# On Perturbation Components Correspondence between Diffusion and Transport

## Abstract

We have established a correspondence between perturbation components in diffusion and transport theory. In particular we have established the correspondence between the leakage perturbation component of the diffusion theory to that of the group self scattering in transport theory. This has been confirmed by practical applications on sodium void reactivity calculations of fast reactors. Why this is important for current investigations? Recently, there has been a renewed interest in designing fast reactors where the sodium void reactivity coefficient is minimized. In particular the ASTRID8,9 reactor concept has been optimized with this goal in mind. The correspondence on the leakage term that has been established here has a twofold implication for the design of this kind of reactors. First, this type of reactor has a radial reflector; therefore, as shown before, the sodium void reactivity coefficient calculation requires the use of transport theory. The minimization of the sodium reactivity coefficient is normally done by increasing the leakage component that has a negative sign. The correspondence established in this paper allows to directly look at this component in transport theory. The second implication is related to the uncertainty evaluation on sodium void reactivity. As it has shown before, the total sodium voidmore »

- Authors:

- Publication Date:

- Research Org.:
- Idaho National Laboratory (INL)

- Sponsoring Org.:
- DOE - NE

- OSTI Identifier:
- 1060973

- Report Number(s):
- INL/CON-12-26363

- DOE Contract Number:
- DE-AC07-05ID14517

- Resource Type:
- Conference

- Resource Relation:
- Conference: ANS Winter Meeting,San Diego, CA,11/11/2012,11/15/2012

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; Diffusion and Transport; Perturbation Components Equivalence; transport equivalent Corss sEctions

### Citation Formats

```
G. Palmiotti.
```*On Perturbation Components Correspondence between Diffusion and Transport*. United States: N. p., 2012.
Web.

```
G. Palmiotti.
```*On Perturbation Components Correspondence between Diffusion and Transport*. United States.

```
G. Palmiotti. Thu .
"On Perturbation Components Correspondence between Diffusion and Transport". United States. https://www.osti.gov/servlets/purl/1060973.
```

```
@article{osti_1060973,
```

title = {On Perturbation Components Correspondence between Diffusion and Transport},

author = {G. Palmiotti},

abstractNote = {We have established a correspondence between perturbation components in diffusion and transport theory. In particular we have established the correspondence between the leakage perturbation component of the diffusion theory to that of the group self scattering in transport theory. This has been confirmed by practical applications on sodium void reactivity calculations of fast reactors. Why this is important for current investigations? Recently, there has been a renewed interest in designing fast reactors where the sodium void reactivity coefficient is minimized. In particular the ASTRID8,9 reactor concept has been optimized with this goal in mind. The correspondence on the leakage term that has been established here has a twofold implication for the design of this kind of reactors. First, this type of reactor has a radial reflector; therefore, as shown before, the sodium void reactivity coefficient calculation requires the use of transport theory. The minimization of the sodium reactivity coefficient is normally done by increasing the leakage component that has a negative sign. The correspondence established in this paper allows to directly look at this component in transport theory. The second implication is related to the uncertainty evaluation on sodium void reactivity. As it has shown before, the total sodium void reactivity effect is the result of a large compensation (opposite sign) between the scattering (called often spectral) component and the leakage one. Consequently, one has to evaluate separately the uncertainty on each separate component and then combine them statistically. If one wants to compute the cross section sensitivity coefficients of the two different components, the formulation established in this paper allows to achieve this goal by playing on the contribution to the sodium void reactivity coming from the group self scattering of the sodium cross section.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {11}

}