By Harald Klingbeil, Ulrich Laier, Dieter Lens (auth.)
ISBN-10: 3319071874
ISBN-13: 9783319071879
ISBN-10: 3319071882
ISBN-13: 9783319071886
This course-tested textual content is a perfect place to begin for engineers and physicists coming into the sphere of particle accelerators. the basics are comprehensively brought, derivations of crucial effects are supplied and a constant notation sort used in the course of the booklet permits readers to speedy familiarize themselves with the sector, supplying an effective theoretical foundation for extra studies.
Emphasis is put on the fundamental good points of the longitudinal movement of charged particle beams, including the corresponding RF iteration and tool amplification units for synchrotron and garage ring structures. specifically, electric engineering features akin to closed-loop keep watch over of method elements are discussed.
The ebook additionally bargains a priceless source for graduate scholars in physics, electronics engineering, or arithmetic trying to find an introductory and self-contained textual content on accelerator physics.
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Extra info for Theoretical Foundations of Synchrotron and Storage Ring RF Systems
Example text
E jn' d' H. t. T e dx: T =2 Due to ! D 2T , the last exponential function equals 1. t dt T =2 holds. 3) 0 instead of Eq. 2). 2 Spectrum of a Dirac Comb In this book, the Dirac delta distribution is used in a heuristic way without the foundations of distribution theory. Therefore, the reader should be aware that the results presented still have to be proven mathematically. x0 /; even though it does not have any meaning in the scope of classical analysis. 1 Fourier Analysis and Application to Beam Signals 11 which is called Dirac comb.
1]). In synchrotrons and storage rings, the particles will be located inside the conducting beam pipe during those time intervals in which the field has the wrong polarity. The electric field may be generated in a so-called ceramic gap. Such a ceramic gap is a short ceramic tube that interrupts the metallic beam pipe. Since its material is nonconducting, a voltage can be induced even though the beam pipe is still evacuated. 1 shows the main elements (cf. [2] for further reading) of a synchrotron or storage ring in a schematic way: • A metallic beam pipe is evacuated so that flying particles will not hit gas molecules.
The voltage VR that is required after one revolution usually does not differ much from the voltage VR in the previous revolution. This is why Fig. 2 shows almost the same voltage after the revolution time TR . The voltage VR is determined by VR D VO sin 'R ; where 'R is the reference phase or the synchronous phase. Please note that in LINACs, the synchronous phase is usually defined in a different way, namely with respect to the crest instead of the zero crossing of the RF voltage. As the figure shows, it is not necessary that the RF frequency fRF D 1=TRF equal the revolution frequency fR D 1=TR for the same voltage VR as in the previous revolution affecting the particle.
Theoretical Foundations of Synchrotron and Storage Ring RF Systems by Harald Klingbeil, Ulrich Laier, Dieter Lens (auth.)
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