# Dynamics of resistive double tearing modes with broad linear spectra

## Abstract

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied with a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable and may peak around m=m{sub peak}{approx}10. In this paper, it is first demonstrated that this result agrees with existing linear theory for DTMs. Based on this theory, a semiempirical formula for the dependence of m{sub peak} on the system parameters is proposed. Second, with the use of nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, where small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant to the understanding of the magnetohydrodynamic activity near the minimum of q and may thus be of interest for studies on stability and confinement of advancedmore »

- Authors:

- Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan)
- (France)
- (Japan)

- Publication Date:

- OSTI Identifier:
- 20974822

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 2; Other Information: DOI: 10.1063/1.2446420; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CYLINDRICAL CONFIGURATION; KINK INSTABILITY; MAGNETIC ISLANDS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; PLASMA; PLASMA CONFINEMENT; PLASMA SIMULATION; SAFETY; STABILITY; TEARING INSTABILITY; TOKAMAK DEVICES

### Citation Formats

```
Bierwage, Andreas, Benkadda, Sadruddin, Hamaguchi, Satoshi, Wakatani, Masahiro, Equipe Dynamique des Systemes Complexes, UMR 6633 CNRS-Universite de Provence, 13397 Marseille, Center for Atomic and Molecular Technologies, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, and Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011.
```*Dynamics of resistive double tearing modes with broad linear spectra*. United States: N. p., 2007.
Web. doi:10.1063/1.2446420.

```
Bierwage, Andreas, Benkadda, Sadruddin, Hamaguchi, Satoshi, Wakatani, Masahiro, Equipe Dynamique des Systemes Complexes, UMR 6633 CNRS-Universite de Provence, 13397 Marseille, Center for Atomic and Molecular Technologies, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, & Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011.
```*Dynamics of resistive double tearing modes with broad linear spectra*. United States. doi:10.1063/1.2446420.

```
Bierwage, Andreas, Benkadda, Sadruddin, Hamaguchi, Satoshi, Wakatani, Masahiro, Equipe Dynamique des Systemes Complexes, UMR 6633 CNRS-Universite de Provence, 13397 Marseille, Center for Atomic and Molecular Technologies, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, and Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011. Thu .
"Dynamics of resistive double tearing modes with broad linear spectra". United States.
doi:10.1063/1.2446420.
```

```
@article{osti_20974822,
```

title = {Dynamics of resistive double tearing modes with broad linear spectra},

author = {Bierwage, Andreas and Benkadda, Sadruddin and Hamaguchi, Satoshi and Wakatani, Masahiro and Equipe Dynamique des Systemes Complexes, UMR 6633 CNRS-Universite de Provence, 13397 Marseille and Center for Atomic and Molecular Technologies, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871 and Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011},

abstractNote = {The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied with a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable and may peak around m=m{sub peak}{approx}10. In this paper, it is first demonstrated that this result agrees with existing linear theory for DTMs. Based on this theory, a semiempirical formula for the dependence of m{sub peak} on the system parameters is proposed. Second, with the use of nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, where small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant to the understanding of the magnetohydrodynamic activity near the minimum of q and may thus be of interest for studies on stability and confinement of advanced tokamaks.},

doi = {10.1063/1.2446420},

journal = {Physics of Plasmas},

number = 2,

volume = 14,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}