  A prescription for the fragment size distribution resulting from dust grain
collisions is essential when modelling a range of astrophysical systems, such
as debris disks and planetary rings. While the slope of the fragment size
distribution and the size of the largest fragment are well known, the behaviour
of the distribution at the small size end is theoretically and experimentally
poorly understood. This leads debris disk codes to generally assume a limit
equal to, or below, the radiation blow-out size. We use energy conservation to
analytically derive a lower boundary of the fragment size distribution for a
range of collider mass ratios. Focussing on collisions between equal-sized
bodies, we apply the method to debris disks. For a given collider mass, the
size of the smallest fragments is found to depend on collision velocity,
material parameters, and the size of the largest fragment. We provide a
physically motivated recipe for the calculation of the smallest fragment, which
can be easily implemented in codes for modelling collisional systems. For
plausible parameters, our results are consistent with the observed predominance
of grains much larger than the blow-out size in Fomalhaut's main belt and in
the Herschel cold debris disks.
