  Giant planet migration is an important phenomenon in the evolution of
planetary systems. Recent works have shown that giant planet growth and
migration can shape the asteroid belt, but these works have not considered
interactions between planetesimals. We have calculated the evolution of
planetesimal disks, including planetesimal-planetesimal collisions, during gas
giant growth and migration. The numbers, locations, and impact velocities of
these collisions depend on the specific growth and migration path. We find that
giant planet growth alone has little effect on impact velocities, and most of
the planetesimals scattered by growing giants do not undergo collisions with
each other during the growth period. In contrast, we find that giant planet
migration induces large numbers of high velocity collisions between
planetesimals. These impacts have sufficient velocities to cause shock-induced
vaporization for both water ice and silicate components of planetesimals, and
to cause catastrophic disruption of the bodies. New bodies may form from impact
debris. Collisional evolution reduces the efficiency of planetesimal
implantation into the asteroid belt via giant planet growth and migration. A
small fraction of the largest planetesimals implanted into the asteroid belt
would have been processed via collisions. We identify important consequences of
planetesimal collisions that have not been considered in planet accretion
models. The prevalence of high velocity collisions during giant planet
migration, and their potential links to the properties of meteorites, and the
formation of chondrules, makes impact vaporization a critically important
phenomenon. The consequences of vaporizing planetesimal constituents require
further detailed study. New collision outcome models for impacts within the
nebula, and models for new planetesimal formation are needed.
