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Performance analysis of a coil launcher is very important for experimental research and electromagnetic optimization design. To check the effect of the improvement and analyze electromagnetic transient in a coil launcher, a field coupling circuit simulation method is introduced in this paper. Initially, the current of drive coils is calculated by the circuit model based on improved current filament method, and then the exciting current is loaded in 2-D axisymmetric field model. The field model is built based on nonoverlapping mortar finite-element method (NO-MFEM). NO-MFEM divides the whole domain into two subdomains: one contains the movable part (armature), and the other contains the source current (coils). The two subdomains are discretized independently and the two sets of meshes are nonconforming on the interface. When the movable part changes its location, it is necessary only to change the node coordinates in movable subdomains and information of mortar nodes and elements. In this paper, performance analysis of a three-stage coaxial induction coil launcher is carried out based on the proposed field-circuit method. The correspondence of the simulation results proves the validity of the field-circuit method.