  Spontaneous formation of spatial structures (patterns) occurs in various
contexts, ranging from sand dunes and rogue wave formation, to traffic jams.
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. However the irregularity of these patterns largely prevented
applications of this powerful source. Here we show how to make the
spatio-temporal patterns regular (and thus the emitted THz power) using a point
of view borrowed from chaos control theory. 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.
