What boundary condition is used for solving the neutron flux distribution in a subcritical reactor core?

In the context of neutron flux distribution in a subcritical reactor core, the appropriate boundary condition is that the neutron flux, represented as φ, approaches zero at a certain distance from the core (r = R_2). This is reflective of physical reality in a subcritical system where the neutron population decreases exponentially away from the reactor core due to absorption and leakage.

Setting φ to zero at r = R_2 signifies that we are modeling the behavior of neutrons as they escape the influence of the reactor core, indicating that beyond this point, there are no significant neutron interactions taking place. The second part of the boundary condition, where φ is specified at a certain value φ_1 at r = R_1, is also important as it represents the neutron flux level present at the boundary closer to the reactor core.

This method of establishing boundary conditions is crucial for accurately solving the diffusion equation that describes how neutrons behave in a reactor, particularly in subcritical configurations where the multiplication factor is less than one, and thus leads to a gradual reduction of the neutron population as distance from the core increases. This approach ensures that the mathematical model reflects the physical behavior of neutrons in the system, leading to essential insights into reactor behavior and safety.