By Levi Schächter
The major subject of this e-book is the interplay of electrons with electromagnetic waves within the presence of periodic and quasi-periodic constructions in vacuum, in view of purposes within the layout and operation of particle accelerators.
The first a part of the e-book is worried with the textbook-like presentation of the fundamental fabric, particularly reviewing undemanding electromagnetic phenomena and electron dynamics. the second one a part of the booklet describes the present types for beam-wave interactions with periodic and quasi-periodic constructions. this is often the foundation for introducing, within the final a part of the publication, a few particle and radiation assets that leisure on those ideas, particularly the free-electron laser, wake-field acceleration schemes and several other complicated particle accelerator concepts.
This moment variation brings this primary textual content up to date in view of the big advances which have been revamped the decade because the first version was once released. All chapters, in addition to the bibliography, were considerably revised and prolonged, and the variety of end-of-chapter workouts has been extra elevated to reinforce this book’s usefulness for instructing really expert graduate classes.
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Extra info for Beam-Wave Interaction in Periodic and Quasi-Periodic Structures
Beam quality, which is associated with fluctuations in the energy around the average value, is another classification criterion. This topic is addressed in Sect. 4 and it is of particular interest in accelerators and in free electron lasers. In the former because the electrons have to travel very long distances and ultimately have to be focused with great precision, therefore both the transverse and longitudinal momentum are important. In free electron lasers, this parameter is important as we go up in frequency and in fact beam quality is one of the major limitations of today’s free electron lasers – at least with regard to optical or shorter wavelengths.
4 Choice and Organization of the Material With such a variety of concepts and paradigms we owe the reader an explanation of how the material was selected, and why we chose to present one topic, whereas another, which might be as important, was left out. The principle that directed me was to have a coherent and thorough presentation of the beam-wave interaction in a few modern devices with most mathematical details that enable a simple description of their operation. From the very beginning, it was clear that it is virtually impossible to meet the requirement of detailed presentation and encompass the whole variety of sources and interaction schemes, discussed above, in one reasonably-sized volume.
19) we obtain Az ðr; z; tÞ ¼ À em0 ð2pÞ2 ! 21) where b ¼ v0 =c and g ¼ ½1 À b2 À1=2 . Using the Lorentz gauge one can determine the scalar electric potential Fðr; z; tÞ ¼ À e 1 1 4pe0 v0 p ! 22) This expression indicates that the field associated with a moving charge is a superposition of cylindrical evanescent waves (for large arguments thepmodiﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ fied Bessel function decays exponentially following K0 ðxÞ ’ expðÀxÞ p=2x Abramowitz and Stegun 1968, p. 378). 2. When scattered by periodic structures, the evanescent waves can be “converted” into propagating waves as we shall see when the Smith-Purcell effect will be discussed in Chap.