To model the interaction between the solar wind and the interstellar wind , magnetic fields must be included . Recently Opher et al . 2003 found that , by including the solar magnetic field in a 3D high resolution simulation using the University of Michigan BATS-R-US code , a jet-sheet structure forms beyond the solar wind Termination Shock . Here we present an even higher resolution three-dimensional case where the jet extends for 150 AU beyond the Termination Shock . We discuss the formation of the jet due to a de Laval nozzle effect and it ’ s subsequent large period oscillation due to magnetohydrodynamic instabilities . To verify the source of the instability , we also perform a simplified two dimensional-geometry magnetohydrodynamic calculation of a plane fluid jet embedded in a neutral sheet with the profiles taken from our 3D simulation . We find remarkable agreement with the full three-dimensional evolution . We compare both simulations and the temporal evolution of the jet showing that the sinuous mode is the dominant mode that develops into a velocity-shear-instability with a growth rate of 5 \times 10 ^ { -9 } sec ^ { -1 } = 0.027 ~ { } years ^ { -1 } . As a result , the outer edge of the heliosphere presents remarkable dynamics , such as turbulent flows caused by the motion of the jet . Further study , e.g. , including neutrals and the tilt of the solar rotation from the magnetic axis , is required before we can definitively address how this outer boundary behaves . Already , however , we can say that the magnetic field effects are a major player in this region changing our previous notion of how the solar system ends .