian, to obtain approximate resonance frequences and eigenfunctions. An appropriate set of trial co-ordinate functions is defined, which leads to frequency and eigenfunction estimates in excellent agreement with the work of Parker et al. (1964).

In absorbing media, where Maxwell's equations are not seif-adjoint, the adjoint field is introduced via the differential operator adjoint to the Maxwell operator. The concomitant vector can be made equal to the time averaged Poynting vector at a boundary with a non-absorbing medium. In general, the adjoint field represents an electromagnetic field in a medium other than the absorbing medium under consideration. To draw conclusions about the latter, a [conjugate field] in this medium is defined, using a conjugating transformation of the Maxwell operator and field. Relations between the conjugate and adjoint fields are established, allowing one to gather physical information about the first absorbing medium from the adjoint field.

The parametric excitation of transverse and Langmuir waves by an externally-driven electromagnetic field of frequency (ω0 > 2ωp) in a warm and collisional plasma is studied, using the fluid equations. By an application of the multiple- time-scale perturbation method, the threshold intensity and the growth rate above threshold are obtained. The results are compared with those of Goldman (1969) and Prasad (1968), both of whom worked with a kinetic model.

The theory of parametric instabilities in plasmas has been the subject of numerous investigations in recent years. Broadly speaking, the instabilities can be grouped into two categories: those for which the excited waves are purely electrostatic (see e.g. DuBois & Goldman 1965, 1967; Silin 1965; Lee & Su 1966; Jackson 1967; Nishikawa 1968; Kaw & Dawson 1969; Tzoar 1969; Sanmartin 1970; McBride 1970; Perkins & Flick 1971; Fejer & Leer 1972a, b; Bezzerides & Weinstock 1972; DuBois & Goldman 1972), and those for which one of the excited waves is electromagnetic (see e.g. Goldman & Dubois 1965; Montgomery & Alexeff 1966; Chen & Lewak 1970; Bodner & Eddleman 1972; Fejer & Leer 1972b; Lee & Kaw 1972; Forslund et al. 1972).

Starting from the kinetic equation and Maxwell's equations, a dispersion relation is obtained for wave propagation through a fully-ionized plasma along a spatially-uniform, external, periodic magnetic field B0 cos ω0t, and several excitation conditions are deduced. The parametri excitation of waves in a plasma by spatially uniform external periodic electric field has been considered by several authors (Aiev & Silim 1965; Montgomery & Alexeff 1966; Jackson 1967; Prasad 1967, 1968; Nishikawa 1968 a, b). The effect of spatially uniform external periodic magnetic field on wave propagation through a hot plasma was considered by Das (1971), who used hydrodynamic equations to study the effect of wave propagation perpendicular to a spatially-uniform, external, periodic magnetic field.

The instability of the ordinary electromagnetic mode, propagating perpendicular to an external magnetic field, is studied for a single-species plasma with ring velocity distribution. The marginal instability boundaries for both the purely growing mode and the propagating growing modes are calculated from the instability criteria. The dispersion characteristics for various sets of plasma parameters are also given. The frequency bands of the propagating growing modes are centered at about (η +½)ωc, where η = 1, 2,…, and the typical growth rates are of the order of the cyclotron frequency and enhanced by increasing fluβ1.

We present measurements proving the successive excitation of two distinct instabilities by electron beam–plasma interaction along a plasma column. The first, appearing near the gun, grows in space, until the beam is trapped in the wave electric field, and decays. In this process the time-averaged distribution function changes, from a δ-type distribution function, into a plateau. This new beam–plasma distribution is also unstable; and another instability grows until the beam is again trapped. Numerical calculations show that the second instability can be explained, assuming that the beam distribution thermalizes when propagating from the first instability to the second.

Experiments by Friedman (1972), and theoretical analysis by Sudan & Lovelace (1973), Rostoker (1972), Rostoker & Poukey (1971) and Wheeler (1974), considered ion emissionin a vacuum diode. The ions emitted (e.g. in the Friedman experiment) were generated by laser irradiation of the anode. Using this technique, multiply-ionized species could be obtained. The ion currentwas limited non-relativistically to the square root of the mass ratio times the electron current, so that energy transfer to the ions was relatively inefficient. Some improvement was obtained at relativistic electron energies.

Sloan & Drummond (1973) proposed a high-current ion accelerator, where the transfer of energy to the ions is achieved by a negative energy cyclotron wave on an intense E beam. Such an accelerator requires an ion source capable of providing several hundred Amperes of protons at energies in the range of a few hundred keV to several MeV. In this article, we propose a suitable ion source for an accelerator.

The compression of plasmas by laser beams to produce a significant thermonuclear energy requires very sophisticated experimental techniques and equipment, costing millions of dollars. We review here comparatively simple techniques which should permit a time-resolved demonstration of an isentropic density compression, using low-powered lasers of a type commonly encountered in university research laboratories, and diagnostic equipment of modest cost. Althoughthermonuclear burn cannot be investigatedwith such simple apparatus, many aspects of flux-limited thermal transport, light absorption, and end-effects (i.e. intensity assymmetries) could be conveniently and quantitatively investigated.

A new, purely growing instability has been found for a bi-Maxwellian plasma in a uniform magnetic field. Instability exists for β;11 = 4βnkT11/B2 > O.591 when Tboxhu;= 0, and ions are neglected. The growth rate is near the electron gyro frequency (or v/c the plasma frequency), and the polarization is almost electrostatic for almost perpendicular propagation. The instability is obtainable only from the complete dispersion relation.