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We present a comprehensive numerical study of the dynamics of magnetized relativistic axisymmetric tori orbiting in the background spacetime of a Schwarzschild black hole. The tori are modeled as having a purely toroidal magnetic field and a constant distribution of the specific angular momentum. Following previous investigations of tori in a purely hydrodynamical context, the dynamics of these objects has been studied upon the introduction of a perturbation which, for the values of thedoi:10.1088/1742-6596/66/1/012061 fatcat:qgibht3m3bamhbc5jpbx3pxv6m