Microbunching instability in storage rings: Link between phase-space structure and terahertz coherent synchrotron radiation radio-frequency spectra

E Roussel,C Szwaj,C Evain,S Bielawski

doi:10.1103/physrevstab.17.010701

Abstract

In storage rings, when the number of electrons in a bunch exceeds a threshold value, microstructures appear spontaneously in the bunch. Experimental observations of these microstructures and their evolution are indirect to obtain. In practice, most information is obtained from the terahertz coherent synchrotron radiation (THz CSR), since microstructures in the millimeter range radiate THz CSR. Here we show, thanks to a simple analytical formula associated to numerical simulations, that a frequency component in the THz CSR signal permits one to obtain information about the structure of the electron bunch longitudinal phase space during the microbunching instability. The proposed formula permits one also to link experimental information together, in particular the bunch length and the THz CSR spectrum.

Highlights

Contrary to the synchrotron radiation emitted by freeelectron lasers, the light emitted by electron bunches circulating in a storage ring is usually incoherent longitudinally, since there is no phase relation between emission by different electrons in a bunch
In special situations, emission can become coherent in the THz domain, and highly more intense. It happens when the electron bunch is shorter than the THz wavelength [1] or when the longitudinal charge density has been modified by an external laser [2,3,4]
Our goal here is to link the frequency fm of the terahertz coherent synchrotron radiation (THz CSR) signal to the angle between branches forming the patterns in the 2D phase space

Summary

INTRODUCTION

Contrary to the synchrotron radiation emitted by freeelectron lasers, the light emitted by electron bunches circulating in a storage ring is usually incoherent longitudinally, since there is no phase relation between emission by different electrons in a bunch. It happens when the electron bunch is shorter than the THz wavelength (typically, with a bunch length of few millimeters) [1] or when the longitudinal charge density has been modified by an external laser [2,3,4] Beside these controlled situations, terahertz coherent synchrotron radiation (THz CSR) is emitted spontaneously in storage rings when the number of electrons exceeds a threshold value, with the apparition of the so-called microbunching instability (e.g., [5,6,7,8,9]). This can be used for example to estimate the value of fm in the case when this value is not known (from experiment or simulation)

EQUATIONS AND PARAMETERS

ORIGIN OF THE RF FREQUENCY IN THE THZ COHERENT SYNCHROTRON RADIATION

LINK BETWEEN ANGLE IN THE PHASE SPACE AND THE FREQUENCY MODULATION f m

CONCLUSION