Starting from hydrodynamic equations, a dispersion relation is obtained for wave propagation through a hot electron plasma perpendicular to a spatially uniform external periodic magnetic field, B0 cos ω0t, and several excitation conditions are deduced.

Dispersion relations for first-order oscillations in an infinite homogeneous two- component plasma, in response to an externally applied constant magnetic field and a right-hand circularly polarized external electric field, and with propagation vector parallel to the magnetic field, has been obtained. The external electric field, assumed to be spatially homogeneous, is perpendicular to the applied magnetic field. It has been shown that the left-hand mode is excited and is unstable when its frequency ≃ ν–ωρ, where ν is the frequency of the external electric field and ωρ is the characteristic plasma frequency. When the applied magnetic field is large, both the left- and right-hand modes are excited and may be unstable when their frequencies ≃ Ωic – ωρ where Ωic represent the electron (i = 1) and the ion (i = 2) cyclotron frequencies. The principal criterion for the validity of these results is the condition of spatial homogeneity of the external electric field.

In this investigation, we study the effects of non-linear interaction of plasma waves in the weak turbulence approximation on a stream-plasma system which is subject to the two-stream instability. The momentum distribution of the stream is assumed to be a Gaussian function and the background plasma is assumed to be a Maxwellian with a temperature T. The non-linear wave-particle interaction of induced scattering on the polarization clouds of ions may lead to stabilization of the stream—plasma waves in the resonant cone are scattered into the nonresonant region. The non-linear wave-particle interaction of induced scattering on the polarization clouds of ions may lead to stabilization of the stream; plasma waves in the resonant cone are scattered into the non-resonant region and vice versa, leading to a well-defined average energy density in plasma waves which is much less than the energy density of the stream. Non-linear scattering also causes transformation of plasma waves into electromagnetic radiation near the fundamental of the electron plasma frequency of the background plasma, and combination of two plasma waves leads to electromagnetic radiation near the second harmonic of this frequency. Expressions are given for the latter process for emission and absorption for arbitrary values of the ratio of the wave number of plasma waves to the wave number of the electromagnetic wave. The major features of the whole phenomenon are illustrated with the help of a numerical example, with conditions typical for the solar corona in which case an ion stream would be stabilized, but an electron or neutral stream (with the chosen density) would not.

The non-linear scattering of circularly polarized electromagnetic waves is studied. Expressions for matrix elements of interaction are derived and for interacting right-handed circularly polarized waves (whistler waves) the matrix is explicitly calculated for particular velocity distribution functions of electrons. Non-linear damping rates are computed.It is shown that non-linear scattering is not in general a dominant process for whistlers in the magnetosphere.

The propagation of small monochromatic disturbances in a stable ideal magnetohydrodynamic fluid is treated by the method of geometric optics. The medium is trirefringent and requires six systems of rays. The problem of a point radiator is solved in the small wave-length limit where the theory holds.

The time asymptotic method of non-linear mechanics (Bogoljubov & Mitropoiski 1961) is used to solve the hierarchy equations of low-amplitude wave correlations. We start with a formal description of individual dispersive and undamped waves and derive the usual kinetic equation for the energy spectrum and the three-wave correlation in the lowest order (three-wave processes). We show that the equations are automatically closed (‘Quasi-Gaussian’) even in the case where the correlations have the same order of magnitude as the corresponding moments. This approach parallels the multiple-time formalism of Sandri and Frieman, but it represents an alternate systematic and unique method (without ‘extension’ in the sense of Sandri).

We discuss the structure of hydomagnetic shock waves of various types. The plasma is treated in the two fluid approximation and coffisional transport coefficients are used. This treatment should be valid in a collisional plasma subject to the usual caveat about the use of transport coefficients in situations where the density, temperature, etc., may change significantly over a mean free path. The approach may also have some validity for collisionless shocks if the dissipation mechanisms involve instabilities of sufficiently fine scale and high frequency that they can be described by effective transport coefficients.

In electrostatic turbulence under appropriate conditions we show that we can have an equation for ϕk (time variation of electrostatic potential amplitude) which is essentially instantaneous in time. The coefficients in this equation are uniquely determined by the Poisson equation of the corresponding order. By applying time asymptotic methods of Bogoljubov and Mitropoiski to the corresponding hierarchy equations we obtain a kinetic equation for the spectrum 〈|ϕk|2〉. The resonant mode coupling terms agree with the usual ones. But the non-linear Landau damping terms, as given, e.g. by Frieman & Rutherford (1964), Kadomtsev (1965), Tsytovich (1968), and Rogister & Oberman (1969) are complemented by additional terms which are, at least formally, non-zero. For simplicity the calculations are only done for the weakly unstable (and weakly damped) modes.

It is shown that the relativistic Vlasov–Maxwell equations admit a solution very much like the transverse Alfvén wave of magnetohydrodynamic theory. This wave propagates as a plane electromagnetic wave of arbitrary amplitude, is noncompressive, is associated with fluctuations in direction (but not magnitude) of magnetic field, is characterized by a non-linear ‘dispersion relation’, and reduces in the limit of small amplitude to the transverse Alfvén mode of linearized plasma wave theory. The dispersion relation yields a criterion for the firehose instability which turns out to be the same as that derived from linearized theory.

The system studied is that of an electrostatic Gaussian wave packet in a cold uniform plasma being excited by a weak resonant beam. To first order in a parameter associated with the weakness of the beam the resonant particle distribution function and resonant particle charge densities are computed.

The interaction of three electrostatic waves in a collisionless plasma is treated to fourth order neglecting the wave—particle interaction (damping). Using the principles of energy conservation, and invariance under time reversal, conditions on the coupling constants are derived, enabling the solution to be expressed as a function of only two coupling constants. Phase plane diagrams of the solutions are sketched showing that the only singular points are stable equili bria. It is suggested how the theory may be applied to the explanation of the ‘floating spike’ resonance observable when one-half the hybrid frequency is the difference between the plasma and gyro frequencies (Hagg & Muldrew 1968).

The effect of stochastic high-frequency fields on the stability of electrostatic plasma oscillations in a magnetostatic field is studied. The stabilizing effect can be provided by diffusion in configuration co-ordinates, as well as in the longitudinal and transverse velocities. The parameters of the stochastic field for effective stabilization are estimated, as well as the influence of the accompanying escape of particles due to the stochastic fields.

The effects of ion-ion collisions, described by a Fokker-Planck operator in the kinetic equation, on an ion-acoustic plasma pulse, are studied. Our investigations show that the coffisions give a broadening of the pulse, and reduce the effect of interaction between the main plasma and the pulse.

The stability of the screw pinch is investigated taking into account the presence of Hall current in Ohm's law. The dispersion relation is obtained as the exact solution of the characteristic value equations governing the general perturbations. It is found that the Hall current has no effect on the hydromagnetic stability of the screw pinch.

The theory of the development of thick sheaths given in an earlier paper (Sander 1969) is applied to planar sheath growth in practical situations. The results are compared with those resulting from a purely numerical method and from certain approximate equations suggested by other workers in the field.

Using a reformulation of ordinary perturbation theory to first and second order, explicit solutions for the penetration of electrostatic waves into a semi-infinite Vlasov plasma are presented. Two types of electron velocity distribution are used, the uniform step (‘water-bag’ model) and the Maxwellian. The existence of propagating modes below the plasma frequency, behaviour of the second harmonic field and the formation of a narrow sheet of electrons near the bounding wall are displayed. Replacement of boundary fields with equivalent charge and current sources is discussed.

Scattering of optical and radio frequency radiation from electron density fluctuations in a plasma has been extensively studied and bids fair to become a useful diagnostic tool (see, for example, Davies & Ramsden, 1964, 1966). The scattered spectrum, although difficult to observe, contains a great deal of information. The electron density, ion and electron temperatures, the shape of the tail of the electron distribution function, spectral fluctuations in unstable systems, the magnitude and direction of the magnetic field and the charge to mass ratio of the ions present all seem to be contained in it.

The propagation and stability of drift waves is examined, by means of a perturbation technique, in geometries where the magnitude of the magnetic field varies periodically along the field lines. Two sets of modes are found which can be driven unstable by resonant particles trapped in the magnetic field non-uniformity. One set of modes consists of standing waves with wavelength twice that of the magnetic field non-uniformity. The other set of modes consists of standing waves composed essentially of the sum of a component which does not vary along the line and a component which is a standing wave with wavelength equal to the wavelength of the magnetic field non-uniformity. The advantage of this method is that it predicts simply and pictorially the real frequency of oscillation for these modes.

Local imperfections in the magnetic field can alter the topology of the magnetic surfaces, thereby allowing plasma to escape. A modest longitudinal magnetic field will maintain the nested surfaces near the plasma boundary, so that the residual topological changes near the separatrix become unimportant.

The voltage refiexion coefficient from a vacuum-plasma boundary in a co-axial transmission line with an axial magnetic field B0 applied has been measured. The results agree well with a previously published theory for conditions where the microwave-, plasma-, electron collision-, and electron cyclotron-frequencies are of the same order. A 9 GHz co-axial microwave probe is mounted along the axis of a 44mm diameter, hydrogen driven, dry air filled, shock tube in an axial d.c. magnetic field. Shock ionized air (Ms = 9–14, T 4000 °K, electron density nc = 1017 to 3 x 1019 m−3, initial pressure p0 = 1–10 Torr, electron collision frequency v = 1010 to 1011/S) fills the coaxial line and partially reflects a microwave signal. Initially this probe, and a similar rectangular waveguide probe, were used with B0 = 0 to calibrate the plasma (ne, v) in terms of the shock tube parameters (p0, Ms). Measurement of the saturated-ion current to electrostatic probes inset into a fiat plate in the shock tube flow showed that the sheath-edge ion density is close to the predicted free-stream equilibrium ion density. The apparent ionization potential derived from electrostatic probe results decreased as p0 was reduced from 10 to 1 Torr.