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    <subfield code="a">Theoretical framework and Thomson backscattering sources.</subfield>
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    <subfield code="a">1. Introduction -- 1.1. The Larmor formula and a classical description of Thomson scattering -- 1.2. Elements of special relativity : inertial frames and Lorentz transformations -- 1.3. Relativistic kinematics and dynamics -- 1.4. The relativistic kinematics of Compton scattering -- 1.5. The kinematics of inverse Compton scattering -- 1.6. The relativistic Doppler shift -- 1.7. Maxwell's equations and special relativity -- 1.8. Comments and exercises</subfield>
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    <subfield code="a">2. Thomson backscattering radiation -- 2.1. Compton scattering and Thomson scattering -- 2.2. Electron dynamics under intense wave excitation -- 2.3. Retarded potentials -- 2.4. Thomson backscattering radiation -- 2.5. Analogy with the emission in magnetic undulators and the Fermi-Weizs&#xFFFD;acker-Williams approximation -- 2.6. Comments and exercises</subfield>
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    <subfield code="a">4. Optical beam transport -- 4.1. Introduction -- 4.2. The ray matrix method -- 4.3. Matrix optics and lens images -- 4.4. A phase-space formalism for optical wave transport -- 4.5. Gaussian beams and the formal quantum theory of light rays -- 4.6. Comments and exercises</subfield>
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    <subfield code="a">5. Beam-beam interactions -- 5.1. Introduction -- 5.2. Spectral broadening in CBS devices : on-axis contributions from energy spread and emittance -- 5.3. Spectral broadening in CBS devices : off-axis contributions from the divergence of scattered photons -- 5.4. A toy model of a real CBS radiation facility -- 5.5. Comments and exercises</subfield>
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    <subfield code="a">6. CBS sources -- 6.1. Introduction -- 6.2. Further comments on the bandwidth of CBS sources -- 6.3. Laser systems in operational CBS sources -- 6.4. Electron accelerators in operational CBS sources -- 6.5. A comparison between theory and experiment -- 6.6. Applications and the costs of CBS sources -- 6.7. Comments and exercises.</subfield>
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    <subfield code="a">The top-performing x-ray and gamma ray sources are synchrotrons and free-electron lasers, which require large investment. Consequently, more affordable and accessible platforms are required for research and applications based on x-rays and gamma rays. Compton backscattering (CBS) is a subset of Thomson and Compton scattering and is the mechanism through which high energy electrons interacting with low energy photons transfer part of their energy to the photons. Accordingly, an infrared photon can e.g. be 'transformed' into an x-ray or gamma ray, in a CBS process. Monochromatic and ultrashort x-ray and gamma ray sources are challenging to make; however, CBS provides a compact and accessible platform for this purpose. Aimed at those entering the field for the first time, this first volume provides a background in classical electromagnetism and relativity to facilitate the understanding of Thomson and Compton particle scattering. The general scattering theories are presented, along with laser and electron beam transport and optics. This first volume should equip the reader with the necessary background and insight to understand more advanced topics in Volume 2.</subfield>
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    <subfield code="a">Dr. Alessandro Curcio obtained a PhD at the School of Accelerator Physics at the University of Rome La Sapienza, before winning a Research Fellowship at the CERN Linear Accelerator for Research. Afterwards, he joined the National Polish Synchrotron SOLARIS as Section Leader in beam diagnostics and instrumentation. Later, he was Senior Scientist at CLPU and, currently, he is Senior Scientist at the Italian National Institute for Nuclear Physics (INFN). His research interests have always been particle acceleration, innovative radiation sources and particle-matter interactions for applications. Giuseppe Dattoli is an ENEA Researcher and has been involved in different research projects, including high-energy accelerators, free-electron lasers, and applied mathematics networks since 1979. Dr. Dattoli has taught in Italian and overseas universities and has received the FEL Prize Award for his outstanding achievements in the field. Emanuele Di Palma received the Laurea degree in mathematics from La Sapienza University of Rome Italy, in 1996, a master's degree in 'Fusion Energy: Science and Engineering' from Tor Vergata University of Rome Italy, in 2013 and a PhD degree in 'Fusion Science and Engineering' from the University of Padova Italy, in 2018. His research interests are in the fields of physics and applications of intense electron beams, computer-aided design and development of CARM device for various novel applications such as in space solar energy harvesting, in fusion energy for high-field Tokamaks and in biomedical applications to develop compact device for nuclear diagnostics.</subfield>
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