AbstractThe one-speed transport equation is solved for a ring reactor. A complete solution is obtained for the space-time relaxation of a pulse of neutrons in a multiplying medium in which delayed neutrons are neglected. The solution consists of a fundamental mode, a finite number of harmonics, and an integral transient. A condition is deduced, which gives the maximum number of harmonics that can exist for a given ring circumference. The limitations of diffusion theory are pointed out with particular reference to the shortcomings of that theory in dealing with the early stages of evolution of the pulse.Delayed neutrons are included and a complete solution is obtained by means of the prompt jump approximation. The results are illustrated by numerical calculations designed to show the onset of instabilities in the harmonics when the reactor is sufficiently large.