Abstract In this paper, a three-dimensional cathode spot erosion model is proposed to study the development of cathode spot motion 
process on the surface of copper cathode. The formation and development process of cathode spots motion without external 
magnetic field is studied. In this model, energy flux density, pressure, and current value are considered as external parameters. 
The simulation results compared the cathode spot ablation trajectories and temperature distribution under different motion 
forms and motion velocities. The results indicated that during the spots expansion process, the flow of liquid metal will form a 
convex structure on the surface of the cathode and a hollow structure inside the cathode. Comparing different motion types, the 
annular motion significantly increased the roughness of the cathode surface. With the increase of the speed of spots movement, 
the interaction between the craters is significantly weakened, which will reduce the temperature and the roughness of the 
cathode surface. The simulation results are consistent with the experimental results.
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