  Next-generation accelerator concepts which hinge on the precise shaping of
beam distributions, demand equally precise diagnostic methods capable of
reconstructing beam distributions within 6-dimensional position-momentum
spaces. However, the characterization of intricate features within
6-dimensional beam distributions using conventional diagnostic techniques
necessitates hundreds of measurements, using many hours of valuable beam time.
Novel phase space reconstruction techniques are needed to substantially reduce
the number of measurements required to reconstruct detailed, high-dimensional
beam features in order to resolve complex beam phenomena, and as feedback in
precision beam shaping applications. In this study, we present a novel approach
to reconstructing detailed 6-dimensional phase space distributions from
experimental measurements using generative machine learning and differentiable
beam dynamics simulations. We demonstrate that for a collection of synthetic
beam distribution test cases that this approach can be used to resolve
6-dimensional phase space distributions using basic beam manipulations and as
few as 20 2-dimensional measurements of the beam profile, without the need for
prior data collection or model training. We also demonstrate an application of
the reconstruction method in an experimental setting at the Argonne Wakefield
Accelerator, where it is able to reconstruct the beam distribution and
accurately predict previously unseen measurements 75x faster than previous
methods.
