Response of the point-reactor telegraph kinetics to time varying reactivities

The new model of the Point Reactor Kinetics (PRK) equations developed based on the Telegraph approximation of the neutron transport equation, is solved for several cases of time varying Reactivities insertions and Temperature feedback while comparing it to that of the diffusion PRK model in an infinite Thermal Homogenous Nuclear Reactor. Diffusion PRK is based on the Neutron Diffusion Equation which is a parabolic differential equation and hence it assumes an infinite velocity of propagation, while neutrons propagate with a finite velocity. By the introduction of the hyperbolic type Telegraph equation which is a more accurate representation of the neutron transport than the diffusion equation and in which neutrons propagate with a finite velocity, one could overcome this paradox that contradicts causality. The new model introduces a new parameter called the relaxation time (τ), which is not present in the diffusion approximation, and affects the neutron density calculations. Both Ramp insertions of reactivity and Sinusoidal insertions of reactivity were studied, as well as the effect of The Adiabatic Temperature feedback. The general phenomena in the solution of the new model is a Relaxation in the time response of the solution. It is found that the Telegraph model with its extra second order time derivative, will give observable different values than that of the diffusion even when we used small (τ) especially for the cases at which the neutron density changes rapidly.