CHAPTER 1 FUNDAMENTALS OF RADIATIVE TRANSFER .................... 1
1.1 The Electromagnetic Spectrum; Elementary Properties of
Radiation .................................................. 1
1.2 Radiative Flux ............................................. 2
Macroscopic Description of the Propagation of Radiation .... 2
Flux from an Isotropic Source-The Inverse Square Law ....... 2
1.3 The Specific Intensity and Its Moments ..................... 3
Definition of Specific Intensity or Brightness ............. 3
Net Flux and Momentum Flux ................................. 4
Radiative Energy Density ................................... 5
Radiation Pressure in an Enclosure Containing an
Isotropic Radiation Field .................................. 6
Constancy of Specific Intensity Along Rays in Free
Space ...................................................... 7
Proof of the Inverse Square Law for a Uniformly Bright
Sphere ..................................................... 7
1.4 Radiative Transfer ......................................... 8
Emission ................................................... 9
Absorption ................................................. 9
The Radiative Transfer Equation ........................... 11
Optical Depth and Source Function ......................... 12
Mean Free Path ............................................ 14
Radiation Force ........................................... 15
1.5 Thermal Radiation ......................................... 15
Blackbody Radiation ....................................... 15
Kirchhoffs Law for Thermal Emission ....................... 16
Thermodynamics of Blackbody Radiation ..................... 17
The Planck Spectrum ....................................... 20
Properties of the Planck Law .............................. 23
Characteristic Temperatures Related to Planck Spectrum .... 25
1.6 The Einstein Coefficients ................................. 27
Definition of Coefficients ................................ 27
Relations between Einstein Coefficients ................... 29
Absorption and Emission Coefficients in Terms of
Einstein Coefficients ..................................... 30
1.7 Scattering Effects; Random Walks .......................... 33
Pure Scattering ........................................... 33
Combined Scattering and Absorption ........................ 36
1.8 Radiative Diffusion ....................................... 39
The Rosseland Approximation ............................... 39
The Eddington Approximation; Two-Stream Approximation ..... 42
PROBLEMS ....................................................... 45
REFERENCES ..................................................... 50
CHAPTER 2 BASIC THEORY OF RADIATION FIELDS ..................... 51
2.1 Review of Maxwell's Equations ............................. 51
2.2 Plane Electromagnetic Waves ............................... 55
2.3 The Radiation Spectrum .................................... 58
2.4 Polarization and Stokes Parameters ........................ 62
Monochromatic Waves ....................................... 62
Quasi-monochromatic Waves ................................. 65
2.5 Electromagnetic Potentials ................................ 69
2.6 Applicability of Transfer Theory and the Geometrical
Optics Limit .............................................. 72
PROBLEMS ....................................................... 74
REFERENCES ..................................................... 76
CHAPTER 3 RADIATION FROM MOVING CHARGES ........................ 77
3.1 Retarded Potentials of Single Moving Charges: The
Lienard-Wiechart Potentials ............................... 77
3.2 The Velocity and Radiation Fields ......................... 80
3.3 Radiation from Nonrelativistic Systems of Particles ....... 83
Larmor's Formula .......................................... 83
The Dipole Approximation .................................. 85
The General Multipole Expansion ........................... 88
3.4 Thomson Scattering (Electron Scattering) .................. 90
3.5 Radiation Reaction ........................................ 93
3.6 Radiation from Harmonically Bound Particles ............... 96
Undriven Harmonically Bound Particles ..................... 96
Driven Harmonically Bound Particles ....................... 99
PROBLEMS ...................................................... 102
REFERENCE ..................................................... 105
CHAPTER 4 RELATIVISTIC CO VARIANCE AND KINEMATICS ............. 106
4.1 Review of Lorentz Transformations ........................ 106
4.2 Four-Vectors ............................................. 113
4.3 Tensor Analysis .......................................... 122
4.4 Covariance of Electromagnetic Phenomena .................. 125
4.5 A Physical Understanding of Field Transformations ........ 129
4.6 Fields of a Uniformly Moving Charge ...................... 130
4.7 Relativistic Mechanics and the Lorentz Four-Force ........ 136
4.8 Emission from Relativistic Particles ..................... 138
Total Emission ........................................... 138
Angular Distribution of Emitted and Received Power ....... 140
4.9 Invariant Phase Volumes and Specific Intensity ........... 145
PROBLEMS ...................................................... 148
REFERENCES .................................................... 154
CHAPTER 5 BREMSSTRAHLUNG ...................................... 155
5.1 Emission from Single-Speed Electrons ..................... 156
5.2 Thermal Bremsstrahlung Emission .......................... 159
5.3 Thermal Bremsstrahlung (Free-Free) Absorption ............ 162
5.4 Relativistic Bremsstrahlung .............................. 163
PROBLEMS ...................................................... 165
REFERENCES .................................................... 166
CHAPTER 6 SYNCHROTRON RADIATION ............................... 167
6.1 Total Emitted Power ...................................... 167
6.2 Spectrum of Synchrotron Radiation: A Qualitative
Discussion ............................................... 169
6.3 Spectral Index for Power-Law Electron Distribution ....... 173
6.4 Spectrum and Polarization of Synchrotron Radiation:
A Detailed Discussion .................................... 175
6.5 Polarization of Synchrotron Radiation .................... 180
6.6 Transition from Cyclotron to Synchrotron Emission ........ 181
6.7 Distinction between Received and Emitted Power ........... 184
6.8 Synchrotron Self-Absorption .............................. 186
6.9 The Impossibility of a Synchrotron Maser in Vacuum ....... 191
PROBLEMS ...................................................... 192
REFERENCES .................................................... 194
CHAPTER 7 COMPTON SCATTERING .................................. 195
7.1 Cross Section and Energy Transfer for the Fundamental
Process .................................................. 195
Scattering from Electrons at Rest ........................ 195
Scattering from Electrons in Motion: Energy Transfer ..... 197
7.2 Inverse Compton Power for Single Scattering .............. 199
7.3 Inverse Compton Spectra for Single Scattering ............ 202
7.4 Energy Transfer for Repeated Scatterings in a Finite,
Thermal Medium: The Compton Y Parameter .................. 208
7.5 Inverse Compton Spectra and Power for Repeated
Scatterings by Relativistic Electrons of Small Optical
Depth .................................................... 211
7.6 Repeated Scatterings by Nonrelativistic Electrons: The
Kompaneets Equation ...................................... 213
7.7 Spectral Regimes for Repeated Scattering by
Nonrelativistic Electrons ................................ 216
Modified Blackbody Spectra; y << 1 ....................... 218
Wien Spectra; y >> l ..................................... 219
Unsaturated Comptonization with Soft Photon Input ........ 221
PROBLEMS ...................................................... 223
REFERENCES .................................................... 223
CHAPTER 8 PLASMA EFFECTS ...................................... 224
8.1 Dispersion in Cold, Isotropic Plasma ..................... 224
The Plasma Frequency ..................................... 224
Group and Phase Velocity and the Index of Refraction ..... 227
8.2 Propagation Along a Magnetic Field; Faraday Rotation ..... 229
8.3 Plasma Effects in High-Energy Emission Processes ......... 232
Cherenkov Radiation ...................................... 233
Razin Effect ............................................. 234
PROBLEMS ...................................................... 236
REFERENCES .................................................... 237
CHAPTER 9 ATOMIC STRUCTURE .................................... 238
9.1 A Review of the Schrodinger Equation ..................... 238
9.2 One Electron in a Central Field .......................... 240
Wave Functions ........................................... 240
Spin ..................................................... 243
9.3 Many-Electron Systems .................................... 243
Statistics: The Pauli Principle .......................... 243
Hartree-Fock Approximation: Configurations ............... 245
The Electrostatic Interaction; LS Coupling and Terms ..... 247
9.4 Perturbations, Level Splittings, and Term Diagrams ....... 248
Equivalent and Nonequivalent Electrons and Their
Spectroscopic Terms ...................................... 248
Parity ................................................... 251
Spin-Orbit Coupling ...................................... 252
Zeeman Effect ............................................ 256
Role of the Nucleus; Hyperfine Structure ................. 257
9.5 Thermal Distribution of Energy Levels and Ionization ..... 259
Thermal Equilibrium: Boltzmann Population of Levels ...... 259
The Saha Equation ........................................ 260
PROBLEMS ...................................................... 263
REFERENCES .................................................... 266
CHAPTER 10 RADIATIVE TRANSITIONS .............................. 267
10.1 Semi-Classical Theory of Radiative Transitions ........... 267
The Electromagnetic Hamiltonian .......................... 268
The Transition Probability ............................... 269
10.2 The Dipole Approximation ................................. 271
10.3 Einstein Coefficients and Oscillator Strengths ........... 274
10.4 Selection Rules .......................................... 278
10.5 Transition Rates ......................................... 280
Bound-Bound Transitions for Hydrogen ..................... 280
Bound-Free Transitions (Continuous Absorption) for
Hydrogen ................................................. 282
Radiative Recombination—Milne Relations .................. 284
The Role of Coupling Schemes in the Determination
off Values ............................................... 286
10.6 Line Broadening Mechanisms ............................... 287
Doppler Broadening ....................................... 287
Natural Broadening ....................................... 289
Collisional Broadening ................................... 290
Combined Doppler and Lorentz Profiles .................... 291
PROBLEMS ...................................................... 291
REFERENCES .................................................... 292
CHAPTER 11 MOLECULAR STRUCTURE ................................ 294
11.1 The Born-Oppenheimer Approximation: An Order of
Magnitude Estimate of Energy Levels ...................... 294
11.2 Electronic Binding of Nuclei ............................. 296
The H2+ Ion .............................................. 297
The H2 Molecule .......................................... 300
11.3 Pure Rotation Spectra .................................... 302
Energy Levels ............................................ 302
Selection Rules and Emission Frequencies ................. 304
11.4 Rotation-Vibration Spectra ............................... 305
Energy Levels and the Morse Potential .................... 305
Selection Rules and Emission Frequencies ................. 306
11.5 Electronic-Rotational-Vibrational Spectra ................ 308
Energy Levels ............................................ 308
Selection Rules and Emission Frequencies ................. 308
PROBLEMS ...................................................... 311
REFERENCES .................................................... 312
SOLUTIONS ..................................................... 313
INDEX ......................................................... 375
|
