## Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering

## Abstract

Recently, the validity of the guiding-center approach to model relativistic runaway electrons in tokamaks has been challenged by full-orbit simulations that demonstrate the breakdown of the standard magnetic moment conservation. In this paper, we derive a new expression for the magnetic moment of relativistic runaway electrons with p∥>>⊥, which is conserved significantly better than the standard one. The new result includes one of the second-order corrections in the standard guiding-center theory which, in case of runaway electrons with p∥>>⊥, can peculiarly be of the same order as the lowest-order term. The better conservation of the new magnetic moment also explains the collisionless pitch-angle-scattering effect observed in full-orbit simulations since it allows momentum transfer between the perpendicular and parallel directions when the runaway electron is accelerated by an electric field. In conclusion, while the derivation of the second-order correction to the magnetic moment in general case would require the full extent of the relativistic second-order guiding-center theory, we exploit the Lie-perturbation method at the limit p∥Gtp⊥ which simplifies the computations significantly. Consequently, we present the corresponding guiding-center equations applicable to runaway electrons.

- Authors:

- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China). School of Physics
- Univ. of Science and Technology of China, Hefei (China). School of Physics

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1460954

- Grant/Contract Number:
- AC02-09CH11466; SC0016268

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Fusion

- Additional Journal Information:
- Journal Volume: 58; Journal Issue: 10; Journal ID: ISSN 0029-5515

- Publisher:
- IOP Science

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Liu, Chang, Qin, Hong, Hirvijoki, Eero, Wang, Yulei, and Liu, Jian. Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering. United States: N. p., 2018.
Web. doi:10.1088/1741-4326/aad2a5.
```

```
Liu, Chang, Qin, Hong, Hirvijoki, Eero, Wang, Yulei, & Liu, Jian. Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering. United States. doi:10.1088/1741-4326/aad2a5.
```

```
Liu, Chang, Qin, Hong, Hirvijoki, Eero, Wang, Yulei, and Liu, Jian. Wed .
"Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering". United States. doi:10.1088/1741-4326/aad2a5. https://www.osti.gov/servlets/purl/1460954.
```

```
@article{osti_1460954,
```

title = {Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering},

author = {Liu, Chang and Qin, Hong and Hirvijoki, Eero and Wang, Yulei and Liu, Jian},

abstractNote = {Recently, the validity of the guiding-center approach to model relativistic runaway electrons in tokamaks has been challenged by full-orbit simulations that demonstrate the breakdown of the standard magnetic moment conservation. In this paper, we derive a new expression for the magnetic moment of relativistic runaway electrons with p∥>>⊥, which is conserved significantly better than the standard one. The new result includes one of the second-order corrections in the standard guiding-center theory which, in case of runaway electrons with p∥>>⊥, can peculiarly be of the same order as the lowest-order term. The better conservation of the new magnetic moment also explains the collisionless pitch-angle-scattering effect observed in full-orbit simulations since it allows momentum transfer between the perpendicular and parallel directions when the runaway electron is accelerated by an electric field. In conclusion, while the derivation of the second-order correction to the magnetic moment in general case would require the full extent of the relativistic second-order guiding-center theory, we exploit the Lie-perturbation method at the limit p∥Gtp⊥ which simplifies the computations significantly. Consequently, we present the corresponding guiding-center equations applicable to runaway electrons.},

doi = {10.1088/1741-4326/aad2a5},

journal = {Nuclear Fusion},

number = 10,

volume = 58,

place = {United States},

year = {2018},

month = {7}

}