Introduction

The formalism developed in Chaps. 3 and 4 needs to be modified to take into account the inhomogeneities present in our universe, and we shall try to reconstruct the observed universe in the following manner: We assume that, at some time in the past, there were small deviations from homogeneity in our universe. These deviations can then grow because of gravitational instability over a period of time and, eventually, form galaxies, clusters etc. The first task is to develop the mathematical machinery capable of describing the growth of structures.

In a universe made of nonbaryonic dark matter, baryons, and radiation, we need to discuss each component separately. The simplest of the three components is the dark matter, which is affected only by gravity and is collisionless. In the fluid limit, we can ignore the velocity dispersion of the dark-matter particles, and there is no effective pressure term in the equations. If the velocity dispersion is important, there will arise an effect called free streaming, which we will discuss in Section 5.6. The physics of radiation is complicated by the fact that a photon can traverse a distance of the order of dH ≈ ct within a cosmic time t; hence any perturbation in δR at length scales λ ≲ ct will be wiped out by the free propagation of photons. At λ > ct, radiation can be treated as a fluid influenced only by the gravitational perturbations.

Introduction

In this chapter several aspects of galactic structure and evolution are discussed. Some of the ideas introduced in Chap. 1 are used and the contents of this chapter will be needed in Chaps. 7–10.

In the study of stellar structure and evolution in Vol. II, we could begin with a series of physically justifiable assumptions, derive the relevant equations describing the stars, and integrate these equations to understand the structure and evolution of stars. Such an approach is impossible in the case of galaxies for several reasons. To begin with, we do not understand how galaxies have formed. (It is true that there are several uncertainties in the case of star formation as well but they refer to details rather than to the fundamental process itself.) Second, observational data related to the galaxies are by no means statistically as well determined and abundant as data related to the stars. The reason essentially has to do with the fact that galaxies are located farther away from us and thus are more difficult to observe with the same level of accuracy. Third, galaxies, being collisionless systems of stars, are intrinsically more complicated compared with stars – which are made of collisional gas – from the point of view of mathematical description.

Given these difficulties, it is better to divide the study of galactic structure and dynamics into several separate aspects and investigate each of them as though they are disconnected from each other.

Introduction

The purpose of this chapter is to give an overview and summarise several observations that are of cosmological relevance. Many of the results (like the existence of dark matter) described here were taken for granted in the earlier chapters, and we shall make an attempt to provide the description of the evidence in support of these results. This chapter also provides a summary of the current knowledge of different parameters of cosmological significance.

Cosmic Distance Scale

The measurement of distances to different celestial bodies is of primary importance not only in understanding their properties but also – for objects at cosmological distances – in determining the geometry of the universe and the cosmological parameters. Obviously the technique used to measure the distance will depend on the properties of the object that is being studied; we shall concentrate on the measurement of extragalactic distances.

The procedures used for distance measurements can be divided into two natural classes. The first one uses what could be called the absolute distance estimator. These estimators are certain properties of (or features in) an object that can be used to directly measure the distance to the object. The second approach uses a relative distance estimator that allows us to determine the ratio between the distances to two different objects. By choosing a wide class of overlapping relative distance estimators, we can build what is known as a cosmic distance ladder.

Introduction

We now take up the study of galaxy formation, which requires understanding the growth of structure in the baryonic component of the universe. This chapter uses concepts from several earlier chapters, especially Chaps. 3–5, and will be needed for Chap. 9.

The study of galaxy formation from fundamental physical considerations is made difficult by a wide variety of physical processes that we need to take into account. To begin with, galaxies by themselves show a variety of morphological and physical properties, even at z = 0. The formation process should be such that, starting from relatively structureless density enhancements at high redshifts (z ≳ 25), one is capable of producing such a variety at z = 0. Second, the observational situation as regards galaxylike structures at high redshifts is still very unsatisfactory. The samples are small in number and often we have to decide how to make the correspondence between the sources seen at high redshifts and those seen at low redshifts. This issue is further complicated by the fact that a certain kind of population could have existed at a certain interval of time and could have vanished outside this epoch. Such a conjecture of invoking new populations is often convenient, but is not very satisfactory unless we could back it with some physical reasoning.

Introduction

Cosmic microwave background radiation (CMBR) is a relic from the redshift z ≈ 103, beyond which the universe is optically thick in most of the wave bands. This radiation therefore carries vital information about the state of the universe at an epoch that is probably as early as we could probe by direct electromagnetic measurements. A considerable amount of theoretical and observational progress has been achieved in this topic in the past decade, and future observations of CMBR hold the promise for allowing us to determine the parameters of the universe with unprecedented accuracy.

The temperature anisotropies in CMBR and related issues are discussed in this chapter. Anisotropies that are due to peculiar velocities and fluctuations in the gravitational potential are derived in Section 6.3 and discussed in detail in Sections 6.4 and 6.5. The damping of anisotropies and the distortions that arise because of the astrophysical processes are studied in Section 6.7.

Processes Leading to Distortions in CMBR

We have seen in Chap. 4 that the photons in the universe decoupled from matter at a redshift of ~ 103. These photons have been propagating freely in space–time since then and can be detected today. In an ideal Friedmann universe, a comoving observer will see these photons as a blackbody spectrum at some temperature T0.

Atoms and ions of the working gas and trace impurities emit radiation when transitions of electrons occur between the various energy levels of the atomic system. The radiation is in the form of narrow spectral lines, unlike the continuum of free-electron radiation such as bremsstrahlung. It was, of course, the study of these spectral lines that originally led to the formation of the quantum theory of atoms.

Because of the enormous complexity of the spectra of multielectron atoms it would be inappropriate here to undertake an introduction to atomic structure and spectra. Many excellent textbooks exist [e.g., Thorne (1974) or, for a more complete treatment, Slater (1968)] that can provide this introduction at various levels of sophistication. Instead we shall assume that the energy level structure of any species of interest is known, because of experimental or theoretical spectroscopic research. Then we shall discuss those aspects of spectroscopy that more directly relate to our main theme, plasma diagnostics. It is fairly well justified for neutral atoms and for simpler atomic systems with only a few electrons, to assume that spectral structure is known (speaking of the scientific enterprise as a whole, not necessarily for the individual student!). It is not so well justified for highly ionized heavy ions that occur in hot plasmas. The spectra of such species are still a matter of active research; therefore, it should not automatically be assumed that all aspects of these spectra are fully understood. However, for those diagnostic purposes that we shall discuss, the gaps in our knowledge are not particularly important.

In many plasmas it is unsatisfactory to use material probes to determine internal plasma parameters, so we require nonperturbing methods for diagnosis. Some of the most successful and accurate of these use electromagnetic waves as a probe into the plasma. Provided their intensity is not too great, such waves cause negligible perturbation to the plasma, but can give information about the internal plasma properties with quite good spatial resolution. In this chapter we are concerned with the uses of the refractive index of the plasma, that is, the modifications to free space propagation of the electromagnetic waves due to the electrical properties of the plasma.

The way waves propagate in magnetized plasmas is rather more complicated than in most other media because the magnetic field causes the electrical properties to be highly anisotropic. This is due to the difference in the electron dynamics between motions parallel and perpendicular to the magnetic field. Therefore, we begin with a brief review of the general problem of wave propagation in anisotropic media before specializing to the particular properties of plasmas.

Interferometry is the primary experimental technique for measuring the plasma's refractive properties and we shall discuss the principles of its use as well as some of the practical details that dominate plasma diagnostic applications.

Electromagnetic waves in plasma

Waves in uniform media

We must first consider the nature and properties of electromagnetic waves in a plasma. We treat the plasma as a continuous medium in which current can flow, but that is otherwise governed by Maxwell's equations in a vacuum.

Plasma diagnostics has grown in accomplishment and importance in the sixteen years since the first edition of this book was written. The fusion research field has reached the threshold of energy breakeven, and of committing to a burning plasma experiment. But more important perhaps, the accuracy and comprehensiveness of measurements on major magnetic plasma confinement devices now give us unprecedented information on plasma behaviour. Plasmas have gained in importance in industrial processes and of course in electronic manufacturing; so the economic necessity of monitoring them accurately has become increasingly evident. Astrophysical and space plasma diagnosis has continued to be the basis of investigations of a host of phenomena from black hole accretion to planetary magnetospheres.

In preparing a second edition, my objective was to retain the original emphasis on the physical principles upon which plasma measurements are based, and to maintain an accessible teaching style. Both of these aspects have proven attractive to students and researchers. Also, the examples are still predominantly drawn from my own field of fusion research, but some discussion of the broader applications is included. It became increasingly pressing in recent years that the book should be updated to include the latest techniques and applications. It has thus been impossible to avoid some expansion of the length, because of the substantial additional material. A few obsolete sections have been removed, but I have endeavored to keep as much of the first edition as possible, bringing the topics up to date by discussions of the recent developments and modern references.

The practice of plasma diagnostics is a vast and diverse subject, far beyond the span of a single volume, such as this, to cover in all its detail. Therefore, some limitations on the objectives adopted here have to be accepted. The title Principles of Plasma Diagnostics refers to the fact that the physical principles used for plasma measurements are to be our main concern. In brief, this book seeks to give a treatment of the fundamental physics of plasma diagnostics, and thus to provide a sound conceptual foundation upon which to base any more detailed study of applications. I hope, therefore, to bring the reader to the point where he or she may, with confidence and understanding, study the details of any diagnostic discussed in the literature.

Most journal articles and reviews on plasma diagnostics tend, of necessity, to begin from a mere citing of the required equations governing the principles employed. For all but the experienced specialist, this means that the reader must accept the equations without much justification or else pursue a deeper understanding through references to original papers. One of my main objectives here is to overcome this difficulty by a systematic presentation from first principles. Therefore, if in some cases it may seem that the development stops just as we approach the point of practicality, I can only plead that, in bringing the reader to the point of being able comfortably to understand the basis of any application, I have fulfilled a major part of my task.

Preliminaries

Perhaps the most natural approach to diagnosing the particle distribution functions within the plasma is to propose insertion of some kind of probe that directly senses the particle fluxes. Indeed, this approach was one of the earliest in plasma diagnostics, with which the name of Irving Langmuir is most notably associated for his investigations of the operation of the electric probe often known as the Langmuir probe.

Just as with internal magnetic probes, the applicability of particle flux probes is limited to plasmas that the probe itself can survive. This means that frequently only the plasma edge is accessible, but the importance of edge effects makes the prospects bright for continued use of such probes even in fusion plasmas. In cooler plasmas, of course, the limitations are less severe and more of the plasma is accessible.

In common also with magnetic probes, the often more important question is: what is the effect of the probe on the plasma? Because of the nonlocal nature of the source of the magnetic field (arising from possibly distant currents), in many cases the local perturbation of the plasma by a magnetic probe can be ignored. In contrast a particle flux measurement is essentially local and as a result the local perturbation of the plasma can almost never be ignored.

Thus, the difficulty with measurements of direct plasma particle flux is rarely in the measurements themselves; rather it is in establishing an understanding of just how the probe perturbs the plasma locally and how the local plasma parameters are then related to the unperturbed plasma far from the probe.