  We have investigated the influence of a velocity shear surface on the linear
and non-linear development of the CD kink instability of force-free helical
magnetic equilibria in 3D. In this study we follow the temporal development
within a periodic computational box and concentrate on flows that are
sub-Alfvenic on the cylindrical jet's axis. Displacement of the initial
force-free helical magnetic field leads to the growth of CD kink instability.
We find that helically distorted density structure propagates along the jet
with speed and flow structure dependent on the radius of the velocity shear
surface relative to the characteristic radius of the helically twisted
force-free magnetic field. At small velocity shear surface radius the plasma
flows through the kink with minimal kink propagation speed. The kink
propagation speed increases as the velocity shear radius increases and the kink
becomes more embedded in the plasma flow. A decreasing magnetic pitch profile
and faster flow enhance the influence of velocity shear. Simulations show
continuous transverse growth in the nonlinear phase of the instability. The
growth rate of the CD kink instability and the nonlinear behavior also depend
on the velocity shear surface radius and flow speed, and the magnetic pitch
radial profile. Larger velocity shear radius leads to slower linear growth,
makes a later transition to the nonlinear stage, and with larger maximum
amplitude than occur for a static plasma column. However, when the velocity
shear radius is much greater than the characteristic radius of the helical
magnetic field, linear and non-linear development can be similar to the
development of a static plasma column.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology