The nonlinear behaviour of a realistic one-dimensional bounded plasma (specifically, the classical plasma slab–condenser system) is computed by an iterative perturbation method. The results indicate, somewhat unexpectedly, that the influence of the r.f. field on the static density profile and on the resonance spectrum is much smaller than would have been inferred from a previous analysis of an unbounded plasma. However, this approach is inherently limited by the fact that, even for not too high r.f. fields, the electron density perturbations can become of the same order of magnitude as the static density in the tenuous plasma sheath near the wall. The resonance curves obtained with this sophisticated model show quite remarkable agreement with existing experimental data.

The three important aspects of wave propagation in a stationary and a moving plasma (namely frequency, polarization and dispersion) are compared, taking the phase refractive index of the wave as the independent variable. Wave propagation and the motion of the plasma are taken to be along the magnetic field. The plasma is assumed to consist of one species only, and the effect of collisions is neglected. Wave propagation in a moving plasma has been shown to possess several important features, such as the absence of cyclotron resonance, reversal of the sense of polarization when the phase velocity becomes equal to the plasma velocity, and the existence of backward waves for very small and very large phase velocities.

By linearizing about the upstream state, the characteristic length for the growth of magnetic field in a laminar wave front, propagating perpendicular to an external magnetic field, is found as a function of βi, the ratio of ion pressure to magnetic pressure. For values of βi, between 10–2 and 1 the thickness is found to scale as . This scaling is in good agreement with the observed scaling of turbulent shocks, suggesting that for such shocks the shock thickness is closely related to that of the corresponding laminar pulse.

The results of two experiments in a weakly ionized turbulent argon plasma are compared with a theory for the spacewisespectrum of the electron – ion density fluctuations of the plasma. It would appear that the theoretical predictions are in reasonable agreement with the results of these experiments. The theory, based on a quasi-static formulation of the Boltzmann equations, is a direct consequence of the Boltzman equations for the electrons, ions and neutrals in theweakly ionized plasma. A Heisenberg model is used for the turbulent diffusion coefficient of the plasma.

Nonlinear stabilization of cold beam plasma instability are studied on the basis of Dupree's theory of strong plasma turbulence. Calculations are carried out to second order in the perturbed electric field, and it is found that, for a narrow spectrum satisfying δκ/κ≪1, stabilization occurs for the trapping frequency ωT ť ∣qeκΕk/me∣½ ť γL the linear growth rate. Nonlinear frequency correction, and also the changes in the kinetic and thermal energy densities of the beam, are calculated as the waves grow. Some points of difference between the resonant and non-resonant instabilities are discussed.

The large-amplitude plasma wave with a trapped-particle distribution monotonically increasing in energy is found to be unstable if the trapped-particle plasma frequency ωt = (4πnte2/m)½ is greater than the bounce frequency ωb = (eΕ0κ0/m)½.

We present a theory of the nonlinear damping of a plasma mode based on a solution of the Vlasov–Poisson system. The formulation is exempt from the objectionable separation of the particles into ‘resonant’ and ‘nonresonant’, and is valid for ion as well as for electron modes. The effect of the damping of the mode on particle motion is taken in account. In particular, we evaluate numerically the damping of an ion mode for a temperature ratio Te/Ti = 16. We also obtain a number of small new shifts in the damping of a plasma mode in general, including contributions from the second derivative of the stationary distribution function.

Dispersion curves of electrostatic electron cyclotron harmonic waves with a phase exp {i(k. r – ωt)}, where ω and k are the angular frequency and wave vector, respectively, are calculated numerically for a case of real ω and complex k that is pertinent for a case of pulsed short dipole excitation of plasma waves. Oblique propagation with respect to the ambient magnetic field direction is considered. There are positive κi and negative κi modes, where k is the imaginary part of the wave number κ = ∣κ∣ in the solutions. The energy propagates in opposite directions in the two modes, and the waves are always subjected to thermal damping. The positive κi mode usually indicates a large κi value (i.e. a large attentuation rate); and it is here called the ‘short-life’ mode.

We analyze energy and momentum exchange associated with Landau damping of hydromagnetic waves, from a macroscopic viewpoint, and compare the conclusions with those of the resonant quasiinear theory. It is found that the heating of protons and electrons is correctly given by the resonant theory, but that the momentum exchange is not correctly described by the resonant theory.

An exact result in the theory of wave propagation in random media is presented. Using the ergodic theory of dynamical systems, it is shown that a semi-infinite, one-dimensional random medium is totally reflecting. A direct numerical study shows that the mean reflection coefficient converges exponentially to one.

The frequency response of the h.f. quadrupole probe is calculated to be used as a diagnostic tool for measurements of electron density and temperature. In §2 the magnetic field is assumed to be zero, and ion motions are neglected. For a Maxwellian plasma, the so-called ‘Landau wave approximation’ is compared with various more sophisticated treatments, such as numerical integration or super-Cauchy and multiple water-bag models. The range of validity of this approximation is shown to be large, and the results can be applied to the most interesting parts of the experimental observations. All results previously established are recovered with greater speed. Having studied various disturbances (collisions, inhomogeneity and relative motion of the probe with respect to the plasma), it is deduced that the best way to determine the electron temperature is to use the anti-resonances due to beating between the Landau wave and the cold plasma field. In § 3 we describe the quadrupole probe, launched in December 1971 as part of the CISASPE rocket experiment. To deduce the electron density and temperature from these measurements, it is necessary to consider the influence of a static magnetic field, such as the earth's magnetic field. The general case could be treated by numerical integration, though with great difficulty, but it is shown that in most ionospheric conditions, in the vicinity of the upper hybrid frequency ωT the above treatment is again possible, the plasma frequency simply being replaced by ωT, and the thermal velocity slightly modified. These assumptions are used to deduce the electron density and temperature profiles.

The motion of a charged particle in a transverse wave of varying amplitude, wavelength and phase speed βp, propagating along a uniform magnetic field, together with a longitudinal electric field, is investigated. The equations of motion, in Hamiltonian form, are reduced to a system with two degrees of freedom in which integrable cases appear naturally. It is shown that particles may be locked in resonance with the wave, and expressions are found for the energy and momentum of such particles in terms of βp.