Characterizing the phase space distribution of particle beams in accelerators
is a central part of accelerator understanding and performance optimization.
However, conventional reconstruction-based techniques either use simplifying
assumptions or require specialized diagnostics to infer high-dimensional (>
2D) beam properties. In this Letter, we introduce a general-purpose algorithm
that combines neural networks with differentiable particle tracking to
efficiently reconstruct high-dimensional phase space distributions without
using specialized beam diagnostics or beam manipulations. We demonstrate that
our algorithm accurately reconstructs detailed 4D phase space distributions
with corresponding confidence intervals in both simulation and experiment using
a single focusing quadrupole and diagnostic screen. This technique allows for
the measurement of multiple correlated phase spaces simultaneously, which will
enable simplified 6D phase space distribution reconstructions in the future