Streaming tearing instability in the current sheet with a super-Alfvénic flow

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Abstract
The tearing instability in a current sheet, which has a sub‐Alfvénic or super‐Alfvénic plasma flow in the current layer, is investigated based on the linearized compressible magnetohydrodynamic (MHD) equations. An initial‐value method is employed to obtain the linear growth rate and eigenmode profiles of the fastest growing mode. The results show that for a sub‐Alfvénic plasma flow parallel to the neutral sheet, the growth rate of the tearing instability is only slightly larger than that of the pure tearing mode without the flow. On the other hand, a large increase in the growth rate of the most unstable mode is observed, when the streaming speed V0m in the central region of the current sheet increases above a critical speed VC≂1.2VA∞. Here VA∞ is the Alfvén speed far away from the current layer. This study shows that when the electric resistivity η is zero, the sausage mode is excited because of a super‐Alfvénic plasma flow parallel to the current sheet. This flow‐induced sausage mode is called the streaming sausage mode. In the presence of a finite resistivity, the streaming sausage mode becomes a mixed sausage–tearing mode, because of the presence of magnetic field line reconnections in the current sheet. This mixed sausage–tearing mode, or simply the streaming tearing mode, has a high growth rate, γ≂0.1τ−1A, where τA is the Alfvén transit time across the current layer. This growth rate is larger than the growth rate of the pure tearing mode, which is approximately the inverse of the geometric mean of the Alfvén time τA and the diffusion time τD across the current layer.