Calculating Neutron Flux using SN Method

[NukeLion]

when we calculate the neutron flux in finite medium using sn method for steady state neutron transport equation, it gives us some numbers up to 1. I am sure its not the real flux, can someone explain how we can calculte the real flux using sn method.

 

[Astronuc]

when we calculate the neutron flux in finite medium using sn method for steady state neutron transport equation, it gives us some numbers up to 1. I am sure its not the real flux, can someone explain how we can calculte the real flux using sn method.

If values are going from 0 to 1 for a value, then it is probably normalized or represents a probability. Then the question is to what quantity I the value normalized. Perhaps the reaction rate or neutron production rate/density, which relates to the fission density.

One can solve for a neutron distribution, but the actual value depends on fission density. A finite critical fission system can have any power level up to some limit, e.g., 1 W to 1 GW. Criticality means steady-state. The local fission density will depend on the relative fission cross-section in comparison to other absorption cross-sections.

 

[NukeLion]

Thanks Astronuc for your reply. So is it means that we need to multiply with power to get the real flux?

 

[Astronuc]

Thanks Astronuc for your reply. So is it means that we need to multiply with power to get the real flux?

Correct, there would have to be some local or average (integrated) power from which to obtain a real flux. In conjunction with power and temperature (assuming some heat transfer), the temperature would have to be consistent with the resonance (doppler) broadening and moderator density.

 

[alphy]

The SN method is a commonly used approach for solving the steady state neutron transport equation in finite media. It involves dividing the problem into discrete angular directions and solving for the neutron flux in each direction separately. This results in a set of equations that can be solved numerically to obtain an approximate solution for the neutron flux in the medium.

The numbers obtained from this method are indeed not the real neutron flux values, but rather an approximation. This is because the SN method assumes that the neutron flux is constant within each angular direction, which is not always the case in real systems. In order to obtain a more accurate solution, one can increase the number of angular directions used in the calculation, but this can become computationally expensive.

To calculate the real neutron flux using the SN method, one can use a technique called "ray effects correction". This involves taking into account the variations in the neutron flux within each angular direction and correcting the values obtained from the SN method accordingly. This can be done using various techniques such as the diamond difference method or the linear interpolation method.

In summary, while the SN method provides a useful and efficient approach for calculating the neutron flux in finite media, it is important to keep in mind that the results obtained are approximations and may need to be corrected for more accurate values.