Analyzing Assumptions for Neutron Flux: Fast & Thermal Groups

In summary, the equations provided by the professor state that in equilibrium, the total neutron density of fast neutrons is equal to the number of neutrons generated by thermal fission. Additionally, the number of thermal neutrons is constant due to absorption and scattering processes, with absorption removing the same number of thermal neutrons as scattering produces.
  • #1
sandon
18
1
Assumptions
1) a=absorption
2) f=fission
3) ∅=neutron flux
4) time independent
5) group 1, fast neutrons
6) group 2, thermal neutrons
7) All fission neutron are boring in fast group
8) All neutrons created by thermal group, thus vƩf2 exists vƩf2 does not
9) Down scattering occurs but up scattering does not, Ʃ1→2 exists, Ʃ2→1 is zero

From the prof produced 2 equations
(1) -(Ʃa1+Ʃ1→2)*∅1 + v*Ʃf2*∅2=0
(2) -Ʃa2*∅2 + Ʃ1→2*∅1=0

(1) Equation says the total neutron density of all fast neutrons(including ones scattered) is equal to the neutrons generated by thermal fission. This is correct by assumptions 7) and 8).

(2) I do not understand equation 2, why is the neutron density of the amount of slow neutrons absorbed equal to the neutron density of scattered neutrons?

Thank in advance
 
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  • #2
In equilibrium (!), the number of thermal neutrons is constant. Absorption removes as many thermal neutrons as scattering produces new thermal neutrons.

7) All fission neutron are boring in fast group
I don't think "boring" is what you mean.
8) All neutrons created by thermal group, thus vƩf2 exists vƩf2 does not
Is that a typo?
 
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  • #3
sorry
7) All fission neutron are born in fast group
 
  • #4
8) All neutrons created by thermal group, thus vƩf2 exists vƩf1 does not
 

1. What are the assumptions made when analyzing neutron flux in fast and thermal groups?

The assumptions made when analyzing neutron flux in fast and thermal groups include:

  • The neutron flux is assumed to be isotropic, meaning it has the same magnitude and direction in all directions.
  • Neutron scattering is assumed to be isotropic and independent of energy.
  • Thermal neutron scattering is assumed to be elastic, meaning no energy is lost during the scattering process.
  • The neutron flux is assumed to be steady-state, meaning it does not change over time.
  • There is no external source of neutrons, so the only source is the fission of the material being analyzed.

2. Why is it important to analyze assumptions when studying neutron flux?

Analyzing assumptions when studying neutron flux is important because it allows for a more accurate and reliable analysis of the data. The assumptions made can greatly impact the results and conclusions drawn from the analysis. By understanding and addressing these assumptions, scientists can ensure that their data and conclusions are as accurate as possible.

3. How do fast and thermal neutron groups differ?

Fast and thermal neutron groups differ in terms of their energies. Fast neutrons have higher energies (usually above 1 MeV) and are more likely to induce fission reactions. Thermal neutrons, on the other hand, have lower energies (usually below 1 eV) and are more likely to be captured by nuclei. This difference in energy also affects their behavior and interactions with materials, making it necessary to analyze them separately.

4. What are some common methods used for analyzing assumptions in neutron flux studies?

Some common methods used for analyzing assumptions in neutron flux studies include:

  • Monte Carlo simulations, which use random sampling and statistical analysis to model the behavior of neutrons in a system.
  • Comparison with experimental data, which can help identify any discrepancies or incorrect assumptions.
  • Sensitivity analysis, which involves varying the assumptions and observing the impact on the results.
  • Validation against other analytical methods, such as diffusion theory or transport theory.

5. What are some possible sources of error when analyzing neutron flux assumptions?

There are several possible sources of error when analyzing neutron flux assumptions, including:

  • Uncertainty in material properties and cross-section data used in the analysis.
  • Limitations in the models and methods used for the analysis.
  • Assumptions that do not accurately reflect the real-world conditions.
  • Experimental error or discrepancies in data used for comparison.
  • Human error in setting up or running the analysis.

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