Simple Analytical Model

We assume that the dust produced in the system is the tail of a collisional equilibrium size distribution which is ultimately due to the destruction of a group of large bodies which we will call comets for convenience. Let Np be the initial number of such bodies with collisional cross section crp and mass Mp. Let these bodies occupy a volume V where they move around and collide with relative velocities vcon = vv^ with vk being the Kepler velocity in the regions where the comets exist, v will be zero for circular orbits in a single plane and approach one for highly excited orbits. If all collisions are destructive, the time derivative of the number of comets in the system is given by

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