Machine learning-based direct solver for one-to-many problems on temporal shaping of relativistic electron beams

doi:10.1007/s11467-022-1205-y

Front. Phys.

2022, Vol. 17

Issue (6) : 64601 https://doi.org/10.1007/s11467-022-1205-y

RESEARCH ARTICLE

Machine learning-based direct solver for one-to-many problems on temporal shaping of relativistic electron beams

Jinyu Wan^1,^2,³, Yi Jiao^1,²(

)

¹. Key Laboratory of Particle Acceleration Physics and Technology, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
². University of Chinese Academy of Sciences, Beijing 100049, China
³. China Spallation Neutron Source, Dongguan 523803, China

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Abstract

To control the temporal profile of a relativistic electron beam to meet requirements of various advanced scientific applications like free-electron-laser and plasma wakefield acceleration, a widely-used technique is to manipulate the dispersion terms which turns out to be one-to-many problems. Due to their intrinsic one-to-many property, current popular stochastic optimization approaches on temporal shaping may face the problems of long computing time or sometimes suggesting only one solution. Here we propose a real-time solver for one-to-many problems of temporal shaping, with the aid of a semi-supervised machine learning method, the conditional generative adversarial network (CGAN). We demonstrate that the CGAN solver can learn the one-to-many dynamics and is able to accurately and quickly predict the required dispersion terms for different custom temporal profiles. This machine learning-based solver is expected to have the potential for wide applications to one-to-many problems in other scientific fields.

Keywords beam shaping one-to-many problem machine learning

Corresponding Author(s): Yi Jiao

About author:

Tongcan Cui and Yizhe Hou contributed equally to this work.

Issue Date: 28 September 2022

Cite this article:

Jinyu Wan,Yi Jiao. Machine learning-based direct solver for one-to-many problems on temporal shaping of relativistic electron beams[J]. Front. Phys. , 2022, 17(6): 64601.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1205-y
https://academic.hep.com.cn/fop/EN/Y2022/V17/I6/64601

Fig.1 Schematic diagram of the CGAN solver in this study. The color of the initial beam from black to white represents the charge-density from low to high. The compressed temporal profile is obtained by letting the initial beam pass through a chicane having specific R

56

, T

566

and U

5666

. By feeding the custom temporal profiles and noise components to the trained generator of the CGAN, the CGAN solver is able to predict the required dispersion terms to realize the input target temporal profiles.

Fig.2 Using stochastic optimization methods to solve temporal shaping problems. (a) and (b) show the grid scan results and the evolutionary trajectory of the PSO and the surrogate model-based PSO in the variable space for a cusp-shaped profile and a double-horn profile, respectively. The z-axis in (a) and (b) is −log(objective function) representing the objective performance. The contour maps of the grid scan results are plotted at the bottom, where the color from blue to yellow represent the objective performance from low to high. For each R

56

-T

566

grid in (a) and (b), only one U

5666

with the highest objective performance is plotted. Two separate predictions of the CGAN solver are also shown in (a) and (b) for comparison. (c) and (d) are the final temporal profiles obtained with the optimization methods for the cusp-shaped profile and double-horn profile, respectively.

R 2

is the determination coefficient to the target temporal profile.

Fig.3 Longitudinal phase space distribution and temporal profiles of two separate CGAN predictions. The left two columns represent the cusp-shaped profile, and the right two columns represent the double-horn profile, respectively.

Fig.4 The average solving time with the CGAN solver, the PSO and the surrogate model-based PSO for five repeated tests.

Fig.5 Beam profiles obtained with CGAN solutions for two target profiles with CSR effect taken into account. (a) and (b) represent a cusp-shape target and a double-horn target, respectively.

Fig.6 The temporal profiles obtained with the CGAN solver for the flat-top profile (a) and the linearly-ramped profile (b). The red/blue solid line represents the results are predicted by the CGAN model without/with CSR effect considered in the training.

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