10 Waveguides and Cavities 118 10.1 The approximation of perfect conductors 118 10.2 Waveguides 119 10.3 Rectangular Waveguide.. 122 10.4 Energy Flow and Attenuation 122 l0.5 Resonant Cavities..··. 125 10.6 Perturbation of Boundary Conditions 128 10.7 Excitation of Waveguide Modes 。。 129 11 Radiation from Localized Sources 133 ll.1 Long Wavelength Limit...........:·· 135 11.2 Beyond the Multipole Expansion 137 11.3 Systematics of the Multipole Expansion..................... 139 11.4 Vector Spherical Harmonics and Multipole Radiation............. 140 12 Scattering of Electromagnetic Waves 143 12.1 Long Wavelength Scattering...... 143 12.2 General Formulation of Scattering..... 145 12.3 The Born Approximation... 146 l2.4 Scattering from a Perfectly Conducting Sphere....,···.. 147 12.5 Short wavelength approximation and diffraction 150 12.6 Short Wavelength Scattering 152 l2.7 The Optical Theorem..·.··. 154 13 Energy Loss and Cherenkov Radiation 157 14 Radiation from a particle in relativistic motion 159 14.1 Lienard-Wiechert Potentials and Fields................ 159 l4.2 Charge in uniform motion···························· 161 l4.3 Charge moving with constant proper acceleration·.············· 162 3 ©2010 by Charles Thorn10 Waveguides and Cavities 118 10.1 The approximation of perfect conductors . . . . . . . . . . . . . . . . . . . . 118 10.2 Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 10.3 Rectangular Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 10.4 Energy Flow and Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . 122 10.5 Resonant Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 10.6 Perturbation of Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 128 10.7 Excitation of Waveguide Modes . . . . . . . . . . . . . . . . . . . . . . . . . 129 11 Radiation from Localized Sources 133 11.1 Long Wavelength Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 11.2 Beyond the Multipole Expansion . . . . . . . . . . . . . . . . . . . . . . . . 137 11.3 Systematics of the Multipole Expansion . . . . . . . . . . . . . . . . . . . . . 139 11.4 Vector Spherical Harmonics and Multipole Radiation . . . . . . . . . . . . . 140 12 Scattering of Electromagnetic Waves 143 12.1 Long Wavelength Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 12.2 General Formulation of Scattering . . . . . . . . . . . . . . . . . . . . . . . . 145 12.3 The Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 12.4 Scattering from a Perfectly Conducting Sphere . . . . . . . . . . . . . . . . . 147 12.5 Short wavelength approximation and diffraction . . . . . . . . . . . . . . . . 150 12.6 Short Wavelength Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 12.7 The Optical Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 13 Energy Loss and Cherenkov Radiation 157 14 Radiation from a particle in relativistic motion 159 14.1 Li´enard-Wiechert Potentials and Fields . . . . . . . . . . . . . . . . . . . . . 159 14.2 Charge in uniform motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 14.3 Charge moving with constant proper acceleration . . . . . . . . . . . . . . . 162 3 c 2010 by Charles Thorn