Emission of light by a single electron moving on a curved trajectory (synchrotron radiation) is one of the most well-known fundamental radiation phenomena. However experimental situations are more complex as they involve many electrons, each being exposed to the radiation of its neighbors. This interaction has dramatic consequences, one of the most spectacular being the spontaneous formation of spatial structures inside electrons bunches. This fundamental effect is actively studied as it represents one of the most fundamental limitations in electron accelerators, and at the same time a source of intense terahertz radiation (Coherent Synchrotron Radiation, or CSR). Here we demonstrate the possibility to directly observe the electron bunch microstructures with subpicosecond resolution, in a storage ring accelerator. The principle is to monitor the terahertz pulses emitted by the structures, using a strategy from photonics, time-stretch, consisting in slowing-down the phenomena before recording. This opens the way to unpreceeded possibilities for analyzing and mastering new generation high power coherent synchrotron sources.

Spontaneous formation of spatial structures (patterns) occurs in various contexts, ranging from sand dunes [1] and rogue wave formation [2,3], to traffic jams [4]. These last decades, very practical reasons also led to studies of pattern formation in relativistic electron bunches used in synchrotron radiation light sources. As the main motivation, the patterns which spontaneously appear during an instability increase the terahertz radiation power by factors exceeding 10000 [5,6]. However the irregularity of these patterns [5][6][7][8][9][10][11] largely prevented applications of this powerful source. Here we show how to make the spatiotemporal patterns regular (and thus the emitted THz power) using a point of view borrowed from chaos control theory [12][13][14]. Mathematically, regular unstable solutions are expected to coexist with the undesired irregular solutions, and may thus be controllable using feedback control. We demonstrate the stabilization of such regular solutions in the Synchrotron SOLEIL storage ring. Operation of these controlled unstable solutions enables new designs of high charge and stable synchrotron radiation sources.Synchrotron light sources are used worldwide to produce brilliant light from THz to hard X-rays, allowing to investigate a very large range of matter properties. In these sources where electron bunches travel at relativistic velocities, an ubiquitous phenomenon occurs when the bunch charge density exceeds a threshold value. Due to the interaction between the electron bunch and its own emitted electric field, micro-structures spontaneously appear in the longitudinal profile (and phase-space) of the bunch [7, 15-17] (see Fig. 1(a) and (b) for the SOLEIL storage ring which will be considered here). In storage rings, these structures are responsible for a huge emission of coherent light in the terahertz range, typically 10 3 − 10 5 times normal synchrotron radiation power density. However, as the micro-structures appear mostly in the form of bursts [ Fig. 1(d)] this type of source is barely usable in user applications. Hence, research in this domain has naturally attempted to find regions for which coherent emission (CSR) occurs while bursting dynamics * Corresponding author : clement.evain@univ-lille.fr is absent. Such "parameter search" methods succeeded in identifying parameter regions with stable coherent emission. However, this corresponds to special configurations (with short and low charge electron bunches, in the so-called low-alpha operation [5,6,10,11,[18][19][20][21][22][23]) which are not compatible with most of the user experiments. Therefore, this type of THz source is used in relatively few synchrotron radiation facilities (SOLEIL, DIAMOND, BESSY-II), and only during a small part of the year."Parameter search approaches" are however not the only possibilities for avoiding instabilities. The point of view that we will use here is directly borrowed from the so-called chaos control theory, introduced by Ott, Grebogi and Yorke (OGY) [12,13]. Mathematically, when an undesi...

In recent synchrotron radiation facilities, the use of short (picosecond) electron bunches is a powerful method for producing giant pulses of terahertz coherent synchrotron radiation. Here we report on the first direct observation of these pulse shapes with a few picoseconds resolution, and of their dynamics over a long time. We thus confirm in a very direct way the theories predicting an interplay between two physical processes. Below a critical bunch charge, we observe a train of identical THz pulses (a broadband Terahertz comb) stemming from the shortness of the electron bunches. Above this threshold, a large part of the emission is dominated by drifting structures, which appear through spontaneous self-organization. These challenging single-shot THz recordings are made possible by using a recently developed photonic time stretch detector with a high sensitivity. The experiment has been realized at the SOLEIL storage ring.

Single-shot recording of terahertz electric signals has recently become possible at high repetition rates, by using the photonic time-stretch electro-optic sampling (EOS) technique. However the moderate sensitivity of time-stretch EOS is still a strong limit for a range of applications. Here we present a variant enabling to increase the sensitivity of photonic time-stretch for free-propagating THz signals. The ellipticity of the laser probe is enhanced by adding a set of Brewster plates, as proposed by Ahmed et al. [Rev. Sci. Instrum. 85, 013114 (2014)] in a different context. The method is tested using the high repetition rate terahertz coherent synchrotron radiation source of the SOLEIL synchrotron radiation facility. The signal-to-noise ratio of our terahertz digitizer could thus be straightforwardly improved by a factor ≈6.5, leading to a noise-equivalent input electric field below 1.25 V/cm inside the electro-optic crystal, over the 0-300 GHz band (i.e., 2.3 μV/cm/Hz). The sensitivity is scalable with respect to the available laser power, potentially enabling further sensitivity improvements when needed.