# From self-organization in relativistic electron bunches to coherent synchrotron light: observation using a photonic time-stretch digitizer

## TL;DR

This paper demonstrates a novel non-destructive method to measure the electric field of relativistic electron bunches in a storage ring, revealing the link between pattern formation and coherent synchrotron radiation.

## Contribution

It introduces a photonic time-stretch digitizer capable of ultrafast, non-invasive electric field measurements of electron bunches in real-time.

## Key findings

- Observed spontaneous pattern formation in electron bunches.
- Linked pattern formation to bursts of coherent synchrotron radiation.
- Achieved terasamples/second acquisition rate for electric field measurement.

## Abstract

In recent and future synchrotron radiation facilities, relativistic electron bunches with increasingly high charge density are needed for producing brilliant light at various wavelengths, from X-rays to terahertz. In such conditions, interaction of electrons bunches with their own emitted electromagnetic fields leads to instabilities and spontaneous formation of complex spatial structures. Understanding these instabilities is therefore key in most electron accelerators. However, investigations suffer from the lack of non-destructive recording tools for electron bunch shapes. In storage rings, most studies thus focus on the resulting emitted radiation. Here, we present measurements of the electric field in the immediate vicinity of the electron bunch in a storage ring, over many turns. For recording the ultrafast electric field, we designed a photonic time-stretch analog-to-digital converter with terasamples/second acquisition rate. We could thus observe the predicted link between spontaneous pattern formation and giant bursts of coherent synchrotron radiation in a storage ring.