# Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

## Abstract

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S{sub n} source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S{sub n} discretization.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 8948

- Report Number(s):
- SAND99-1698C

TRN: US0102009

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Conference

- Resource Relation:
- Conference: American Nuclear Society 1999 Winter Meeting, Long Beach, CA (US), 11/14/1999--11/18/1999; Other Information: PBD: 8 Jul 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; CROSS SECTIONS; PARITY; SCATTERING; PHOTON TRANSPORT; ELECTRON TRANSFER; EQUATIONS; COUPLING

### Citation Formats

```
Liscum-Powell, J.L., Lorence, L.J. Jr., Morel, J.E., and Prinja, A.K.
```*Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport*. United States: N. p., 1999.
Web.

```
Liscum-Powell, J.L., Lorence, L.J. Jr., Morel, J.E., & Prinja, A.K.
```*Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport*. United States.

```
Liscum-Powell, J.L., Lorence, L.J. Jr., Morel, J.E., and Prinja, A.K. Thu .
"Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport". United States. https://www.osti.gov/servlets/purl/8948.
```

```
@article{osti_8948,
```

title = {Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport},

author = {Liscum-Powell, J.L. and Lorence, L.J. Jr. and Morel, J.E. and Prinja, A.K.},

abstractNote = {Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S{sub n} source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S{sub n} discretization.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {7}

}