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Transverse Beam Emittance Measurement and Control

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

Abstract

The beam emittance xyz represents the volume of the beam occupied in the six dimensional phase space (x, x′, y, y′, φ, δ), where x and y are the transverse positions, x′ and y′ are the transverse angles, φ is the time-like variable representing the relative phase of the beam, and δ is the relative beam momentum error. Using the notation of the beam matrix Σbeam introduced in Chap. 1, the 6-dimensional emittance is
$${\varepsilon _{xyz}} = \det \Sigma _{beam}^{xyz}.$$
(4.1)
Considering now only the horizontal plane, the corresponding 2-dimensional horizontal emittance is obtained from
$${\varepsilon _x} = \sqrt {\left\langle {{x^2}} \right\rangle \left\langle {{{x'}^2}} \right\rangle- {{\left\langle {xx'} \right\rangle }^2}} ,$$
(4.2)
where the first moments have been subtracted, and the average (〈…〉) is taken over the distribution function of the beam; recall also (1.27–1.29). An analoguous expression holds for the vertical plane. For a coupled system, the general form of (4.1) must be taken.

Keywords

Emittance Measurement Phase Advance Beam Emittance Partition Number Emittance Growth 
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.

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© 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.

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Authors and Affiliations

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

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