# VARIATIONAL METHODS IN NEUTRON THERMALIZATION

## Abstract

Variational methods for calculating thermal flux distribu tion in reactors for design purposes are described. The methods relate the nature and essential features of the scattering kernel to the characteristics of the neutron distributions that have engineering significance. Information is given on variational principles, adjoint functions, and their various interpretations. Typical problems in neutron thermalization are evaluated by this method. The first problem considered is the asymptotic behavior of the neutron distribution, due to a discontinuity in an infinite medium which 1eads to an exponentially decaying space distribution, or a pulse in a b1ock of material which leads to an analogous eigenvalue problem for the calculation of the decay constant for the time-dependent distribution. The second problem is the calculation of the spectrum of neutrons in an infinite medium generated by a uniform source of fission neutrons, and its use in calculating thermal group constants for simplified models of a reactor. The final problem concerns the calculation of the thermal flux distribution in space and energy in a system with many regions having different compositions and temperatures, which is necessary for accurate reactor design. (N.W.R.)

- Authors:

- Publication Date:

- Research Org.:
- Knolls Atomic Power Lab., Schenectady, N.Y.

- OSTI Identifier:
- 4774719

- Report Number(s):
- TID-12780

- NSA Number:
- NSA-16-029713

- DOE Contract Number:
- W-31-109-ENG-52

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-62

- Country of Publication:
- United States

- Language:
- English

- Subject:
- PHYSICS; MATHEMATICS; SCATTERING; VARIATIONAL METHOD

### Citation Formats

```
Selengut, D.S.
```*VARIATIONAL METHODS IN NEUTRON THERMALIZATION*. United States: N. p., 1961.
Web.

```
Selengut, D.S.
```*VARIATIONAL METHODS IN NEUTRON THERMALIZATION*. United States.

```
Selengut, D.S. Mon .
"VARIATIONAL METHODS IN NEUTRON THERMALIZATION". United States.
```

```
@article{osti_4774719,
```

title = {VARIATIONAL METHODS IN NEUTRON THERMALIZATION},

author = {Selengut, D.S.},

abstractNote = {Variational methods for calculating thermal flux distribu tion in reactors for design purposes are described. The methods relate the nature and essential features of the scattering kernel to the characteristics of the neutron distributions that have engineering significance. Information is given on variational principles, adjoint functions, and their various interpretations. Typical problems in neutron thermalization are evaluated by this method. The first problem considered is the asymptotic behavior of the neutron distribution, due to a discontinuity in an infinite medium which 1eads to an exponentially decaying space distribution, or a pulse in a b1ock of material which leads to an analogous eigenvalue problem for the calculation of the decay constant for the time-dependent distribution. The second problem is the calculation of the spectrum of neutrons in an infinite medium generated by a uniform source of fission neutrons, and its use in calculating thermal group constants for simplified models of a reactor. The final problem concerns the calculation of the thermal flux distribution in space and energy in a system with many regions having different compositions and temperatures, which is necessary for accurate reactor design. (N.W.R.)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1961},

month = {5}

}