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).

A model for the kinetic formulation of a weakly-ionized monatomic gas, which interacts with thermal radiation, is proposed. The collision terms for particle-initiated ionization, developed in terms of a non-equilibrium degree of ionization, and the collision terms for photon-initiated ionization, developed by assuming particles remain in local equilibrium during photon relaxation, all satisfy the usual conservation principles. It is also shown that the proposed model leads to an H theorem.

Limiting currents in annular unneutralized relativistic electron beams are calculated and compared with experiment. The limiting factor for short beams is found to be the space-charge depression of the potential due to the unneutralized beam; in longer beams self-magnetic and electric fields impose a power limit. Typical beam impedances are found to be of the order of 15 Ω with a 350 keV beam. The role of shear in the axial velocity of the beam is discussed.

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.

Physically acceptable solutions of the time-independent Vlasov–Poisson system are found by applying a method which is analogous to the soliton method in Korteweg–de Vries theory. Cnoidal wave solutions for small-amplitude Langmuir and ion acoustic waves are derived, in which the nonlinearity is determined by trapped electrons. The class of weakly distorted waves is shown to be modulational unstable.

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).

This paper considers an example of the propagation of a finite wave-train in a plasma of relatively simple dispersive properties. In this case, the wave field can be evaluated exactly. The concept of a wave-packet moving at the group speed can therefore be tested rigorously. Various approximations to the field, physically more transparent than the exact solution, are presented and compared with the latter. One of these, relevant in the neighbourhood of the ideal group front, is in fact applicable to a wide range of dispersion laws. The paper demonstrates broadening with time, and eventual disappearance, of the pulse.

The paper describes a model, in which ions are accelerated against the direction of the electric field at a density gradient. A one-dimensional, inhomogeneous, steady-state is constructed, in which cold electrons stream relative to cold ions. The wavenumber and amplitude of the fluctuating potential are calculated, then used to compute the trajectories of representative ions trapped in the potential troughs. Ion acceleration to energies an order of magnitude greater than the applied potential is demonstrated.

It is common practice to define reflexion and transmission coefficients for waves propagating through isotropic and anisotropic inhomogeneous plasma in terms of coefficients of waves existing within homogeneous regions of the plasma below and above the inhomogeneity. This concept is shown to be very restricted, and corresponding coefficients are defined for solutions existing within the inhomogeneous regions of the plasma. The extended concept is shown to satisfy conditions usually associated with the more common definitions, notably energy conservation and reciprocity. The theory is developed using integral equations and matrix theory, and special precautions are taken so that the results extend from the inhomogeneous plasma into free-space domains.

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.

The instability of the ordinary mode propagating perpendicular to the magnetic field is discussed for two ion beams counter-streaming along the magnetic field through a plasma of stationary electrons and ions. The instability criterion gives the necessary and sufficient condition for a purely growing mode. Although the instability threshold is high (u/Voi ≳ (2βoiNoi/Noi)-½ if the streaming velocity is 10% larger than the threshold value), large growth rates of the order of the ion cyclotron frequency result.

It is found that, for a fully-ionized, homogeneous plasma in a high-frequency electric field, the fundamental term 1 in the kinetic-energy correction is defined by the intensity and frequency of the electric field and by the collision frequency v1. We obtain the Debye–Hükel energy correction in 2, too, as did Theimer & Wright, but this term is much smaller than 1, and its coefficient is no longer a constant.

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.

In this paper we consider the stability of one-dimensional stationary waves set up by two counter-streaming beams of electrons in a background of stationary ions. The perturbations considered are long-wave in a direction perpendicular to the wave. The presence of a uniform magnetic field in the direction of the wave and the effect of a perpendicular pressure are taken into account. In the long-wavelength limit growth rates are diminished by the nonlinear wave. When the amplitude of this wave tends to its maximum value, the growth rates tend to zero. Thus the wave has a stabilizing effect for long-wave perturbations. Three- dimensional effects lead to additional instabilities which are also quenched by the nonlinear wave, but not as fast as the one-dimensional calculation indicates.

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.

Demehenko & Hussein (1973) discussed some properties of nonlinear magneto-sonic waves in a collisionless plasma. The relevant equation describing the space dependence x of the magnetic field may be written in the form d2y/dx2+f(y) = 0, (1) where f(y) is a nonlinear function of y only.