Linear analysis of the double-tearing mode

Abstract

The linear behavior of the double‐tearing mode is investigated within the framework of magnetohydrodynamics. A two‐space‐scale analysis in which resistive solutions valid near the rational surfaces are joined to ideal solutions outside these regions is performed and used to derive the dispersion relation for the mode. If the separation of the rational surfaces at x=±x_s is sufficiently small [x_s/a<(k_ya)^−7/9S^−1/9], the growth rate is predicted to scale as S^−1/3, and the structure of the mode proves to be essentially identical with that of the m=1 tearing mode in cylindrical geometry. With increasing separation, the mode makes a transition to the S^−3/5 scaling and structure of the standard tearing mode. These predictions are confirmed by direct numerical solution of the magnetohydrodynamic equations, and the S^−1/3 scaling is shown to be correlated with violations of the constant‐ψ approximation. Possible physical implications of the double‐tearing mode are discussed.