Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch

We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x₁=0 and 1. Periodic boundary conditions are assumed in the x₂ and x₃ directions and the magnetofluid is driven by an electric field in the x₃ direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,J₃). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L₂ and L₃ in the x₂ and x₃ directions, and the mean values B₂ and B₃ of the magnetic-field components in these directions. {} 1996 The American Physical Society.