DocumentCode
1964612
Title
Multi-dimensional beam emittance and β-functions
Author
Buoa, J.
Author_Institution
Lab. de l´Accel. Lineaire, Univ. de Paris-Sud, Orsay
fYear
1993
fDate
17-20 May 1993
Firstpage
469
Abstract
The concept of r.m.s. emittance is extended to the case of several degrees of freedom that are coupled. The multidimensional emittance is lower than the product of the emittances attached to each degree of freedom, but is conserved in a linear motion. An envelope-hyperellipsoid is introduced to define the p-functions of the beam envelope. On the contrary for one-degree of freedom motion, it is emphasized that these envelope functions differ from the amplitude functions of the normal modes of motion as a result of the difference between the Liouville and Lagrange invariants
Keywords
particle beam diagnostics; statistical analysis; β-functions; Lagrange invariant; Liouville invariant; beam envelope; envelope-hyperellipsoid; multidimensional beam emittance; p-functions; rms emittance; Covariance matrix; Eigenvalues and eigenfunctions; Extraterrestrial measurements; Multidimensional systems; Optical coupling; Phase measurement; Symmetric matrices; Volume measurement;
fLanguage
English
Publisher
ieee
Conference_Titel
Particle Accelerator Conference, 1993., Proceedings of the 1993
Conference_Location
Washington, DC
Print_ISBN
0-7803-1203-1
Type
conf
DOI
10.1109/PAC.1993.308879
Filename
308879
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