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

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.

Physics‐informed neural network method for modelling beam‐wall interactions

“…Importantly, this demonstrates the behaviour of resistive wall wake field as well explained in [1]. These results indicate that both the resistive wall wake field and space charge field can be simulated with the constructed PINNs, unlike our previous study [8].…”

“…These are similar to those used in [Appendix B, 8]. The prediction accuracy of PINNs and its general trend were already discussed in [7, 8] and demonstrated for different PDEs. Therefore, their properties are believed to be the same in this study.…”

“…N PDE random points are generated inside a chamber and N SIBC grid points are generated on the chamber wall. These are similar to those used in [Appendix B,8]. The prediction accuracy of PINNs and its general trend were already discussed in [7,8] and demonstrated for different PDEs.…”

“…Note that a neural network is used as a solution surrogate. Unlike the previous study [8], although the space‐charge field has only a purely imaginary part, the resistive wall wake field has both real and imaginary parts. Therefore, the constructed NN also has two outputs $$( {e_z^r,e_z^i} )$$ corresponding to the real ( r ) and imaginary ( i ) parts of E z .…”

“…This letter first introduces the PINN into the resistive wall impedance modelling. The main focus is to extend our recent study [8] on the perfectly electric conducting (PEC) wall to the resistive wall. This approach is not yet addressed in other publications [9,10].…”