  We present a numerical study of a MEMS-based design of a fiber cavity
integrated with an ion trap system. Each fiber mirror is supported by a
microactuator that controls the mirror's position in three dimensions. The
mechanical stability is investigated by a feasibility analysis showing that the
actuator offers a stable support of the fiber. The actuators move the fibers'
positions continuously with a stroke of more than 10 $\mu$m, with mechanical
resonance frequencies on the order of kHz. A calculation of the trapping
potential shows that a separation between ion and fiber consistent with strong
ion-cavity coupling is feasible. Our miniaturized ion-photon interface
constitutes a viable approach to integrated hardware for quantum information.
