Formulas for coherent synchrotron radiation microbunching in a bunch compressor chicane

Zhirong Huang,Kwang-Je Kim

doi:10.1103/physrevstab.5.074401

Abstract

A microbunching instability driven by coherent synchrotron radiation (CSR) in a bunch compressor chicane is studied using an iterative solution of the integral equation that governs this process. By including both one-stage and two-stage amplifications, we obtain analytical expressions for CSR microbunching that are valid in both low-gain and high-gain regimes. These formulas can be used to explore the dependence of CSR microbunching on compressed beam current, energy spread, and emittance, and to design stable bunch compressors required for an x-ray free-electron laser.

Highlights

Coherent synchrotron radiation (CSR) is one of the most challenging issues associated with the design of bunch compressor chicanes required for an x-ray free-electron laser (FEL) [1,2]
A self-consistent treatment of CSR microbunching, including the electron energy chirp and the emittance effect, is developed in Ref. [8], and the microbunching process is described by an integral equation
The numerical solution of the integral equation for beam parameters and lattice functions corresponding to the second bunch compressor of the Linac Coherent Light Source (LCLS) [1] yields very low gain (,3) over a wide wavelength range

Summary

INTRODUCTION

Coherent synchrotron radiation (CSR) is one of the most challenging issues associated with the design of bunch compressor chicanes required for an x-ray free-electron laser (FEL) [1,2]. Computer simulations have shown that small density modulations can be significantly amplified by the CSR force in bunch compressor chicanes, giving rise to a microbunching instability [4]. Such an instability is currently under intense study [5,6,7,8] as it may impact the design of an x-ray FEL calling for kiloampere, subpicosecond electron bunches. In this paper we analyze the microbunching process in a typical bunch compressor chicane and obtain the iterative solution of the integral equation that is valid in both high-gain and low-gain regimes.

INTEGRAL EQUATION FOR CSR MICROBUNCHING

STAGED AMPLIFICATION OF CSR MICROBUNCHING

Microbunching due to initial density modulation

DLs2 r0

Microbunching due to initial energy modulation

NUMERICAL EXAMPLES