Exact 1-D Model for Coherent Synchrotron Radiation with Shielding and Bunch Compression

TL;DR

This paper presents an exact 1D model for coherent synchrotron radiation that accounts for shielding and bunch compression effects, improving accuracy over previous approximations and providing new formulas for radiated power.

Contribution

It introduces an exact Maxwell-based model for CSR wake-fields in multiple bends with shielding, extending to bunch compression scenarios and deriving a precise power formula.

Findings

Previous bends influence subsequent ones significantly.

Shielding effects are accurately modeled using image charges.

Simpler bunch compression models tend to overestimate effects.

Abstract

Coherent Synchrotron Radiation has been studied effectively using a 1-dimensional model for the charge distribution in the realm of small angle approximations and high energies. Here we use Jefimenko's form of Maxwell's equations, without such approximations, to calculate the exact wake-fields due to this effect in multiple bends and drifts. It has been shown before that the influence of a drift can propagate well into a subsequent bend. We show, for reasonable parameters, that the influence of a previous bend can also propagate well into a subsequent bend, and that this is especially important at the beginning of a bend. Shielding by conducting parallel plates is simulated using the image charge method. We extend the formalism to situations with compressing and decompressing distributions, and conclude that simpler approximations to bunch compression usually overestimates the effect. Additionally, an exact formula for the coherent power radiated by a Gaussian bunch is derived by considering the coherent synchrotron radiation spectrum, and is used to check the accuracy of wake-field calculations.