By Levi Schächter
The major subject of this booklet is the interplay of electrons with electromagnetic waves within the presence of periodic and quasi-periodic buildings in vacuum, in view of purposes within the layout and operation of particle accelerators.
The first a part of the publication is worried 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 versions for beam-wave interactions with periodic and quasi-periodic buildings. this is often the foundation for introducing, within the final a part of the booklet, a few particle and radiation assets that relaxation on those rules, specifically the free-electron laser, wake-field acceleration schemes and several other complex particle accelerator concepts.
This moment version brings this basic textual content updated in view of the big advances which were 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 extra elevated to augment this book’s usefulness for educating really expert graduate classes.
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Extra info for Beam-Wave Interaction in Periodic and Quasi-Periodic Structures
2 Boundary Conditions At sharp discontinuities the differential operators are not defined therefore an integral approach has to be adopted. 1 Maxwell’s Equations 25 solved in each region separately, away of the discontinuity, and the question that needs to be addressed is the relation between the various field components from both sides of a discontinuity. Consider two regions (subscripts 1 and 2) separated by a surface which is locally characterized by its local normal n. 16) Here Js is the surface current density and rs is the surface charge density.
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. Energy conversion efficiency brings us to another possible way of classification, based on whether the initial beam is uniform or pre-bunched.
This current distribution excites the z component of the magnetic vector potential that in turn satisfies ! 17) where az ðr; k; oÞ satisfies ! 19) where K0 ðxÞ is the zero order modified Bessel function of the second kind. In order to determine the amplitude Aþ there are two ways to proceed: (1) calculate the azimuthal magnetic field and then impose the boundary conditions at r ¼ 0. 18) from r ¼ 0 to r ¼ d ! 0. 3 Guided Waves 37 subsequently. For small arguments the modified Bessel function behaves as K0 ðxÞ ’ À lnðxÞ (see Abramowitz and Stegun 1968, p.