Abstract
The concept of r.m.s. emittance is extended to the case of several degrees of freedom that are coupled. That multi-dimensional 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 {beta}-functions of the beam envelope. On the contrary of an 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. (author) 4 refs.
Citation Formats
Buon, J.
Multi-dimensional beam emittance and {beta}-functions.
France: N. p.,
1993.
Web.
Buon, J.
Multi-dimensional beam emittance and {beta}-functions.
France.
Buon, J.
1993.
"Multi-dimensional beam emittance and {beta}-functions."
France.
@misc{etde_10138099,
title = {Multi-dimensional beam emittance and {beta}-functions}
author = {Buon, J}
abstractNote = {The concept of r.m.s. emittance is extended to the case of several degrees of freedom that are coupled. That multi-dimensional 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 {beta}-functions of the beam envelope. On the contrary of an 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. (author) 4 refs.}
place = {France}
year = {1993}
month = {May}
}
title = {Multi-dimensional beam emittance and {beta}-functions}
author = {Buon, J}
abstractNote = {The concept of r.m.s. emittance is extended to the case of several degrees of freedom that are coupled. That multi-dimensional 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 {beta}-functions of the beam envelope. On the contrary of an 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. (author) 4 refs.}
place = {France}
year = {1993}
month = {May}
}