Beam-Beam Fields with Full Six-Dimensional Coupling: Theory and Computational Methods

TL;DR

This paper introduces a comprehensive theoretical and computational framework for calculating beam-beam fields with full six-dimensional coupling, improving accuracy over traditional models and aiding future collider design.

Contribution

It develops a generalized theory and computational methods for beam-beam fields with full 6D coupling, including a practical case study for the Electron-Ion Collider.

Findings

Standard slice models underestimate longitudinal fields

The new framework offers more accurate beam-beam field calculations

Potential to improve simulation and design of particle colliders

Abstract

This work presents a generalized theoretical framework for calculating beam-beam fields induced by a Gaussian beam with full six-dimensional coupling. We also develop computational techniques for evaluating these fields. A case study based on the Electron-Ion Collider (EIC) electron storage ring illustrates the practical application of the framework. Our results suggest that the standard slice model for the beam-beam kick can significantly underestimate the longitudinal field. The proposed theory may provide a foundation for developing improved simulation models and guiding future design studies.