Under what conditions would negative buckling (B^2) be possible?
Never. Buckling is a function of physical parameters (sphere radius, reaction cross-sections, diffusion coefficient), none of which can ever be negative.
Buckling of a structure (mechanical analysis) is not the same as 'buckling' with respect to the neutron flux in a nuclear reactor.
I believe B2 < 0 implies the system is subscritical.
Let B2 = (νΣf - Σa)/D = (k∞ - 1)/L2, then the buckling is negative if k∞ < 1, or Σa > νΣf.
Geometric buckling would not be negative.
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