  We consider whether equilibrium size distributions from collisional cascades
match the frequency of impactors derived from New Horizons crater counts on
Charon (Singer et al 2019). Using an analytic model and a suite of numerical
simulations, we demonstrate that collisional cascades generate wavy size
distributions; the morphology of the waves depends on the binding energy of
solids $Q_d^\star$ and the collision velocity $v_c$. For an adopted minimum
size of solids, $r_{min}$ = 1 micron, and collision velocity $v_c$ = 1-3
km/sec, the waves are rather insensitive to the gravitational component of
$Q_d^\star$. If the bulk strength component of $Q_d^\star$ is $Q_s r^{e_s}$ for
particles with radius $r$, size distributions with small $Q_s$ are much wavier
than those with large $Q_s$; systems with $e_s \approx -0.4$ have stronger
waves than systems with $e_s \approx 0$. Detailed comparisons with the New
Horizons data suggest that a collisional cascade among solids with a bulk
strength intermediate between weak ice (Leinhardt & Stewart 2012) and normal
ice (Schlichting et al 2013) produces size distributions fairly similar to the
size distribution of impactors on Charon. If the surface density $\Sigma$ of
the protosolar nebula varies with semimajor axis $a$ as $\Sigma \approx 30~{\rm
g~cm^{-2}} (a / {\rm 1~au})^{-3/2}$, the time scale for a cascade to generate
an approximate equilibrium is 100-300 Myr at 45 au and 10-30 Myr at 25 au.
Although it is necessary to perform more complete evolutionary calculations of
the Kuiper belt, collisional cascades are a viable model for producing the size
distribution of solids that impacted Charon throughout its history.
