Knowing the axial and radial flux shapes, Section

7.4.1 of this chapter, it may be readily shown using the one group theory that:

Pnl * 1/(1 + (x/L’)2 + (2.405/R’)2M2]

where M is the ‘migration length’ of the neutrons in the reactor material (M2 is sometimes called the ‘migration, ^rea’); it is a measure of the crow-flight range neutrons travel between ‘birth’ by fission and final absorption.

4.6.5 The critical reactor

As keff = k*, Pnl» and using from the expression for Pnl in Section 7.4.3, it follows that for a critical reactor where keff = 1 that:

(k. — 1)/M2 = (x/L’)2 + (2.405/R’)2

The quantity on the left of the equation (к» — 1)/ M2, is determined solely by the core materials and their arrangement within the core. It is called the material buckling Bm2.

Similarly the quantity on the right (x/L’)2 + (2.405/R’)2, is determined solely by the overall geo­metry of the core and is called the geometric buck­ling Bg2. (The term buckling comes from an analogy drawn between the degree of curvature of the neutron flux shape and equations describing a strut buckling

under longitudinal compression.) Hence, the condition for a critical reactor is that:

Bg2 = Bm2