Three-Dimensional Relativistic Magnetohydrodynamic Simulations of   Current-Driven Instability with A Sub-Alfvenic Jet: Temporal Properties
  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. 
Yosuke Mizuno, Philip E. Hardee, Ken-Ichi Nishikawa
astro-ph.HE gr-qc