Electromagnetic field computation of multilayer vacuum chambers with physics-informed neural networks

Abstract

The electromagnetic interaction of a charged particle beam with multilayer vacuum chambers is of particular interest in accelerator physics. This paper presents a deep learning-based approach for calculating electromagnetic fields generated by the beam in infinitely long multilayer vacuum chambers with arbitrary cross section. The presented approach is based on physics-informed neural networks and the surface impedance boundary condition of a multilayer structure derived from the transmission line theory. Deep neural networks (DNNs) are utilized to approximate the solution of partial differential equations (PDEs) describing the physics of electromagnetic fields self-generated by a charged particle beam traveling in a particle accelerator. A residual network is constructed from the output of DNNs, the PDEs and boundary conditions are embedded into the loss function and differential operators are calculated using the automatic differentiation. As a result, the presented approach is regarded to be mesh-free. The approach is applied to circular and elliptical vacuum chambers with a three-layer structure. It is verified in comparison with the recently proposed boundary element method. The effects of chamber geometries and multilayer structure on the beam coupling impedance are demonstrated.