Beam-Wave Interaction in Periodic and Quasi-Periodic by Levi Schächter

By Levi Schächter

The major subject matter of this booklet 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 publication is anxious with the textbook-like presentation of the fundamental fabric, specifically reviewing straightforward electromagnetic phenomena and electron dynamics. the second one a part of the e-book describes the present types for beam-wave interactions with periodic and quasi-periodic constructions. this can be the foundation for introducing, within the final a part of the e-book, a couple of particle and radiation resources that leisure on those ideas, specifically the free-electron laser, wake-field acceleration schemes and several complex particle accelerator concepts.

This moment variation brings this primary textual content up to date in view of the big advances which have been remodeled 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 additional elevated to reinforce this book’s usefulness for educating really expert graduate courses. 

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B) Propagation of a transverse magnetic (TM) mode in a circular waveguide - see Sect. 2. (c) Propagation of transverse electric (TE) mode in rectangular waveguide - Sect. 4 1 Jz(r,w) = 1 - b(r) . 2a illustrates schematically the system under consideration. 3) and A+ is determined by the discontinuity at r the close vicinity of r = 0, - Az(r,w) ] [ rdd r r=O+ = 0. , H~2)(x) ~ - j In(x)2/7r [Abramowitz and Stegun (1968) p. Lo/4. 5) 40 2. Elementary Electromagnetic Phenomena respectively. 6) and the total power radiated is P = Re [21frdSr (r)] = ~ (~d) 1}O/2 .

11 in the book by Haus and Melcher (1989). fJ(r)] . 25) F(r, w) is called the phasor associated with the function F(r, t). To illustrate the use of this notation, Maxwell's equations read V' x E+jwB = 0, V' x ii - jwD V'·D=e, V'·B=O. 29) The main advantage of this notation is now evident since the differential operator a/at was replaced by a simple algebric operator jw. 2. 5 Complex Poynting's Theorem The phasor notation, as introduced above, cannot be directly applied to Poynting's theorem since all quantities are quadratic in the electromagnetic field.

2 Simple Wave Phenomena The wave equation developed in the previous section for the scalar electric potential and the three components of the magnetic vector potential will be next solved for several simple cases. A few of the examples presented here will be used later in this text to develop models which in turn enable the investigation of complex structures. In the context of these examples we formulate the radiation condition. 1 Simple Propagating Waves With the source terms, constitutive relations and boundary conditions determined, one can proceed towards solution of a few simple wave phenomena.

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