Formulation of a point reactor kinetics model based on the neutron telegraph equation

• Developed a point reactor kinetics model based on the telegraph equation.
• Found the inhour equation, the matrix form and some known (PRK) field approximations, based on the model.
• Solution of the model shows the phenomenon of retardation in time.
• The model is considered a generalization of the Diffusion Point Reactor Kinetics (DPRK) model.

A Telegraph model of the Point Reactor Kinetics (TPRK) is developed based on the monoenergetic, non-fractional order telegraph approximation of the neutron transport equation. The model was used to develop a complete theory of the point reactor kinetics based on the non-fractional neutron telegraph equation. The inhour equation in the new form was obtained alongside different known reactor kinetics approximations applied to the model and their analytical solutions. The matrix form of the model was also obtained, which is needed for numerical solutions of the model. We solved this model for a step insertion of reactivity for an infinite thermal nuclear reactor system. In our model the value of the velocity of the neutrons propagation is finite and equals v/3 because of the neutron telegraph equation. Although this value is still under research, it is different from infinite as in the diffusion approximation which contradicts causality. Values of the relaxation time (τ), which is the main difference between the (TPRK) and the Diffusion Point Reactor Kinetics (DPRK), is studied for different materials based on theoretical approach and its effect on the neutron density calculations have been calculated. The most important notice in the solution of the (TPRK) model is that there is a relaxation (retardation) in the time response of the solution. This is similar to what was found earlier in the literature concerning the solutions of the neutron telegraph equation.