# Chain Rule Approach for Calculating the Time-Derivative of Flux

## Abstract

The reaction history (gamma-flux observable) is mathematically studied by using the chain rule for taking the total-time derivatives. That is, the total time-derivative of flux is written as the product of the ion temperature derivative with respect to time and the derivative of the flux with respect to ion temperature. Some equations are derived using the further simplification that the fusion reactivity is a parametrized function of ion temperature, T. Deuterium-tritium (D-T) fusion is used as the application with reactivity calculations from three established reactivity parametrizations.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Booker Scientific, Fredericksburg, TX (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA). Office of Defense Nuclear Security (NA-70)

- OSTI Identifier:
- 1398942

- Report Number(s):
- LA-UR-17-29223

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; fusion

### Citation Formats

```
Langenbrunner, James R., and Booker, Jane M..
```*Chain Rule Approach for Calculating the Time-Derivative of Flux*. United States: N. p., 2017.
Web. doi:10.2172/1398942.

```
Langenbrunner, James R., & Booker, Jane M..
```*Chain Rule Approach for Calculating the Time-Derivative of Flux*. United States. doi:10.2172/1398942.

```
Langenbrunner, James R., and Booker, Jane M.. Tue .
"Chain Rule Approach for Calculating the Time-Derivative of Flux". United States.
doi:10.2172/1398942. https://www.osti.gov/servlets/purl/1398942.
```

```
@article{osti_1398942,
```

title = {Chain Rule Approach for Calculating the Time-Derivative of Flux},

author = {Langenbrunner, James R. and Booker, Jane M.},

abstractNote = {The reaction history (gamma-flux observable) is mathematically studied by using the chain rule for taking the total-time derivatives. That is, the total time-derivative of flux is written as the product of the ion temperature derivative with respect to time and the derivative of the flux with respect to ion temperature. Some equations are derived using the further simplification that the fusion reactivity is a parametrized function of ion temperature, T. Deuterium-tritium (D-T) fusion is used as the application with reactivity calculations from three established reactivity parametrizations.},

doi = {10.2172/1398942},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Oct 03 00:00:00 EDT 2017},

month = {Tue Oct 03 00:00:00 EDT 2017}

}

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