Statistical study of the muon catalyzed d-t fusion cycle

In this paper we discuss the statistics of the main branch species of the muon catalyzed d-t fusion. From a master equation we derive and numerically solve kinetic equations for the average density and the covariances of a system composed of muons, muonic deuterium and muonic tritium atoms, muon molecular d-t ions, muonic helium, helium and neutrons. The system consists of an initial fixed amount of muons in a 50–50% D₂ + T₂ mixture without any external muon source. It is known that the probability distribution function of the population species with the exception of the neutron and helium follow a multinomial distribution function.