Analytical theory of coherent synchrotron radiation wakefield of short bunches shielded by conducting parallel plates

TL;DR

This paper presents a comprehensive analytical model for coherent synchrotron radiation wakefields of short electron bunches shielded by parallel conducting plates, enabling new insights into various beam trajectories and benchmarking against simulations.

Contribution

The authors develop a versatile analytical framework for CSR impedance with shielding, extending previous models to new geometries and providing exact formulas for different orbits.

Findings

Derived new analytical formulas for CSR impedance with shielding.

Validated formulas against numerical simulations with CSRZ.

Expanded understanding of CSR effects in complex beam trajectories.

Abstract

We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to the situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked agains numerical simulations with the CSRZ computer code.