Advertisement

Solutions to Exercises

  • Michiko G. Minty
  • Frank Zimmermann
Open Access
Chapter
Part of the Particle Acceleration and Detection book series (PARTICLE)

Abstract

From (1.12) at a fixed location s we can write \(x = \sqrt {2{I_x}{\beta _x}} \cos {\phi _x},\) where φx includes the initial phase φ0 We then have
$$\begin{array}{*{20}{c}}{{{ \in }_{x}} = \frac{{\left\langle {{{x}^{2}}\left( s \right)} \right\rangle }}{{{{\beta }_{x}}\left( s \right)}}} \\{ = \int {d{{\phi }_{x}}d{{I}_{x}}2{{I}_{x}}{{{\cos }}^{2}}{{\phi }_{x}}\rho \left( {{{I}_{x}},{{\phi }_{x}}} \right)} } \\{ = \int {d{{\phi }_{x}}d{{I}_{x}}2{{I}_{x}}{{{\cos }}^{2}}{{\phi }_{x}}\rho \left( {{{I}_{x}}} \right)\frac{1}{{2\pi }}} } \\{ = \int {d{{I}_{x}}{{I}_{x}}\rho \left( {{{I}_{x}}} \right) = \left\langle {{{I}_{x}}} \right\rangle .} } \\\end{array}$$
(12.1)

Keywords

Bunch Length Beam Position Monitor Equilibrium Emittance Beam Lifetime Synchronous Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    R. Assmann, A. Chao: Dispersion in the Presence of Strong Transverse Wake- fields. In: Proc. PAC 97, Vancouver, 1997 (IEEE, Piscataway 1998) P. 1523Google Scholar

Copyright information

© The Author(s) 2003

Open Access This chapter was originally published with exclusive rights reserved by the Publisher in 2003 and was licensed as an open access publication in November 2019 under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license if changes were made.

The images or other third party material in this chapter may be included in the chapter’s Creative Commons license, unless indicated otherwise in a credit line to the material or in the Correction Note appended to the chapter. For details on rights and licenses please read the Correction  https://doi.org/10.1007/978-3-662-08581-3_13. If material is not included in the chapter’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Authors and Affiliations

  • Michiko G. Minty
    • 1
  • Frank Zimmermann
    • 2
  1. 1.DESY - MDEHamburgGermany
  2. 2.AB Division, ABP GroupCERNGeneva 23Switzerland

Personalised recommendations