Determination of the cricital nuclear size via the two group diffision theory

The only known energy source that can be used as a continuous power source except fossil fuels is the nuclear energy. Exploitation of the nuclear energy takes place via the fission reaction that takes place inside the nuclear reactors. Being able to keep the fission reaction under control depends on satisfying the criticality condition. In this work, the neutrons that trigger the fission reaction have been regarded as two different groups that are low energy thermal neutrons and high energy fast neutrons. Two group neutron diffusion theory that arises as a result of this yields two group criticality equation. The reactor size that satisfies the criticality condition for a given reactor composition has been determined by solving the two group criticality equation numerically. In this way, the effects of the changes in the core radius, the reflector thickness and the extrapolation length on the critical reactor size in spherical geometry have been investigated in detail. Keywords: Nuclear Energy, Fission, Criticality, Neutron Diffusion