# Adjoint Fokker-Planck equation and runaway electron dynamics

## Abstract

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.

- Authors:

- Princeton Univ., NJ (United States)
- Columbia Univ., New York, NY (United States)

- Publication Date:

- Research Org.:
- Columbia Univ., NY (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1468793

- Alternate Identifier(s):
- OSTI ID: 1234783

- Grant/Contract Number:
- FG02-03ER54696

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 1; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Liu, Chang, Brennan, Dylan P., Bhattacharjee, Amitava, and Boozer, Allen H. Adjoint Fokker-Planck equation and runaway electron dynamics. United States: N. p., 2016.
Web. doi:10.1063/1.4938510.
```

```
Liu, Chang, Brennan, Dylan P., Bhattacharjee, Amitava, & Boozer, Allen H. Adjoint Fokker-Planck equation and runaway electron dynamics. United States. doi:10.1063/1.4938510.
```

```
Liu, Chang, Brennan, Dylan P., Bhattacharjee, Amitava, and Boozer, Allen H. Wed .
"Adjoint Fokker-Planck equation and runaway electron dynamics". United States. doi:10.1063/1.4938510. https://www.osti.gov/servlets/purl/1468793.
```

```
@article{osti_1468793,
```

title = {Adjoint Fokker-Planck equation and runaway electron dynamics},

author = {Liu, Chang and Brennan, Dylan P. and Bhattacharjee, Amitava and Boozer, Allen H.},

abstractNote = {The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.},

doi = {10.1063/1.4938510},

journal = {Physics of Plasmas},

number = 1,

volume = 23,

place = {United States},

year = {2016},

month = {1}

}

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