Double tearing mode induced by parallel electron viscosity in tokamak plasmas

The linear behaviors of the double tearing mode (DTM) mediated by parallel electron viscosity in cylindrical plasmas with reversed magnetic shear and thus two resonant rational flux surfaces is numerically investigated. The distance between the two surfaces is found to play an important role for modes with poloidal mode number m>1. Two modes, one of which is centered at the inner rational surface and the other is located between the two surfaces, are simultaneously unstable and the growth rates show the standard single tearing mode (STM) scaling as γ∝R−1/3 when the distance is large (here, the Reynolds number R≡τυ/τh, τυ, and τh are, respectively, the viscosity penetration time of the magnetic field and the Alfvén time for a plasma sheet of width a). The latter is unstable only and the growth rate transits to the standard DTM scaling as γ∝R−1/5 for low-m (e.g., m<4) modes and keeps the STM scaling γ∝R−1/3 for high-m (e.g., m∼10) modes, which are found dominant, when the distance is decreased. In contrast, two unstable modes extending from plasma center to the two rational surfaces, respectively, coexist and the growth rates always show the scaling of γ∝R−1/5, independent of the distance, when the poloidal mode number m=1. The DTMs mediated by electron viscosity are enhanced by plasma resistivity of the range where the growth rate of the mode induced by the latter alone is comparable with that mediated by the former alone and vice versa. Otherwise, the growth rate of the mode is equal to the higher of the modes mediated by resistivity or electron viscosity alone when both of them are taken into account.