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A quench protection circuit is designed and the three-dimensional (3-D) thermal-electromagnetic coupled model is built for simulating the quench process of a 7 T actively shielded superconducting magnet for animal MRI. The magnet has a warm bore diameter of 210 mm. It consists of five concentric epoxy-impregnated NbTi/Cu windings and operates in the persistent mode with a total energy of 1.52 MJ. The protection circuit design applies subdivision technology and actively triggered quench heaters, and the 3-D thermal-electromagnetic coupled problem is solved by a commercial finite element method code. To improve the accuracy of analysis, magnetic field and temperature dependence of thermal and electromagnetic characteristics of the magnet materials are taken into account. The hot spot temperature rise of the windings, the temporal variation of the current, and the maximum interlayer voltage are calculated.