Question

Explain the physics meaning of material buckling and geometry buckling.

Answer 1

In the reactor, physics buckling plays a vital role. Criticality is achieved in a nuclear reactor when the rate of neutron production is equal to the rate of neutron losses, including both neutron absorption and neutron leakage. So, Geometric buckling is a measure of neutron leakage. It only depends on geometry. On the other hand, material buckling is a measure of neutron production minus absorption. Generally, in the simplest case of a bare, homogeneous, steady-state reactor, the geometric and material buckling must be equal.

Precisely, we can say that geometric buckling is a measure of the curvature of the neutron flux distribution of a reactor at equilibrium due to its geometry. For a slab reactor, B_g² = (pi/a)² where a is the extrapolation distance where the flux is zero. Material buckling is a description of the characteristics of the fuel material in an infinite medium. B_m² = n*S_f-S_a / D (neutron production rate minus absorption rate divided by the neutron diffusion coefficient).  

The three basic states ( subcritical, critical and supercritical ) may be defined also according to the material and geometrical bucklings:

• B_m < B_g. When a reactor is smaller (i.e. higher B_g and higher relative curvature) than the critical size for a given material, B_m < B_g, then the reactor is subcritical.
• B_m = B_g. When a reactor size matches the critical size for a given material, B_m = B_g, then the reactor is critical.
• B_m > B_g. When a reactor is larger than the critical size for a given material, B_m > B_g, then the reactor is supercritical.