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

R. Roussel, A. Edelen, C. Mayes, D. Ratner, J. P. Gonzalez-Aguilera, S. Kim, E. Wisniewski, and J. Power

Phys. Rev. Lett. 130, 145001 – Published 5 April 2023

Abstract

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 ( $> 2 D$ ) 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.

Received 9 September 2022
Accepted 3 March 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.145001

Physics Subject Headings (PhySH)

Beam code development & simulation techniques Beam diagnostics

Artificial neural networks

Machine learning

Accelerators & Beams

Authors & Affiliations

R. Roussel ^*, A. Edelen, C. Mayes , and D. Ratner

SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA

J. P. Gonzalez-Aguilera

Department of Physics, University of Chicago, Chicago, Illinois 60637, USA

S. Kim , E. Wisniewski, and J. Power

Argonne National Laboratory, Argonne, Illinois 60439, USA

^*rroussel@slac.stanford.edu

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Vol. 130, Iss. 14 — 7 April 2023

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Images

Figure 1
Description of our approach for reconstructing phase space beam distributions. First, randomly generated samples drawn from a Multivariate normal distribution are transformed via a neural network, parametrized by $θ_{t}$ , into a proposed initial distribution. This distribution is then transported through a differentiable accelerator simulation of the tomographic beam line. The quadrupole is scanned to produce a series of images on the screen, both in simulation and on the operating accelerator. The images produced both from the simulation $Q_{n}^{(i, j)}$ and the accelerator $R_{n}^{(i, j)}$ are then compared with a custom loss function, which attempts to maximize the entropy of the proposal distribution, constrained on accurately reproducing experimental measurements. This loss function is then used to update the neural network parameters $θ_{t} \to θ_{t + 1}$ via gradient descent. The neural network transformation that minimizes the loss function generates the beam distribution that has the highest likelihood of matching the real initial beam distribution.
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Figure 2
Comparisons between the synthetic and reconstructed beam probability distributions using our method. (a)–(e) Plots of the mean predicted phase space density projections in 4D transverse phase space. Contours that denote the 50th (black) and 95th (white) percentiles of the synthetic ground truth (dashed) and reconstructed (solid) distributions. (f)–(j) Plots of the predicted phase space density uncertainty.
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Figure 3
Evolution of the proposal distribution during training on synthetic data. (a) Learning rate schedule for snapshot ensembling. (b) Second order moments of beam reconstruction during training for each phase space coordinate. Dashed lines denote ground truth values. Vertical lines denote snapshot locations after burn-in period.
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Figure 4
Reconstruction results from experimental measurements at AWA. Comparison between measured and predicted beam centroids (a) and second-order beam moments (b) on the diagnostic screen as a function of geometric quadrupole focusing strength ( $k$ ). Points denote training samples and crosses denote test samples. Dashed line shows second order polynomial fit of training data and solid line shows predictions from image-based phase space reconstruction. We also compare (c)–(h) screen images and reconstructed predictions for a subset of quadrupole strengths. Contours denote the 50th (black) and 95th (white) percentiles of the measured (dashed) and predicted (solid) screen distributions. Orange borders denote test samples.
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