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The 3-dimensional trajectories of a single, charged particle within the fields of a resonant microwave cavity and a DC magnetic mirror were computed. The RF fields were due to the TM011 mode of a cylindrical cavity which produces a closed, 3-dimensional, axisymmetric containment region in the center of the cavity. The mirror field was produced by current carrying rings at the ends of the cylinder. The combined fields were able to contain particles which would escape the RF containment well alone. Similarly, the loss cone angles at the ends of the mirror were decreased, a result noted by Gray  for a mirror simulated by parabolic magnetic fields aided by a 1-dimensional RF containment well.