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Two-stage Convolutional Neural Network for six-dimensional phase space reconstruction

Sayantan Mukherjee, Masao Kuriki, Zachary John Liptak, Hitoshi Hayano, Masakazu Kurata, Nobuhiro Terunuma, Toshiyuki Okugi, Yasuchika Yamamoto

TL;DR

A two-stage convolutional neural network (CNN) is developed that reconstructs the 6D phase space from only sixteen transverse $x-y$ screen images taken at a place with dispersion by different phase space rotation angles, enabling the provision of a more practical 6D phase space measurement method.

Abstract

In particle accelerators, full knowledge of the six-dimensional (6D) beam phase space is crucial but difficult to obtain with conventional beam diagnostics. We develop a two-stage convolutional neural network (CNN) that reconstructs the 6D phase space from only sixteen transverse $x-y$ screen images taken at a place with dispersion by different phase space rotation angles. The model is trained with simulation data of KEK-Accelerator Test Facility (ATF) injector with ASTRA. The real-space images in the chicane orbit at the KEK-ATF injector were acquired by varying the RF phase of the RF electron gun and the solenoid magnetic field. From these data, we reconstructed the 6D phase space distribution at the cathode surface and visualized it as 15 two-dimensional images covering all pairwise coordinate combinations. The time width and spatial spread of the electron beam at the cathode showed values consistent with the measured values at KEK-ATF. Compared to existing 6D beam imaging measurement techniques such as tomography, it significantly reduces measurement time and required computational resources, enabling the provision of a more practical 6D phase space measurement method.

Two-stage Convolutional Neural Network for six-dimensional phase space reconstruction

TL;DR

A two-stage convolutional neural network (CNN) is developed that reconstructs the 6D phase space from only sixteen transverse screen images taken at a place with dispersion by different phase space rotation angles, enabling the provision of a more practical 6D phase space measurement method.

Abstract

In particle accelerators, full knowledge of the six-dimensional (6D) beam phase space is crucial but difficult to obtain with conventional beam diagnostics. We develop a two-stage convolutional neural network (CNN) that reconstructs the 6D phase space from only sixteen transverse screen images taken at a place with dispersion by different phase space rotation angles. The model is trained with simulation data of KEK-Accelerator Test Facility (ATF) injector with ASTRA. The real-space images in the chicane orbit at the KEK-ATF injector were acquired by varying the RF phase of the RF electron gun and the solenoid magnetic field. From these data, we reconstructed the 6D phase space distribution at the cathode surface and visualized it as 15 two-dimensional images covering all pairwise coordinate combinations. The time width and spatial spread of the electron beam at the cathode showed values consistent with the measured values at KEK-ATF. Compared to existing 6D beam imaging measurement techniques such as tomography, it significantly reduces measurement time and required computational resources, enabling the provision of a more practical 6D phase space measurement method.
Paper Structure (22 sections, 15 equations, 26 figures, 2 tables)

This paper contains 22 sections, 15 equations, 26 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Principles of phase-space rotation and measurement for beam reconstruction
  3. Transverse phase-space rotation
  4. Longitudinal phase-space rotation
  5. CNN Algorithm for 6D phase space reconstruction
  6. Model Architecture
  7. Loss function
  8. Training process
  9. Cross validation performance
  10. Performance evaluation with synthetic distributions
  11. Validation on simulated test sets
  12. Experimental Demonstration
  13. The KEK-ATF injector
  14. Experimental Results
  15. Summary of 6D Phase Space Reconstruction
  16. ...and 7 more sections

Figures (26)

  • Figure 1: Rotation of $x-x'$ phase space by varying the solenoid peak field, $B$. The motion is influenced by solenoid focusing, dispersion due to chicane and space charge effects.
  • Figure 2: Rotation of $y-y'$ phase space by varying the solenoid peak field, $B$. The overall effect comes from solenoid focusing, edge focusing by chicane and space charge effects.
  • Figure 3: Rotation of $t-p_z$ phase space in the presence of different RF phases ($\phi$). The net effect is due to the change in energy spread and space charge forces.
  • Figure 4: The detailed network architecture of the two-stage CNN model. In Stage 1, the model learns from one beam image at a time while keeping the RF phase and solenoid setting fixed, and this training is repeated across all cathode phase spaces and multiple RF-solenoid configurations. In Stage 2, the model takes all 16 chicane beam images together with their RF-solenoid settings and learns to combine them to predict a single cathode phase space distribution.
  • Figure 5: Cathode beam distributions that are generated using Fourier series functions. These provide various beam shapes for the model training. By providing Fourier generated functions we improved the CNN's ability to extrapolate to experimental beam shapes.
  • ...and 21 more figures