  We use a new multiannulus planetesimal accretion code to investigate the
evolution of a planetesimal disk following a moderately close encounter with a
passing star. The calculations include fragmentation, gas and
Poynting-Robertson drag, and velocity evolution from dynamical friction and
viscous stirring. We assume that the stellar encounter increases planetesimal
velocities to the shattering velocity, initiating a collisional cascade in the
disk. During the early stages of our calculations, erosive collisions damp
particle velocities and produce substantial amounts of dust. For a wide range
of initial conditions and input parameters, the time evolution of the dust
luminosity follows a simple relation, L_d/L_{\star} = L_0 / [alpha +
(t/t_d)^{beta}]. The maximum dust luminosity L_0 and the damping time t_d
depend on the disk mass, with L_0 proportional to M_d and t_d proportional to
M_d^{-1}. For disks with dust masses of 1% to 100% of the `minimum mass solar
nebula' (1--100 earth masses at 30--150 AU), our calculations yield t_d approx
1--10 Myr, alpha approx 1--2, beta = 1, and dust luminosities similar to the
range observed in known `debris disk' systems, L_0 approx 10^{-3} to 10^{-5}.
Less massive disks produce smaller dust luminosities and damp on longer
timescales. Because encounters with field stars are rare, these results imply
that moderately close stellar flybys cannot explain collisional cascades in
debris disk systems with stellar ages of 100 Myr or longer.
