Transverse Beam Emittance Measurement and Control

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


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
$${\varepsilon _{xyz}} = \det \Sigma _{beam}^{xyz}.$$
Considering now only the horizontal plane, the corresponding 2-dimensional horizontal emittance is obtained from
$${\varepsilon _x} = \sqrt {\left\langle {{x^2}} \right\rangle \left\langle {{{x'}^2}} \right\rangle- {{\left\langle {xx'} \right\rangle }^2}} ,$$
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.


Emittance Measurement Phase Advance Beam Emittance Partition Number Emittance Growth 
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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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