Exploring the neutron diffusion system under reflector boundaries via an ansatz approach: Time-dependent solution

Essam R El-Zahar¹Abdelhalim Ebaid^2*Laila F Seddek¹

• ¹Prince Sattam bin Abdulaziz University, Al Kharj, Saudi Arabia
• ²University of Tabuk, Tabuk, Saudi Arabia

This paper analyzes the dynamics of the neutron diffusion kinetic system under reflector boundaries/zero-flux gradient. An ansatz approach is proposed to exactly solve the governing system. The time-dependent solutions are exactly obtained in explicit forms, where spatial variations violate and the temporal behavior dominates the dynamics. Robust physical interpretation is provided for the neutron flux and the precursor concentration under three different cases, supercritical, critical, and sub-critical conditions. A key strength of the study lies in the effectiveness of the solution technique, particularly the use of the ansatz approach, which allows accurate handling of both short-term transients and long-term steady states. The method proves computationally efficient and stable across a wide range of reactivity levels.