# Plasmoid instability in double current sheets

## Abstract

The linear behavior of plasmoid instability in double current sheet configurations, namely, double plasmoid mode (DPM), is analytically and numerically investigated within the framework of a reduced magnetohydrodynamic model. Analytical analysis shows that if the separation of double current sheets is sufficiently small [κx{sub s}≪κ{sup 2/9}S{sub L}{sup 1/3}], the growth rate of DPMs scales as κ{sup 2/3}S{sub L}{sup 0} in the non-constant-ψ regime, where κ=kL{sub CS}/2 is the wave vector measured by the half length of the system L{sub CS}/2, 2x{sub s} is the separation between two resonant surfaces, and S{sub L}=L{sub CS}V{sub A}/2η is Lundquist number with V{sub A} and η being Alfven velocity and resistivity, respectively. If the separation is very large [κx{sub s}≫κ{sup 2/9}S{sub L}{sup 1/3}], the growth rate scales as κ{sup −2/5}S{sub L}{sup 2/5} in the constant-ψ regime. Furthermore, it is also analytically found that the maximum wave number scales as x{sub s}{sup −9/7}S{sub L}{sup 3/7} at the transition position between these two regimes, and the corresponding maximum growth rate scales as x{sub s}{sup −6/7}S{sub L}{sup 2/7} there. The analytically predicted scalings are verified in some limits through direct numerical calculations.

- Authors:

- Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)
- School of Mathematical Sciences, Dalian University of Technology, Dalian 116024 (China)

- Publication Date:

- OSTI Identifier:
- 22407984

- 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; ALFVEN WAVES; CONFIGURATION; CURRENTS; PLASMA INSTABILITY; PLASMA SHEET; RESONANCE; SCALING; SURFACES; VECTORS

### Citation Formats

```
Nemati, M. J., Wang, Z. X., E-mail: zxwang@dlut.edu.cn, Wei, L., and Selim, B. I.
```*Plasmoid instability in double current sheets*. United States: N. p., 2015.
Web. doi:10.1063/1.4906052.

```
Nemati, M. J., Wang, Z. X., E-mail: zxwang@dlut.edu.cn, Wei, L., & Selim, B. I.
```*Plasmoid instability in double current sheets*. United States. doi:10.1063/1.4906052.

```
Nemati, M. J., Wang, Z. X., E-mail: zxwang@dlut.edu.cn, Wei, L., and Selim, B. I. Thu .
"Plasmoid instability in double current sheets". United States.
doi:10.1063/1.4906052.
```

```
@article{osti_22407984,
```

title = {Plasmoid instability in double current sheets},

author = {Nemati, M. J. and Wang, Z. X., E-mail: zxwang@dlut.edu.cn and Wei, L. and Selim, B. I.},

abstractNote = {The linear behavior of plasmoid instability in double current sheet configurations, namely, double plasmoid mode (DPM), is analytically and numerically investigated within the framework of a reduced magnetohydrodynamic model. Analytical analysis shows that if the separation of double current sheets is sufficiently small [κx{sub s}≪κ{sup 2/9}S{sub L}{sup 1/3}], the growth rate of DPMs scales as κ{sup 2/3}S{sub L}{sup 0} in the non-constant-ψ regime, where κ=kL{sub CS}/2 is the wave vector measured by the half length of the system L{sub CS}/2, 2x{sub s} is the separation between two resonant surfaces, and S{sub L}=L{sub CS}V{sub A}/2η is Lundquist number with V{sub A} and η being Alfven velocity and resistivity, respectively. If the separation is very large [κx{sub s}≫κ{sup 2/9}S{sub L}{sup 1/3}], the growth rate scales as κ{sup −2/5}S{sub L}{sup 2/5} in the constant-ψ regime. Furthermore, it is also analytically found that the maximum wave number scales as x{sub s}{sup −9/7}S{sub L}{sup 3/7} at the transition position between these two regimes, and the corresponding maximum growth rate scales as x{sub s}{sup −6/7}S{sub L}{sup 2/7} there. The analytically predicted scalings are verified in some limits through direct numerical calculations.},

doi = {10.1063/1.4906052},

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}

}