Topics: Neutron transport equation
Starting from expanding flux dependence to even include direction and energy. ø( position, energy, direction, time), we write down the neutron balance equation. And then, omit direction dependence first and focus on energy dependence from now on.
ø( vector r, E, t)
Notice that not only flux has a energy dependence, some parameters like cross section, velocity or diffusion coefficients are also energy dependent now.
Some changes in neutron balance equation:
1. Fission neutrons come from fission reactions of neutrons of all energy.
2. Losing neutrons by scattering from objective energy to any other energy.
3. Gaining neutrons by scattering from any other energy to objective energy.
Then we define g group of flux ø_g by integrate the flux from E_g to E_g-1. By this, we have the neutron balance equation of group g.
For example, we had taken a look of two group, G=2. Some simplifications are used like up-scattering, fission neutrons being all fast