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.

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Abstract-We describe and demonstrate a time-domain boundary-element method for numerical computation of wake fields. The accelerator structure is modeled with a surface mesh, and the wake field is easily split from the self fields of the source particles. The formulation for three-dimensional structures is introduced first, followed by two formulations for axisymmetric structures. We briefly describe methods for computing the wake potential in a boundary-element code. Finally, we compare the fully axisymmetric formulation with codes based on the finite integration technique (

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A mesh‐free approach for modelling beam‐wall interactions in particle accelerators is proposed. The key idea of our method is to use a deep neural network as a surrogate for the solution to a set of partial differential equations involving the particle beam, and the surface impedance concept. The proposed approach is applied to the coupling impedance of an infinitely long vacuum chamber with a thin conductive coating, and also verified in comparison with traditional numerical methods.