Search

Recently, Istomin, Petviashvili, and Pokhotelov, 1 referred to in what follows as IPP (we must warn the reader that there are a number of minor errors in this paper), have developed a theory to explain the terrestrial or auroral kilometric radiation (AKR). We refer to IPP and a paper by Gurnett2 for a survey of the experimental data. The IPP model has been analyzed in considerable detail by Cole and Pokhotelov,3 who found that the model could explain many features of the AKR quantitatively and especially the fact that the power in the AKR is roughly 10% of the power in the auroral electron beams which excite the plasma turbulence in the region where the AKR originates. The IPP model uses the fact that the electron beams will excite shortwavelength electrostatic cyclotron waves which will be concentrated in solitonlike structures—called cyclotron solitons. Energy will be pumped into these solitons until the electric field in the soliton reaches a certain value. The oscillating charges in the structure will then produce electromagnetic radiation at twice the gyrofrequency which in the region where the AKR is produced corresponds to kilometric radiation.

I want to report here on some work from our group at Oxford, mainly by John Gibbons, Steve Thornhill, and Martin Wardrop, details of which can be found in a forthcoming paper (Gibbons, Thornhill, Wardrop and ter Haar 1976). We have in Oxford for some time been interested in various manifestations of plasma effects in astrophysics. Due to the enormous amounts of energy available, it is likely that many astrophysical objects, such as pulsar magnetospheres, accretion discs, galactic nuclei, quasars, and supernova remnants may contain turbulent plasmas. One way to approach this problem was the introduction by Tsvtovich and Chikhachev of plasma turbulent reactors (for a review of their theory see Norman and ter Haar 1975), but it now appears that these systems — at least in the simplified form in which they have been considered so far — are not adequate. It was therefore felt advisable to see whether one might find a theory of plasma turbulence which could easily be built into astrophical theory. The work by Kingsep, Rudakov, and Sudan (1973) sugested that perhaps a strongly Langmuir-turbulent plasma might be..lescribed as a gas of Langmuir solitons. This was the reason for a programme for studying the properties of Langmuir solitons and I am presenting some of the results of this programme, I should perhaps add that we are no longer very optimistic about the soliton approach to strong turbulence.

This thesis is a partial investigation of instabilities in the interstellar gas which are driven by a coupling between the ambient radiation field and the gas, and which do not arise when this coupling is missed out. The modes of couplings considered are, firstly, the attenuation of the radiation with the concomitant effects on the temperature, density and composition of the gas, in various combinations. Secondly, velocity dependent effects are examined in various circumstances and thirdly, radiation pressure, not included in the other two, is looked at in the simple case in which temperature and compositional changes are excluded. The explanation of why these instabilities may be of interest, and an outline of the extent to which similar instabilities have been investigated, is given in Chapter 1. Chapter 2 gives details of the basic equations used in the case in which the absorption line shape is ignored. Many of the equations are used in the other chapters. The equations are linearised in perturbations of the density, temperature, radiation field and composition, and the resulting dispersion relationship is found for a harmonic perturbation. Because of the attenuation term in the radiative transfer equation, the polynomial has complex coefficients. In Chapter 3 we investigate the properties of the roots of a complex polynomial by an extension of Routh's methods, and derive a set of criteria to determine the number of roots which have positive real part. These roots correspond to exponentially growing perturbations, or, in other words, they correspond to instabilities. Later in the chapter we apply these methods to Field's dispersion relationship for thermal instabilities and derive many of his conclusions in a fairly simple way. By a slight extension the method yields estimates of the growth times of the instabilities. Some related situations are also examined in a similar way. After the detour of Chapter 3, Chapter 4 gives details of some models of the heating and cooling of the interstellar gas as well as of the reactions to be considered, namely the formation and destruction of H2 and of carbon ions. Some of the limitations of the models are also discussed and the roots of the dispersion relation are given for different values of the parameters. New instabilities do appear; for H2 their timescales of growth are rather too long to be of interest; for carbon no short timescale instabilities are discovered. Chapter 5 gives similar details for a system of pure hydrogen gas which may be of interest in studies of the formation of the first generation of stars. In Chapter 6 there is a criticism of an earlier work by Schatzman on a similar subject, in which it is shown that his analysis was wrong. Chapter 7 deals with a new possibility, namely that, as the gas moves, photons will be seen to be shifted in frequency and so the molecules will be exposed to a new set of destructive photons at frequencies which have not been selectively absorbed in the unperturbed gas. First the simplest case, that in which the temperature is unperturbed, is treated analytically. The attenuation of the radiation field is not considered. The effectiveness of this doppler-induced effect depends upon both the absorption profile and the radiation spectrum; these factors as well as temperature perturbations are included next. Both line absorption and continuum absorption are considered. The former is used to investigate the stability of the interstellar gas and of pure hydrogen gas, where hydrogen molecules are dissociated by line absorption; the latter is used in connection with HII regions and also the interstellar gas where the photodissociated species are hydrogen atoms and neutral carbon respectively. Radiation pressure was not included in the previous chapters but in Chapter 8 a modified version of Field's theory of instabilities driven by radiation pressure is presented. The new feature is that the frequency dependence of the absorption coefficient is included in the equations and this, in the case of a flat radiation spectrum, leads to an exact cancellation of the dominant term in Field's equation. Several restrictive features of Field's conclusions are thus modified and seem to make this instability rather more useful in the study of instabilities in the interstellar gas than it appeared in Field's work.

In this thesis we consider turbulent fluid systems. We develop a closure scheme in which the mean velocity field of an incompressible fluid is driven by a turbulent velocity field possessing a non-zero mean helicity. We use this to investigate the formation of large scale vortices and the behaviour of the mean kinetic energy, enstrophy and helicity. The same technique is then applied to the equations of magneto-hydrodynamics, in order to explain the self-generation of mean magnetic fields, and the joint formation of current and vortex structures. We then discuss the convection of a passive scalar by the fluid and determine an equation for the mean temperature. Finally we present a theory to account for the behaviour of a two-dimensional electrically conducting fluid subject to a constant external magnetic field driven by external forces. We explain the peaks in the power spectrum, the saturation of the magnetic and kinetic energies, and the insensitiveness of their equilibrium value on the external field. All of these are observed in numerical experiments.

Plasma physics is nowadays a fast-developing field. This is to a large extent due to its importance in the search for terrestrial thermonuclear energy-sources. Of course, it is also a subject which is of interest both in its own merit and because of its applications to such more academic fields as astrophysics. All these aspects are well represented at this symposium. The programme before us promises a rich feast. The first day we shall hear about experimental results, a useful reminder to all theorists present that physics is an empirical science and that we should be sure never to stray too far from our experimental base. The remainder of the programme looks like having mainly a theoretical bias. No doubt some of the theoretical talks will be dealing with possible explanations of experiments, but I suspect that many of us will indulge in unbridled theorizing. As a theorist with a great interest in astrophysics I have also noted a few talks about astrophysical applications.

The vibrations of the electronic plasma are considered, which arise as a result of an arbitrary initial non-equilibrium distribution in it. It is shown that the vibrations of the field in the plasma are always damped, and the dependence of the frequency and of the damping decrement on the wave vector is determined for small and for large values of the latter. The penetration of a periodical external electric field into the plasma is considered. The case of the frequency of the external field being almost at resonance with the proper frequency of plasma is considered separately.

A transport equation is derived for a system consisting of charged particles taking their interactions into account. The order of magnitude of the mean free path of the particles in such a system is determined. The rate at which the temperatures of the ions and electrons in the plasma become equal is evaluated.

It is shown that the formulae for the distribution of nuclear energy levels which Bethe has obtained by considering the nucleus as an ideal gas, can also result from quite general considerations. A formula is derived for determining the width of the nuclear energy levels which are associated with scattering. Both inelastic scattering of neutrons, and emission of γ-rays are considered.

It is shown by considering possible methods of measurement that all the physical quantities occurring in wave mechanics can in general no longer be defined in the relativistic range. This is related to the well-known failure of the methods of wave mechanics in that range.