# Calculations in the theory of tearing instability

## Abstract

Recent studies have suggested that the tearing instability may play a significant role in magnetic turbulence. In this work we review the theory of the magnetohydrodynamic tearing instability in the general case of an arbitrary tearing parameter, which is relevant for applications in turbulence. We discuss a detailed derivation of the results for the standard Harris profile and accompany it by the derivation of the results for a lesser known sine-shaped profile. We devote special attention to the exact solution of the inner equation, which is the central result in the theory of tearing instability. We also briefly discuss the influence of shear flows on tearing instability in magnetic structures. Our presentation is self-contained; we expect it to be accessible to researchers in plasma turbulence who are not experts in magnetic reconnection

- Authors:

- Publication Date:

- DOE Contract Number:
- SC0016215

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

- OSTI Identifier:
- 1880263

- DOI:
- https://doi.org/10.7910/DVN/MOCDDK

### Citation Formats

```
Boldyrev, Stanislav, and Loureiro, Nuno F.
```*Calculations in the theory of tearing instability*. United States: N. p., 2018.
Web. doi:10.7910/DVN/MOCDDK.

```
Boldyrev, Stanislav, & Loureiro, Nuno F.
```*Calculations in the theory of tearing instability*. United States. doi:https://doi.org/10.7910/DVN/MOCDDK

```
Boldyrev, Stanislav, and Loureiro, Nuno F. 2018.
"Calculations in the theory of tearing instability". United States. doi:https://doi.org/10.7910/DVN/MOCDDK. https://www.osti.gov/servlets/purl/1880263. Pub date:Thu Nov 01 00:00:00 EDT 2018
```

```
@article{osti_1880263,
```

title = {Calculations in the theory of tearing instability},

author = {Boldyrev, Stanislav and Loureiro, Nuno F.},

abstractNote = {Recent studies have suggested that the tearing instability may play a significant role in magnetic turbulence. In this work we review the theory of the magnetohydrodynamic tearing instability in the general case of an arbitrary tearing parameter, which is relevant for applications in turbulence. We discuss a detailed derivation of the results for the standard Harris profile and accompany it by the derivation of the results for a lesser known sine-shaped profile. We devote special attention to the exact solution of the inner equation, which is the central result in the theory of tearing instability. We also briefly discuss the influence of shear flows on tearing instability in magnetic structures. Our presentation is self-contained; we expect it to be accessible to researchers in plasma turbulence who are not experts in magnetic reconnection},

doi = {10.7910/DVN/MOCDDK},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {11}

}

Works referencing / citing this record:

##
Calculations in the theory of tearing instability

journal, October 2018

- Boldyrev, Stanislav; Loureiro, Nuno F.
- Journal of Physics: Conference Series, Vol. 1100