An Introduction to the Linear Theories and Methods of Electrostatic Waves in Plasmas
Published on 6. December 2012
XV, 312 pages
978-1-4757-0211-8 (ISBN)
Description
Modern plasma physics, encompassing wave-particle interactions and collec tive phenomena characteristic of the collision-free nature of hot plasmas, was founded in 1946 when 1. D. Landau published his analysis of linear (small amplitude) waves in such plasmas. It was not until some ten to twenty years later, however, with impetus from the then rapidly developing controlled fusion field, that sufficient attention was devoted, in both theoretical and experimental research, to elucidate the importance and ramifications of Landau's original work. Since then, with advances in laboratory, fusion, space, and astrophysical plasma research, we have witnessed important devel opments toward the understanding of a variety of linear as well as nonlinear plasma phenomena, including plasma turbulence. Today, plasma physics stands as a well-developed discipline containing a unified body of powerful theoretical and experimental techniques and including a wide range of appli cations. As such, it is now frequently introduced in university physics and engineering curricula at the senior and first-year-graduate levels. A necessary prerequisite for all of modern plasma studies is the under standing oflinear waves in a temporally and spatially dispersive medium such as a plasma, including the kinetic (Landau) theory description of such waves. Teaching experience has usually shown that students (seniors and first-year graduates), when first exposed to the kinetic theory of plasma waves, have difficulties in dealing with the required sophistication in multidimensional complex variable (singular) integrals and transforms.
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12/2012
Springer
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W. D. Jones | William Jones
An Introduction to the Linear Theories and Methods of Electrostatic Waves in Plasmas
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11/1985
Plenum Publishing Corporation
€111.73
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Content
1. The Cookbook: Fourier, Laplace, and Hilbert Transforms.- 1.1. Introduction.- 1.2. A Basic Example: Electromagnetic-Wave Propagation in Vacuum.- 1.3. The Fourier-Laplace Transforms.- 1.4. Laplace Transforms and Causality.- 1.5. Hilbert Transforms.- 1.6. Appendix A: Functions of Complex Variables.- 2. Waves in a Conductivity-Tensor-Defined Medium: A Cold-Plasma Example.- 2.1. Introduction.- 2.2. Waves in Idealized Media.- 2.3. Waves in Plasmas.- 2.4. Waves in a Cold Plasma.- 2.5. Applications of the Cold-Plasma-Theory Results.- 2.6. Selected Experiment: A Simple Transmission Experiment Using the Extraordinary Wave to Measure Plasma Density.- 3. Electrostatic Waves in a Warm Plasma: A Fluid-Theory Example.- 3.1. Introduction.- 3.2. Dispersion Relation for Purely Electrostatic Waves in a Warm Plasma.- 3.3. Electrostatic Modes in a Warm Plasma.- 3.4. Selected Experiments.- 4. Ion-Acoustic Waves with Ion-Neutral and Electron-Neutral Collisions.- 4.1. Introduction.- 4.2. Dispersion Relation with Collisions.- 4.3. Initial-Value Problem.- 4.4. Boundary-Value Problem.- 4.5. Selected Experiment: Boundary-Value Problem for Ion-Acoustic Waves in a Collision-Dominated Discharge Plasma.- 5. Finite-Size-Geometry Effects.- 5.1. Introduction.- 5.2. Electron Plasma Waves in a Cold Plasma Supported by a Strong Magnetic Field.- 5.3. Ion-Acoustic Waves in a Warm Plasma Supported by a Strong Magnetic Field.- 5.4. Selected Experiments.- 6. Ion-Acoustic Waves in a Small Density Gradient.- 6.1. Introduction.- 6.2. Wave Equation.- 6.3. Wave Propagation in a Nonuniform Plasma Having a Gaussian Density Profile.- 6.4. Wave Propagation in a Nonuniform Plasma Having an Arbitrary Density Profile.- 6.5. Wave Propagation in a Uniform Plasma Having a Subsonic Density Gradient at its Edge.- 6.6. Selected Experiments.- 7. Landau Damping: An Initial-Value Problem.- 7.1. Introduction.- 7.2. Collisionless Damping Due to Free Streaming.- 7.3. Longitudinal Oscillations in an Infinite, Homogeneous Plasma with No Applied Fields-The Electron Plasma Wave.- 7.4. Ion-Acoustic Waves.- 8. Kinetic Theory of Forced Oscillations in a One-Dimensional Warm Plasma.- 8.1. Introduction.- 8.2. Microscopic Theory of Forced Oscillations.- 8.3. Difficulties Encountered in the Forced-Oscillations Problem.- 8.4. Free-Streaming and Collective Effects.- 8.5. Physical Meaning of Landau Damping.- 9. Computing Techniques for Electrostatic Perturbations.- 9.1. Introduction.- 9.2. Dielectric Constant of a Maxwellian Electron Cloud.- 9.3. The Gould Technique.- 9.4. The Derfler-Simonen Technique.- 9.5. The Hybrid Technique.- 9.6. Conclusions.- 9.7. Appendix: Plasma Wave Functions.- 10. Ion-Acoustic Waves in Maxwellian Plasmas: A Boundary-Value Problem.- 10.1. Introduction.- 10.2. Dispersion Relation for Ion-Acoustic Waves.- 10.3. Ion-Acoustic Waves in an Isothermal Plasma.- 10.4. Selected Experiment: Landau Damping of Ion-Acoustic Waves in a Nonisothermal Plasma.- 11. Numerical Methods.- 11.1. Introduction.- 11.2. Numerical Evaluation of Hilbert Transforms.- 11.3. Hunting the Roots of a Dispersion Relation.- 11.4. Appendix.- References.
