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Filling a gap in the literature, this introduction to the topic covers the physics of the standard microwave diagnostics established on modern fusion experiments, and the necessary technological background from the field of microwave engineering. Written by well-known mm-wave diagnosticians in the field of fusion physics, the textbook includes such major diagnostic techniques as electron cyclotron emission, interferometry, reflectometry, polarimetry, and scattering.

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Preface XIII

1 Fusion Research 1

1.1 Reaction Scheme 1

1.2 Magnetic Plasma Confinement 4

1.2.1 Tokamak 5

1.2.2 Stellarator 6

1.2.3 Physics Issues of Magnetic Confinement 7

1.2.4 Plasma Heating 10

1.3 Plasma Diagnostic 11

1.3.1 Generic Arrangements 12

1.3.2 Microwave Diagnostics 15

References 17

2 Millimeter-Waves in Plasmas 19

2.1 Basic Equations 20

2.2 Plasma Dielectric Tensor, General Properties 23

2.3 Dielectric Tensor from Kinetic Theory 25

2.4 Cold-Plasma Limit 29

2.5 Derivation within Fluid Description 32

2.6 Discussion of Cold-Plasma Dispersion Relations 34

2.6.1 Nonmagnetized Plasma, B0 = 0 34

2.6.2 Magnetized Plasma, Parallel Propagation, kB0 37

2.6.3 Magnetized Plasma, Perpendicular Propagation, k B0 39

2.6.4 Slightly Oblique Propagation 41

2.7 Finite-Temperature Correction to Cold-Plasma Dielectric Tensor 42

2.7.1 Finite Larmor Radius Expansion 42

2.7.2 Warm-Plasma Approximation 44

2.7.3 Relativistic Corrections 46

2.8 Inhomogeneous Plasma 48
2.8.1 WKB Approximation 49

2.8.2 Refraction 51

2.8.3 Ray Tracing 53

2.9 Finite-Size Probing Beam 54

2.9.1 Gaussian Beam Description 54

2.10 Radiation Transfer 58

2.10.1 Transparent Plasma 58

2.10.2 Plasma Emitting and Absorbing 60

2.10.3 Multiple Chords, Imaging 61

References 62

3 Active Diagnostics 65

3.1 Interferometry 65

3.1.1 Single-Chord Interferometry 68

3.1.2 Multiple Chords 69

3.2 Polarimetry 70

3.2.1 Faraday Effect 71

3.2.2 Cotton-Mouton Effect 75

3.2.3 Common Generalized Description 77

3.3 Reflectometry 83

3.3.1 Time Delay Measurement 86

3.3.2 Phase Change at Cutoff 89

3.3.3 Profile Reconstruction 92

3.3.4 Localization of Reflecting Layer 93

3.3.5 Relativistic Corrections 95

3.3.6 Influence of Density Fluctuations 95

3.4 Scattering 100

3.4.1 Single-Particle Thomson Scattering 101

3.4.2 Doppler Shift 102

3.4.3 Incoherent Scattering 104

3.4.4 Relativistic Incoherent Scattering Spectrum 106

3.4.5 Role of Density Fluctuations 108

3.4.6 Coherent Scattering 108

3.4.7 Electron and Ion Feature 110

3.4.8 Summarizing Comments 113

References 115

4 Passive Diagnostics 117

4.1 Bremsstrahlung 118

4.2 Electron Cyclotron Emission 122

4.2.1 Electron Motion in a Static B-Field 122

4.2.2 Electric Field and Spectrum, Single Electron 123

4.2.3 Perpendicular Observation, Characteristic Modes 126

4.2.4 Spectrum, Electron Ensemble 128

4.2.5 Absorption Coefficient 130

4.2.6 Emission Profile 132

4.2.7 B0-Field Varying along Sightline 135

4.2.8 Optical Depth of Most Relevant Modes 137

4.2.9 Visibility Depth and Localization 139

4.2.10 Electron Cyclotron Absorption Measurement 142

4.3 Electron Bernstein Wave Emission 143

4.3.1 Electron Bernstein Waves 144

4.3.2 Mode Conversion 146

References 149

5 Guided Waves 151

5.1 Transmission Line Properties 151

5.1.1 Waves on a Lossy Transmission Line 151

5.1.2 Terminated Transmission Line 153

5.1.3 Classification of Transmission Lines 157

5.1.4 Surface Currents 160

5.2 Coaxial Transmission Line 161

5.2.1 Characteristic Properties 162

5.2.2 Losses and Limits of Coaxial Lines 162

5.3 Rectangular Waveguides 163

5.3.1 TE Waves 164

5.3.2 TM Waves 166

5.3.3 Attenuation in Rectangular Waveguides 166

5.3.4 Fundamental TE10 Wave 167

5.4 Circular Waveguides 170

5.4.1 Fields in Circular Waveguides 171

5.4.2 TM Waves 172

5.4.3 TE Waves 173

5.4.4 Loss in Circular Waveguides 175

5.5 Multimode Waveguides 176

5.5.1 Number of Modes Propagating 176

5.5.2 Multimode Propagation 178

5.5.3 TE11 Mode in Overmoded Circular Waveguides 179

5.6 Corrugated Circular Waveguides 182

5.6.1 Fields of Corrugated Circular Waveguides 183

5.6.2 Characteristics of HE11 Hybrid Mode 185

5.7 Gaussian Beams 185

5.7.1 Solution of Approximate Wave Equation 185

5.7.2 Transformation

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