Self-consistent study of tearing mode with finite current gradient in the resistive-inertial and viscous-resistive regimes

Via the two-field reduced magneto-hydrodynamics model, a self-consistent theory of tearing mode evolution is developed to study the stability of tearing mode in the resistive-inertial and viscous-resistive regimes. Based on the series expansion method, we obtain a closed system for tearing mode evolution with the finite current gradient (FCG) effect. Solving the closed system with correlated approximations, the dispersion relation of tearing mode with FCG in the resistive-inertial and resistive-viscous regimes is derived and discussed. Self-consistent calculations adopted in this work show that assumptions used in previous studies are not always appropriate. Furthermore, deviation from those assumptions provides a non-negligible effect to the stability of tearing mode.