Magnetogasdynamics and Plasma Dynamics

ISBN-13: 9783709180853 / Angielski / Miękka / 2014 / 197 str.

Shih-I Pai

Opis

This book is based on the lecture notes which the author gave in a seminar of the same title in the Institut fur theoretische Gasdynamik, D. V. L. e. V., Aachen, Germany, during the academic year of 1957-1958. The subject matter has been rewritten and expanded after the author's return to the University of Maryland. The purpose of this book is to give a theoretical introduction to plasma dynamics and magnetogasdynamics from the gasdynamic point of view. Attention is given to the basic assumptions and the formulation of the theory of the flow problems of a plasma, an ionized gas, as well as to the various methods of solving these problems. Since plasma dynamics is still in a developing stage, the author hopes that this book _may furnish the readers some basic elements in the theory of plasma -dynamics so that they may find it useful for further study and research in this new field. After the introduction in which the scope of plasma. dynamics is briefly discussed, the fundamental equations of plasma dynamics from the macro- scopic point of view, i. e., the theory of continuum has been analyzed, in detail in chapters IT to IV, including many simplified cases sUQh as m,agneto- gasdynamics, magnetohydrodynamics, electromaguetodynamics, radiation- magnetogasdynamics etc. In chapter V, the important parameters and their range of applicatIons have been treated. The parameters are useful in the correlation of experi- mental results.

Spis treści

I. Introduction.- 1. Plasma and plasma dynamics.- 2. Methods of treatment.- 3. Microscopic point of view: — Kinetic theory of plasma.- 4. Macroscopic point of view: — Theory of continuum.- 5. Magnetogasdynamics and magnetohydrodynamics.- References.- II. Fundamental Equations of Plasma Dynamics.- 1. Introduction.- 2. Equation of state.- 3. Equation of continuity.- 4. Equation of motion.- 5. Equation of energy.- 6 Maxwell’s equations of electromagnetic field.- 7. Gross variables of the plasma as a whole.- 8. Fundamental equations for the gross quantities of the plasma.- 9. Fundamental equations of plasma dynamics.- 10. Fundamental equations of electro-magneto-gasdynamies.- References.- III. Electromagnetic Equations in Plasma Dynamics.- 1. Introduction.- 2. Maxwell’s equations.- 3. Equation of conservation of electrical charge.- 4. Equation of electrical current.- 5. Vector and scalar potentials.- 6. Boundary conditions.- 7. Units in electromagnetic theory.- References.- IV. Magnetogasdynamics and Electromagnetogasdynamics.- 1. Introduction.- 2. Magnetogasdynamic approximations.- 3. Fundamental equations of magnetogasdynamics.- 4. Important parameters in magnetogasdynamics.- 5. Some properties of the fundamental equations of magnetogasdynamics.- 6. Electromagnetogasdynamics.- References.- V. Dimensional Analysis and Important Parameters.- 1. Introduction.- 2. Fully ionized plasma.- 3. Some characteristic velocities, frequencies and lengths in plasma dynamics.- 4. Important parameters of plasma dynamics.- 5 Important parameters for special cases.- References.- VI. Magnetohydrodynamics.- 1. Introduction.- 2. Laminar flow between parallel plates.- 3. Laminar flow in a pipe under external magnetic field.- 4. Laminar flow near a stagnation point.- 5. Inviscid flow past a magnetized sphere.- 6. Boundary layer flow of a fluid of very small electrical conductivity.- 7. Boundary layer flow of fluid of large or infinite electrical conductivity.- 8. Unsteady motion of a plate. Rayleigh’s problem.- 9. The temperature distribution in magnetohydrodynamics.- References.- VII. Stability of Magnetogasdynamic Flows.- 1. Introduction.- 2. Stability equations for parallel flow in magnetohydrodynamics.- 3. Stability of laminar flow between parallel planes in the presence of a coplanar magnetic field.- 4. Stability of laminar flow between parallel planes under a transverse magnetic field.- 5. Stability of boundary layer flow.- 6. Stability of laminar flow between rotating cylinders.- 7. Stability, of a layer of fluid heated below.- 8. Stability of pinch effect.- 9. Experiment of stability of flow in magnetohydrodynamics.- References.- VIII. Turbulence in Magnetohydrodynamics.- 1. Introduction.- 2. Double and triple correlation in isotropic turbulence.- 3. Generalized von Kármán-Howarth equation.- 4. Equations in terms of vector potential.- 5. The dissipation of energy.- 6. Invariants of Loitsiansky’s type.- 7. A spontaneous magnetic field in conducting fluid.- 8. Stationary turbulence.- 9. The partition of energy in hydromagnetic turbulence.- References.- IX. One Dimensional Flow in Magnetogasdynamics.- 1. Introduction.- 2. Fundamental equations of one dimensional unsteady flow of magnetogasdynamics.- 3. Steady one dimensional flow.- 4. Generalized Rankine-Hugoniot relations.- 5. Shock wave structure in an inviscid and non-heat-conducting fluid of finite electrical conductivity.- 6. Shock wave structure in a fluid of infinite electrical conductivity.- 7. Shock wave structure in a plasma.- 8. Unsteady flow of an ideal plasma.- 9. Characteristics of the fundamental equations of one-dimensional unsteady flow of magnetogasdynamics.- 10. Steady flow through a nozzle.- 11. Approximate one-dimensional flow in a transverse electromagnetic field.- 12. Magnetohydrodynamic (MHD) power generation.- References.- X. Wave Motion in a Plasma.- 1. Introduction.- 2. Linearized equations of electromagnetogasdynamics.- 3. Electromagnetic waves.- 4. Gasdynamic waves.- 5 Magnetogasdynamic waves.- 6. Electromagnetogasdynamic waves.- References.- XI. Shock Wave Propagation in Magnetogasdynamics.- 1. Introduction.- 2. Oblique shock in magnetogasdynamics.- 3. Oblique shock wave structure in magnetogasdynamics.- 4. Shock wave propagation in an infinitely electrically conductive plasma with transverse magnetic field and gravitation.- 5. Cylindrical shock waves produced by instantaneous energy release.- 6. The penetration of a shock wave into a magnetic field.- References.- XII. Two- and Three-Dimensional Flows in Magnetogasdynamics.- 1. Introduction.- 2. Three-dimensional unsteady flow of an ideal plasma.- 3. Two-dimensional steady flow over a thin body in fluids of large or infinite magnetic Reynolds number.- 4. Linearized theory of airfoils in fluids of low electric conductivity.- 5. Hypersonic flow past a blunt body in magnetogasdynamics.- 6. Two-dimensional boundary layer flow.- References.- XIII. Some Problems of Plasma Dynamics.- 1. Introduction.- 2. Ionization.- 3. Saha relation.- 4. Flow of plasma with variable degree of ionization.- 5. Plasma oscillation.- 6. Electrical conductivity.- 7. Flow with radiation.- 8. Particle motions of a plasma.- References.- XIV. Plasma Dynamics from Microscopic Point of View.- 1. Introduction.- 2. Molecular velocity and its distribution function.- 3. Generalized Boltzmann equation.- 4. Maxwellian distribution.- 5. Relations between kinetic theory and conservation equations.- 6. Transfer equations.- 7. Expressions for the coefficients of diffusion, heat conduction and viscosity.- 8. Plasma oscillations.- 9. Some dimensional considerations of plasma dynamics.- References.- Author Index.