Phase Space Reconstruction from Accelerator Beam Measurements Using Neural Networks and Differentiable Simulations

Characterizing the phase space distribution of particle beams in accelerators is a central part of understanding beam dynamics and improving accelerator performance. However, conventional analysis methods either use simplifying assumptions or require specialized diagnostics to infer high-dimensional ($>2\mathrm{D}$) 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 limited number of measurements from 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.