Thermal Plasmas Fundamentals and Applications Volume 1
Thermal Plasmas Fundamentals and Applications Volume 1 Maher I. Boulos University 0/ Sherbrooke Sherbrooke, Quebec, Canada Pierre Fauchais University 0/ Limoges Limoges, France and Emil Pfender University 0/ Minnesota Minneapolis, Minnesota Springer Science+Business Media, LLC
Library of Congress Cataloging in Publication Data Boulos. Maher I. Thermal plasmas: fundamentals and applications, Yolume 1 / Maher I. Boulos, Pierre Fauchais, and Emil Pfender. p. cm. IncIudes bibliographical references and index. 1. High temperature plasmas. 2. High temperature plasmas-industrial applications. I. Fauchais, Pierre. 11. Pfender. Emil, 1925-. 111. Title. QC718.5.H5B68 1994 530.4'4-dc20 94-6326 CIP ISBN 978-1-4899-1339-5 DOI 10.1007/978-1-4899-1337-1 ISBN 978-1-4899-1337-1 (ebook) 1994 Springer Science+Business Media New York Originally published by Plenum Press, New York in 1994. Softcover reprint of the hardcover 1st edition 1994 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher
Preface Thermal plasma technology has evolved over the past decade into an advanced interdisciplinary science that is attracting increasing attention. Its principal applications are in materials processing, including extractive metallurgy, melting and refining of metals and alloys, plasma chemical synthesis, plasma chemical vapor deposition, plasma and arc spraying, plasma waste destruction, and plasma synthesis of advanced ceramics. Although some of these applications are presently well-established technologies such as arc plasma welding, plasma cutting, arc spraying, and atmospheric and vacuum plasma spraying, present research activities indicate that refinement and optimization of these processes and especially intelligent processing and automation are still in the forefront of research endeavors. Plasma synthesis of fine particles down to the nanometer size range, the plasma chemical vapor deposition of thin films, and the plasma destruction of toxic waste materials are among the more recent applications of thermal plasmas, which are still in their early stages of development. As engineers or research scientists undertake a design or an R & D project in any of these areas, they are faced with the major difficulty of having to be acquainted with a wide range of scientific disciplines varying from plasma physics, statistical thermodynamics, hightemperature chemical kinetics, advanced transport phenomena, and materials science. Publications dealing with thermal plasma technology te nd to be dispersed over a wide range of scientific journals, which makes it rather difficult for the expert as weil as the newcomer to follow progress in this field. Having maintained an active involvement in this field over the past 20 years, and having taught graduate level and continuing education courses covering different aspects of thermal plasma technology, we have decided to put our knowledge and diverse experiences and backgrounds v
vi Preface together in a single reference textbook devoted to the fundamentals and applications of thermal plasma technology. We choose to address the book to practicing engineers and research scientists looking for a simple and clear review of the principal fundamental concepts involved rather than an exhaustive survey of the subject. But this book mayaiso serve as an introductory text for graduate students entering the field of thermal plasma technology. Ample references are given in each chapter for a more in-depth study of the topics covered. Because of the diversity of the topics to be covered, it was not possible to cover all of them in a single volume. Our choice was, therefore, to present the subject matter of this book in two complementary volumes, the first devoted to the more fundamental concepts of plasma physics and gaseous electronics, thermodynamics and transport properties of plasmas, while the second deals more with the engineering aspects of plasma generation, transport phenomena under plasma conditions, diagnostic techniques, and industrial applications of thermal plasma technology. This first volume ls divided into eight chapters preceded by abrief introduction. In the first chapter, the plasma state is defined and various methods of thermal plasma generation are introduced along with abrief discussion of thermal plasma properties and applications of thermal plasmas. Chapters 2, 3, and 4 cover the essential elements of atomic and molecular theory, kinetic theory, and gaseous electronics, respectively, which are needed for an understanding of material presented in the following chapters. After deriving the plasma equations in Chapter 5, thermodynamic and transport properties are considered in the following two chapters. The most up-to-date values of these properties for selected gases and gas mixtures are presented in the Appendix in the form of tables. The last chapter (8) is devoted to radiation transport. This book has grown out of work done by the authors and their co-workers at their respective universities. Thanks are due to many present and former students and co-workers of the authors who contributed direct1y or indirect1y to this book. Mrs. Pierrette Robidoux painstakingly typed the manuscript and Mrs. P. McMurry provided assistance in technical editing. Very special thanks are due to the wives of the authors-alice, Paulette, and Maja-for their patience, understanding, and support. M. Boulos P. Fauchais E. Pfender
Contents 1. The Plasma State 1 1.1. Preliminary Definition of the Plasma State 1 1.1.1. What Is a Plasma?. 1 1.1.2. Temperature in a Plasma. 2 1.1.3. Different Types of Plasmas 5 1.2. Generation of Thermal Plasmas. 8 1.2.1. High-Intensity Ares 9 1.2.2. Thermal RF Diseharges. 16 1.2.3. Mierowave Diseharges 19 1.3. Properties of Thermal Plasmas 22 1.3.1. Plasma Composition 22 1.3.2. Thermodynamie Properties 25 1.3.3. Fluxes and Transport Properties. 28 1.4. Thermal Plasma Teehnology 33 1.4.1. Plasma Deposition. 34 1.4.2. Plasma Synthesis of Fine Powders 37 1.4.3. Thermal Plasma Deeomposition 37 1.4.4. Plasma Metallurgy. 38 1.4.5. Plasma Densifieation. 41 1.4.6. Plasma Welding and Cutting 43 List of Symbols 43 General Bibliography 45 Referenees 46 vii
viii Contents 2. Basic Atomic and Molecular Theory. 49 2.1. Atomic Models... 2.1.1. Bohr's Model. 2.1.2. Line Emission. 2.1.3. Line Absorption. 2.1.4. Franck-Hertz Experiment 2.2. The Hydrogen Atom and Its Eigenfunctions 2.2.1. The Schrödinger Equation... 2.2.2. Solution of the Schrödinger Equation 2.2.3. Quantum Numbers 2.2.4. Prob ability Distribution.... 49 50 51 55 56 57 57 59 60 61 2.3. The Structure of More Complex Atoms 2.3.1. Atomic Structure.... 2.3.2. Electronic States of Atoms... 2.3.3. Designation of Electron Configurations. 2.4. Excited States of Diatomic Moleeules.... 77 2.4.1. Energy States............ 77 2.4.2. Classification of the Electronic States of Diatomic Moleeules............... 80 2.4.3. General Remarks about Molecular Spectra 85 2.4.4. The Nt(l-) Spectra 86 List of Symbols... 95 General Bibliography 97 References..... 98 63 63 67 69 3. Kinetic Theory.... 99 3.1. Particles and Collisions. 99 3.2. Cross Sections and Collision Frequencies. 101 3.2.1. Collision Probabilities...... 101 3.2.2. Collision Cross Sections..... 102 3.2.3. Collision Frequencies and Scattering Cross Sections 104 3.2.4. Mean Free Paths.............. 105 3.2.5. Total Effective Cross Seetion Qi(V) for Collision Processes.................. 107
Contents ix 3.3. Elementary Processes for Elastic Collisions. 3.4. Elementary Processes for Inelastic Collisions 3.4.1. Excitation............. 3.4.2. Ionization............. 3.4.3. Inelastic Collisions of the Second Kind. 107 109 109 111 114 3.5. Distribution Functions 115 3.5.1. Definition... 116 3.5.2. Particle Fluxes. 116 3.5.3. The Boltzmann Equation. 118 3.5.4. The Maxwellian Distribution 121 3.5.5. Collision Probabilities and Mean Free Paths in a Particle Ensemble. 123 3.6. Reaction Rates..... 3.6.1. Binary Reactions. 3.6.2. Three-Body Reactions 3.6.3. Recombination 124 124 127 128 List of Symbols... 129 General Bibliography 132 References..... 132 4. Fundamental Concepts in Gaseous Electronics 133 4.1. Generation of Charge Carriers 133 4.1.1. Direct Ionization 134 4.1.2. Indirect Ionization. 134 4.2. Loss of Charge Carriers. 134 4.3. Motion of Charge Carriers 135 4.3.1. Drift in Electric Fields 135 4.3.2. Diffusion of Charge Carriers 140 4.3.3. Motion of Charge Carriers in Magnetic Fields. 144 4.4. Thermal Excitation and Ionization. 4.4.1. Boltzmann Distribution... 4.4.2. Saha Equilibrium..... 4.4.3. Complete Thermal Equilibrium (CTE). 151 151 158 162
x Contents 4.4.4. Concept of Local Thermodynamic Equilibrium (LTE) 164 4.4.5. Deviations from LTE..... 168 4.5. Rigorous Definition of the Plasma State 169 4.5.1. Debye Length in a Plasma... 169 4.5.2. Characteristic Lengths in a Plasma. 172 4.6. Quasi-Neutrality............ 174 4.6.1. Charge-Carrier Separation by Diffusion. 174 4.6.2. Charge-Carrier Separation by Magnetic Fields. 175 4.7. Plasma Sheaths 177 List of Symbols 180 General Bibliography 182 References..... 182 5. Derivation of the Plasma Equations. 185 5.1. Definitions...... 185 5.2. Conservation Equations 186 5.2.1. Conservation of Mass 186 5.2.2. Conservation of Momentum. 187 5.2.3. Conservation of Energy.. 187 5.2.4. Entropy Balance...... 188 5.3. Onsager's Reciprocity Relations and Some Phenomenological Theorems............ 192 5.4. Heat of Transition and Energy Fluxes 196 5.5. Diffusion and Energy Fluxes in Chemically Reacting Gases 199 5.6. An Example of Mass and Energy Fluxes in a Chemically Reacting Gas................ 201 5.7. Transport Equations for a Fully Ionized Plasma. 204 5.7.1. Plasma Exposed to an Electric Field... 205 5.7.2. Plasma Exposed to an Electric Field and an Arbitrarily Directed Magnetic Field of Induction B....... 206
Contents 6.5. Composition and Thermodynamic Properties of a Two- Temperature Plasma...... 252 6.5.1. Composition...... 253 6.5.2. Thermodynamic Properties 260 List of Symbols... 260 General Bibliography 262 References..... 263 xi 5.8. Determination of Transport Coefficients List of Symbols References.. 210 211 212 6. Thermodynamic Properties 213 6.1. Introduction........ 6.2. Thermodynamic Functions for CTE 6.2.1. Notation........ 6.2.2. Partition Functions..... 6.2.3. Thermodynamic Functions. 6.2.4. Calculation of Partition Functions 6.3. Composition of a Plasma in CTE 6.3.1. Equilibrium Relationships. 6.3.2. Law of Mass Action... 6.3.3. Calculation of the Plasma Composition. 6.4. Thermodynamic Properties of Plasmas in CTE 6.4.1. Specific Heat at Constant Pressure... 6.4.2. Enthalpy and Entropy........ 213 214 214 216 217 221 225 225 227 230 244 244 248 7. Transport Properties. 7.1. Definition...... 7.2. Simplified Derivation of the Transport Coefficients 7.2.1. SeIf-Diffusion Coefficient 7.2.2. Viscosity...... 7.2.3. Thermal Conductivity 7.2.4. Electrical Conductivity 265 265 266 267 268 271 273
xii Contents 7.3. Derivation of the Transport Coefficients from the Boltzmann Equation...... 274 7.3.1. Basic Equations.......... 275 7.3.2. Fluxes.............. 280 7.3.3. Calculation of Distribution Functions. 281 7.3.4. Interaction Potentials and Collision Integrals 285 7.3.5. Transport Properties........... 287 7.4. Contribution of Other Transport Mechanisms to the Thermal Conductivity............ 291 7.4.1. Reactional Contribution... 291 7.4.2. Contribution of Internal Energy. 294 7.5. Transport Coefficients of Simple Gases and Complex Gas Mixtures in CTE............ 296 7.5.1. Examples for Simple Gases..... 297 7.5.2. Examples for Complex Gas Mixtures. 303 7.5.3. Mixing Rules and Their Limitations. 311 7.6. Transport Coefficients for a Two-Temperature Plasma: Example for an Ar-H 2 Plasma Mixture 314 List of Symbols... 318 General Bibliography 321 References..... 322 8. Radiation Transport 8.1. General Concepts.. 8.1.1. Definitions.. 8.1.2. Blackbody Radiation. 8.1.3. Gaseous Radiation.. 325 325 325 327 329 8.2. Radiation Mechanisms in Plasmas 332 8.2.1. Spontaneous Emission 332 8.2.2. Induced Emission.... 332 8.2.3. Absorption....... 333 8.2.4. Microreversibility Principle 333 8.2.5. Effective Radiative Lifetime of an Excited State. 335
Contents 8.3. Radiation Emission and Absorption 8.3.1. Classification of Emitted Radiation 8.3.2. Line Radiation 8.3.3. Continuum Radiation 8.3.4. Total Effective Radiation of Plasmas. 8.4. Examples of Results..... 8.4.1. Classical Plasma Gases. 8.4.2. Plasma Seeded with Metallic Vapors. 8.5. Blackbody Radiation of High-Temperature Gases List of Symbols General Bibliography References xiii 336 336 340 348 358 366 366 372 377 378 381 381 Appendix: Thermodynamic and Transport Properties of Pure Gases and Their Mixtures at Atmospheric Pressure over the Temperature Range 500-24,000 K. 385 A.1. Introduction.......... 385 A.2. Calculation Method....... 386 A.2.1. Thermodynamic Properties. 386 A.2.2. Transport Properties 387 A.3. Plasma Tables 387 References.. 448 Index.... 1 449
Thermal Plasmas Fundamentals and Applications Volume 1