  Based on a new approach on modeling the magnetically dominated outflows from
AGNs (Li et al. 2006), we study the propagation of magnetic tower jets in
gravitationally stratified atmospheres (such as a galaxy cluster environment)
in large scales ($>$ tens of kpc) by performing three-dimensional
magnetohydrodynamic (MHD) simulations. We present the detailed analysis of the
MHD waves, the cylindrical radial force balance, and the collimation of
magnetic tower jets. As magnetic energy is injected into a small central volume
over a finite amount of time, the magnetic fields expand down the background
density gradient, forming a collimated jet and an expanded ``lobe'' due to the
gradually decreasing background density and pressure. Both the jet and lobes
are magnetically dominated. In addition, the injection and expansion produce a
hydrodynamic shock wave that is moving ahead of and enclosing the magnetic
tower jet. This shock can eventually break the hydrostatic equilibrium in the
ambient medium and cause a global gravitational contraction. This contraction
produces a strong compression at the head of the magnetic tower front and helps
to collimate radially to produce a slender-shaped jet. At the outer edge of the
jet, the magnetic pressure is balanced by the background (modified) gas
pressure, without any significant contribution from the hoop stress. On the
other hand, along the central axis of the jet, hoop stress is the dominant
force in shaping the central collimation of the poloidal current. The system,
which possesses a highly wound helical magnetic configuration, never quite
reaches a force-free equilibrium state though the evolution becomes much slower
at late stages. The simulations were performed without any initial
perturbations so the overall structures of the jet remain mostly axisymmetric.
