A comprehensive textbook on the foundational principles of plasmas, including material on advanced topics and related disciplines such as optics, fluid dynamics, and astrophysics
Foundations of Plasma Physics for Physicists and Mathematicians covers the basic physics underlying plasmas and describes the methodology and techniques used in both plasma research and other disciplines such as optics and fluid mechanics. Designed to help readers develop physical understanding and mathematical competence in the subject, this rigorous textbook discusses the underlying theoretical foundations of plasma physics as well as a range of specific problems, focused on those principally associated with fusion.
Reflective of the development of plasma physics, the text first introduces readers to the collective and collisional behaviors of plasma, the single particle model, wave propagation, the kinetic effects of gases and plasma, and other foundational concepts and principles. Subsequent chapters cover topics including the hydrodynamic limit of plasma, ideal magneto-hydrodynamics, waves in MHD plasmas, magnetically confined plasma, and waves in magnetized hot and cold plasma. Written by an acknowledged expert with more than five decades' active research experience in the field, this authoritative text:
* Identifies and emphasizes the similarities and differences between plasmas and fluids
* Describes the different types of interparticle forces that influence the collective behavior of plasma
* Demonstrates and stresses the importance of coherent and collective effects in plasma
* Contains an introduction to interactions between laser beams and plasma
* Includes supplementary sections on the basic models of low temperature plasma and the theory of complex variables and Laplace transforms
Foundations of Plasma Physics for Physicists and Mathematicians is the ideal textbook for advanced undergraduate and graduate students in plasma physics, and a valuable compendium for physicists working in plasma physics and fluid mechanics.
Plasma often called 'the fourth state of matter' is the most abundant form of observable matter in the universe. Nonetheless plasma physics is a relatively new discipline, unknown before 1900. Ionisation studies originated in the experimental study of gas breakdown in strong electric fields by Paschen (1889). The inception of low temperature plasma physics may be considered to have been the result of the discovery by Thomson (1897) of the negatively charged electron in gas discharges in 1897, although plasma physics as we know it today did not evolve until the mid-1920s. Positively charged ions, essentially gas molecules which had lost an electron, were found soon after. In the early years of the twentieth century, gas discharges and arcs were empirically investigated. The related topics of breakdown of gases and ionisation and recombination dominated this field known as ionised gases. This activity becoming progressively more realistic during the early years of the twentieth century as the mobile role of molecules and particles became better understood; but still only in media of low ionisation, where the number of charged particles is small compared to that of the background gas. von Engel (1965) gives an interesting history of the study of ionised gases up to about to 1900. The early studies of breakdown, glow discharges and arcs are covered in detail by von Engel (1965), Cobine (1958), and Loeb (1955). By 1930 an essential understanding of the low temperature plasma had been developed exemplified by the two volume text (von Engel and Steenbeck 1932). At that time quantum physics was not well developed and essentially relatively simple classical models had to used. These yielded basic formal structures with functional relationships but with coefficients to be determined by experiment - an approach which has worked well and is still used today, exemplified by volumes such as Brown (1967). The field, now known as low temperature plasma physics has become increasingly developed (Raizer, 1997; Lieberman and Lichtenberg, 2005; Smirnov, 2015) as the earlier models have been progressively refined and improved. Although the basic theory has remained unchanged since the 1930s the detailed methodology has been refined and agreement between experiment and theory improved. In recent years a wide range of direct uses for both direct current and microwave discharges has been found such as gas laser pumping. Important commercial applications now include plasma processing, coating, etching, lighting, and lightning (Lieberman and Lichtenberg, 2005).
In the 1920s, the subject broadened after it became realised that the interior of stars for example must be at such high temperatures that they could contain only fully stripped bare atomic nuclei and electrons (Eddington, 1959). Astrophysical plasmas became an important subject area today embracing a much wider field than simply stellar interiors. Nowadays plasma physics embraces the whole gamut of astronomical bodies from aurora, the magnetosphere to the edge of black holes and led to many conceptual advances in subject (Alfvén, 1950). This area remains an active and important discipline in its own right. At this stage, the end of 1920s, we see the identification of the essential criteria defining plasma through two seminal works. Both involve the nature of the interactive force between charged particle in the plasma.
The first important conceptual step forward towards distinctive plasma physics was taken in 1923 by the publication of the paper by Debye and Hückel (1923) relating to the behaviour of electrolyte ions in solution. Considering the behaviour of positively and negatively charged particles with equal average charge density, Debye and Hückel argued that each ion of one charge is surrounded more closely by ions of the opposite charge thereby decreasing the field of the primary ion below that associated with Coulomb force law over distances in excess of a characteristic length, known as the Debye length (Section 1.3), which tends to zero as the particle temperature tends to zero.
The second key step was the identification of collective waves by Langmuir (1928) (and more fully Tonks and Langmuir 1929). It was proposed that cold plasma moved as a 'block', the individual particles oscillating in the field of their neighbours through the Coulomb force in a plasma wave Section 1.2. Again the medium is acting collectively through the Coulombic interparticle field, and not through the individual particle fields (see Section 6.2).
Realising that they were observing behaviour not described by conventional nomenclature Langmuir coined the name plasma in Langmuir (1928). More details on the origin of the name are given by Tonks (1967) and Mott-Smith (1971) who state that it arose from similarities with blood plasma as a transport fluid. In fact the word plasma stems from the Greek p?ásµa meaning a 'maleable substance' which is appropriate in view of the uncanny ability of the positive column of a glow discharge to fill the space available to it. The name was slow to become adopted but by the 1950s was widely used, particularly in connection with controlled fusion.
The following decade was characterised by the development of plasma kinetic theory.
Firstly Landau (1936) developed a form of Fokker-Planck equation Section 7.3 to account for the fact that most particle interactions are long range and therefore weak involving many particles simultaneously. In contrast to earlier work analogous to gases where the interaction was assumed short range and the Chapman-Enskog method, Section 4.11, used for fluids, had been incorrectly used to determine the hydrodynamic behaviour in plasma. This approach was followed by an improved more formal stochastic picture by Chandrasekhar (1943) (see Section 7.2) in an astrophysical context. The method was completed for application in plasma by Rosenbluth, MacDonald and Judd (1957), the final element being the introduction of the Coulomb logarithm by Cohen, Spitzer, and Routly (1950) following several early workers. The development of magneto-hydrodynamics, the plasma equivalent of fluid theory which treats ensembles of large numbers of particles averaged over velocity, was now complete.
The second development of kinetic theory was in the area of the microscopic distribution in which the particle motions are treated individually before a final averaging. Recognising the relative importance of collective behaviour over collisional, Vlasov (1938) introduced what is essentially a collisionless Boltzmann equation Section 6.2. This kinetic equation has proved very successful in dealing with the large number of plasma modes of oscillation. An important development of the theory due to Landau (1946) took account of the velocity resonance at the wave phase speed in warm plasma to develop damping Appendix 12.A. The approach has been widely used to identify micro-instability and damping.
These two approaches complete the underlying theoretical structure of plasma physics, individually appropriate for different problems. By about 1960 the formal structure of plasma physics was well established. Further development involved the development of theoretical pictures to investigate specific problems.
The successful achievement of man-made thermo-nuclear reactions in 1952 led to a marked increase in activity on the possibility of controlled reactions suitable for the generation of electrical power in the USA, UK, and USSR, which was mostly hidden behind security barriers. One of the first, and probably best known, was by John Lawson at Harwell, initially issued as a secret report (Lawson, 1955), but later a revised form in the open literature (Lawson, 1957), introducing the familiar Lawson criterion giving a necessary condition for useful thermo-nuclear power. His final conclusion (Lawson, 1955) remains as true today as it was 60 years ago.
Even with the most optimistic possible assumptions, it is evident that the conditions for the operation of a useful thermonuclear reactor are very severe.
Nonetheless as we shall see in the course of this book, a major part of the road to controlled nuclear fusion has now been achieved.
Despite these problems, the possibility of such a device and its anticipated rewards led to surge in activity in plasma physics as it is was clear that the lowest temperatures require the working medium to be plasma. The general interest in the possibility of achieving fusion power using plasma as the medium has led to an enormous increase in the resources allocated to these problems and a wide variety of experimental device (Glasstone and Lovberg, 1960). As a consequence, the subject as a whole has moved rapidly forward with particular emphasis on conditions required for stable confined plasma, particularly toroidal geometries (tokamaks). Since 1970, laser generated plasma has offered an alternative route to fusion through inertial confinement.
It is a characteristic of any new field, that its development is likely to be reflected in the way plasma physics has developed over the years, namely in fits and starts. 1900-1940 the era of gas discharges, and collisional effects, 1940-1950 the start of what we might call the modern era where collective behaviour was being understood. 1950-1970 the age of major theoretical...