Physics of Shock Waves in Gases and Plasmas

ISBN-13: 9783642706011 / Angielski / Miękka / 2012 / 388 str.

Michael A. Libermann; Alexander L. Velikovich; Michael A. Libermann

Opis

As Emile Jouguet remarked, "the shock wave flew off the tip of the pen of a theoretician for the first time" about a hundred years ago. The physics of shock waves has since grown into an independent branch of science closely linked with a wide range of research areas, from astrophysics and plasma physics to solid-state physics. Since the beginning, theoretical investiga tion has kept its leading role. The present book is devoted to actual problems of the theory of shock waves in gases and plasmas, that are of general interest to physicists. It con tains the results of studies on shock structure, stability, evolutionarity and dynamics. Of special interest is the theory of shock phenomena in mag netic fields, which is important for applied research on controlled nuclear fusion. A substantial contribution to this theory has been made by these authors. This monograph is the first attempt in the literature to make a systematic presentation of the shock-structure theory.The theory is consistently sub stantiated by relevant experimental results obtained recently with the use of high-power electromagnetic shock tubes. The material contained here is applicable to the solution of a wide variety of problems arising in plasma physics, nuclear fusion and cosmic gasdynamics. I believe that this book will be of help and interest for a broad circle of research workers (physi cists, astrophysicists and engineers concerned with energy accumulation, shock phenomena and other related problems of plasma hydrodynamics) as well as for university staff, post- and undergraduates."

Spis treści

1. Introduction to the Theory of Gasdynamic Shock Waves.- 1.1 Equations of Motion.- 1.1.1 Conservation Laws and the Euler Equation.- 1.1.2 Viscosity and Heat Transfer in a Fluid. The Navier-Stokes Equation.- 1.2 Kinetic Theory and Gasdynamic Equations.- 1.2.1 Kinetic Equations for a Gas.- 1.2.2 Obtaining the Gasdynamic Equations.- 1.3 Limits of Applicability of the Gasdynamic Equations in Studying Shock-Wave Structure.- 1.4 Linear and Nonlinear Waves.- 1.4.1 Linear and Sonic Waves.- 1.4.2 Nonlinear Plane Waves.- 1.4.3 The Riemann Invariants.- 1.4.4 Simple Waves.- 1.4.5 Expansion Waves.- 1.5 Origins of Discontinuities.- 1.5.1 Profile Distortion of a Running Wave.- 1.5.2 Breakdown of the Sonic Wave Front.- 1.5.3 Burgers’ Equation. Evolution of Spectral Composition of the Sonic Wave.- 1.6 Discontinuities and Shocks.- 1.6.1 Discontinuous Solutions.- 1.6.2 The Solution of Burgers’ Equation for the Profile of a Weak Shock Wave.- 1.6.3 The Shock Adiabat.- 1.6.4 Production of Shock Waves. Elementary Theory of a Shock Tube.- 1.7 Criteria of Stability and Evolutionarity of Discontinuities.- 1.7.1 Evolutionarity.- 1.7.2 Evolutionarily Condition and Existence of the Shock Structure. Basic and Additional Relations on the Front.- 1.7.3 Spectra of Dissipative Waves, Corresponding to Shock-Wave Structure Described by Burgers’ Equation.- 1.7.4 Stability and Evolutionarity of Plane Discontinuities in Three Dimensions.- 1.8 Structures of Gasdynamic Shock Waves.- 1.8.1 Equations of the Shock Layer.- 1.8.2 Shock Structure Shaped by Viscosity Alone.- 1.8.3 Shock-Front Structure in a Gas with High Heat Conductivity.- 1.9 Detonation and Deflagration.- 1.9.1 Propagation of an Exothermal Reaction. Equations of Structure of the Reaction Zone.- 1.9.2 Structures of the Detonation and Deflagration Fronts.- 1.9.3 Realization of Different Propagation Regimes of the Reaction. The Piston Problem.- 2. Gas Shock Ionization and Shock-Wave Structures in Plasmas.- 2.1 Shock Structures in a Completely Ionized Plasma.- 2.1.1 Equations for the Shock Layer and Boundary Conditions.- 2.1.2 Structure of a Weak Shock Wave.- 2.1.3 Structure of a Strong Shock Wave.- 2.1.4 Polarization of Plasma in Shock Waves.- 2.2 Shock Structure in a Plasma with Ionization.- 2.2.1 Shock-Layer Equations and Boundary Conditions.- 2.2.2 Shock Structure Associated with Multiple Ionization.- 2.2.3 Shock Structure in Partially Ionized Argon.- 2.3 Structure of an Ionizing Shock Wave.- 2.3.1 Morphology.- 2.3.2 Structure of the Precursor Region.- 2.3.3 Precursor Ionization in Electromagnetic Shock Tubes.- 2.3.4 Structure of the Ionization-Relaxation and Radiative Cooling Regions.- 2.4 Effects of Plasma Flow Nonunidimensionality in Ionizing Shock Waves.- 2.4.1 Effects of the Wall Boundary Layer in a Shock Tube on the Structure of the Relaxation Region.- 2.4.2 Instability of Ionizing Shock Waves.- 3. Magnetohydrodynamic Shock Waves in Plasmas.- 3.1 Basic Equations.- 3.1.1 Magnetohydrodynamic Equations.- 3.1.2 Two-Fluid Transfer Equations for a Plasma.- 3.2 Magnetohydrodynamic Waves.- 3.2.1 Linear MHD Waves.- 3.2.2 Damping and Dispersion of Linear MHD Waves.- 3.2.3 Nonlinear Simple MHD Waves.- 3.3 Discontinuities and Shock Waves in Magnetohydrodynamics.- 3.3.1 Classification of Discontinuities.- 3.3.2 Boundary Conditions and the Shock Adiabat in Magnetohydrodynamics.- 3.3.3 Evolutionarity Conditions for MHD Shock Waves.- 3.3.4 Shock Structures in the MHD Approximation.- 3.3.5 Evolutionarity of Singular MHD Shock Waves.- 3.4 Structures of Transverse Shocks.- 3.4.1 Boundary Conditions and the Shock Adiabat.- 3.4.2 Structure of Transverse Shock Waves in Magnetized Plasmas.- 3.4.3 Structures of Transverse Shock Waves in Nonmagnetized and Partly Magnetized Plasmas.- 3.4.4 Plasma Polarization in Transverse Shock Waves.- 3.4.5 Experimental Investigations of Transverse Shock Waves in Plasma.- 3.5 Structures of Switch-On Shock Waves.- 3.5.1 Boundary Conditions and the Shock Adiabat.- 3.5.2 Switch-On Shock-Wave Structures in Nonmagnetized Plasma.- 3.5.3 Switch-On Shock-Wave Structure in Magnetized Plasma.- 3.6 Structures of Switch-Off Shock Waves.- 4. Ionizing Shock Waves in Magnetic Fields: Structures and Stability.- 4.1 Classification and the Problem of Boundary Conditions.- 4.1.1 The Basic Boundary Conditions.- 4.1.2 Evolutionarity Conditions.- 4.2 Shock Structures and Additional Boundary Conditions.- 4.2.1 Magnetic Structures of Ionizing Shocks as Pm? 0.- 4.2.2 The Criterion for Distinguishing Between Ionizing and MHD Shock Propagation Regimes.- 4.2.3 Precursor Ionization in a Magnetic Field. Conditions for the Ionization Stability of the Upstream Flow.- 4.2.4 Additional Boundary Conditions and the Magnetic Structures of Ionizing Shocks.- 4.2.5 Limiting Regimes.- 4.3 Transverse Ionizing Shock Waves.- 4.3.1 Magnetic Structures.- 4.3.2 Additional Boundary Conditions and Structures of Transverse Ionizing Shocks.- 4.3.3 Structure of Transverse MHD Shocks in Partially Ionized Plasma.- 4.4 Normal Ionizing Shock Waves.- 4.4.1 Magnetic Structures.- 4.4.2 Tensor Conductivity and Joule Heating of Plasmas in Normal Ionizing Shocks.- 4.4.3 Switch-On MHD Shocks in Partially Ionized Plasmas.- 4.5 Switch-Off Ionizing Shock Waves.- 5. Dynamics of Shock Waves in Magnetic Fields.- 5.1 Electromagnetic Shock Tubes.- 5.1.1 Design and Operation of Electromagnetic Shock Tubes.- 5.1.2 Elementary Theory of Electromagnetic Shock Tubes: The Snowplow Model.- 5.1.3 Effects of Nonunidimensionality of the Plasma Flow in Coaxial Electromagnetic Shock Tubes.- 5.2 Piston Problem.- 5.2.1 Self-Similar Magnetic Piston Problem in Magnetohydrodynamics.- 5.2.2 Self-Similar Piston Problem for Flows with Ionizing Shock Waves.- 5.3 Dynamics of Transverse Shocks in Magnetized Plasma.- 5.4 Evolution of the Initial Ionizing Discontinuity in the Transverse Magnetic Field.- 5.5 Shaping the Structure of the Normal Ionizing Shock.- References.