Question

Construct the geometric bucklings and critical flux profiles in finite cylinder reactor.

Answer 1

Geometrical buckling is a measure of neutron leakage, while material buckling is a measure of neutron production minus absorption. With this terminology the criticality condition may also be stated as the material and geometric buckling being equal:

The quantity Bg2 is called the geometrical buckling of the reactor and depends only on the geometry. This term is derived from the notion that the neutron flux distribution is somehow ‘‘buckled’’ in a homogeneous finite reactor. It can be derived the geometrical buckling is the negative relative curvature of the neutron flux (Bg2 = ∇2Ф(x) / Ф(x)). In a small reactor the neutron flux have more concave downward or ‘‘buckled’’ curvature (higher Bg2) than in a large one.

The value of geometrical buckling for infinite slab reactor can be derived, when the vacuum boundary condition is applied on the solution of diffusion equation. The physically acceptable solution for infinite slab reactor is:

Φ(x) = C.cos(Bg x)

Criticality Condition

The basic classification of states of a reactor is according to the multiplication factor as eigenvalue which is a measure of the change in the fission neutron population from one neutron generation to the subsequent generation.

    keff < 1. This condition is known as the subcritical state.
    keff = 1. This condition is known as the critical state.
    keff > 1. This condition is known as the supercritical state.

But these three basic states may be defined also according to the material and geometrical bucklings:

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