Nonlinear evolution of double tearing modes

Abstract

The linear and nonlinear behaviors of the tearing mode is systematically studied for nonmonotonic q-profiles on the basis of the reduced magnetohydrodynamics (MHD) equations in cylindrical geometry, and some new features about the double tearing mode are revealed. The linear eigenmode scales as a resistive internal mode for a small distance between two rational surfaces with the same q-value, Δrs, and as the tearing one for large Δrs. New nonlinear phenomena appear in the tearing mode regime and for shorter Δrs. The linear eigenfunction shows sharply localized fluid motion at both resonant surfaces and small but global convective motion between the resonant surfaces; consequently the mode goes through a Rutherford-type regime. When the islands have grown enough, the mode shows explosive growth. This results from the nonlinear coupling among the higher harmonics, so that the inner and outer magnetic islands interact with each other leading to an internal disruption.

Dynamics of resistive double tearing modes with broad linear spectra

“…Equilibria with larger inter-resonance distance D 12 than in Case (D-3) have a dominant m = 1 mode and the dynamics proceed as described in earlier studies (e.g., Refs. [9,18]). …”

“…Resistive and neoclassical q s = 2 DTMs were investigated in Axisymmetric Divertor Experiment (ASDEX)-Upgrade, one motivation being the possible interaction * Electronic address: abierwag@uci.edu † Electronic address: benkadda@up.univ-mrs.fr ‡ Electronic address: hamaguch@ppl.eng.osaka-u.ac.jp § deceased ¶ Present address: Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA of these modes with internal transport barriers (ITBs) [7,8]. In Japan Atomic Energy Agency Tokamak Upgrade (JT-60U) q s = 3 DTMs are thought to play a crucial role in disruptions, as indicated by experimental observations and numerical results [9,10,11].…”

Investigation of Trigger Mechanism in the Explosive Nonlinear Growth of the Double Tearing Mode

“…1). In recent years, nonlinear evolution of the DTM depending on the distance between the rational surfaces has also been systematically studied [3][4][5][6][7]. Interestingly, the intermediate coupling defined for…”

“…However, instead of saturating, the mode sud- denly enters a fast growth regime. Ishii et al [3,4], who investigated the onset of the rapid growth, explained this dynamics by triangular deformation of the magnetic structure and the resulting current point formation. If the localized current amplitude reaches a certain level, fast growth is triggered.…”

Nonlinear acceleration of the electron inertia-dominated magnetohydrodynamic modes due to electron parallel compressibility

“…The nonlinear behavior of the double tearing mode has been studied with the reduced MHD model with resistivity 16,17 and the kinetic model with electron inertia. 18 From the analogy to the m = 1 mode, it is expected that the effect of electron parallel compressibility becomes important for the nonlinear evolution of the collisionless double tearing modes in the ␦ e ജ s region.…”