  We describe planetesimal accretion calculations in the Kuiper Belt.
  Our evolution code simulates planetesimal growth in a single annulus and
includes velocity evolution but not fragmentation. Test results match analytic
solutions and duplicate previous simulations at 1 AU.
  In the Kuiper Belt, simulations without velocity evolution produce a single
runaway body with a radius of 1000 km on a time scale inversely proportional to
the initial mass in the annulus. Runaway growth occurs in 100 Myr for 10 earth
masses and an initial eccentricity of 0.001 in a 6 AU annulus centered at 35
AU. This mass is close to the amount of dusty material expected in a minimum
mass solar nebula extrapolated into the Kuiper Belt.
  Simulations with velocity evolution produce runaway growth on a wide range of
time scales. Dynamical friction and viscous stirring increase particle
velocities in models with large (8 km radius) initial bodies. This velocity
increase delays runaway growth by a factor of two compared to models without
velocity evolution. In contrast, collisional damping dominates over dynamical
friction and viscous stirring in models with small (80--800 m radius) initial
bodies. Collisional damping decreases the time scale to runaway growth by
factors of 4--10 relative to constant velocity calculations. Simulations with
minimum mass solar nebulae, 10 earth masses, reach runaway growth on time
scales of 20-40 Myr with 80 m initial bodies, 50-100 Myr with 800 m bodies, and
75-250 Myr for 8 km initial bodies. These growth times vary linearly with the
mass of the annulus but are less sensitive to the initial eccentricity than
constant velocity models.
