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.

Introduction

During the past few decades, plasma physics has become established as a major research field. As a result, the field includes a very substantial body of knowledge covering a wide variety of branches, from the most theoretical to the most practical, comparable to any other subdiscipline of physics. As with any other science, progress has been made most effectively when an early quantitative confrontation between theory and experiment has been possible. This confrontation places strong demands upon theory to do calculations in realistic configurations and circumstances, but it also requires that the properties of plasmas be measured experimentally as completely and accurately as possible. For this reason much of the effort in experimental plasma physics is devoted to devising, developing, and proving techniques for diagnosing the properties of plasmas: plasma diagnostics.

A major driving force behind the research on plasmas has been, and still is, the prospect of generating economically significant amounts of power from controlled thermonuclear fusion. Fusion has its own imperatives of temperature, density, confinement, and so on, which provide a stimulating and relevant environment in which plasma research is conducted. Moreover, the vitally important diagnosis of fusion plasmas poses problems that are often enhanced by the nature of the fusion goal. For example, the high temperatures sought for fusion frequently eliminate the possibility of internal diagnosis by material probes.

The overall objective of plasma diagnostics is to deduce information about the state of the plasma from practical observations of physical processes and their effects.

The errors that can enter into any kind of measurement, and so limit its accuracy, may be classified into two main types.

First, systematic errors arise from inaccuracies in calibration or the general performance of experimental instruments. The errors are systematic when they are consistent and reproducible. For example, in measuring the length of an object using a ruler whose own length markings are, say 1% too close together, a consistent overestimate by 1% will be obtained. The measurement may be repeated many times using the same ruler, but will give the same error. Of course, in the complicated electronic and mechanical systems used in sophisticated diagnostics, many more complicated possibilities exist for systematic errors to arise. Nevertheless, the principle remains that these errors cannot be revealed by repeated measurement with the same instrument. There is very little to be said in the way of general analysis of systematic errors except that the best way to reveal them is to compare measurements of the same quantity using different instruments (or even different techniques). In the absence of such a check, the experimenter must attempt to estimate the systematic uncertainties from a fundamental knowledge of how an instrument works and what potential flaws there are, or else from his own experience.

The second type of error is random or statistical. There are many possible sources of such errors. In our length measurement example they may arise from slight misreadings of the scale due to misalignment or parallax, for example.

Diagnostics based on manipulating neutral atoms in the plasma are particularly important for magnetically confined plasmas because, unlike the charged ions, the atoms travel freely across the field. As a result, it is possible to use atoms that are emitted from the plasma to provide information about the plasma interior. It is also possible to send a beam of atoms into the plasma in a controlled way so as to produce a particular desired diagnostic configuration. This active probing often uses other phenomena, such as line radiation induced by the presence of the beam, to complete the diagnosis. However, because the beam propagation and related atomic processes are such a critical part of the diagnostic implementation, we gather together discussion of all these diagnostics within the present chapter.

Neutral particle analysis

Although most hot plasmas are almost completely ionized, there are, nevertheless, neutral atoms that are continually being formed within the plasma. Because these travel straight across any confining magnetic field, significant numbers can escape from the plasma without suffering a collision. These atoms then carry information out of the plasma about the state of the inner regions. They are called fast neutrals to distinguish them from the more numerous neutrals that tend to surround even a relatively hot plasma and that are edge particles, providing no information about the interior.

Collision processes

The proportion of fast neutrals that can reach the plasma edge (and hence be detected) without suffering a collision depends upon the collision cross sections for the various possible collisions.

The purpose of this appendix is to provide a brief overview of the technology of radiation detection and generation. Through this material an impression may be gained and guidance obtained on what is technically feasible in terms of plasma experiments. The tables of detectors and sources are far from complete and give only representative examples of what was available at the time of writing of the first edition (1985). In a few areas, technological progress has made the examples obsolete, but in most cases, the progress has been predominantly in integration, permitting, for example, multiple detector imaging where previously only single-channel detectors might have been used, and inconvenience and reliability. Naturally, complete design of experiments requires much more detailed information, which is usually available only from manufacturers of the equipment. In the Further reading section some guidance is given on how to go about obtaining the details one needs as well as references to more general texts and reference works on radiation technology.

Detectors

The performance of detectors of electromagnetic radiation may be characterized by a variety of parameters. These parameters are not all independent and are not all appropriate for describing any specific detector, but the more important of them are described in the following.

The most immediate question concerning a detector's operation is what frequency of electromagnetic radiation it is sensitive to. This may, of course, also be specified in terms of wavelength λ or photon energy, the latter being more appropriate for radiation, such as x-rays, in which the photon energy is large.