  Debris disks are thought to be sculptured by neighboring planets. The same is
true for the Edgeworth-Kuiper debris disk, yet no direct observational evidence
for signatures of giant planets in the Kuiper belt dust distribution has been
found so far. Here we model the dust distribution in the outer solar system to
reproduce the dust impact rates onto the dust detector onboard the New Horizons
spacecraft measured so far and to predict the rates during the Neptune orbit
traverse. To this end, we take a realistic distribution of transneptunian
objects to launch a sufficient number of dust grains of different sizes and
follow their orbits by including radiation pressure, Poynting-Robertson and
stellar wind drag, as well as the perturbations of four giant planets. In a
subsequent statistical analysis, we calculate number densities and lifetimes of
the dust grains in order to simulate a collisional cascade. In contrast to the
previous work, our model not only considers collisional elimination of
particles, but also includes production of finer debris. We find that particles
captured in the 3:2 resonance with Neptune build clumps that are not removed by
collisions, because the depleting effect of collisions is counteracted by
production of smaller fragments. Our model successfully reproduces the dust
impact rates measured by New Horizons out to ~23AU and predicts an increase of
the impact rate of about a factor of two or three around the Neptune orbit
crossing. This result is robust with respect to the variation of the vaguely
known number of dust-producing scattered disk objects, collisional outcomes,
and the dust properties.
