High-dimensional maximum-entropy phase space tomography using normalizing flows

TL;DR

This paper introduces a novel method using normalizing flows to perform maximum-entropy tomography of six-dimensional phase space distributions in particle accelerators, enabling accurate reconstruction from limited measurements.

Contribution

It extends maximum-entropy tomography to six-dimensional phase space using invertible generative models, improving reconstruction accuracy and efficiency.

Findings

Consistent with exact 2D maximum-entropy solutions

Able to fit complex 6D distributions

Performs well with large measurement sets in reasonable time

Abstract

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage normalizing flows -- invertible generative models -- to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time.