Modeling and Particle Tracking through Longitudinal Gradient Bending Magnets

TL;DR

This paper develops a versatile, symplectic particle tracking model for longitudinal gradient bending magnets, enabling accurate simulation of magnetic fields and stable particle trajectories in accelerator physics.

Contribution

It introduces a new general model for LGBs, implements a symplectic integrator, and demonstrates its effectiveness through particle tracking and stability analysis.

Findings

Successfully modeled arbitrary magnetic field profiles.

Produced stable phase space trajectories.

Compared lattice implementations with preliminary results.

Abstract

This report documents the development of a versatile model for longitudinal gradient bending magnets (LGB's) and its implementation in particle tracking simulations. The model presented below may be used to represent an arbitrary magnetic field profile, and was successfully implemented to represent two different LGB's. After building a symplectic integrator for our model, we were able to perform particle tracking studies. By producing phase space plots which depicted stable trajectories, we were able to demonstrate that we had in fact correctly implemented our symplectic integration scheme. In addition, we produced stack representations for the bending component of the magnetic field for each LGB and made preliminary comparisons between lattices implementing this model and our own.