  We have performed nonlinear ideal magnetohydrodynamic simulations of the long
term evolution of a magnetized low-density "bubble" plasma formed by a radio
galaxy in a stratified cluster medium. It is found that about 3.5% of the
initial magnetic energy remains in the bubble after $\sim 8 \times 10^{9}$
years, and the initial magnetic bubble expansion is adiabatic. The bubble can
survive for at least $8 \times 10^9$ years due to the stabilizing effect of the
bubble magnetic field on Rayleigh-Taylor and Kelvin-Holmholtz instabilities,
possibly accounting for "ghost cavities" as observed in<EMAIL_ADDRESS>A filament
structure spanning about 500 kpc is formed along the path of bubble motion. The
mean value of the magnetic field inside this structure is $\sim 0.88$ $\mu$G at
$\sim8\times10^9$ years. Finally, the initial bubble momentum and rotation have
limited influence on the long term evolution of the bubble.
