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The convection of liquid helium in the superconducting magnet was analyzed by means of lattice Boltzmann method in order to study the cryogenic stability of the magnet. Since the cooling capability is determined by the convection of liquid helium, the cryogenic stability of the superconducting magnet should be analyzed considering the effects of the convection. In the calculation, we applied the lattice Boltzmann method which is suitable for the analysis of the complex flows and the heat transfer. By calculating both the convection of liquid helium and the heat transfer, the propagation of the normal state zone was studied.