Jeans's criterion for instability is found to be changed only for the case of perturbations perpendicular to the magnetic field and rotation parallel to it, when rotation and finite Larmor radius effects tend to stabilize the plasma.

Small amplitude electrostatic oscillations in a cold plasma with continuously varying density have been investigated. The problem is the same as that treated by Barston (1964) but instead of his normal-mode analysis we employ the Laplace transform approach to solve the corresponding initial-value problem. We construct the Green function of the differential equation of the problem to show that there are branch-point singularities on the real axis of the complex frequency-plane, which correspond to the singularities of the Barston eigenmodes and which, asymptotically, give rise to non-collective oscillations with position-dependent frequency and damping proportional to negative powers of time. In addition we find an infinity of new singularities (simple poles) of the analytic continuation of the Green function into the lower half of the complex frequency-plane whose position is independent of the spatial co-ordinate so that they represent collective, exponentially damped modes of plasma oscillations. Thus, although there may be no discrete spectrum, in a more general sense a dispersion relation does exist but must be interpreted in the same way as in the case of Landau damping of hot plasma oscillations.

The problem of the linear stability of a plasma with density profiles

in a homogeneous magnetic field B = îzB0 has been solved exactly. The dispersion relation leads to stability criteria less severe than those obtained in the local approximation. As examples, we consider Bernstein waves and the low-frequency drift instability. In the second example the marginal stability curve

is given for different values of the parameters kx, Ri, Ri n′/n, with Ti = Te. Further, the same method is applied to a plasma with equilibrium distribution function in a linear electric potential φ = αx and a homogeneous magnetic field B = îxB0.

An infinite, inhomogeneous electron plasma driven by a spatially uniform oscillating electric field is investigated. The multi-time perturbation method is used to analyze possible parametric excitations of transverse waves and to evaluate their growth rates. It is shown that there exist subharmonic excitations of: (1) a pair of transverse waves in an unmagnetized plasma and (2) a pair of one right and one left circularly polarized wave in a magnetoplasma. Additionally, parametric excitation of two right or two left circularly polarized waves with different frequencies can exist in a magnetoplasma. The subharmonic excitations are impossible whenever the density gradient and the applied electric field are perpendicular. However, parametric excitation is possible with all configurations.

It is shown that the reported absence of a contribution of electronic excitation on to the total specific heats of helium and nitrogen (10,000–35,000°K, 10−1−10 atm) should be attributed to the presence of compensation effects among the various terms into which the total specific heat can be separated and that these terms are influenced by the electronic contribution.

The interaction of homogeneous wave turbulence and a magnetohydrodynamic tangential discontinuity is studied. Attention is focused on the turbulent shear stress produced as a result of such an interaction. A magnetohydrodynamic description is used which is believed to be adequate for plasma problems in interplanetary space. As a model for wave turbulence, it is assumed that the turbulent wave field is made up of the seven modes of magnetohydrodynamic waves. They are the entropy waves, the Alfvn waves (two independent modes), the fast and slow waves (each with two independent modes). It is found that to a first approximation the turbulent shear stress acting on the surface of discontinuity is linearly proportional to the energy density of the fluctuating magnetic field and to the kinetic energy density of the plasma fluctuations. On applying the present theory to the problem of interaction between the turbulent waves in the magnetosheath and the magnetopause, it is found that the turbulent shear stress produced is too weak to produce any large-scale internal magnetospheric convection as was previously contemplated.

The observed response of a low-density magnetoplasma column to a pair of RF pulses near the cyclotron frequency is a series of pulses known as two-pulse echoes. A similar three-pulse echo train may be obtained by applying a third pulse. This behaviour involves some type of non-linearity, and for a low-density plasma the most promising mechanism appears to be velocity-dependent electron-neutral collisions. This gives velocity-dependent decay to induced currents, and velocity-dependent diffusion. The latter may be important in three-pulse echo formation. In this paper computations from these theories are compared with experimental data with these findings: (1) diffusion is not primarily responsible for three-pulse echoes; (2) the predictions of the collisional current decay theory are in reasonable agreement with the experimental results.

This paper considers the non-linear interaction between three resonant, modified ordinary electromagnetic waves, which propagate perpendicular to a constant magnetic field in a spatially homogeneous electron plasma. The coupling coefficients are calculated and discussed. Finally, a general formula, describing the interaction between three waves propagating at arbitrary angles to the static field, is derived.

We first discuss wave propagation perpendicular to a magnetic field. Variables depend on x only. The medium is collision-free, described by the Vlasov theory. We can prove that there exist two, and only two, unique constants of the motion, that are independent of y, z and t, and that at least one of them depends on x. Thus a necessary condition for the existence of stationary shocks is fulfilled. Examples show that the existence proof also suggests a practical tool for solving problems. The oblique case which is also briefly discussed turns out to be qualitatively different in that, owing to the presence of reflected particles, a uniform upstream state cannot be prescribed a priori.

The hydromagnetic analogue of the Kelvin–Helmholtz problem is extended to include the effects of the Hall term. In contrast to other results in the literature it is shown that, in the case of incompressible fluids, the stability of a shear plane is unaffected by the introduction of the Hall term. The special case of a hot, uninagnetized fluid on one side of the interface and a cold, magnetized fluid on the other is studied in some detail. In this case it is shown that the presence of the Hall term can have either a stabilizing or a destabilizing effect, depending upon whether the sound speed in the hot fluid is very much greater than the Alfvén speed in the cold fluid or vice versa.

The oscillations, excited by a pulsed dipole antenna at the upper hybrid resonance in a weakly inhomogeneous plasma, are investigated by the Wentzel—Kramers—Brillouin (WKB) approximation. In addition to a direct component, the field at a given distance from the transmitter is shown to consist in two obliquely reflected rays when the upper hybrid frequency WT is less than twice the electron gyro-frequency WH. The analytical expressions of the frequencies of the echoes intercepted by a moving receiver are given and the influence of the reception time t, the velocity VS of the receiver and the parameters of the plasma are thus pointed out.

As distinct from previous studies, the static magnetic field B0, the velocity of the receiver, and the gradient of the electron density ∂N/∂X, are here vectors of arbitrary directions. The choice of such a general model makes it possible to interpret most of the experimental data concerning the upper hybrid resonance in the ionosphere.

A recent paper on quasiinear theory by Klozenberg & Bernstein is commented upon. It is argued that improper treatment of the perturbed electron distribution for damped waves has led to a diffusion-type equation with a negative diffusion coefficient.

The effect of a test particle, moving through a two-dimensional Maxwellian plasma, has been studied both analytically and by computer simulation. For a stationary test particle, Debye shielding occurs. When the velocity of the test particle approaches the electron thermal velocity, there is a concentration of electrons several Debye lengths downstream, an effect which is essentially a heavily damped plasma oscillation. The analytic results agree closely with the computer simulation. As the velocity of the test particle increases, it is shown analytically that the damping diminishes, and eventually a fully developed plasma oscillation is established in the wake of the particle.

The criticisms of Montgomery & Bodner (preceding paper) seem to stem from a misunderstanding of the claims in the paper of Klozenberg & Bernstein (1970) in part perhaps semantic. The derivation criticized was intended to apply only to those particle velocities v corresponding to the range in phase velocities βк/к for which there is an appreciable wave excitation. The term ‘resonant phase velocity’ was intended to mean those phase velocities in a small interval Δ such that ν − ½Δ < βк/к < ν + ½Δ, which interval in the integral determining the diffusion coefficients leads to the familiar expression involving δ(βк кν). When this contribution is non-vanishing it determines the lowest significant order contribution, in the small parameters of the problem, of ∂ƒ0/∂t, assuming that the wave excitation at the time in question is so large that effects associated with initial conditions are indeed negligible.

Inside any symmetrical double-humped plasma velocity distribution, all growing waves with real wave-number have zero phase velocity. Growth rates of such plasma oscillations are calculated for distributions made up of resonance functions and of Gaussian functions. The results are compared with an earlier calculation made with less realistic distribution functions with no infinite tails.

We wish to point out that the revised quasilinear equations found recently by Klozenberg & Bernstein (1970) for continuous wave-number spectra, which are a simplified version of those derived by us for discrete wave spectra (Abraham-Shrauner 1970), can be derived easily from the conventional quasilinear equations (Drummond & Pines 1962; Vedenov, Veliklov & Sagdeev 1962) by analytic continuation. The analytic continuation is the same type used in discussions of the plasma dispersion relation for the linearized Vlasov equation and of the weakly unstable kinetic equation (Balescu 1963; Rogister & Obermann 1969).

Stable, phase coherent ion plasma oscillations are found superimposed on the d.c. potential and current of positive coaxial corona discharges in air at pressures of the order of 1/100 of one atmosphere. The frequency of these oscillations, typically several hundred kHz, is a function of air density, and varies with the concentration of gaseous trace contaminants.