Fast growing double tearing modes in a tokamak plasma

Abstract

Configurations with nearby multiple resonant surfaces have broad spectra of linearly unstable coupled tearing modes with dominant high poloidal mode numbers m. This was recently shown for the case of multiple q = 1 resonances [Bierwage et al., Phys. Rev. Lett. 94 (6), 65001 (2005)]. In the present work, similar behavior is found for double tearing modes (DTM) on resonant surfaces with q >= 1. A detailed analysis of linear instability characteristics of DTMs with various mode numbers m is performed using numerical simulations. The mode structures and dispersion relations for linearly unstable modes are calculated. Comparisons between low- and higher-m modes are carried out, and the roles of the inter-resonance distance and of the magnetic Reynolds number S_Hp are investigated. High-m modes are found to be destabilized when the distance between the resonant surfaces is small. They dominate over low-m modes in a wide range of S_Hp, including regimes relevant for tokamak operation. These results may be readily applied to configurations with more than two resonant surfaces.Comment: 11 pages, 15 figure

Dynamics of resistive double tearing modes with broad linear spectra

“…The purpose of the present paper is (i) to shown that the findings of Ref. [4] agree with linear DTM theory, and (ii) to present first nonlinear simulation results involving high-m DTMs for cases with q s = 1 and q s > 1. For simplicity, a reduced magnetohydrodynamic (RMHD) model is employed.…”

“…Despite the lack of a distinguished band of weakly coupled modes in the cases considered here, we conjecture that an estimate for the mode number of the fastest growing mode m peak may be obtained from the transition criterion in Eq. [4]), which suggests that m peak ≈ m trans + 1. Tests with other configurations gave similarly good agreement, despite the fact that the x s dependence is described only approximately under the assumption that q(r) is parabolic around r = r 0 .…”

“…The linear instability of DTMs for equilibria with small inter-resonance distances was studied numerically in Ref. [4]. The purpose of the present paper is (i) to shown that the findings of Ref.…”

“…The RMHD model governs the evolution of the magnetic flux function ψ and the electrostatic potential φ, as described previously in Ref. [4]. The normalized RMHD equations are…”

“…Results for the linearized system are obtained using initial-value and eigenvalue solvers as described in Ref. [4]. The nonlinear RMHD equations are solved numerically using the simulation code described in Ref.…”