The reconnexion of magnetic field lines is described for a special case of steady, incompressible hydromagnetic flow in two dimensions. A similarity solution is obtained which corresponds to the flow of a perfectly conducting, inviscid fluid such that magnetic field lines are carried from two sides toward, then on the other two sides away from, the centre of an X-configuration. The effects of viscosity are important in shocks which form in the vicinity of the X-lines of the configuration. The effects of finite electrical conductivity must be taken into account near the centre of the configuration which, in the symmetrical case discussed, is an X-type neutral point. From an approximate solution valid in this region it is found that the fluid must flow from the larger to the smaller wedges of the X-configuration. Hence, the reconnexion process is such that oppositely directed magnetic field lines move towards the neutral point in the larger wedges, become reconnected at the neutral point, and move away in the smaller wedges. Since the solution in the vicinity of the neutral point appears to be no more than a response to the external flow, which is in turn controlled by conditions far from the neutral point and is essentially unaffected by viscosity and finite electrical conductivity, it is tentatively concluded that the rate of re-connexion of magnetic field lines does not depend on these quantities, and that, in general, re-connexion can be expected to take place rapidly if circumstances are favourable.

Parts I and II of this paper present a comprehensive picture of longitudinal wave propagation in a warm homogeneous magnetoplasma. Part I discusses computed dispersion characteristics for propagation perpendicular to the static magnetic field. For a ring electron velocity distribution it is found that mode coupling and absolute instability can occur. Similar effects are predicted for a spherical shell distribution. The Maxwellian distribution gives rise to stable propagation of undamped waves, and attenuating standing waves. A mixture of ring and Maxwellian distributions can give absolute instability with stronger growth and lower instability thresholds than for the ring distribution alone. Propagation oblique to the static magnetic field will be dealt with in Part II.

Part I of this paper has discussed longitudinal wave propagation, perpendicular to the static magnetic field, in a warm homogeneous magnetoplasma. Part II extends the work to oblique propagation. The ring and Maxwellian transverse velocity distributions, which are absolutely unstable and stable, respectively, for perpendicular propagation, are shown here to be both absolutely unstable for oblique propagation. Their instabilities are radically affected by the introduction of axial velocity spread. A detailed study is made for the cases of a Maxwellian transverse distribution with resonance and resonance-squared axial velocity distributions. It is shown that abolute instabilities occur at high energy anisotropies. These become convectively unstable as teh anistropy is reduced, and are quenched as isotropy is approached. The isotropic Maxwellian is treated in detail, and shows both cyclotron and Landau collisionless damping.

Within the hydromagnetic approximation, the effects of resistive, viscous, and thermal conduction dissipation on the structure of shock waves is studied. A Perturbation analysis about the upstream and downstream stationary points is developed, which, when coupled with the shock evolutionary conditions, determines the conditions for the formation of discontinuities in the shock structure. The Viscous subshock for fast shock waves and the hydromagnetic analogue of the gas dynamic isothermal discontinuity for fast and slow shocks are analyzed. Very oblique fast shocks require both resistive and viscous dissipation for a steady shock structure. Strong slow shocks propagationg nearly along the magnetic field fail to steepen if only resistive dissipation is included. The rotational discontinuity does not possess a stable shock structure for any of the dissipation processes considered.

The first-order temperature terms for the anisotropic-temperature plasma susceptibility are calculated for each species, using the velocity moment equations and circular polarized co-ordinates. The results agree with the expanded terms for the Vlasov equation solution, for which a usefully simple derivation is given. An electrostatic wave result is given. Drift can be included by a transformation of the results for zero drift.

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).

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.

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.

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.

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 method of matched asymptotic expansions is applied to the fluid model of the low-pressure positive column. The expansion of the eigenvalue in the plasma balance equation is obtained to second order in plane and in cylindrical geometry, and uniformly valid expressions for charged particle densities and fluid velocity in two separate regions are indicated.

The free-fall model is also examined and the scales of the transition layer and sheath layer found. Comparison is made with the results of direct numerical integration of the equations involved for both models.

The suppression of runaway electrons in a Lorentz plasma is demonstrated for a two-component, fully ionized plasma in the presence of a high frequency, weak, uniform electric field. The time for runaway to occur for electric field frequencies high compared to the collision frequency is longer than the runaway time for low electric field frequencies or zero frequency, by the ratio of the frequency of the electric field to the collision frequency squared. Both the resolvant method developed by Prigogine and co-workers and the double perturbation scheme of the Poincaré—Lighthill method are employed to derive the diffusion equation for the modified one-particle distribution function in the collision-dominated region of velocity space.

The Chew—Goldberger—Low theory of a collisionless plasma, modified to include the effect of finite Larmor radius of the ion and the electron, is applied to a linearized problem of two-dimensional steady flow. The zeroth-order terms in the Larmor radius expansions of the velocity distribution functions of the ion and the electron are assumed to be anisotropic Maxwellian. The spatial development of a given velocity profile is investigated for flows with either crossed or aligned magnetic fields, and for various values of Mach number, Alfvén Mach number, and anisotropic pressure ratios in the main flow.