Download An Introduction to the Linear Theories and Methods of by W. D. Jones, H. J. Doucet, J. M. Buzzi (auth.) PDF

By W. D. Jones, H. J. Doucet, J. M. Buzzi (auth.)

Modern plasma physics, encompassing wave-particle interactions and collec­ tive phenomena attribute of the collision-free nature of sizzling plasmas, was once based in 1946 whilst 1. D. Landau released his research of linear (small­ amplitude) waves in such plasmas. It was once no longer till a few ten to 20 years later, besides the fact that, with impetus from the then swiftly constructing managed­ fusion box, that enough cognizance was once committed, in either theoretical and experimental study, to clarify the significance and ramifications of Landau's unique paintings. for the reason that then, with advances in laboratory, fusion, area, and astrophysical plasma learn, now we have witnessed very important devel­ opments towards the certainty of quite a few linear in addition to nonlinear plasma phenomena, together with plasma turbulence. this day, plasma physics stands as a well-developed self-discipline containing a unified physique of strong theoretical and experimental ideas and together with a variety of appli­ cations. As such, it really is now usually brought in college physics and engineering curricula on the senior and first-year-graduate degrees. an important prerequisite for all of recent plasma experiences is the below­ status oflinear waves in a temporally and spatially dispersive medium similar to a plasma, together with the kinetic (Landau) thought description of such waves. instructing event has frequently proven that scholars (seniors and first-year graduates), whilst first uncovered to the kinetic thought of plasma waves, have problems in facing the necessary sophistication in multidimensional complicated variable (singular) integrals and transforms.

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Extra info for An Introduction to the Linear Theories and Methods of Electrostatic Waves in Plasmas

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68) 20 CHAPTER 1 (\ A f\ A f\ x V V V V V Fig. 5. Wave generation described by Eq. 68) showing B z as a function of x at a given time. Thus, as shown in Fig. 5 which gives the shape of the magnetic field of the wave as a function of x, at a given time, electromagnetic waves are generated and propagate away from the antenna in both the backward and forward directions. 4. , after Laplace inversion of the Fourier-Laplace transform function M(w,k), we found that M(k, t < 0) = O. At that time it was stated without proof that this intuitively reasonable result, which we referred to as causality, was a direct result of having made a Laplace transform in time (in which t varies from 0 to 00) rather than a Fourier transform in time (in which t varies from - 00 to + 00 ).

INTRODUCTION The aim of this chapter is to introduce and briefly describe the propagation of electromagnetic waves in a medium where anisotropic conductivity tensor (J can be defined. This approach provides a valid description of the wave phenomena possible in many plasmas of interest. Since such a description can be found in many places [see, for example, Denisse and Delcroix (1961), Stix (1962), Allis, Buchsbaum, and Bers (1963), Quemada (1968), Chen (1974), and Nicholson (1983)], we present here only the cold-plasma theory as an example of the utility of this approach.

9. Transformation of the Path of Integration The use of either Cauchy's equation or of the residues theorem requires that the paths of integration be closed. Very often in plasma physics, however, the paths of integration required in nontrivial problems are not closed paths but are, rather, open paths such as (- 00 + ia, + 00 + ia), which is a path parallel to the real axis. Therefore, because of the extreme usefulness of Cauchy's equation and of the residues theorem in problems involving complex variables, we give two very useful theorems for transforming open-path integrals into closed-path integrals.

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