  We show that collisional damping of adiabatic primordial fluctuations yields
constraints on the possible range of mass and interaction rates of Dark Matter
particles. Our analysis relies on a general classification of Dark Matter
candidates, that we establish independently of any specific particle theory or
model. From a relation between the collisional damping scale and the Dark
Matter interaction rate, we find that Dark Matter candidates must have
cross-sections at decoupling smaller than $ 10^{-33} \frac{m_{dm}}{1 MeV} cm^2$
with photons and $10^{-37} \frac{m_{dm}}{1 MeV} cm^2$ with neutrinos, to
explain the observed primordial structures of $10^9$ Solar mass. These damping
constraints are particularly relevant for Warm Dark Matter candidates. They
also leave open less known regions of parameter space corresponding to
particles having rather high interaction rates with other species than
neutrinos and photons.
