  We study a ballistic agglomeration process in the reaction-controlled limit.
Cluster densities obey an infinite set of Smoluchowski rate equations, with
rates dependent on the average particle energy. The latter is the same for all
cluster species in the reaction-controlled limit and obeys an equation
depending on densities. We express the average energy through the total cluster
density that allows us to reduce the governing equations to the standard
Smoluchowski equations. We derive basic asymptotic behaviors and verify them
numerically. We also apply our formalism to the agglomeration of dark matter.
