Adaptive optics will play a crucial role in achieving the full potential of the next generation of large diameter telescopes. In this paper, we present an optical design for a multi-conjugate adaptive optics system for the Giant Magellan Telescope, a 25.7 m telescope with a primary mirror consisting of seven 8.4 m segments. The tri-conjugate MCAO optics is based on adaptive secondary technology developed for the MMT telescope and incorporates dynamic refocus optics for the laser guide star wavefront sensors. We use the results of analytic (non-Monte-Carlo) numerical simulations to determine the optimal configuration of deformable mirrors as well as laser and natural guide stars. The simulation results are extended to include and quantify the effects of wavefront sensor and control loop delay noise as well as dynamic refocus and fitting error on the expected system performance and sky coverage
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