Diffusion equation from neutron flux

The diffusion equation, based on Fick’s law, provides an analytical solution of spatial neutron flux distribution in the multiplying system.

Links:

1. NuclearPower, possible similar formula.

diffusion_coefficient

neutron_diffusion_coefficient.

Symbol:

D

Latex:

\(D\)

Dimension:

length

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

effective_multiplication_factor

effective_multiplication_factor.

Symbol:

k_eff

Latex:

\(k_\text{eff}\)

Dimension:

dimensionless

position

position.

Symbol:

x

Latex:

\(x\)

Dimension:

length

neutron_flux

neutron_flux as a function of position.

Symbol:

Phi(x)

Latex:

\(\Phi{\left(x \right)}\)

Dimension:

1/(area*time)

neutron_flux_laplacian

Laplacian of the neutron_flux as a function of position.

Symbol:

Laplace(Phi)(x)

Latex:

\(\nabla^{2} \Phi{\left(x \right)}\)

Dimension:

1/(length**4*time)

law

-D * Laplace(Phi)(x) + Sigma_a * Phi(x) = nu / k_eff * Sigma_f * Phi(x)

Latex:

\[- D \nabla^{2} \Phi{\left(x \right)} + \Sigma_\text{a} \Phi{\left(x \right)} = \frac{\nu}{k_\text{eff}} \Sigma_\text{f} \Phi{\left(x \right)}\]