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A design for a passive magnetic bearing system that can stably levitate a rotor in all directions is described. The bearing system consists of levitation magnets coupled with a Halbach array stabilizer, which induces currents in stabilization coils, in order to overcome the inherent instability of a system composed only of permanent magnets. The levitation magnet system consists of two pairs of annular ring magnets which provide an upward magnetic levitation force to counteract the downward gravitational force of the rotor. The Halbach array stabilizer consists of two stabilization coils shifted in angular position with respect to one another and centered in the vertical direction between two rotating Halbach arrays. Magnetic fields from permanent magnets are calculated using superposition of fields due to patches of magnetization charge at surfaces where the magnetization is discontinuous. Induced currents in the stabilization coils are calculated by computing the time derivative of the magnetic flux through those coils. Magnetic forces on the rotor are computed using a superposition of forces on each patch of magnetization charge. The entire magnetic bearing system, consisting of both the levitation magnets and the Halbach array stabilizer, is stable to both vertical and lateral displacements. Results are compared with a simpler straightened approximation of the Halbach array stabilizer.