Ionization and Ion Transport

A primer for the study of non-equilibrium, low-temperature gas discharges and plasmas

By (author) David B. Go

Publication date:

04 April 2018

Length of book:

106 pages

Publisher

Morgan & Claypool Publishers

ISBN-13: 9781681746036

BOOK DESCRIPTION
TABLE OF CONTENTS

This text introduces engineering and science students to the basic underlying physics and chemistry concepts that form the foundation of plasma science and engineering. It is an accessible primer directed primarily at those students who, like the general public, simply do not understand exactly what a plasma or gas discharge is, nor do they even necessarily have the fundamental background in statistical thermodynamics, gas dynamics, ﬂuid dynamics, or solid-state physics to effectively understand many plasma and gas discharge principles. At the conclusion of this text, the reader should understand what an ion is, how they move, the equations we use to describe these basic concepts, and how they link to the aforementioned topics of plasmas and gas discharges. This book is focused on specific concepts that are important to non-equilibrium, low-temperature gas discharges. These discharges ﬁnd wide applicability today and are of significant interest to the scientific and engineering communities.

Contents

Preface

PART I Ionization

1 Foundations from Gas Dynamics 3

1.1 The Atom, The Molecule, and Excited States . . . . . . . . . . . . . . . . 3

1.2 The Statistics of a Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.1 Collision Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.2 Equilibrium Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 Elementary Electron Behavior 18

2.1 Electron-Driven Gaseous Reactions . . . . . . . . . . . . . . . . . . . . . 18

2.1.1 Elastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.2 Excitation Collisions . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.3 Ionization Collisions . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Electron-Neutral Collisions and the Collision Cross-Section . . . . . . . . 21

2.2.1 The Nature of Electron-Driven Collisions . . . . . . . . . . . . . . 21

2.2.2 Differential Collision Cross-Section . . . . . . . . . . . . . . . . . 21

2.2.3 Elementary Collision Dynamics . . . . . . . . . . . . . . . . . . . 23

2.2.4 Realistic Collision Cross-Sections . . . . . . . . . . . . . . . . . . 25

2.3 Electron Energy Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Electron Collision Frequency and Reaction Rates . . . . . . . . . . . . . . 29

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Gaseous Ionization Processes 33

3.1 Electron Impact Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.1 Temporal Electron Avalanche . . . . . . . . . . . . . . . . . . . . 34

3.1.2 Spatial Electron Avalanche . . . . . . . . . . . . . . . . . . . . . . 34

3.1.3 Townsend’s First Ionization Coefﬁcientα . . . . . . . . . . . . . . 37

3.2 Ion Impact Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3 Photoionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 Thermal Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5 Step Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.6 Penning Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7 Electron Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Electrode Processes 43

4.1 Importance of Electron Emission . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 Foundational Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.1 The Solid State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.2 Fermi-Dirac Distribution and the Work Function . . . . . . . . . . 46

4.3 General Electron Emission . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3.1 Thermionic Emission . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3.2 Photoelectric Emission . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.3 Field Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Secondary Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4.1 Ion-Induced Secondary Emission . . . . . . . . . . . . . . . . . . 52

4.4.2 Secondary Emission Coefﬁcientγ . . . . . . . . . . . . . . . . . . 56

4.4.3 Metastable-Induced Secondary Emission . . . . . . . . . . . . . . 57

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

PART II Ion Transport 60

5 Foundations from General Transport Theory 62

5.1 Basics of Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.1.1 Application of Kinetics to Transport . . . . . . . . . . . . . . . . . 63

5.2 Transport Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2.1 Continuum Perspective - Scalar Transport Equation . . . . . . . . . 66

5.2.2 Kinetic Perspective - Boltzmann Transport Equation . . . . . . . . 69

5.2.3 From the Boltzmann Transport Equation to Macroscopic Properties 70

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6 Transport Equations for Gas Discharges 73

6.1 Equations for the Charged Particles . . . . . . . . . . . . . . . . . . . . . . 73

6.1.1 Particle/Charge Conservation . . . . . . . . . . . . . . . . . . . . . 73

6.1.2 Momentum Conservation . . . . . . . . . . . . . . . . . . . . . . . 75

6.1.3 Energy Conservation . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.1.4 Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.2 The Drift-Diffusion Approximation . . . . . . . . . . . . . . . . . . . . . 78

6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Whence and Whither………81