# Collisionless kinetic theory of oblique tearing instabilities

## Abstract

The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.

- Authors:

- Univ. of Iowa, Iowa City, IA (United States). Dept. of Physics and Astronomy
- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Iowa, Iowa City, IA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); National Science Foundation (NSF)

- OSTI Identifier:
- 1429052

- Alternate Identifier(s):
- OSTI ID: 1421302; OSTI ID: 1438147

- Report Number(s):
- LA-UR-18-21045

Journal ID: ISSN 1070-664X; TRN: US1802606

- Grant/Contract Number:
- SC0016159; AGS-0962698; AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 2; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; kinetic theory; dispersion; magnetic reconnection; ionospheric physics; plasma dynamics; magnetospheric dynamics; physical optics; plasma instabilities; plasma interactions; flow boundary effects

### Citation Formats

```
Baalrud, S. D., Bhattacharjee, A., and Daughton, W. Collisionless kinetic theory of oblique tearing instabilities. United States: N. p., 2018.
Web. doi:10.1063/1.5020777.
```

```
Baalrud, S. D., Bhattacharjee, A., & Daughton, W. Collisionless kinetic theory of oblique tearing instabilities. United States. doi:10.1063/1.5020777.
```

```
Baalrud, S. D., Bhattacharjee, A., and Daughton, W. Thu .
"Collisionless kinetic theory of oblique tearing instabilities". United States. doi:10.1063/1.5020777. https://www.osti.gov/servlets/purl/1429052.
```

```
@article{osti_1429052,
```

title = {Collisionless kinetic theory of oblique tearing instabilities},

author = {Baalrud, S. D. and Bhattacharjee, A. and Daughton, W.},

abstractNote = {The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.},

doi = {10.1063/1.5020777},

journal = {Physics of Plasmas},

number = 2,

volume = 25,

place = {United States},

year = {2018},

month = {2}

}

#### Figures / Tables:

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*