Formation of double rings around evolved stars

I propose a scenario for the formation of double-ring systems, as observed in some planetary nebulae and in the outer rings of SN 1987A. In this scenario, two jets, one jet on each side of the equatorial plane, expand into a thin, dense shell. Such a flow is expected in binary systems in which the mass-losing primary undergoes an impulsive mass-loss episode that forms a thin, dense shell. I assume that a small fraction of that mass is accreted onto a companion that blows the jets. Each jet accelerates the shell's material that it hits sideways, forming a higher density ring. Using several simplifying assumptions, I derive an expression for the radius of the ring, which depends relatively weakly on the jets and impulsive mass-loss episode properties. This shows that such a scenario is feasible. If there are several such impulsive mass-loss episodes, more double rings will be formed. Because of the binary interaction and orbital motion, the double-ring system is displaced from the symmetry axis of the main nebula, as observed.