<p>Electrical arc machining (EAM) provides a novel approach for efficiently machining difficult-to-cut materials, allowing for significant material removal. The arc removal is fundamentally a thermal erosion process, where the formation and evolution of the arc channel plasma play a crucial role in discharge machining. As a high-temperature heat source, the arc directly influences the distribution of energy within the discharge channel and the material erosion characteristics. A novel electromagnetic-thermal-hydraulic multi-physics coupling model for EAM is employed to analyze the distribution characteristics of the electric, magnetic, fluid, and thermal fields in the discharge channel based on magnetohydrodynamic theory. This model integrates the workpiece, arc discharge channel, and tool electrode, while considering heat transfer effects within the discharge channel. The study also investigates the thermal erosion characteristics of the plasma on both the workpiece and tool electrode, illustrating the physical nature and distribution patterns of the various fields within the discharge channel. Single-pulse discharge experiments were conducted, and the variations in the arc discharge channel were observed using a high-speed camera. The arc column diameter, workpiece crater morphology, and tool electrode erosion were compared with simulation results to validate the accuracy of the model. The study demonstrates that the discharge channel in EAM acts as a temporally formed high-temperature heat source with a broad scale, enhancing the understanding of the arc discharge channel evolution and the material thermal erosion process.</p>