The effect of rarefaction, optical depth and ratio of conduction to radiation on the heat transfer through stagnant diatomic gas between parallel plates is investigated. A three-fluid formulation (translator–rotator–photon) at low temperature and [translator–(rotator and vibrator)–photon] at high temperature, based on continuous distribution functions, molecule–molecule elastic collisions, molecule–photon inelastic collisions, grey gas, and local equilibrium is solved by the linearized moment procedure for fully accommodating surfaces. Results include the error involved in decoupled total heat flux.

Suppression of runaway of electrons in a weak, uniform electric field in a fully ionized Lorentz plasma by crossed magnetic and electric fields is analysed. A uniform, constant magnetic field parallel to a constant or harmonically time varying electric field does not alter runaway from that in the absence of the magnetic field. For crossed, constant fields the passage to runaway or to free motion as described by constant drift motion and spiral motion about the magnetic field is lengthened in time for strong magnetic fields. The new ‘runaway’ time scale is roughly the ratio of the cyclotron frequency to the collision frequency squared for cyclotron frequencies much greater than the collision frequency. All ‘runaway’ time scales may be given approximately by t2E Teff where tE is the characteristic time of the electric field and Teff is the ffective collision time as estimated from the appropriate component of the electrical conductivity.

The stability of a non-conducting, compressible fluid (gas) flowing across the surface of incompressible conducting fluid (liquid) is discussed. Finite resistivity and Hall current are included in the hydromagnetic equations, together with surface tension. Both subsonic and supersonic flows are treated and some new instabilities are found, together with modifications to real and oscillatory modes obtained in earlier treatments.

A self-consistent Vlasov equation treatment will be given for a type of echo which arises due to the relativistic velocity dependence of the gyrofrequency. We consider a relativistic plasma in a homogeneous magnetic field. If at t = 0 and t = T a spatially homogeneous external r.f. electric field is applied perpendicular to B0, then an echo response is produced at t = 2T. The amplitude of the echo is proportional to the amplitude of the first pulse multiplied by the square of the amplitude of the second pulse.

The influence of shock-induced precursor ionization on the steady-state structure of switch-on shock waves with non-equilibrium ionization and radiation is examined theoretically. A single-temperature monatomic gas is assumed, together with a Clarke–Ferrari model for photoionization of the upstream gas. It is found that the effect of the precursor depends in general on the ratio of a characteristic precursor length to a characteristic magnetic interaction length. For the slightly ionized case treated in some detail, this ratio is much greater than unity, indicating a precursor-independence for the magnetohydrodynamic shock structure.

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.

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.

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.

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.

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.

The effect of finite ion-Larmor radius is considered on the Rayleigh–Taylor instability of a plasma. The macroscopic equations of motion are used where the finite ion-Larmor radius effects are incorporated in the stress tensor. The finite ion-Larmor radius stabilization of the interchange mode is demonstrated. For disturbances propagating along the magnetic field, it is found that the inclusion of gyro-viscosity has a stabilizing effect; it increases the critical wavenumber (compared to its value in the absence of gyro-viscosity) beyond which all modes are unstable.

A laser produced plasma expanding in a uniform magnetic field emits far infrared radiation. The time-dependent radiation history is calculated assuming spherical symmetry and compared with experiment. General features of the radiation history agree well with experimental observation. However, a detailed comparison is difficult because of the oversimplified theoretical model employed.

This paper considers the non-linear resonant interaction between three waves, which propagate in the direction of a constant magnetic field in a homogeneous plasma. A coupled-mode theory, which makes it possible to derive the coupling coefficients within a kinetic description, is developed.

A new derivation of quasilinear theory for plasma oscillations is given, subject to the neglect of wave-wave interactions. The theory, which applies equally to damping and growing waves, requires that the individual wave resonances be narrow and the electric field spectrum sufficiently broad.

When a sheath grows into a plasma at a slower speed than the local ion speed of sound, an ion rarefaction wave propagates into the plasma ahead of the sheath. It is shown that, in the frame of reference of the sheath edge, the speed of ions arriving at the sheath edge cannot exceed (kTe/M)½.

This paper deals with the problem of classification of the two-stream instability for hot plasmas. The method is based on the criterion of Fainberg, Kurilko & Shapiro (1961). The basis of the analysis is the ‘resonance’ distribution, but a modified resonance distribution, leading to better results, is also investigated. The stability limit, classification into absolute and convective instabilities, as well as asymptotic growth rates are given for some chosen values of stream densities and temperatures, and arbitrary stream velocities. A method for finding the maximum temporal growth rates is also outlined.

Ion-acoustic waves propagating in a collision-free, gravity-supported plasma in a static magnetic field are studied with a linearized Vlasov equation. The dispersion relation is derived in the limit of vanishing electron to ion mass ratio and wavelength much larger than the Debye length. From this dispersion relation it is shown that the well-known fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is competing with the effect of Landau damping. Depending on the ratio of electron and ion temperatures, the direction of propagation and the strength of the static magnetic field, waves of wavelengths of the order of the scale height or even greater are shown to be damped. Several special cases are discussed.

The effects of dissipation due to a week firehose instability on steady planar flow of a collisionless plasma are investigated on the basis of the quasi-linear fluid equations. Dissipation terms remain non-linear even within the perturbation theory, and their effects tend to resemble relaxation effects in an ordinary reacting gas rather than ordinary viscous dissipation. As an example, a steady half-jet flow with aligned magnetic field is considered. It is found that the disturbed field decays within a finite distance for some upstream conditions, but grows without limit for others.

‘MHD Rankine-Hugoniot equations applied to earth's bow shock’

by J. D. Mihalov, C. P. Sonett and J. H. Wolfe

J. Plasma Physics (1969), vol. 3, part 3, pp. 449–463

The bottom entry of column 2, Table 2, page 455, should read ‘–20’ instead of ‘20’. Recent work suggests the possibility of a systematic error as large as ˜ –3 deg in ø(‘spacecraft’ co-ordinates) of Table 1, page 453. The calculations have been repeated with the ø values decreased by 2·8 deg, with the result that none of the conclusions of the paper are changed since the detailed numerical results are not significantly different.

On page 463, the fifteenth of the list of references should read:

Ness, N. F. & Taylor, H. E. 1969 Annals of the IQSY, 3, 366.

On the same page, the fifth to the last of the list of references should read:

Wilcox, J. M. 1969 Solar Flares and Space Research, p. 294 (edited by C. de Jager and Z. Švestka). Amsterdam: North-Holland Publishing Co.