Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Kazuhiro Fujita

doi:10.1109/access.2021.3132942

Abstract

The electromagnetic coupling of a charged particle beam with vacuum chambers is of great interest for beam dynamics studies in the design of a particle accelerator. A deep learning-based method is proposed as a mesh-free numerical approach for solving the field of space charges of a particle beam in a vacuum chamber. Deep neural networks based on the physical model of a relativistic particle beam with transversally nonuniform charge density moving in a vacuum chamber are constructed using this method. A partial differential equation with the Lorentz factor, transverse charge density, and boundary condition is embedded in its loss function. The proposed physics-informed neural network method is applied to round, rectangular, and elliptical vacuum chambers. This is verified in comparison with analytical solutions for coupling impedances of a round Gaussian beam and an elliptical bi-Gaussian beam. The effects of chamber geometries, charge density, beam offset, and energy on the beam coupling impedance are demonstrated.

Highlights

Electromagnetic coupling of a charged particle beam with vacuum chambers is of great interest for beam dynamics studies in the design of a particle accelerator [1,2]
When using volume meshes for the impedance computations, the standard finite integration technique (FIT) with structured grids suffers from the so-called staircasing error of curved boundaries, and the finite element method (FEM) with unstructured grids allows accurate boundary modeling but may require the generation of dense meshes owing to a large variation in the field in the vicinity of the space charge (SC) of a relativistic beam traversing in a vacuum chamber [7]
The physics-informed neural network (PINN) method for the calculation of beam coupling impedances of accelerator vacuum chambers is proposed as a mesh-free approach

Summary

Introduction

Electromagnetic coupling of a charged particle beam with vacuum chambers is of great interest for beam dynamics studies in the design of a particle accelerator [1,2] Such coupling effects are quantified using the concept of the beam coupling impedance [2] in the frequency domain. Deep neural networks based on a physical model of the beam coupling effect due to the SC field are constructed. By virtue of the use of the NN, our approach includes no mesh in the computational domain This offers the advantage of modeling the SC effect compared to the FIT [6] and FEM [7]. The main purpose of this study is to demonstrate the feasibility of the proposed method for modeling the SC effect

Objectives

Results

Conclusion