  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 $150AU$ beyond the Termination
Shock. We discuss the formation of the jet due to a de Laval nozzle effect and
it's su bsequent 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.
