Computing Eigen-Emittances from Tracking Data

TL;DR

This paper introduces a new iterative method to accurately compute eigen-emittances from tracking data in nonlinear systems by suppressing tail contributions, applicable to complex coupled beam dynamics.

Contribution

A novel iterative algorithm for extracting eigen-emittances from phase space data that effectively suppresses tail effects in nonlinear, coupled systems.

Findings

Efficient suppression of tail contributions in covariance matrices.

Successful application to 6D muon ionization cooling data.

Retrieval of coupled optics functions from the sigma matrix.

Abstract

In a strongly nonlinear system the particle distribution in the phase space may develop long tails which contribution to the covariance (sigma) matrix should be suppressed for a correct estimate of the beam emittance. A method is offered based on Gaussian approximation of the original particle distribution in the phase space (Klimontovich distribution) which leads to an equation for the sigma matrix which provides efficient suppression of the tails and cannot be obtained by introducing weights. This equation is easily solved by iterations in the multi-dimensional case. It is also shown how the eigen-emittances and coupled optics functions can be retrieved from the sigma matrix in a strongly coupled system. Finally, the developed algorithm is applied to 6D ionization cooling of muons in HFOFO channel.