Bifurcation analysis of the plane sheet pinch

A numerical bifurcation analysis of the electrically driven plane sheet pin ch is presented. The electrical conductivity varies across the sheet such a s to allow instability of the quiescent basic state at some critical Hartma nn number. The most unstable perturbation is the two-dimensional tearing mo de. Restricting the whole problem to two spatial dimensions, this mode is f ollowed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primar y instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying p arameters of the sheet pinch. The instability with respect to three-dimensi onal perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the sy stem parameters, the unstably perturbed state is followed up in its nonline ar evolution and is found to approach a three-dimensional steady state.