In this work we evaluate the anomalous high-frequency conductivity arising from particle—wave interactions in a multi-species turbulent plasma with no external magnetic field. The calculation is made by using the full three-dimensional model of the quasi-linear theory of plasma turbulence for a wide range of frequencies embracing the electron plasma frequency. It is found that the conductivity tensor is anisotropic and slowly time dependent; this reflects the slow time dependence and the anisotropic character of the distribution functions of the velocities of the particles. It is also found that there is a very narrow range of frequencies (just above the electron plasma frequency) for which the components of the conductivity tensor are negative. The particular case of the two- stream instability is examined in detail. The anisotropic character of the components of the conductivity tensor and their dependence on the frequency of the external field is studied. Finally some possible means for an experimental check of our calculations are suggested.

The jump conditions across a transverse ionizing MHD shock wave, where the magnetic field is in the plane of the shock, are examined. The conservation laws, in conjunction with Maxwell's laws and the equation of state, yield three jump equations in four unknowns. To uniquely describe jumps across an ionizing wave requires an additional descriptive relationship. The theory of Kulikovskii & Lyubimov and, later, Chu, in which the internal structure of the shock itself supplies the missing relationship, is examined. In particular, Kulikovskii & Lyubimov show, for appropriate ratios of thermal to magnetic diffusivities, that for low-speed waves the magnetic field compression across the shock is unity and the jump equations reduce to the ordinary Rankine—Hugoniot relations. For high-speed shock waves, the magnetic field compression, B2/B1, equals the gas compression across the wave, p2/p1, and the jump equations become the magnetohydrodynamic shock jump relations. Furthermore, intermediate speed shocks induce magnetic field compressions between 1 and p2/p1. An experiment was performed in an inverse pinch where E behind the shock, the shock and piston velocities, and the magnetic field compression across the shock, were measured over a wide range of initial conditions and shock velocities in hydrogen. The jump relations were written with B2/B1 as a parameter and programmed into a digital computer. The program was written for real, equilibrium hydrogen. The program provided easy access to a unique solution of the jump equations for any B2/B1. The experiment tends to confirm the Kulikovskii—Lyubimov—Chu theory. Ordinary shock waves were observed at low speeds and near-MilD shocks were observed at high speeds. Further, the relation was verified for the plasma behind the shock for low-speed shock waves, and was verified to within experimental accuracy for the intermediate class of shock waves.

The shock-tube side-wall boundary layer in a 1 eV, high-density argon plasma was studied experimentally using anew, simple, quantitative schlieren technique. The angular refraction of light which enters the shock-tube test section parallel to a side wall and passes through typically 1 mm thick boundary layers was determined in two separate wavelengths. This was done by measuring the displacements of two shadows formed by two thin wires placed in the point source light, which is reflected non-centrally by a concave spherical mirror. The experiments were of exploratory nature only, but clearly demonstrated the feasibility of the new technique in analysing plasma-boundary-layer flows. Measured electron density profiles in the high-temperature region of the sidewall boundary layers agreed within experimental errors with those calculated from the equilibrium-boundary-layer theory.

The mathematical formulation for the problem of non-linear oscillations in a self-consistent, non-uniform, collisionless plasma is considered. The fully nonlinear treatment illuminates the effect of the wave on the background distribution of the plasma through which it is passing. It is assumed that, although the overall non-uniformity may be large, significant changes occur only over time or length scales which are large compared with the plasma period or Debye length respectively. Exclusion of secular terms from the solution leads to a Liouvile type equation, which must be satisfied by the background distribution, and to propagation laws for the waves.

The theory is restricted to almost one-dimensional electrostatic waves and a general presentation is given from a relativistically-invariant point of view. Then the equations are derived in terms of physical variables for the special case in which: (i) the distribution functions and electrostatic potential depend on one space co-ordinate (that of propagation of the wave) and the former on the corresponding particle velocity component only, (ii) the wave is slowly-varying only with respect to this co-ordinate and time, and (iii) the magnetic field is zero. Finally, the non-relativistic limit of this case is considered in more detail. The boundary conditions satisfied by the distribution functions are discussed and this leads to the conclusion that in some circumstances thin sheets of probability fluid are formed in phase space and the background distribution cannot be strictly defined. This motivates a reformulation and subsequent re-solution of the problem (for this non-relativistic special case) in terms of weak functions, corresponding to the physical assumption of the presence of a small-scale mixing mechanism, which is excited by and smears the sheeted distribution but is otherwise dormant.

The results of the investigation are given as a system of differentio-integral equations which must be solved if necessary conditions for the absence of nonsecular solutions (of the Vlasov and Maxwell equations) are to be satisfied. No solution of this system is attempted here.

The dispersion equation for helicon waves in a plasma-filled wave-guide is derived. The relation between the solution and the quasi-static modes of Trivelpiece & Gould is discussed. An approximate dispersion relation, appropriate for cases where Ωe≫ ν ≫ ω, is obtained allowing the real and imaginary parts of the propagation constant to be expressed very simply in a normalized form. Curves are presented for this approximation.

J. Plasma Physics (1968) vol 2, part 2, pp. 105–118.

Page 115, legend to figure 4 should read as follows:

Figure 4.(a)Plot of

(b) Plot of

‘On the a.c. electrical conductivity of a Lorentz gas’ by J. H. M. Fu and R. S. B.Ong, J. Plasma Phys. 2, 1968, P. 1.

Calculation of the electrical conductivity

The current density is expressed by

Using the dimensionless velocity c = (m/2θ;)½v and noting that the current density associated with the equilibrium distribution function f0 vanishes, we can write

g(k, c, w) is given formally by

where gns(k, c, w) is given by (2.15) in the original paper, and

with λ = (2θ/m)½/(w/k and δ the Dirac delta function.

‘Propagation along the magnetic field of a pulse current originated dlisturbance in a cold two-fluid plasma’, by G. J. Lewak, J. Plasma Physics, vol. 1, 1967 p. 435.

On page 449, the sixth of the list of references should read

Davis, L., Lust, R. & Schluter, A. 1958 Z. Naturforsch. 13a, 916.