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Introduction

A plasma, for the physicist, is not a jelly-like substance. It is a gas containing a very high density of electrons and ions. The name ‘plasma’ for such a gas was coined by the late Irving Langmuir in the course of his theoretical and experimental investigations of gas discharges at General Electric Research Laboratories during the 1920s. In a gaseous discharge, such as one finds in a fluorescent light, only a minute fraction of the atoms present are ionized, that is disassociated into positive ions and electrons; none the less a study of the motion of the ions and electrons shows that many new and interesting

phenomena can take place. In most highly-ionized gases, such as one finds in the ionosphere (the layer of free ions and electrons present toward the top of our atmosphere), the motion of the electrons and ions is, in fact, organized to a remarkable extent. The organization takes two forms, neither of which is characteristic of ordinary dilute gases made up of neutral atoms. First, a given particle, ion or electron, does not move independently of its neighbors. Rather, such a particle is always accompanied by a cloud of other particles, which move along with it in such a way as to screen out the electric field produced by its charge. Second, the electrons carry out long-wavelength, high-frequency oscillations, which involve the coherent motion of many thousands of particles. Langmuir’s studies of the possibilities for organized behavior in such a system led him to believe that here was a new state of matter—neither solid, liquid or gas. He called it plasma.

part such investigations could be classified as basic research; in other words, physicists studied plasmas out of a sense of curiosity as to their behavior. During the war the size of that group increased somewhat; one of the methods of obtaining separated isotopes of uranium, the so-called calutron, invented at the University of California at Berkeley, involved the use of highly ionized arc sources, i.e. plasmas. Also toward the end of the war, and in the years immediately following it, physicists began to be interested in plasmas as possible devices for the production and amplification of electromagnetic waves in the microwave region. Thus in 1950, at the time I received my PhD degree from Princeton University under David Bohm for a thesis entitled The role of plasma oscillations in electron interactions,’ there were likely no more than a hundred physicists in this country and abroad who were, in one sense or another, working on plasmas. Some were electrical engineers, working on electron vacuum tubes; some were still concerned with gaseous discharges. Others were astrophysicists, interested not so much in the ionosphere as in the plasma of charged particles which surround the sun, or that very dilute plasma which makes up all of inter-planetary and intergalactic space. Bohm and I were interested in plasmas for yet another reason—as offering a clue to a fundamental understanding of the behavior of electrons in metals.

Today the number of physicists engaged in working on plasmas is in the thousands. There is a Plasmas Physics Division of the American Physical Society; it boasts some 2,000 members and represents only a modest fraction of the physicists and electrical engineers in the United States interested in such problems. This hundred-fold growth in plasma research has been due primarily to the launching of large-scale programs designed to harness the power liberated in the fusion of light atoms at high temperatures. Such attempts at controlled thermonuclear fusion involve the use of plasmas. At the temperatures at which a thermonuclear reactor might operate, the matter within would be a plasma; moreover, the screening action of plasmas permits one to envisage the possibility of a thermonuclear reactor with its interior at millions of degrees centigrade and its walls at room temperature.

Interest in plasmas grew, too, because theoretical physicists came to recognize that an idealized model for a plasma represents a particularly simple, and often soluble, example of a many-body problem. The many-body problem is one of the problems of principal concern to the theoretical physicist today. It may be formally defined as ‘_{a study of the behavior of systems in which the simultaneous presence and interaction of many particles markedly}

alters their isolated individual behavior.’ Less formally, we could describe it as a study of all condensed systems and most gases—that is liquids, solids, plasmas and not-too-dilute gases. The kinds of many-body problems the

physicist is interested in range from the behavior of metals to the motion of nucleons in the nucleus and the interior of neutron stars. They comprise the greater part of chemistry, solid-state physics and nuclear physics.

The theoretical physicist who works on a many-body problem such as the plasma would seem, at first sight, to be faced with an insuperable handicap. How can someone who is unable to solve precisely any problem involving the interactions between three bodies hope to solve one involving millions of billions of particles? The theorist’s first reaction is to make a virtue of necessity; to hope and expect that just this feature—the large number of

particles—will make life simple again. In part it does, in that it makes possible a statistical description of the average behavior of the system; furthermore, the fluctuations about that average behavior are small. However, the use of a statistical description is not in itself enough; the problems under consideration are still too complicated to be understood in precise mathematical detail.

In any approach to understanding the behavior of complex systems, the theorist must begin by choosing a simple, yet realistic, model for the behavior of the system in which he is interested. Two models are commonly taken to represent the behavior of plasmas. In the first, the plasma is assumed to be a fully ionized gas; in other words, as being made up of electrons and positive ions of a single atomic species. The model is realistic for experimental situations in which the neutral atoms and impurity ions, present in all laboratory plasmas, play a negligible role. The second model is still simpler; in it the discrete nature of the positive ions is neglected altogether. The plasma is thus regarded as a collection of electrons moving in a background of uniform positive charge. Such a model can obviously only teach us about electronic behavior in plasmas. It may be expected to account for experiments conducted under

circumstances such that the electrons do not distinguish between the model, in which they interact with the uniform charge, and the actual plasma, in which they interact with positive ions. We adopt it in what follows as a model for the electronic behavior of both classical plasmas and the quantum plasma formed by electrons in solids.

In this article I shall try to put in historical perspective the key physical ideas and mathematical approaches which David Bohm and I used in our development of a collective description of electron interactions in metals during the period 1948–53. This work led to the identification of quantized plasma oscillations as the dominant long-wavelength mode of excitation of electrons in most solids. It justified the application of the independent electron model to the low-frequency motion of electrons in metals, and made possible a consistent and accurate calculation of metallic cohesion. I shall then describe briefly how the extension of those ideas to systems of strongly interacting

neutral particles, the helium liquids, has, some thirty years later, enabled us to understand effective particle interactions, elementary excitations and transport in the helium liquids. As a result we now possess a unified picture of excitations and transport in both charged and neutral strongly-interacting quantum many-body systems.