  We present cosmological magnetohydrodynamic simulations of the formation of a
galaxy cluster with magnetic energy feedback from an active galactic nuclei
(AGN). We demonstrate that X-ray cavities can be produced by the magnetically
dominated jet-lobe system that is supported by a central axial current. The
cavities are magnetically dominated and their morphology is determined
jointedly by the magnetic fields and the background cluster pressure profile.
The expansion and motion of the cavities are driven initially by the Lorentz
force of the magnetic fields, and the cavities only become buoyant at late
stages ($> 500$ Myr). We find that up to $80%-90%$ of the injected magnetic
energy goes into doing work against the hot cluster medium, heating it, and
lifting it in the cluster potential.
