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...

Low-temperature (LT) plasmas have a substantial role in diverse scientific areas and modern technologies. Their stochastic and nonlinear dynamics strongly determine the efficiency and effectiveness of LT plasma-based procedures involved in applications such as etching, spectrochemical analysis, deposition of thin films on substrates, and others. Understanding and controlling complex behaviors in LT plasmas have become a serious research problem. Modeling their behavior is also a major problem. However, models based on hydrodynamic equations have proven to be useful in their study. In this chapter, we expose the use of fluid models taking into account relevant kinetic processes to describe out from equilibrium LT plasma behavior. Selected topics on the stability, stochastic, and nonlinear dynamics of LT plasmas are discussed. These include the coexistence of diffusive and wave-like particle transport and delayed feedback control of oscillatory regime with relaxation.

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