Reactor dynamics model for the molten salt reactor based on P₁approximation

In this paper, we study the use of the Telegraph Point Reactor Kinetics (TPRK) to model the kinetics and dynamics of Molten Salt Reactors (MSRs). TPRK is based on the full form of the P₁approximation of the neutron transport equation without neglecting the time derivative of the neutron current term in the final form of the P₁approximation system of equations. Inclusion of the neutron current time derivative term results in the addition of a new physical parameter called the relaxation time τ that will affect the solution and the dynamics of MSRs due to the homogeneity of the molten salt fuel. We used eight precursors groups of delayed neutrons in our analysis. We found that the general behavior of relaxation effect associated with the telegraph model in solid fuel systems is still persistent in this analysis. The first peak of the telegraph-based approximation shows similar behavior to other detailed spatial based models of MSRs in contrast to the diffusion model. Also, we found that when τ → 0, TPRK results tend to agree with the diffusion model. If a high amount of reactivity is inserted through any external contributions (control rod movements or any changes of state parameters such as fuel temperature feedback coefficient α_Fand the fuel salt mass flow rate m_F) the difference between the two models is higher than for low reactivity insertions. This result, we contribute to the relaxation effect of the telegraph model.