A General Slice Moment Decomposition of RMS Beam Emittance

TL;DR

This paper presents a comprehensive mathematical framework for decomposing the RMS beam emittance into meaningful slice contributions, aiding in understanding and reconstructing beam properties in phase space.

Contribution

It introduces a general slice moment decomposition formalism for RMS beam emittance, linking projected and slice beam quantities with geometric interpretation.

Findings

Decomposition of RMS emittance into four nonnegative slice contributions.

Method to reconstruct beam moments from subpopulation moments.

Insights into slice and interslice effects on emittance growth.

Abstract

The square of the horizontal projected (rms) beam emittance is expressed as the sum of four nonnegative contributions, each described using the slice moments of the beam and possessing a natural interpretation in terms of the geometrical properties of the beam in the six-dimensional phase space. The mathematical formalism describing the relationships between projected beam quantities and slice beam quantities is reviewed. The results may be used to reconstruct the moments and emittances of the beam from the moments of its subpopulations, as well as to isolate and better understand a variety of slice and interslice dynamical contributions to the projected beam emittance growth.