The Herlofson paradox is exemplified by a capacitor containing cold, collisionless, inhomogeneous plasma as the dielectric: its response to a sinusoidal driving signal can exhibit continuous energy absorption, even though the system is lossless. The underlying mechanism has been explained generally by Barston in terms of the transient response of the system. In this paper, we confirm Barston 's conclusions by examining in detail several analytically tractable cases of delta-function and sinusoidal excitation, and consider the effects of collisions and non-zero electron temperature in determining the steady state fields and dissipation. Energy absorption without dissipation in plasmas is analogous to that occurring after application of a signal to a network of lossless resonant circuits. This analogy is pursued, and extended to cover Landau damping in a warm homogeneous plasma, in which the resonating elements are the electron streams making up the velocity distribution. Some of the practical consequences of resonant absorption are discussed, together with a number of paradoxical plasma phenomena which can also be elucidated by considering a superposition of normal modes rather than a single Fourier component.

From a basic discussion of the behaviour of VLF waves propagated almost perpendicularly to the earth 's magnetic field, the lower hybrid resonance (LHR) frequency is seen as a boundary between compressional Alfv én waves and electrostatic sound waves. The disparity of the wavelengths involved leads to a fundamental difference between the characteristics of the AC electric field far from and close to the source.

Some detailed observations of this field are presented, from an experiment that used both a mother-daughter technique for large distance measurements and a quadrupole probe technique for the local field, and that was performed in the equatorial ionosphere. The frequency dispersion of quasi-transverse (QT) waves received at a large distance and the amplitude-frequency response of the VLF quadrupole probe are compared with a theoretical analysis for the warm ionospheric plasma. From this analysis, the possibility is established of using the properties of fast and slow waves in active experiments, for measuring simultaneously the LHR, the electron density, a hybrid ion-electron thermal velocity and possibly the plasma drift velocity.

The experimental modifications of the classical Landau mode (modification of the first pole, and occurrence of a new propagating mode below the plasma frequency) are due to a peculiar distribution function. This distribution function is approximated by a simple model (i.e. a Maxwellian function plus a water-bag function). A numerical calculation with this model gives new dispersion curves, which agree with experiment.

Measurements of sheath thickness in a low-pressure plasma are reported. The sheath is ion-rich and contains both ions and electrons; the sheath edge is taken as a boundary for ion acoustic waves. The thickness of the sheath is estimated from a frequency shift of the wave. Despite the actually continuous transition from plasma to sheath, a clear-cut sheath edge is observed. It should be emphasized that even a very small increase in thickness, such as 0·1mm, can be measured by this frequency-analysis method. The experimentally obtained sheath boundary is in agreement with the Tonks–Langmuir value as modified by Self.

The equations of motion of an ideally conducting medium, in the magnetohydrodynamic approximation, are solved exactly under the hypotheses that (i) one component of the magnetic field is constant everywhere, (ii) the magnetic and hydrodynamic pressures are in equilibrium, and (iii) the solution is invariant under a continuous group of transformations which preserves the symmetry of the uniform magnetic field. It is seen that the invariants of the group of transformations form the basis for a parametric description of the full solution that describes the propagation of cylindrically symmetric magneto-sonic waves in the direction of the uniform field. A number of general features of the motion are deduced, and an integral expression is given for the amplitude of the component of velocity, perpendicular to the uniform magnetic field, which undergoes potential well oscillations.

We study the resonant interaction of particles with a monochromatic wave in an inhomogeneous plasma. The effects of the inhomogeneity are represented by a variable phase velocity of the wave. This introduces, in the wave frame, an inertial force due to the non-Galilean transformation of co-ordinates. Asymptotic expressions are obtained for the spatial damping coefficient of the wave in two physically different cases.

(i) When the inertial force is greater than the force due to the trapping (strong inhomogeneity case) instead of the null asymptotic behaviour that one obtains in the homogeneous case, the spatial nonlinear damping coefficient behaves asymptotically like the linear Landau damping coefficient.

(ii) When the inertial force is lower than the trapping force (weakinhomogeneity case), the spatial nonlinear damping coefficient for short distances is proportional to the ratio of the inertial force to the trapping force. For long distances, this coefficient is proportional to the square of the preceding ratio multiplied by the number of trapping lengths. In both cases, the proportionality coefficient is the linear spatial Landau damping rate.

The kinetic theory of a two-dimensional one-species plasma in a uniform d.c. magnetic field is investigated in the small plasma parameter limit. The plasma consists of charged rods interacting through the logarithmic Coulomb potential. Vahala & Montgomery earlier derived a Fokker –;Planck equation for this system, but it contained a divergent integral, which had to be cut-off on physical grounds. This cut-off is compared to the standard cut-off introduced in the two-dimensional unmagnetized Fokker –;Planck equation. In the small plasma parameter limit, it is shown (under the assumption that for large integer n, γn/γn+1 = O(np), with p < 2, where γn = ωn −nΩ. with ωn the nth. Bernstein mode and Q the electron gyro frequency) that the Balescu-Lenard collision term is zero in the long time average limit if one considers only two-body interactions. The energy transfer from a test particle to an equilibrium plasma is discussed and also shown to be zero in the long time average limit. This supports the unexpected result of zero Balescu-Lenard collision term.

The BBGKY hierarchy for a two-dimensional magnetized plasma is considered in the weak-coupling and small plasma parameter limits for very large magnetic fields. The Fokker-Planck and Balescu-Lenard equations satisfy an H-theorem and conservation laws, and exhibit two cut-offs related to the periodicity of the particle orbits and to the distance of closest approach of a thermal particle.

The effect of thermal anisotropies on the Drummond-Rosenbiuth two-stream ion cyclotron instability is studied. The properties of the instability are found to be dependent on the ratio of parallel electron temperature to perpendicular ion temperature, T∥e /T⊥ ι which can alternatively be viewed as the product ofT∥e /T⊥ ι and the ion anisotropyT∥e /T⊥ ιThe critical drift velocity decreases and the growth rate increases with T∥e /T⊥ ι. However, the dependence on T∥e /T⊥ ι becomes less sensitive as this temperature ratio increases, and, in the limit of T∥e /T⊥ ι>1, the instability becomes independent of the perpendicular temperatures.

The stability of hydrodynamic longitudinal oscillations of an inhomogeneous magnetoactive plasma is analysed. If the non-uniformity of density is taken into account, it is shown to result in parametric-like instability at sub- and ultra- harmonics of natural plasma oscillation frequencies. The conditions for the development of unstable oscillations and their growth rates are determined.

The dispersion relation for gravitational instability has been given within the framework of a two-fluid theory. It has been shown that the Jeans criterion is changed by finite Larmor radius and by collisions for waves propagating perpendicular to the magnetic field. The critical wavenumber for instability decreases with increasing Alfvén velocity and with increasing gyroviscosity. Instability does not set in with overstabiity.