Title :
Multi-dimensional beam emittance and β-functions
Author_Institution :
Lab. de l´Accel. Lineaire, Univ. de Paris-Sud, Orsay
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;
Conference_Titel :
Particle Accelerator Conference, 1993., Proceedings of the 1993
Conference_Location :
Washington, DC
Print_ISBN :
0-7803-1203-1
DOI :
10.1109/PAC.1993.308879
