skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 » tokamaks.« less

Authors:
; ; ;  [1];  [2];  [3];  [3]
  1. Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan)
  2. (France)
  3. (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}
}
  • Phases of nonlinear double tearing modes are studied numerically. The first two phases lead to the formation and growth of magnetic islands and are followed by a fast reconnection phase to complete the process, driven by a process of neighboring magnetic separatrices merging and magnetic islands coupling. The fast growth can be understood as a result of the island interaction equivalent to a steadily inward flux boundary driven. Resistivity dependences for various phases are studied and shown by scaling analysis for the first time. It is found that after an early Sweet-Parker phase with a {eta}{sup 1/2}-scale, a slow nonlinearmore » phase in a Rutherford regime with a {eta}{sup 1}-scale is followed by the fast reconnection phase with a {eta}{sup 1/5}-scale.« less
  • The tearing instability with sub-Alfvénic streaming flow along the external magnetic field is investigated using resistive MHD simulation. It is found that the growth rate of the tearing mode instability is larger than that without the streaming flow. With the streaming flow, there exist two Alfvén resonance layers near the central current sheet. The larger perturbation of the magnetic field in two closer Alfvén resonance layers could lead to formation of the observed cone structure and can largely enhance the development of the tearing mode for a narrower streaming flow. For a broader streaming flow, a larger separation of Alfvénmore » resonance layers reduces the magnetic reconnection. The linear growth rate decreases with increase of the streaming flow thickness. The growth rate of the tearing instability also depends on the plasma beta (β). When the streaming flow is embedded in the current sheet, the growth rate increases with β if β < β{sub s}, but decreases if β > β{sub s}. The existence of the specific value β{sub s} can be attributed to competition between the suppressing effect of β and the enhancing effect of the streaming flow on the magnetic reconnection. The critical value β{sub s} increases with increase of the streaming flow strength.« less
  • The effect of sheared plasma flow on the m/n = 2/1 tearing mode is studied numerically (m and n are the poloidal and toroidal mode numbers). It is found that in the linear phase the plasma flow with a weak or moderate shear plays a stabilizing effect on tearing mode. However, the mode is driven to be more unstable by sufficiently strong sheared flow when approaching the shear Alfvén resonance (AR). In the nonlinear phase, a moderate (strong) sheared flow leads to a smaller (larger) saturated island width. The stabilization of tearing modes by moderate shear plasma flow is enhanced for amore » larger plasma viscosity and a lower Alfvén velocity. It is also found that in the nonlinear phase AR accelerates the plasma rotation around the 2/1 rational surface but decelerates it at the AR location, and the radial location satisfying AR spreads inwards towards the magnetic axis.« less
  • The evolution of magnetic islands at two resonant surfaces during the development of a global tearing mode is investigated via numerical simulations of a reduced set of magneto-hydrodynamic equations in slab plasmas. The explosive dynamics of the islands resulting in an interchange follows a Rutherford-like regime, also referred to as a weakly coupled double tearing mode. It is found that the latent mechanism of this dynamics is the reduction of the total pressure around the opposite X-point and the abrupt growth is associated with an imbalance of the pressure around the islands. Once this imbalance is well established, each plasmoidmore » is pushed to the opposite X-point, increasing the drive for the field merging. A feedback loop then takes place as the reconnection itself decreases the strength of the magnetic field between the tearing layers, i.e., reinforces the pressure imbalance. This loop accelerates reconnection, thus leading to the observed explosive growth.« less
  • A study is made of the effect of a resistive wall and rigid plasma rotation on kink modes. It is shown that modes with mode rational surfaces in the plasma, for example, [beta]-driven external kinks in a torus, are stabilized just below the ideal threshold by becoming resistive (tearing-like) modes, which can be stabilized in the presence of a resistive wall and rotation. Explicit calculations are shown for reduced magnetohydrodynamics (MHD) in a cylinder, and arguments are made regarding the applicability to the finite [beta] toroidal case.