Kan, Y.-K., & Qiang, J. (2024). On the Electromagnetic Field of a Focusing Charged Particle Beam and Its Two-Dimensional Approximation. arXiv preprint arXiv:2409.13965v2.
This paper aims to provide a rigorous derivation of the electromagnetic potential generated by a focusing charged particle beam, a crucial aspect of beam physics often simplified using the quasistatic approximation. The authors aim to clarify the assumptions underlying this approximation and demonstrate how a commonly used two-dimensional (2D) model can be derived from the more general three-dimensional (3D) case.
The authors begin by revisiting the inhomogeneous wave equations governing electromagnetic fields. They then introduce the quasistatic approximation, explicitly stating the assumptions involved. Using these assumptions, they derive the 3D potential for a Gaussian-distributed focusing beam. Finally, they demonstrate the reduction of this 3D potential to a 2D approximation under specific limiting conditions.
The paper provides a comprehensive theoretical framework for understanding and calculating the electromagnetic fields generated by focusing charged particle beams. By explicitly stating the assumptions and limitations of the quasistatic approximation and its 2D reduction, the authors offer valuable insights for researchers and practitioners in beam physics, particularly in areas like beam-beam interaction studies.
This work contributes significantly to the field of beam physics by providing a rigorous and clear explanation of the commonly used quasistatic approximation and its 2D counterpart. The explicit derivation of these models from fundamental electromagnetic theory enhances their applicability and allows researchers to use them with a deeper understanding of their limitations.
The paper focuses on Gaussian-distributed beams. Exploring other beam profiles and their impact on the derived potentials could be a potential avenue for future research. Additionally, investigating the effects of relaxing the quasistatic assumptions and their implications for beam dynamics could provide further insights.
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by Yi-Kai Kan, ... at arxiv.org 10-24-2024
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