# The double-gradient magnetic instability: Stabilizing effect of the guide field

## Abstract

The role of the dawn-dusk magnetic field component in stabilizing of the magnetotail flapping oscillations is investigated in the double-gradient model framework (Erkaev et al., Phys. Rev. Lett. 99, 235003 (2007)), extended for the magnetotail-like configurations with non-zero guide field B{sub y}. Contribution of the guide field is examined both analytically and by means of linearized 2-dimensional (2D) and non-linear 3-dimensional (3D) MHD modeling. All three approaches demonstrate the same properties of the instability: stabilization of current sheet oscillations for short wavelength modes, appearing of the typical (fastest growing) wavelength λ{sub peak} of the order of the current sheet width, decrease of the peak growth rate with increasing B{sub y} value, and total decay of the mode for B{sub y}∼0.5 in the lobe magnetic field units. Analytical solution and 2D numerical simulations claim also the shift of λ{sub peak} toward the longer wavelengths with increasing guide field. This result is barely visible in 3D simulations. It may be accounted for the specific background magnetic configuration, the pattern of tail-like equilibrium provided by approximated solution of the conventional Grad-Shafranov equation. The configuration demonstrates drastically changing radius of curvature of magnetic field lines, R{sub c}. This, in turn, favors the “double-gradient” modemore »

- Authors:

- Saint Petersburg State University, 198504, Ulyanovskaya 1, Petrodvoretz (Russian Federation)
- (Sweden)
- Institute of Computational Modelling, Russian Academy of Sciences, Siberian Branch, 660036 Krasnoyarsk (Russian Federation)
- (Russian Federation)
- Space Research Institute RAS, Profsoyuznaya 84/32, Moscow 117997 (Russian Federation)
- Centrum voor Plasma-Astrofysica, Departement Wiskunde, Katholieke Universiteit Leuven, B-3001 Leuven (Belgium)
- PDC Center for High Performance Computing, KTH Royal Institute of Technology, SE-100 44 Stockholm (Sweden)
- Space Research Institute, Austrian Academy of Sciences, 8042 Graz (Austria)
- (Austria)

- Publication Date:

- OSTI Identifier:
- 22408010

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; APPROXIMATIONS; BALLOONING INSTABILITY; COMPUTERIZED SIMULATION; GRAD-SHAFRANOV EQUATION; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MAGNETOTAIL; OSCILLATIONS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS; WAVELENGTHS

### Citation Formats

```
Korovinskiy, D. B., E-mail: daniil.korovinskiy@gmail.com, Semenov, V. S., Ivanova, V. V., Divin, A. V., Swedish Institute of Space Physics, SE-751 21 Uppsala, Erkaev, N. V., Siberian Federal University, 660041 Krasnoyarsk, Artemyev, A. V., Ivanov, I. B., Theoretical Physics Division, Petersburg Nuclear Physics Institute, 188300 Gatchina, Lapenta, G., Markidis, S., Biernat, H. K., and Institute of Physics, University of Graz, 8010 Graz.
```*The double-gradient magnetic instability: Stabilizing effect of the guide field*. United States: N. p., 2015.
Web. doi:10.1063/1.4905706.

```
Korovinskiy, D. B., E-mail: daniil.korovinskiy@gmail.com, Semenov, V. S., Ivanova, V. V., Divin, A. V., Swedish Institute of Space Physics, SE-751 21 Uppsala, Erkaev, N. V., Siberian Federal University, 660041 Krasnoyarsk, Artemyev, A. V., Ivanov, I. B., Theoretical Physics Division, Petersburg Nuclear Physics Institute, 188300 Gatchina, Lapenta, G., Markidis, S., Biernat, H. K., & Institute of Physics, University of Graz, 8010 Graz.
```*The double-gradient magnetic instability: Stabilizing effect of the guide field*. United States. doi:10.1063/1.4905706.

```
Korovinskiy, D. B., E-mail: daniil.korovinskiy@gmail.com, Semenov, V. S., Ivanova, V. V., Divin, A. V., Swedish Institute of Space Physics, SE-751 21 Uppsala, Erkaev, N. V., Siberian Federal University, 660041 Krasnoyarsk, Artemyev, A. V., Ivanov, I. B., Theoretical Physics Division, Petersburg Nuclear Physics Institute, 188300 Gatchina, Lapenta, G., Markidis, S., Biernat, H. K., and Institute of Physics, University of Graz, 8010 Graz. Thu .
"The double-gradient magnetic instability: Stabilizing effect of the guide field". United States.
doi:10.1063/1.4905706.
```

```
@article{osti_22408010,
```

title = {The double-gradient magnetic instability: Stabilizing effect of the guide field},

author = {Korovinskiy, D. B., E-mail: daniil.korovinskiy@gmail.com and Semenov, V. S. and Ivanova, V. V. and Divin, A. V. and Swedish Institute of Space Physics, SE-751 21 Uppsala and Erkaev, N. V. and Siberian Federal University, 660041 Krasnoyarsk and Artemyev, A. V. and Ivanov, I. B. and Theoretical Physics Division, Petersburg Nuclear Physics Institute, 188300 Gatchina and Lapenta, G. and Markidis, S. and Biernat, H. K. and Institute of Physics, University of Graz, 8010 Graz},

abstractNote = {The role of the dawn-dusk magnetic field component in stabilizing of the magnetotail flapping oscillations is investigated in the double-gradient model framework (Erkaev et al., Phys. Rev. Lett. 99, 235003 (2007)), extended for the magnetotail-like configurations with non-zero guide field B{sub y}. Contribution of the guide field is examined both analytically and by means of linearized 2-dimensional (2D) and non-linear 3-dimensional (3D) MHD modeling. All three approaches demonstrate the same properties of the instability: stabilization of current sheet oscillations for short wavelength modes, appearing of the typical (fastest growing) wavelength λ{sub peak} of the order of the current sheet width, decrease of the peak growth rate with increasing B{sub y} value, and total decay of the mode for B{sub y}∼0.5 in the lobe magnetic field units. Analytical solution and 2D numerical simulations claim also the shift of λ{sub peak} toward the longer wavelengths with increasing guide field. This result is barely visible in 3D simulations. It may be accounted for the specific background magnetic configuration, the pattern of tail-like equilibrium provided by approximated solution of the conventional Grad-Shafranov equation. The configuration demonstrates drastically changing radius of curvature of magnetic field lines, R{sub c}. This, in turn, favors the “double-gradient” mode (λ > R{sub c}) in one part of the sheet and classical “ballooning” instability (λ < R{sub c}) in another part, which may result in generation of a “combined” unstable mode.},

doi = {10.1063/1.4905706},

journal = {Physics of Plasmas},

number = 1,

volume = 22,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}