  Binary fraction and orbital characteristics provide indications on the
conditions of star formation, as they shed light on the environment they were
born in. Multiple systems are more common in low density environments rather
than in higher density ones. In the current debate about the formation of
Globular Clusters and their multiple populations, studying the binary incidence
in the populations they host offers a crucial piece of information on the
environment of their birth and their subsequent dynamical evolution.
  Through a multi-year observational campaign using FLAMES at VLT, we monitored
the radial velocity of 968 Red-Giant Branch stars located around the half-light
radii in a sample of 10 Galactic Globular Clusters. We found a total of 21
radial velocity variables identified as {\it bona fide} binary stars, for a
binary fraction of 2.2%$\pm$0.5%. When separating the sample into first
generation and second generation stars, we find a binary fraction of
4.9%$\pm$1.3% and 1.2%$\pm$0.4% respectively. Through simulations that take
into account possible sources of bias in detecting radial velocity variations
in the two populations, we show that the difference is significant and only
marginally affected by such effects.
  Such a different binary fraction strongly suggests different conditions in
the environment of formation and evolution of first and second generations
stars, with the latter being born in a much denser environment. Our result
hence strongly supports the idea that the second generation forms in a dense
subsystem at the center of the loosely distributed first generation, where
(loose) binaries are efficiently destroyed.

Solar and Stellar Astrophysics;Astrophysics of Galaxies