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.Comment: 9 pages, 5 figure