Theory for small growth rates of the tearing mode in a sheet pinch

In the theory of tearing modes, analytical expressions for the growth rate γ are only known for large values γ >> 1/τR. However, since resistive instabilities cannot be externally suppressed, they will be rather observed at small growth rates. In this paper, the described gap in the tearing theory is closed. The expressions obtained for small growth rates are as simple as the ones for large growth rates but differ from them appreciably. Their good quality was confirmed by numerical solution of the full tearing equations. In addition, an implicit analytical formula is presented that bridges the gap between small and large growth rates. (author) 1 ref., 2 figs