The problem of a monochromatic plane electromagnetic wave incident from vacuum on the plane boundary of a plasma half-space is considered. The method of solution is based on the representation of the disturbance in the plasma half- space as that generated by some current source in the complementary half-space into which, for the purpose of the representation, the plasma is conceived to extend. The specular reflexion boundary conditions and the diffuse scattering boundary conditions are treated in turn, first for normal incidence and then for oblique incidence.

The stability of relativistic anisotropic plasmas to the magnetosonic (or righthand compressional Alfvén) wave, near the ion cyclotron frequency, propagating perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and large ion plasma frequency () the dispersion relation is obtained in a simple form and solved. It is shown that for T‖ ╪ T⊥ (even T‖ ≥ T⊥) no instability occurs. This conclusion applies also to the case of the anisotropic interplanetary medium.

We note a peculiarity of the dispersion relation. Zero-order and first-order terms cancel so that the relation is of second order in our expansion parameter. The non-relativistic numerical results of Fredricks and Kennel are recovered.

The problem considered here is that of growing longitudinal waves which propagate in a hot plasma parallel to any magnetic field which may be present (i.e. the magnetic field is neglected in the Vlasov equation). The necessary and sufficient condition for stability was obtained by Penrose (1960) and growth rates for plasmas obeying a Maxwell zero-order velocity distribution were computed by Fried & Conte (1961).

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized, Maxwellian electrons. The linear dispersion relation is derived for waves in a perpendicular shock such that the most important sources of instability are the E × B and ∇B electron drifts. For the case of cold ions, propagation perpendicular to the applied magnetic field, and the E × B drift alone, a numerical analysis of frequency vs. wave-number is presented. The effects of the ∇B drift are also considered, and it is shown that the maximum growth rate can be larger than the maximum growth rate for the zero magnetic field ion acoustic instabifity under comparable conditions.

A large class of solutions to the steady-state Vlasov equations for a two component one-dimensional plasma for which the electric potential ø is monotonic is shown to exist. Some of these solutions are shock-like in the sense that the particle densities are also monotonic. If the particle and energy densities at infinity are not constraints of the problem, it is shown that there are always solutions for an arbitrary monotonic ø, and the solutions themselves contain arbitrary functions.

We investigate the structure of the hydromagnetic boundary layer formed by the mixing of two streams of fluid containing oppositely directed magnetic fields. The flow and magnetic field are aligned at infinity. The fluid is considered to be compressible, viscous, and electrically and thermally conducting. Solutions are presented for the density, velocity, and magnetic field variations through the boundary layer.

This paper presents an analysis of the linear dispersion relation for electrostatic waves in a Vlasov plasma of unmagnetized, Maxwellian ions and magnetized, Maxwellian electrons. The electrons undergo E × B and ∇B drifts, and the electron β is small. For propagation in the perpendicular direction, maximum growth rates can be substantially larger than those of the zero magnetic field ion acoustic instability. For propagation outside a few degrees from the perpendicular the dispersion characteristics are essentially those of the ion acoustic instability.

The collective approach of Pines & Bohm has been applied to the problem of the thermodynamics of the N-particle electron gas including transverse radiation. Partitioning of the internal energy and certain of the other thermodynamic quantities is discussed generally. The system is seen to divide itself into three approximately independent subsystems: (1) an infinite set of free harmonic oscillators, corresponding to the transverse field, with an energy spectrum given by ωT(κ), where ωT(κ), is given by the dispersion relation for transverse electromagnetic waves in a plasma; (2) a set of 8 free harmonic oscillators corresponding to the longitudinal (plasma) oscillations, with an energy spectrum ωT(κ), given by the dispersion relation for plasma oscillations; and (3) a set of (N — 2s/3) quasi-particles of mass approximately equal to the electron mass, interacting via a short-range potential which is essentially screened Coulomb. Analytical expressions for the energy, pressure, and constant-volume specific heat of the transverse oscillators are given, together with approximate expressions applicable to the high-density—low-temperature and low-density—high-temperature limits. Detailed numerical calculations of the internal energy and pressure of the longitudinal modes are presented. In addition, the contributions to the energy and pressure from the particle portion are evaluated in the low-density—high-temperature limit as functions of the cut-off wave vector κc; κc is the maximum k-vector of the longitudinal oscillators.

The propagation of a packet of weakly non-linear dispersive cold plasma waves is studied by means of a two-time scale expansion. The effects of amplitude dispersion and the coupling to the mean plasma motion are taken into account. The governing equations are put into a conservation form. It is found that this system of equations is elliptic or hyperbolic depending on the wave-number of the dispersive waves. In the elliptic case modulations in the wave train grow exponentially in time and a periodic wave train will be unstable in this sense. In the hyperbolic case, slow variations in the wave train propagate and the characteristic velocities give a non-linear generalization of the linear group velocity. It is shown that except for waves which have their wave vectors nearly at right angle to the unperturbed magnetic field only fast waves with wave-number less than 0.585 (Ωi Ωe)½/Vα are stable; where Va is the Alfvén velocity and Ωι Ωε, are the ion and electron cyclotron frequencies respectively. A process of steepening of these waves into shocks with dissipation due to wave turbulence at the head of the wave packet is suggested.

The character of equilibrium of an inviscid, incompressible, infinitely conducting fluid of variable density in the presence of a horizontal magnetic field has been investigated taking into account the effects of Hall-currents. The solution is shown to be characterized by a variational principle. Making use of the existence of variational principle the solution is developed in the case of continuously stratified fluid of exponentially varying density confined between two horizontal planes at finite distance, from which the necessary and sufficient conditions of stability are obtained. The Hall-currents are found to destabilize the wave-number range which is stable otherwise.

Continuum theory is adopted to describe the steady, spherically symmetric flow of an unbounded expanse of quiescent, slightly ionized fluid about a perfectly catalytic conductor. The negative charge carrier is taken to be an electron, the potential bias of the probe φP is taken to be negative, and recombination and ionization effects are taken to be negligible. Matched asymptotic expansions are used to study the limit of small Debye number ∈, where ∈ is the ratio of Debye length to conductor radius. The current collected at the probe is found for three ranges of applied potential: small bias, including φp = O(1); moderate bias in which φP = O(log(1/∈)); and large bias in which φP = O(log(1/∈);). The current collected does not saturate (become independent of φP) for the range of c studied here; however, for φP, the current collected remains of order unity while the potential bias varies over several orders of magnitude. The previous asymptotic treatments of this problem, principally due to Su & Lam and to Cohen, are critically reviewed and compared with the results developed here.

Whitham's averaged Lagrangian method is used to yield a relativistically covariant formalism for wave packets in a weakly inhomogeneous (and time dependent) medium. Provided the physics of the medium can be based on a Lagrangian density, a procedure of expansion and averaging is available which gives separate Lagrangians for the dynamics of the background and of the waves. The Euler—Lagrange equations then give immediately the equations of motion for the background, including non-linear reaction of the waves, and the dispersion relation, equations for ray tracing, conservation of wave action and non-linear coupling coefficients, for the waves. Many of these results can be interpreted in an illuminating way by considering the corresponding expansion of the canonical four-dimensional stress tensor.

The loading resistance of a coil-plasma system operated near the lower hybrid resonance in hydrogen and argon has been measured. The results are consistent with the predictions of a theoretical model that includes finite plasma effects.

Thermodynamic properties and compositions of gases in thermal equilibrium at high temperature can in principle be derived quite accurately once the partition functions of the relevant species have been calculated.

A self-consistent solution of the Vlasov—Poisson equations is obtained for a low-temperature, bounded, Maxwellian plasma of arbitrary non-uniform density. An eigenvalue equation for the central frequencies and electric fields of the resonance oscillations is obtained, which agrees with the equation obtained by a low-temperature expansion of the orbital-integral solution. The Landau damping rate is given in a general, explicit form in terms of the central frequencies and fields of the resonances.

The equations governing the collapse of a cylindrical, ionizing shock in an applied axial magnetic field are solved numerically using a method involving characteristics. Initially the collapsing shock accelerates, but subsequently the increasing magnetic forces at the shock produce a retardation and this cools the gas behind the shock. The numerical solution describes the behaviour of the shock until the gas behind ceases to conduct. The decomposition of the ionizing shock is examined.

In a previous paper [Lewak (1969), see also Pflrsch (1966) for related treatment], it was shown that the Vlasov equation in the Semi-Lagrangian (S.L.) formulation, may be written in a form resembling the fluid equations.

plus Maxwell's equations with the source terms given by

where n is the determinant of the tensor Tij = ∂gi/∂ζj, and N is the constant mean number density of electrons. The averaging notation < > here is defined by

where f(σ) is the electron distribution function to be specified. The equations assume for simplicity a uniform fixed ion background, although this is not a necessary restriction and equations (1) and (2) need only an obvious modification to account for ions. The force fields in (1) are related to the electric field E and magnetic field B in the plasma by .

The parametric effect of an applied uniform oscillating electric field on both unmagnetized and magnetized plasmas is investigated. By using a perturbation method of multitime scales, we have shown that parametric excitation of transverse waves propagating obliquely to the applied field in an unmagnetized plasma is possible. The growth rate of the excited waves reaches a maximum for transverse propagation. Ion motion does not change the character of the parametric excitation except by reducing the growth rate. In a magnetized plasma it is shown that excitation of a pair of waves is possible where one is a Langmuir wave, propagating along the magnetic field and the other is a circularly polarized transverse wave propagating in the opposite direction.

The motion of a test particle in a plasma whose average properties vary along one direction in space, but are independent of time, is considered. A method is given which enables this problem to be treated similarly to existing theories for a homogeneous plasma.

An exact solution to the steady-state Vlasov equations and Poisson's equation for a one-dimensional plasma of electrons and protons is obtained by splitting the energy equation into two integral equations for the trapped particle distributions. This solution has the properties that the number densities and electric potential are moiiotonic functions of space and do most of their changing over a distance of the order of the Debye length for electrons. The distributions are everywhere differentiable in phase space and are Maxwellian-like, and in terms of elementary functions. Evidence is given to support stability for restricted shock strengths.