Geometric and Material Buckling - Derivation

Derivation

Both buckling terms are derived from the diffusion equation:

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where k is the criticality eigenvalue, is the neutrons per fission, is the macroscopic cross section for fission, and from diffusion theory, the diffusion coefficient is defined as:

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In addition, the diffusion length is defined as:

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Rearranging the terms, the diffusion equation becomes:

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The left side of the equation is the geometric buckling and the right side is the material buckling.