Solution of the two point nuclear reactor kinetic model for one group delayed neutron precursors

Physics is the foundation of the natural sciences that studies the relationship between matter and energy. Matter consists of atoms, while atoms consist of baryons and electrons with a triple quark structure. Neutrons, which are electrically unstable and unstable baryons, play an important role in the formation of the physical universe, in the transformation between matter and energy, together with protons in the atomic nucleus. With the development of technology, the need for energy is increasing day by day. It is necessary to analyze the behavior of neutrons in nuclear power reactors, which is one of the solutions to meet the energy needs. The amount of energy obtained from nuclear power reactors, which is a viable alternative to renewable energy sources because it provides uninterrupted power, still maintains its attractiveness in terms of construction and operating costs and the amount of fuel used. The commercial use of nuclear energy is through the controlled fission reaction that takes place in nuclear reactors. In this study, the neutrons that trigger the fission reaction are divided into two as fast and delayed neutrons, and the two-point kinetic model for a supercritical reactor is solved numerically and iteratively. For the case where the reactivity increases linearly, the number of nuclei, reflectors and delayed neutrons were calculated as a function of time by choosing the initial values. Our results show that increasing lagging neutron ratio  breaks the exponential increase trend of neutron numbers in the core and reflector. When  =0.5 is reached, the number of neutrons in the core and reflector stabilizes, and in the region of  >0.5, it converges to zero asymptotically. When delayed neutrons are β=0.5, the number of delayed neutrons converges asymptotically to a nonzero value. In this way, it has been observed that the fission reaction can be kept under control in a supercritical reactor by increasing the delayed neutron ratio.