Geometric buckling from macroscopic cross sections and diffusion coefficient

Geometrical buckling is a quantity describing the reactor which depends only on its geometry. It can also be calculated from the macroscopic cross sections and the diffusion coefficient as well as the effective multiplicative factor and the neutron production rate.

Links:

  1. Wikipedia, second part of second equation.

neutrons_per_fission

The average number of neutrons produced per fission. See particle_count.

Symbol:

nu

Latex:

\(\nu\)

Dimension:

dimensionless

effective_multiplication_factor

effective_multiplication_factor.

Symbol:

k_eff

Latex:

\(k_\text{eff}\)

Dimension:

dimensionless

macroscopic_fission_cross_section

macroscopic_cross_section of fission.

Symbol:

Sigma_f

Latex:

\(\Sigma_\text{f}\)

Dimension:

1/length

macroscopic_absorption_cross_section

macroscopic_cross_section of absorption.

Symbol:

Sigma_a

Latex:

\(\Sigma_\text{a}\)

Dimension:

1/length

diffusion_coefficient

neutron_diffusion_coefficient.

Symbol:

D

Latex:

\(D\)

Dimension:

length

geometric_buckling

geometric_buckling.

Symbol:

B_g^2

Latex:

\(B_\text{g}^2\)

Dimension:

1/area

law

B_g^2 = (nu / k_eff * Sigma_f - Sigma_a) / D

Latex:
\[B_\text{g}^2 = \frac{\frac{\nu}{k_\text{eff}} \Sigma_\text{f} - \Sigma_\text{a}}{D}\]