PUBLISHED in JINST at October 21, 2010
ABSTRACT: Presently, there are two most frequently used parameterezations of linear x−y coupled
motion used in the accelerator physics. They are the Edwards-Teng and Mais-Ripken parameterizations.
The article is devoted to an analysis of close relationship between the two representations,
thus adding a clarity to their physical meaning. It also discusses the relationship between the eigenvectors,
the beta-functions, second order moments and the bilinear form representing the particle
ellipsoid in the 4D phase space. Then, it considers a further development of Mais-Ripken parameteresation
where the particle motion is described by 10 parameters: four beta-functions, four
alpha-functions and two betatron phase advances. In comparison with Edwards-Teng parameterization
the chosen parametrization has an advantage that it works equally well for analysis of coupled
betatron motion in circular accelerators and in transfer lines. Considered relationship between second
order moments, eigen-vectors and beta-functions can be useful in interpreting tracking results
and experimental data. As an example, the developed formalism is applied to the FNAL electron
cooler and Derbenev’s vertex-to-plane adapter.