Abstract:

Background: Probability of neutron-initiating persistent fission chain, which has to be calculated in analysis of critical safety, start-up of reactor, burst waiting time on pulse reactor, bursting time on pulse reactor, etc., is an inherent parameter in a multiplying assembly. Purpose: We aim to derive time-dependent integro-differential equation for such probability in relative velocity space according to the probability conservation, and develop the deterministic code Dynamic Segment Number Probability (DSNP) based on the multi-group SN method. Methods: The reliable convergence of dynamic calculation was analyzed and numerical simulation of the evolvement process of dynamic probability for varying concentration was performed under different initial conditions. Results: On Highly Enriched Uranium (HEU) Bare Spheres, when the time is long enough, the results of dynamic calculation approach to those of static calculation. The most difference of such results between DSNP and Partisn code is less than 2%. On Baker model, over the range of about 1 ?s after the first criticality, the most difference between the dynamic and static calculation is about 300%. As for a super critical system, the finite fission chains decrease and the persistent fission chains increase as the reactivity aggrandizes, the dynamic evolvement curve of initiation probability is close to the static curve within the difference of 5% when the Keff is more than 1.2. The cumulative probability curve also indicates that the difference of integral results between the dynamic calculation and the static calculation decreases from 35% to 5% as the Keff increases. This demonstrated that the ability of initiating a self-sustaining fission chain reaction approaches stabilization, while the former difference (35%) showed the important difference of the dynamic results near the first criticality with the static ones. The DSNP code agrees well with Partisn code. Conclusions: There are large numbers of finite fission chains near the first criticality, which can survive until after the second criticality. So the results of dynamic calculation here will be greater than those of static calculation. The numerical simulation on HEU Bare Spheres and Baker model validated the accuracy of the DSNP code, which can calculate initiation probability of dynamic system. Relative to the static method, the DSNP code can describe perfectly the evolvement process of probability of ignition of fissile system.

Key words: Probability of persistent fission chain, Dynamic fissile system, Multi-group SN method