  Very recently Spitler et al. (2016) and Scholz et al. (2016) reported their
detections of sixteen additional bright bursts from the direction of the fast
radio burst (FRB) 121102. This repeating FRB is inconsistent with all the
catastrophic event models put forward previously for hypothetically
non-repeating FRBs. Here we propose a different model, in which highly
magnetized pulsars travel through asteroid belts of other stars. We show that a
repeating FRB could originate from such a pulsar encountering lots of asteroids
in the belt. During each pulsar-asteroid impact, an electric field induced
outside the asteroid has such a large component parallel to the stellar
magnetic field that electrons are torn off the asteroidal surface and
accelerated to ultra-relativistic energies instantaneously. Subsequent movement
of these electrons along magnetic field lines will cause coherent curvature
radiation, which can account for all the properties of an FRB. In addition,
this model can self-consistently explain the typical duration, luminosity, and
repetitive rate of the seventeen bursts of FRB 121102. The predicted occurrence
rate of repeating FRB sources may imply that our model would be testable in the
next few years.
