Resistive tearing in line-tied magnetic fields - Slab geometry

The resistive tearing-mode instability of a current carrying plasma sheet is investigated, including the stabilizing photospheric line-tying boundary conditions. This end condition prohibits a single Fourier mode, and so requires a series expansion in harmonics of the fundamental sheet excitation. Equilibria in which there exist field lines that do not connect to the photosphere are unstable provided that the ratio of the sheet length to characteristic transverse scale is smaller than a critical value that depends on the equilibrium profile. Line-tying has strong stabilizing effect on the fundamental periodic mode. The tearing mode harmonic which develops close to the instability threshold leads to a configuration with one X point and one O point.