{"id":537,"date":"2025-07-15T08:11:16","date_gmt":"2025-07-15T08:11:16","guid":{"rendered":"https:\/\/synchrotron-light.net\/wp\/?page_id=537"},"modified":"2025-07-16T03:24:02","modified_gmt":"2025-07-16T03:24:02","slug":"table-of-content","status":"publish","type":"page","link":"https:\/\/synchrotron-light.net\/wp\/?page_id=537","title":{"rendered":"Full table of contents"},"content":{"rendered":"\r\n
    \r\n
  1. Prologue<\/strong>\r\n
      \r\n
    1. Let the journey begin<\/li>\r\n
    2. Overview of the content<\/li>\r\n
    3. Multiple paths through the book<\/li>\r\n
    4. Resources, units, and conventions<\/li>\r\n<\/ol>\r\n<\/li>\r\n
    5. Introduction to special relativity<\/strong>\r\n
        \r\n
      1. Light and time<\/li>\r\n
      2. Inertial frames and the Lorentz transformations<\/li>\r\n
      3. Consequences of the Lorentz transformations\r\n
          \r\n
        1. Relativity of simultaneity<\/li>\r\n
        2. Length contraction and time dilation<\/li>\r\n
        3. Non-relativistic limit<\/li>\r\n<\/ol>\r\n<\/li>\r\n
        4. Transformation of velocities and accelerations<\/li>\r\n
        5. Relativistic aberration and Doppler shift<\/li>\r\n
        6. The inertia of energy<\/li>\r\n
        7. Mass, momentum, and energy<\/li>\r\n
        8. Steps towards general relativity<\/li>\r\n<\/ol>\r\n<\/li>\r\n
        9. Emission from accelerated charges<\/strong>\r\n
            \r\n
          1. Introduction<\/li>\r\n
          2. Why do accelerated charges radiate?<\/li>\r\n
          3. Radiation emitted by relativistic charges<\/li>\r\n
          4. Angular distribution of the emitted radiation<\/li>\r\n
          5. Radiation emitted by charges in circular motion<\/li>\r\n
          6. Radiation emitted by charges in linear motion<\/li>\r\n<\/ol>\r\n<\/li>\r\n
          7. Radiation emitted by charges in bending magnets<\/strong>\r\n
              \r\n
            1. Introduction<\/li>\r\n
            2. Moving charge in a constant magnetic field<\/li>\r\n
            3. Energy loss and time structure of synchrotron light<\/li>\r\n
            4. Spectrum of light emitted by a dipole magnet: qualitative discussion<\/li>\r\n
            5. Spectrum of light emitted by a dipole magnet: quantitative discussion\r\n
                \r\n
              1. Power radiated into each harmonic<\/li>\r\n
              2. Characteristic harmonic and critical harmonic<\/li>\r\n
              3. Large-order approximation of the spectrum<\/li>\r\n
              4. Maximum-emission harmonic<\/li>\r\n
              5. Angular spectral density and asymptotic expansion of the spectrum<\/li>\r\n
              6. Number of emitted photons per revolution<\/li>\r\n<\/ol>\r\n<\/li>\r\n
              7. Polarisation of synchrotron light<\/li>\r\n
              8. Final remarks<\/li>\r\n<\/ol>\r\n<\/li>\r\n
              9. Insertion devices<\/strong>\r\n
                  \r\n
                1. Introduction<\/li>\r\n
                2. Equations of motion in a wiggler\r\n
                    \r\n
                  1. Electron trajectory in a periodic magnetic field<\/li>\r\n
                  2. Deflection angle and deflection parameter<\/li>\r\n
                  3. Critical energy<\/li>\r\n
                  4. Electron trajectory revisited<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                  5. Spectrum of the emission from an insertion device\r\n
                      \r\n
                    1. Qualitative description<\/li>\r\n
                    2. Simplified model for an insertion device<\/li>\r\n
                    3. Qualitative model for the transition from an undulator to a wiggler<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                    4. Planar undulators: the undulator equation\r\n
                        \r\n
                      1. The undulator equation from relativistic aberration and Doppler shift<\/li>\r\n
                      2. The undulator equation obtained via an interference condition<\/li>\r\n
                      3. Pulse duration, line width, and divergence of an undulator beam<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                      4. Relativistic effects in the undulator spectrum\r\n
                          \r\n
                        1. Basic considerations<\/li>\r\n
                        2. Higher-order harmonics<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                        3. Polarisation of the light from insertion devices\r\n
                            \r\n
                          1. Generating linear polarisation by combining elliptically polarised waves with opposite helicity<\/li>\r\n
                          2. Polarisation of insertion-device emission<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                          3. Source comparison and final remarks<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                          4. Quantum effects in synchrotron radiation<\/strong>\r\n
                              \r\n
                            1. Introduction<\/li>\r\n
                            2. Breakdown of electron-trajectory concept<\/li>\r\n
                            3. Compton scatter<\/li>\r\n
                            4. Inverse Compton scatter\r\n
                                \r\n
                              1. Basic formalism<\/li>\r\n
                              2. Analogy between inverse Compton scattering and undulator radiation<\/li>\r\n
                              3. A hypothetical case study<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                              4. Breakdown of classical synchrotron emission model: Schwinger magnetic field\r\n
                                  \r\n
                                1. Shrinking a storage ring<\/li>\r\n
                                2. Electron recoil<\/li>\r\n
                                3. Storage-ring radius and the Compton wavelength<\/li>\r\n
                                4. Shining too weakly<\/li>\r\n
                                5. Shining too strongly<\/li>\r\n
                                6. Radiative damping<\/li>\r\n
                                7. Critical energy density<\/li>\r\n
                                8. Schwinger magnetic field: discussion<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                9. Quantum effects in relativistic charged-particle orbits<\/strong>\r\n
                                    \r\n
                                  1. Introduction<\/li>\r\n
                                  2. Relativistic quantum mechanics of circular charged-particle trajectories\r\n
                                      \r\n
                                    1. Plane waves and wave-functions<\/li>\r\n
                                    2. Correspondence rules<\/li>\r\n
                                    3. Klein\u2013Gordon equation<\/li>\r\n
                                    4. Klein\u2013Gordon model for a relativistic charged particle in a uniform magnetic field<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                    5. Radiative polarisation and spin light\r\n
                                        \r\n
                                      1. Sokolov\u2013Ternov relaxation time: rough estimate<\/li>\r\n
                                      2. The Golden Rule<\/li>\r\n
                                      3. Sokolov\u2013Ternov relaxation via the Golden Rule<\/li>\r\n
                                      4. Spin light<\/li>\r\n
                                      5. Discussion<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                      6. Comparison of characteristic timescales\r\n
                                          \r\n
                                        1. Some characteristic timescales associated with synchrotron light<\/li>\r\n
                                        2. Comparison of characteristic timescales associated with synchrotron light<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                        3. The free-electron laser<\/strong>\r\n
                                            \r\n
                                          1. Light\u2013matter interaction: absorption and emission\r\n
                                              \r\n
                                            1. Planck\u2019s law<\/li>\r\n
                                            2. Absorption, spontaneous emission, and stimulated emission by atomic electrons<\/li>\r\n
                                            3. Phenomenological model of a low-gain laser<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                            4. Low-gain regime for free-electron laser\r\n
                                                \r\n
                                              1. Microscopic interactions in an FEL<\/li>\r\n
                                              2. Why do FELs need an undulator?<\/li>\r\n
                                              3. Low-gain FEL: the FEL pendulum equation<\/li>\r\n
                                              4. Approximate solution to the pendulum equation: the gain function<\/li>\r\n
                                              5. Gain and undulator bandwidth: Madey\u2019s theorem<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                              6. One-dimensional high-gain FEL theory\r\n
                                                  \r\n
                                                1. Revisiting the FEL pendulum equation<\/li>\r\n
                                                2. The laser field<\/li>\r\n
                                                3. Space-charge effects<\/li>\r\n
                                                4. An equation for the current density<\/li>\r\n
                                                5. Numerical solution of coupled system of high-gain FEL equations<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                6. Introduction to phase-space dynamics\r\n
                                                    \r\n
                                                  1. The concept of phase space<\/li>\r\n
                                                  2. Dynamical evolution and Hamilton\u2019s equations<\/li>\r\n
                                                  3. Beam emittance<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                  4. Phase-space filamentation and chaotic dynamics in FELs\r\n
                                                      \r\n
                                                    1. Phase-space filamentation<\/li>\r\n
                                                    2. Laminar mixing in the low-gain FEL model<\/li>\r\n
                                                    3. Turbulent chaotic evolution<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                    4. Synchrotron light in the cosmos<\/strong>\r\n
                                                        \r\n
                                                      1. Introduction<\/li>\r\n
                                                      2. Motion of charged particles in magnetic fields, revisited<\/li>\r\n
                                                      3. Radiated power and emitted spectrum<\/li>\r\n
                                                      4. Synchrotron emission from an ensemble of particles\r\n
                                                          \r\n
                                                        1. Effect of electron velocity distribution on synchrotron-emission spectrum<\/li>\r\n
                                                        2. Effect of electron energy distribution on synchrotron-emission spectrum<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                        3. Self-absorption of synchrotron light<\/li>\r\n
                                                        4. Distortion of initial electron spectra by synchrotron emission\r\n
                                                            \r\n
                                                          1. Synchrotron cooling<\/li>\r\n
                                                          2. Diffusion\u2013loss equation<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                          3. Fermi model for acceleration of cosmic rays\r\n
                                                              \r\n
                                                            1. Second-order Fermi acceleration<\/li>\r\n
                                                            2. First-order Fermi acceleration<\/li>\r\n
                                                            3. The emergence of power-law spectra<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                            4. Minimum energy and equipartition<\/li>\r\n
                                                            5. Curvature radiation<\/li>\r\n
                                                            6. Synchrotron radiation in planetary magnetic fields\r\n
                                                                \r\n
                                                              1. Geomagnetic emission in cosmic-ray air showers<\/li>\r\n
                                                              2. Synchrotron radiation from Jupiter\u2019s magnetosphere<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                              3. Synchrotron radiation in galactic magnetic fields\r\n
                                                                  \r\n
                                                                1. Synchrotron emission from the Galaxy<\/li>\r\n
                                                                2. Synchrotron emission from supernova remnants<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                3. Cosmic sources of synchrotron radiation\r\n
                                                                    \r\n
                                                                  1. Synchrotron emission from active galactic nuclei<\/li>\r\n
                                                                  2. Synchrotron emission from accreting black holes<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                  3. Non-photon analogues of synchrotron radiation<\/strong>\r\n
                                                                      \r\n
                                                                    1. Introduction<\/li>\r\n
                                                                    2. The four known fundamental forces\r\n
                                                                        \r\n
                                                                      1. Particle-exchange model for the forces of nature<\/li>\r\n
                                                                      2. Some generic aspects of the Standard Model<\/li>\r\n
                                                                      3. Photons as carriers of the electromagnetic force<\/li>\r\n
                                                                      4. W and Z bosons as carriers of the weak force<\/li>\r\n
                                                                      5. Gluons as carriers of the strong force<\/li>\r\n
                                                                      6. Gravitons as carriers of the gravitational force<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                      7. Generalised forms of synchrotron radiation\r\n
                                                                          \r\n
                                                                        1. First generalisation: synchrotron radiation is not exclusive to synchrotron accelerators<\/li>\r\n
                                                                        2. Second generalisation: the accelerating force is not necessarily electromagnetic<\/li>\r\n
                                                                        3. Third generalisation: the particle radiation mechanism is not necessarily electromagnetic<\/li>\r\n
                                                                        4. Caveat emptor<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                        5. Weak-force analogues of synchrotron radiation\r\n
                                                                            \r\n
                                                                          1. Neutrino synchrotron radiation<\/li>\r\n
                                                                          2. Further weak-force synchrotron-radiation analogues<\/li>\r\n
                                                                          3. How synchrotron photons can influence neutrino emission<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                          4. Strong-force analogues of synchrotron radiation\r\n
                                                                              \r\n
                                                                            1. Strong-force analogue of a bending magnet<\/li>\r\n
                                                                            2. Gluon and photon synchrotron radiation induced by QCD vacuum domains<\/li>\r\n
                                                                            3. QCD analogue of Sokolov\u2013Ternov effect<\/li>\r\n
                                                                            4. Hadron jets<\/li>\r\n
                                                                            5. QCD dead cone<\/li>\r\n
                                                                            6. Jet quenching in the quark\u2013gluon plasma<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                            7. Gravitational-wave analogues of synchrotron radiation<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                            8. Calculation of synchrotron radiation from first principles<\/strong>\r\n
                                                                                \r\n
                                                                              1. Maxwell equations, electromagnetic potentials, and gauge invariance\r\n
                                                                                  \r\n
                                                                                1. Maxwell equations<\/li>\r\n
                                                                                2. Electromagnetic potentials and gauge invariance<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                3. Scalar and vector potential for an electron in circular motion\r\n
                                                                                    \r\n
                                                                                  1. Doppler effect, revisited<\/li>\r\n
                                                                                  2. Model for a charge in circular motion<\/li>\r\n
                                                                                  3. Vector-potential harmonics<\/li>\r\n
                                                                                  4. Green functions for scalar and vector potentials<\/li>\r\n
                                                                                  5. Electric-field and magnetic-field harmonics<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                  6. Spectrum of synchrotron radiation by electrons in circular motion\r\n
                                                                                      \r\n
                                                                                    1. Far-field approximation<\/li>\r\n
                                                                                    2. Far-field expressions for harmonics of electromagnetic potentials and fields<\/li>\r\n
                                                                                    3. Poynting vector and electromagnetic energy density<\/li>\r\n
                                                                                    4. Far-field expressions for radiated Poynting vector and energy density: general case<\/li>\r\n
                                                                                    5. Power radiated by a charge in circular motion<\/li>\r\n
                                                                                    6. Large-order approximation for the spectral density<\/li>\r\n
                                                                                    7. Spatial and temporal structure<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                    8. Quantum optics of synchrotron light<\/strong>\r\n
                                                                                        \r\n
                                                                                      1. What is a photon?<\/li>\r\n
                                                                                      2. First answer to \u2018What is a photon?\u2019<\/li>\r\n
                                                                                      3. Second answer to \u2018What is a photon?\u2019\r\n
                                                                                          \r\n
                                                                                        1. Photons via the Poynting vector<\/li>\r\n
                                                                                        2. Poisson photon statistics, part one<\/li>\r\n
                                                                                        3. An illustrative numerical model<\/li>\r\n
                                                                                        4. Poisson photon statistics, part two<\/li>\r\n
                                                                                        5. Some omissions<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                        6. Interlude<\/li>\r\n
                                                                                        7. Third answer to \u2018What is a photon?\u2019\r\n
                                                                                            \r\n
                                                                                          1. Single-mode and multi-mode photon states<\/li>\r\n
                                                                                          2. Localisation<\/li>\r\n
                                                                                          3. Single-photon and multi-photon states<\/li>\r\n
                                                                                          4. Entanglement<\/li>\r\n
                                                                                          5. Photon detection and the intensity operator<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                          6. Coherent states of the photon field\r\n
                                                                                              \r\n
                                                                                            1. Coherent states: properties and definition<\/li>\r\n
                                                                                            2. Coherent states: number-state expansion<\/li>\r\n
                                                                                            3. Coherent states: Poisson statistics<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                            4. Photon radiation from prescribed classical currents\r\n
                                                                                                \r\n
                                                                                              1. Coherent-state displacement operator<\/li>\r\n
                                                                                              2. Coherent states from prescribed currents, part one<\/li>\r\n
                                                                                              3. Interlude: Schr\u00f6dinger, Heisenberg, and interaction pictures<\/li>\r\n
                                                                                              4. Coherent states from prescribed currents, part two<\/li>\r\n
                                                                                              5. Looping back, from photons to classical electrodynamics<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                              6. Quantum optics using synchrotron light\r\n
                                                                                                  \r\n
                                                                                                1. On the plausibility of quantum optics using synchrotron light<\/li>\r\n
                                                                                                2. Interlude<\/li>\r\n
                                                                                                3. Photon beam splitters<\/li>\r\n
                                                                                                4. Parametric down-conversion<\/li>\r\n
                                                                                                5. Synchrotron-light pseudo-temperature and the Unruh effect<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                                6. Some omissions<\/li>\r\n
                                                                                                7. Hierarchy of physical models for light<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                                8. Epilogue<\/strong>\r\n
                                                                                                    \r\n
                                                                                                  1. Introduction<\/li>\r\n
                                                                                                  2. Synchrotron radiation as a connecting thread<\/li>\r\n
                                                                                                  3. Recurring themes<\/li>\r\n
                                                                                                  4. Omissions<\/li>\r\n
                                                                                                  5. Valediction<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n
                                                                                                      \r\n
                                                                                                    1. Bessel-function sums and trigonometric integrals<\/strong>\r\n
                                                                                                        \r\n
                                                                                                      1. Two infinite Bessel-function sums\r\n
                                                                                                          \r\n
                                                                                                        1. Bessel\u2019s differential equation<\/li>\r\n
                                                                                                        2. Normal form of Bessel\u2019s equation<\/li>\r\n
                                                                                                        3. Differential equation for [J_n(x)]^2<\/span><\/li>\r\n
                                                                                                        4. Zeroth Bessel sum<\/li>\r\n
                                                                                                        5. First Bessel sum<\/li>\r\n
                                                                                                        6. Second Bessel sum<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                                        7. Two trigonometric definite integrals\r\n
                                                                                                            \r\n
                                                                                                          1. Trigonometric integral \\mathcal{I}_1<\/span><\/li>\r\n
                                                                                                          2. Trigonometric integral \\mathcal{I}_2<\/span><\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                                          3. Planck\u2019s radiation law and radiometric quantities<\/strong>\r\n
                                                                                                              \r\n
                                                                                                            1. Rayleigh\u2013Jeans law<\/li>\r\n
                                                                                                            2. Planck\u2019s law<\/li>\r\n
                                                                                                            3. Radiometric quantities and different formulations of Planck\u2019s law<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                                            4. Schott\u2019s pioneering contributions to synchrotron light<\/strong>\r\n
                                                                                                                \r\n
                                                                                                              1. Contributions to the physics of synchrotron light<\/li>\r\n
                                                                                                              2. Upheavals of physical theory in the early 1900s<\/li>\r\n
                                                                                                              3. The enduring success of Schott\u2019s failure<\/li>\r\n
                                                                                                              4. Influence of modern computing devices<\/li>\r\n<\/ol>\r\n<\/li>\r\n
                                                                                                              5. Pad\u00e9 approximant for maximum-emission harmonic<\/strong>\r\n
                                                                                                                  \r\n
                                                                                                                1. Pad\u00e9 approximant and Taylor series<\/li>\r\n
                                                                                                                2. Taylor expansion of g(\\tau)<\/span><\/li>\r\n
                                                                                                                3. Relation between Taylor and Pad\u00e9 coefficients of g(\\tau)<\/span><\/li>\r\n
                                                                                                                4. Final remarks<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n","protected":false},"excerpt":{"rendered":"

                                                                                                                  Prologue Let the journey begin Overview of the content Multiple paths through the book Resources, units, and conventions Introduction to special relativity Light and time Inertial frames and the Lorentz transformations Consequences of the Lorentz transformations Relativity of simultaneity Length contraction and time dilation Non-relativistic limit Transformation of velocities and accelerations Relativistic aberration and Doppler […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"off","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-537","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/537","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=537"}],"version-history":[{"count":22,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/537\/revisions"}],"predecessor-version":[{"id":624,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/537\/revisions\/624"}],"wp:attachment":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}